xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 03e6d32953ff6d123393c3df7e15df579e2665b4)
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 <../src/mat/utils/petscheap.h>
10 #include <petscbt.h>
11 #include <petsc/private/isimpl.h>
12 #include <../src/mat/impls/dense/seq/dense.h>
13 
14 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);
15 
16 #if defined(PETSC_HAVE_HYPRE)
17 PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*);
18 #endif
19 
20 #undef __FUNCT__
21 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
22 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
23 {
24   PetscErrorCode ierr;
25 #if !defined(PETSC_HAVE_HYPRE)
26   const char     *algTypes[6] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed"};
27   PetscInt       nalg = 6;
28 #else
29   const char     *algTypes[7] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","hypre"};
30   PetscInt       nalg = 7;
31 #endif
32   PetscInt       alg = 0; /* set default algorithm */
33 
34   PetscFunctionBegin;
35   if (scall == MAT_INITIAL_MATRIX) {
36     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
37     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[0],&alg,NULL);CHKERRQ(ierr);
38     ierr = PetscOptionsEnd();CHKERRQ(ierr);
39     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
40     switch (alg) {
41     case 1:
42       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
43       break;
44     case 2:
45       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
46       break;
47     case 3:
48       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
49       break;
50     case 4:
51       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
52       break;
53     case 5:
54       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
55       break;
56 #if defined(PETSC_HAVE_HYPRE)
57     case 6:
58       ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr);
59       break;
60 #endif
61     default:
62       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
63      break;
64     }
65     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
66   }
67 
68   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
69   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
70   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
71   PetscFunctionReturn(0);
72 }
73 
74 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
75 {
76   PetscErrorCode     ierr;
77   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
78   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
79   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
80   PetscReal          afill;
81   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
82   PetscTable         ta;
83   PetscBT            lnkbt;
84   PetscFreeSpaceList free_space=NULL,current_space=NULL;
85 
86   PetscFunctionBegin;
87   /* Get ci and cj */
88   /*---------------*/
89   /* Allocate ci array, arrays for fill computation and */
90   /* free space for accumulating nonzero column info */
91   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
92   ci[0] = 0;
93 
94   /* create and initialize a linked list */
95   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
96   MatRowMergeMax_SeqAIJ(b,bm,ta);
97   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
98   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
99 
100   ierr = PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);CHKERRQ(ierr);
101 
102   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
103   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
104 
105   current_space = free_space;
106 
107   /* Determine ci and cj */
108   for (i=0; i<am; i++) {
109     anzi = ai[i+1] - ai[i];
110     aj   = a->j + ai[i];
111     for (j=0; j<anzi; j++) {
112       brow = aj[j];
113       bnzj = bi[brow+1] - bi[brow];
114       bj   = b->j + bi[brow];
115       /* add non-zero cols of B into the sorted linked list lnk */
116       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
117     }
118     cnzi = lnk[0];
119 
120     /* If free space is not available, make more free space */
121     /* Double the amount of total space in the list */
122     if (current_space->local_remaining<cnzi) {
123       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
124       ndouble++;
125     }
126 
127     /* Copy data into free space, then initialize lnk */
128     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
129 
130     current_space->array           += cnzi;
131     current_space->local_used      += cnzi;
132     current_space->local_remaining -= cnzi;
133 
134     ci[i+1] = ci[i] + cnzi;
135   }
136 
137   /* Column indices are in the list of free space */
138   /* Allocate space for cj, initialize cj, and */
139   /* destroy list of free space and other temporary array(s) */
140   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
141   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
142   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
143 
144   /* put together the new symbolic matrix */
145   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
146   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
147 
148   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
149   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
150   c                         = (Mat_SeqAIJ*)((*C)->data);
151   c->free_a                 = PETSC_FALSE;
152   c->free_ij                = PETSC_TRUE;
153   c->nonew                  = 0;
154   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
155 
156   /* set MatInfo */
157   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
158   if (afill < 1.0) afill = 1.0;
159   c->maxnz                     = ci[am];
160   c->nz                        = ci[am];
161   (*C)->info.mallocs           = ndouble;
162   (*C)->info.fill_ratio_given  = fill;
163   (*C)->info.fill_ratio_needed = afill;
164 
165 #if defined(PETSC_USE_INFO)
166   if (ci[am]) {
167     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
168     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
169   } else {
170     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
171   }
172 #endif
173   PetscFunctionReturn(0);
174 }
175 
176 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
177 {
178   PetscErrorCode ierr;
179   PetscLogDouble flops=0.0;
180   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
181   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
182   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
183   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
184   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
185   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
186   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
187   PetscScalar    *ab_dense;
188 
189   PetscFunctionBegin;
190   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
191     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
192     c->a      = ca;
193     c->free_a = PETSC_TRUE;
194   } else {
195     ca        = c->a;
196   }
197   if (!c->matmult_abdense) {
198     ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr);
199     c->matmult_abdense = ab_dense;
200   } else {
201     ab_dense = c->matmult_abdense;
202   }
203 
204   /* clean old values in C */
205   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
206   /* Traverse A row-wise. */
207   /* Build the ith row in C by summing over nonzero columns in A, */
208   /* the rows of B corresponding to nonzeros of A. */
209   for (i=0; i<am; i++) {
210     anzi = ai[i+1] - ai[i];
211     for (j=0; j<anzi; j++) {
212       brow = aj[j];
213       bnzi = bi[brow+1] - bi[brow];
214       bjj  = bj + bi[brow];
215       baj  = ba + bi[brow];
216       /* perform dense axpy */
217       valtmp = aa[j];
218       for (k=0; k<bnzi; k++) {
219         ab_dense[bjj[k]] += valtmp*baj[k];
220       }
221       flops += 2*bnzi;
222     }
223     aj += anzi; aa += anzi;
224 
225     cnzi = ci[i+1] - ci[i];
226     for (k=0; k<cnzi; k++) {
227       ca[k]          += ab_dense[cj[k]];
228       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
229     }
230     flops += cnzi;
231     cj    += cnzi; ca += cnzi;
232   }
233   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
234   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
235   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
236   PetscFunctionReturn(0);
237 }
238 
239 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
240 {
241   PetscErrorCode ierr;
242   PetscLogDouble flops=0.0;
243   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
244   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
245   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
246   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
247   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
248   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
249   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
250   PetscInt       nextb;
251 
252   PetscFunctionBegin;
253   /* clean old values in C */
254   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
255   /* Traverse A row-wise. */
256   /* Build the ith row in C by summing over nonzero columns in A, */
257   /* the rows of B corresponding to nonzeros of A. */
258   for (i=0; i<am; i++) {
259     anzi = ai[i+1] - ai[i];
260     cnzi = ci[i+1] - ci[i];
261     for (j=0; j<anzi; j++) {
262       brow = aj[j];
263       bnzi = bi[brow+1] - bi[brow];
264       bjj  = bj + bi[brow];
265       baj  = ba + bi[brow];
266       /* perform sparse axpy */
267       valtmp = aa[j];
268       nextb  = 0;
269       for (k=0; nextb<bnzi; k++) {
270         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
271           ca[k] += valtmp*baj[nextb++];
272         }
273       }
274       flops += 2*bnzi;
275     }
276     aj += anzi; aa += anzi;
277     cj += cnzi; ca += cnzi;
278   }
279 
280   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
281   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
282   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
283   PetscFunctionReturn(0);
284 }
285 
286 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
287 {
288   PetscErrorCode     ierr;
289   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
290   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
291   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
292   MatScalar          *ca;
293   PetscReal          afill;
294   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
295   PetscTable         ta;
296   PetscFreeSpaceList free_space=NULL,current_space=NULL;
297 
298   PetscFunctionBegin;
299   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
300   /*-----------------------------------------------------------------------------------------*/
301   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
302   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
303   ci[0] = 0;
304 
305   /* create and initialize a linked list */
306   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
307   MatRowMergeMax_SeqAIJ(b,bm,ta);
308   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
309   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
310 
311   ierr = PetscLLCondensedCreate_fast(Crmax,&lnk);CHKERRQ(ierr);
312 
313   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
314   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
315   current_space = free_space;
316 
317   /* Determine ci and cj */
318   for (i=0; i<am; i++) {
319     anzi = ai[i+1] - ai[i];
320     aj   = a->j + ai[i];
321     for (j=0; j<anzi; j++) {
322       brow = aj[j];
323       bnzj = bi[brow+1] - bi[brow];
324       bj   = b->j + bi[brow];
325       /* add non-zero cols of B into the sorted linked list lnk */
326       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
327     }
328     cnzi = lnk[1];
329 
330     /* If free space is not available, make more free space */
331     /* Double the amount of total space in the list */
332     if (current_space->local_remaining<cnzi) {
333       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
334       ndouble++;
335     }
336 
337     /* Copy data into free space, then initialize lnk */
338     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
339 
340     current_space->array           += cnzi;
341     current_space->local_used      += cnzi;
342     current_space->local_remaining -= cnzi;
343 
344     ci[i+1] = ci[i] + cnzi;
345   }
346 
347   /* Column indices are in the list of free space */
348   /* Allocate space for cj, initialize cj, and */
349   /* destroy list of free space and other temporary array(s) */
350   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
351   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
352   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
353 
354   /* Allocate space for ca */
355   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
356   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
357 
358   /* put together the new symbolic matrix */
359   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
360   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
361 
362   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
363   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
364   c          = (Mat_SeqAIJ*)((*C)->data);
365   c->free_a  = PETSC_TRUE;
366   c->free_ij = PETSC_TRUE;
367   c->nonew   = 0;
368 
369   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
370 
371   /* set MatInfo */
372   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
373   if (afill < 1.0) afill = 1.0;
374   c->maxnz                     = ci[am];
375   c->nz                        = ci[am];
376   (*C)->info.mallocs           = ndouble;
377   (*C)->info.fill_ratio_given  = fill;
378   (*C)->info.fill_ratio_needed = afill;
379 
380 #if defined(PETSC_USE_INFO)
381   if (ci[am]) {
382     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
383     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
384   } else {
385     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
386   }
387 #endif
388   PetscFunctionReturn(0);
389 }
390 
391 
392 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
393 {
394   PetscErrorCode     ierr;
395   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
396   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
397   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
398   MatScalar          *ca;
399   PetscReal          afill;
400   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
401   PetscTable         ta;
402   PetscFreeSpaceList free_space=NULL,current_space=NULL;
403 
404   PetscFunctionBegin;
405   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
406   /*---------------------------------------------------------------------------------------------*/
407   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
408   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
409   ci[0] = 0;
410 
411   /* create and initialize a linked list */
412   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
413   MatRowMergeMax_SeqAIJ(b,bm,ta);
414   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
415   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
416   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
417 
418   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
419   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
420   current_space = free_space;
421 
422   /* Determine ci and cj */
423   for (i=0; i<am; i++) {
424     anzi = ai[i+1] - ai[i];
425     aj   = a->j + ai[i];
426     for (j=0; j<anzi; j++) {
427       brow = aj[j];
428       bnzj = bi[brow+1] - bi[brow];
429       bj   = b->j + bi[brow];
430       /* add non-zero cols of B into the sorted linked list lnk */
431       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
432     }
433     cnzi = lnk[0];
434 
435     /* If free space is not available, make more free space */
436     /* Double the amount of total space in the list */
437     if (current_space->local_remaining<cnzi) {
438       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
439       ndouble++;
440     }
441 
442     /* Copy data into free space, then initialize lnk */
443     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
444 
445     current_space->array           += cnzi;
446     current_space->local_used      += cnzi;
447     current_space->local_remaining -= cnzi;
448 
449     ci[i+1] = ci[i] + cnzi;
450   }
451 
452   /* Column indices are in the list of free space */
453   /* Allocate space for cj, initialize cj, and */
454   /* destroy list of free space and other temporary array(s) */
455   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
456   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
457   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
458 
459   /* Allocate space for ca */
460   /*-----------------------*/
461   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
462   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
463 
464   /* put together the new symbolic matrix */
465   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
466   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
467 
468   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
469   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
470   c          = (Mat_SeqAIJ*)((*C)->data);
471   c->free_a  = PETSC_TRUE;
472   c->free_ij = PETSC_TRUE;
473   c->nonew   = 0;
474 
475   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
476 
477   /* set MatInfo */
478   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
479   if (afill < 1.0) afill = 1.0;
480   c->maxnz                     = ci[am];
481   c->nz                        = ci[am];
482   (*C)->info.mallocs           = ndouble;
483   (*C)->info.fill_ratio_given  = fill;
484   (*C)->info.fill_ratio_needed = afill;
485 
486 #if defined(PETSC_USE_INFO)
487   if (ci[am]) {
488     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
489     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
490   } else {
491     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
492   }
493 #endif
494   PetscFunctionReturn(0);
495 }
496 
497 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
498 {
499   PetscErrorCode     ierr;
500   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
501   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
502   PetscInt           *ci,*cj,*bb;
503   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
504   PetscReal          afill;
505   PetscInt           i,j,col,ndouble = 0;
506   PetscFreeSpaceList free_space=NULL,current_space=NULL;
507   PetscHeap          h;
508 
509   PetscFunctionBegin;
510   /* Get ci and cj - by merging sorted rows using a heap */
511   /*---------------------------------------------------------------------------------------------*/
512   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
513   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
514   ci[0] = 0;
515 
516   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
517   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
518   current_space = free_space;
519 
520   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
521   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
522 
523   /* Determine ci and cj */
524   for (i=0; i<am; i++) {
525     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 */
526     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
527     ci[i+1] = ci[i];
528     /* Populate the min heap */
529     for (j=0; j<anzi; j++) {
530       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
531       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
532         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
533       }
534     }
535     /* Pick off the min element, adding it to free space */
536     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
537     while (j >= 0) {
538       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
539         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
540         ndouble++;
541       }
542       *(current_space->array++) = col;
543       current_space->local_used++;
544       current_space->local_remaining--;
545       ci[i+1]++;
546 
547       /* stash if anything else remains in this row of B */
548       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
549       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
550         PetscInt j2,col2;
551         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
552         if (col2 != col) break;
553         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
554         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
555       }
556       /* Put any stashed elements back into the min heap */
557       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
558       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
559     }
560   }
561   ierr = PetscFree(bb);CHKERRQ(ierr);
562   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
563 
564   /* Column indices are in the list of free space */
565   /* Allocate space for cj, initialize cj, and */
566   /* destroy list of free space and other temporary array(s) */
567   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
568   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
569 
570   /* put together the new symbolic matrix */
571   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
572   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
573 
574   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
575   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
576   c          = (Mat_SeqAIJ*)((*C)->data);
577   c->free_a  = PETSC_TRUE;
578   c->free_ij = PETSC_TRUE;
579   c->nonew   = 0;
580 
581   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
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_BTHeap(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   PetscBT            bt;
615 
616   PetscFunctionBegin;
617   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
618   /*---------------------------------------------------------------------------------------------*/
619   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
620   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
621   ci[0] = 0;
622 
623   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
624   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
625 
626   current_space = free_space;
627 
628   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
629   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
630   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
631 
632   /* Determine ci and cj */
633   for (i=0; i<am; i++) {
634     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 */
635     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
636     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
637     ci[i+1] = ci[i];
638     /* Populate the min heap */
639     for (j=0; j<anzi; j++) {
640       PetscInt brow = acol[j];
641       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
642         PetscInt bcol = bj[bb[j]];
643         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
644           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
645           bb[j]++;
646           break;
647         }
648       }
649     }
650     /* Pick off the min element, adding it to free space */
651     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
652     while (j >= 0) {
653       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
654         fptr = NULL;                      /* need PetscBTMemzero */
655         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
656         ndouble++;
657       }
658       *(current_space->array++) = col;
659       current_space->local_used++;
660       current_space->local_remaining--;
661       ci[i+1]++;
662 
663       /* stash if anything else remains in this row of B */
664       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
665         PetscInt bcol = bj[bb[j]];
666         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
667           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
668           bb[j]++;
669           break;
670         }
671       }
672       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
673     }
674     if (fptr) {                 /* Clear the bits for this row */
675       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
676     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
677       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
678     }
679   }
680   ierr = PetscFree(bb);CHKERRQ(ierr);
681   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
682   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
683 
684   /* Column indices are in the list of free space */
685   /* Allocate space for cj, initialize cj, and */
686   /* destroy list of free space and other temporary array(s) */
687   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
688   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
689 
690   /* put together the new symbolic matrix */
691   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
692   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
693 
694   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
695   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
696   c          = (Mat_SeqAIJ*)((*C)->data);
697   c->free_a  = PETSC_TRUE;
698   c->free_ij = PETSC_TRUE;
699   c->nonew   = 0;
700 
701   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
702 
703   /* set MatInfo */
704   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
705   if (afill < 1.0) afill = 1.0;
706   c->maxnz                     = ci[am];
707   c->nz                        = ci[am];
708   (*C)->info.mallocs           = ndouble;
709   (*C)->info.fill_ratio_given  = fill;
710   (*C)->info.fill_ratio_needed = afill;
711 
712 #if defined(PETSC_USE_INFO)
713   if (ci[am]) {
714     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
715     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
716   } else {
717     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
718   }
719 #endif
720   PetscFunctionReturn(0);
721 }
722 
723 /* concatenate unique entries and then sort */
724 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
725 {
726   PetscErrorCode     ierr;
727   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
728   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
729   PetscInt           *ci,*cj;
730   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
731   PetscReal          afill;
732   PetscInt           i,j,ndouble = 0;
733   PetscSegBuffer     seg,segrow;
734   char               *seen;
735 
736   PetscFunctionBegin;
737   ierr  = PetscMalloc1(am+1,&ci);CHKERRQ(ierr);
738   ci[0] = 0;
739 
740   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
741   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
742   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
743   ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr);
744   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
745 
746   /* Determine ci and cj */
747   for (i=0; i<am; i++) {
748     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 */
749     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
750     PetscInt packlen = 0,*PETSC_RESTRICT crow;
751     /* Pack segrow */
752     for (j=0; j<anzi; j++) {
753       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
754       for (k=bjstart; k<bjend; k++) {
755         PetscInt bcol = bj[k];
756         if (!seen[bcol]) { /* new entry */
757           PetscInt *PETSC_RESTRICT slot;
758           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
759           *slot = bcol;
760           seen[bcol] = 1;
761           packlen++;
762         }
763       }
764     }
765     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
766     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
767     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
768     ci[i+1] = ci[i] + packlen;
769     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
770   }
771   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
772   ierr = PetscFree(seen);CHKERRQ(ierr);
773 
774   /* Column indices are in the segmented buffer */
775   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
776   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
777 
778   /* put together the new symbolic matrix */
779   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
780   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
781 
782   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
783   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
784   c          = (Mat_SeqAIJ*)((*C)->data);
785   c->free_a  = PETSC_TRUE;
786   c->free_ij = PETSC_TRUE;
787   c->nonew   = 0;
788 
789   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
790 
791   /* set MatInfo */
792   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
793   if (afill < 1.0) afill = 1.0;
794   c->maxnz                     = ci[am];
795   c->nz                        = ci[am];
796   (*C)->info.mallocs           = ndouble;
797   (*C)->info.fill_ratio_given  = fill;
798   (*C)->info.fill_ratio_needed = afill;
799 
800 #if defined(PETSC_USE_INFO)
801   if (ci[am]) {
802     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
803     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
804   } else {
805     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
806   }
807 #endif
808   PetscFunctionReturn(0);
809 }
810 
811 /* This routine is not used. Should be removed! */
812 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
813 {
814   PetscErrorCode ierr;
815 
816   PetscFunctionBegin;
817   if (scall == MAT_INITIAL_MATRIX) {
818     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
819     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
820     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
821   }
822   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
823   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
824   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
825   PetscFunctionReturn(0);
826 }
827 
828 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
829 {
830   PetscErrorCode      ierr;
831   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
832   Mat_MatMatTransMult *abt=a->abt;
833 
834   PetscFunctionBegin;
835   ierr = (abt->destroy)(A);CHKERRQ(ierr);
836   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
837   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
838   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
839   ierr = PetscFree(abt);CHKERRQ(ierr);
840   PetscFunctionReturn(0);
841 }
842 
843 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
844 {
845   PetscErrorCode      ierr;
846   Mat                 Bt;
847   PetscInt            *bti,*btj;
848   Mat_MatMatTransMult *abt;
849   Mat_SeqAIJ          *c;
850 
851   PetscFunctionBegin;
852   /* create symbolic Bt */
853   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
854   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
855   ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
856 
857   /* get symbolic C=A*Bt */
858   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
859 
860   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
861   ierr   = PetscNew(&abt);CHKERRQ(ierr);
862   c      = (Mat_SeqAIJ*)(*C)->data;
863   c->abt = abt;
864 
865   abt->usecoloring = PETSC_FALSE;
866   abt->destroy     = (*C)->ops->destroy;
867   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
868 
869   ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
870   if (abt->usecoloring) {
871     /* Create MatTransposeColoring from symbolic C=A*B^T */
872     MatTransposeColoring matcoloring;
873     MatColoring          coloring;
874     ISColoring           iscoloring;
875     Mat                  Bt_dense,C_dense;
876     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
877     /* inode causes memory problem, don't know why */
878     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
879 
880     ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
881     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
882     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
883     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
884     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
885     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
886     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
887 
888     abt->matcoloring = matcoloring;
889 
890     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
891 
892     /* Create Bt_dense and C_dense = A*Bt_dense */
893     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
894     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
895     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
896     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
897 
898     Bt_dense->assembled = PETSC_TRUE;
899     abt->Bt_den   = Bt_dense;
900 
901     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
902     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
903     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
904     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
905 
906     Bt_dense->assembled = PETSC_TRUE;
907     abt->ABt_den  = C_dense;
908 
909 #if defined(PETSC_USE_INFO)
910     {
911       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
912       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);
913     }
914 #endif
915   }
916   /* clean up */
917   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
918   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
919   PetscFunctionReturn(0);
920 }
921 
922 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
923 {
924   PetscErrorCode      ierr;
925   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
926   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
927   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
928   PetscLogDouble      flops=0.0;
929   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
930   Mat_MatMatTransMult *abt = c->abt;
931 
932   PetscFunctionBegin;
933   /* clear old values in C */
934   if (!c->a) {
935     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
936     c->a      = ca;
937     c->free_a = PETSC_TRUE;
938   } else {
939     ca =  c->a;
940   }
941   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
942 
943   if (abt->usecoloring) {
944     MatTransposeColoring matcoloring = abt->matcoloring;
945     Mat                  Bt_dense,C_dense = abt->ABt_den;
946 
947     /* Get Bt_dense by Apply MatTransposeColoring to B */
948     Bt_dense = abt->Bt_den;
949     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
950 
951     /* C_dense = A*Bt_dense */
952     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
953 
954     /* Recover C from C_dense */
955     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
956     PetscFunctionReturn(0);
957   }
958 
959   for (i=0; i<cm; i++) {
960     anzi = ai[i+1] - ai[i];
961     acol = aj + ai[i];
962     aval = aa + ai[i];
963     cnzi = ci[i+1] - ci[i];
964     ccol = cj + ci[i];
965     cval = ca + ci[i];
966     for (j=0; j<cnzi; j++) {
967       brow = ccol[j];
968       bnzj = bi[brow+1] - bi[brow];
969       bcol = bj + bi[brow];
970       bval = ba + bi[brow];
971 
972       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
973       nexta = 0; nextb = 0;
974       while (nexta<anzi && nextb<bnzj) {
975         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
976         if (nexta == anzi) break;
977         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
978         if (nextb == bnzj) break;
979         if (acol[nexta] == bcol[nextb]) {
980           cval[j] += aval[nexta]*bval[nextb];
981           nexta++; nextb++;
982           flops += 2;
983         }
984       }
985     }
986   }
987   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
988   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
989   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
990   PetscFunctionReturn(0);
991 }
992 
993 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
994 {
995   PetscErrorCode ierr;
996 
997   PetscFunctionBegin;
998   if (scall == MAT_INITIAL_MATRIX) {
999     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1000     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1001     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1002   }
1003   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1004   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1005   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1006   PetscFunctionReturn(0);
1007 }
1008 
1009 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1010 {
1011   PetscErrorCode ierr;
1012   Mat            At;
1013   PetscInt       *ati,*atj;
1014 
1015   PetscFunctionBegin;
1016   /* create symbolic At */
1017   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1018   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1019   ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1020 
1021   /* get symbolic C=At*B */
1022   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1023 
1024   /* clean up */
1025   ierr = MatDestroy(&At);CHKERRQ(ierr);
1026   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1027   PetscFunctionReturn(0);
1028 }
1029 
1030 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1031 {
1032   PetscErrorCode ierr;
1033   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1034   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1035   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1036   PetscLogDouble flops=0.0;
1037   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1038 
1039   PetscFunctionBegin;
1040   if (!c->a) {
1041     ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
1042 
1043     c->a      = ca;
1044     c->free_a = PETSC_TRUE;
1045   } else {
1046     ca = c->a;
1047   }
1048   /* clear old values in C */
1049   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1050 
1051   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1052   for (i=0; i<am; i++) {
1053     bj   = b->j + bi[i];
1054     ba   = b->a + bi[i];
1055     bnzi = bi[i+1] - bi[i];
1056     anzi = ai[i+1] - ai[i];
1057     for (j=0; j<anzi; j++) {
1058       nextb = 0;
1059       crow  = *aj++;
1060       cjj   = cj + ci[crow];
1061       caj   = ca + ci[crow];
1062       /* perform sparse axpy operation.  Note cjj includes bj. */
1063       for (k=0; nextb<bnzi; k++) {
1064         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1065           caj[k] += (*aa)*(*(ba+nextb));
1066           nextb++;
1067         }
1068       }
1069       flops += 2*bnzi;
1070       aa++;
1071     }
1072   }
1073 
1074   /* Assemble the final matrix and clean up */
1075   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1076   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1077   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1078   PetscFunctionReturn(0);
1079 }
1080 
1081 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1082 {
1083   PetscErrorCode ierr;
1084 
1085   PetscFunctionBegin;
1086   if (scall == MAT_INITIAL_MATRIX) {
1087     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1088     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1089     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1090   }
1091   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1092   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1093   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1094   PetscFunctionReturn(0);
1095 }
1096 
1097 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1098 {
1099   PetscErrorCode ierr;
1100 
1101   PetscFunctionBegin;
1102   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1103 
1104   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1105   PetscFunctionReturn(0);
1106 }
1107 
1108 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1109 {
1110   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1111   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
1112   PetscErrorCode    ierr;
1113   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1114   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1115   const PetscInt    *aj;
1116   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n;
1117   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;
1118 
1119   PetscFunctionBegin;
1120   if (!cm || !cn) PetscFunctionReturn(0);
1121   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);
1122   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);
1123   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);
1124   b = bd->v;
1125   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1126   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1127   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1128   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1129     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1130       r1 = r2 = r3 = r4 = 0.0;
1131       n  = a->i[i+1] - a->i[i];
1132       aj = a->j + a->i[i];
1133       aa = a->a + a->i[i];
1134       for (j=0; j<n; j++) {
1135         aatmp = aa[j]; ajtmp = aj[j];
1136         r1 += aatmp*b1[ajtmp];
1137         r2 += aatmp*b2[ajtmp];
1138         r3 += aatmp*b3[ajtmp];
1139         r4 += aatmp*b4[ajtmp];
1140       }
1141       c1[i] = r1;
1142       c2[i] = r2;
1143       c3[i] = r3;
1144       c4[i] = r4;
1145     }
1146     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1147     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1148   }
1149   for (; col<cn; col++) {   /* over extra columns of C */
1150     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1151       r1 = 0.0;
1152       n  = a->i[i+1] - a->i[i];
1153       aj = a->j + a->i[i];
1154       aa = a->a + a->i[i];
1155       for (j=0; j<n; j++) {
1156         r1 += aa[j]*b1[aj[j]];
1157       }
1158       c1[i] = r1;
1159     }
1160     b1 += bm;
1161     c1 += am;
1162   }
1163   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1164   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1165   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1166   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1167   PetscFunctionReturn(0);
1168 }
1169 
1170 /*
1171    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1172 */
1173 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1174 {
1175   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1176   Mat_SeqDense   *bd = (Mat_SeqDense*)B->data;
1177   PetscErrorCode ierr;
1178   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1179   MatScalar      *aa;
1180   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1181   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1182 
1183   PetscFunctionBegin;
1184   if (!cm || !cn) PetscFunctionReturn(0);
1185   b = bd->v;
1186   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1187   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1188 
1189   if (a->compressedrow.use) { /* use compressed row format */
1190     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1191       colam = col*am;
1192       arm   = a->compressedrow.nrows;
1193       ii    = a->compressedrow.i;
1194       ridx  = a->compressedrow.rindex;
1195       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1196         r1 = r2 = r3 = r4 = 0.0;
1197         n  = ii[i+1] - ii[i];
1198         aj = a->j + ii[i];
1199         aa = a->a + ii[i];
1200         for (j=0; j<n; j++) {
1201           r1 += (*aa)*b1[*aj];
1202           r2 += (*aa)*b2[*aj];
1203           r3 += (*aa)*b3[*aj];
1204           r4 += (*aa++)*b4[*aj++];
1205         }
1206         c[colam       + ridx[i]] += r1;
1207         c[colam + am  + ridx[i]] += r2;
1208         c[colam + am2 + ridx[i]] += r3;
1209         c[colam + am3 + ridx[i]] += r4;
1210       }
1211       b1 += bm4;
1212       b2 += bm4;
1213       b3 += bm4;
1214       b4 += bm4;
1215     }
1216     for (; col<cn; col++) {     /* over extra columns of C */
1217       colam = col*am;
1218       arm   = a->compressedrow.nrows;
1219       ii    = a->compressedrow.i;
1220       ridx  = a->compressedrow.rindex;
1221       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1222         r1 = 0.0;
1223         n  = ii[i+1] - ii[i];
1224         aj = a->j + ii[i];
1225         aa = a->a + ii[i];
1226 
1227         for (j=0; j<n; j++) {
1228           r1 += (*aa++)*b1[*aj++];
1229         }
1230         c[colam + ridx[i]] += r1;
1231       }
1232       b1 += bm;
1233     }
1234   } else {
1235     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1236       colam = col*am;
1237       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1238         r1 = r2 = r3 = r4 = 0.0;
1239         n  = a->i[i+1] - a->i[i];
1240         aj = a->j + a->i[i];
1241         aa = a->a + a->i[i];
1242         for (j=0; j<n; j++) {
1243           r1 += (*aa)*b1[*aj];
1244           r2 += (*aa)*b2[*aj];
1245           r3 += (*aa)*b3[*aj];
1246           r4 += (*aa++)*b4[*aj++];
1247         }
1248         c[colam + i]       += r1;
1249         c[colam + am + i]  += r2;
1250         c[colam + am2 + i] += r3;
1251         c[colam + am3 + i] += r4;
1252       }
1253       b1 += bm4;
1254       b2 += bm4;
1255       b3 += bm4;
1256       b4 += bm4;
1257     }
1258     for (; col<cn; col++) {     /* over extra columns of C */
1259       colam = col*am;
1260       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1261         r1 = 0.0;
1262         n  = a->i[i+1] - a->i[i];
1263         aj = a->j + a->i[i];
1264         aa = a->a + a->i[i];
1265 
1266         for (j=0; j<n; j++) {
1267           r1 += (*aa++)*b1[*aj++];
1268         }
1269         c[colam + i] += r1;
1270       }
1271       b1 += bm;
1272     }
1273   }
1274   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1275   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1276   PetscFunctionReturn(0);
1277 }
1278 
1279 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1280 {
1281   PetscErrorCode ierr;
1282   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1283   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1284   PetscInt       *bi      = b->i,*bj=b->j;
1285   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1286   MatScalar      *btval,*btval_den,*ba=b->a;
1287   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1288 
1289   PetscFunctionBegin;
1290   btval_den=btdense->v;
1291   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1292   for (k=0; k<ncolors; k++) {
1293     ncolumns = coloring->ncolumns[k];
1294     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1295       col   = *(columns + colorforcol[k] + l);
1296       btcol = bj + bi[col];
1297       btval = ba + bi[col];
1298       anz   = bi[col+1] - bi[col];
1299       for (j=0; j<anz; j++) {
1300         brow            = btcol[j];
1301         btval_den[brow] = btval[j];
1302       }
1303     }
1304     btval_den += m;
1305   }
1306   PetscFunctionReturn(0);
1307 }
1308 
1309 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1310 {
1311   PetscErrorCode ierr;
1312   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1313   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1314   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1315   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1316   PetscInt       nrows,*row,*idx;
1317   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1318 
1319   PetscFunctionBegin;
1320   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1321 
1322   if (brows > 0) {
1323     PetscInt *lstart,row_end,row_start;
1324     lstart = matcoloring->lstart;
1325     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1326 
1327     row_end = brows;
1328     if (row_end > m) row_end = m;
1329     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1330       ca_den_ptr = ca_den;
1331       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1332         nrows = matcoloring->nrows[k];
1333         row   = rows  + colorforrow[k];
1334         idx   = den2sp + colorforrow[k];
1335         for (l=lstart[k]; l<nrows; l++) {
1336           if (row[l] >= row_end) {
1337             lstart[k] = l;
1338             break;
1339           } else {
1340             ca[idx[l]] = ca_den_ptr[row[l]];
1341           }
1342         }
1343         ca_den_ptr += m;
1344       }
1345       row_end += brows;
1346       if (row_end > m) row_end = m;
1347     }
1348   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1349     ca_den_ptr = ca_den;
1350     for (k=0; k<ncolors; k++) {
1351       nrows = matcoloring->nrows[k];
1352       row   = rows  + colorforrow[k];
1353       idx   = den2sp + colorforrow[k];
1354       for (l=0; l<nrows; l++) {
1355         ca[idx[l]] = ca_den_ptr[row[l]];
1356       }
1357       ca_den_ptr += m;
1358     }
1359   }
1360 
1361   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1362 #if defined(PETSC_USE_INFO)
1363   if (matcoloring->brows > 0) {
1364     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1365   } else {
1366     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1367   }
1368 #endif
1369   PetscFunctionReturn(0);
1370 }
1371 
1372 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1373 {
1374   PetscErrorCode ierr;
1375   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1376   const PetscInt *is,*ci,*cj,*row_idx;
1377   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1378   IS             *isa;
1379   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1380   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1381   PetscInt       *colorforcol,*columns,*columns_i,brows;
1382   PetscBool      flg;
1383 
1384   PetscFunctionBegin;
1385   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1386 
1387   /* bs >1 is not being tested yet! */
1388   Nbs       = mat->cmap->N/bs;
1389   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1390   c->N      = Nbs;
1391   c->m      = c->M;
1392   c->rstart = 0;
1393   c->brows  = 100;
1394 
1395   c->ncolors = nis;
1396   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1397   ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr);
1398   ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr);
1399 
1400   brows = c->brows;
1401   ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1402   if (flg) c->brows = brows;
1403   if (brows > 0) {
1404     ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr);
1405   }
1406 
1407   colorforrow[0] = 0;
1408   rows_i         = rows;
1409   den2sp_i       = den2sp;
1410 
1411   ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr);
1412   ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr);
1413 
1414   colorforcol[0] = 0;
1415   columns_i      = columns;
1416 
1417   /* get column-wise storage of mat */
1418   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1419 
1420   cm   = c->m;
1421   ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr);
1422   ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr);
1423   for (i=0; i<nis; i++) { /* loop over color */
1424     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1425     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1426 
1427     c->ncolumns[i] = n;
1428     if (n) {
1429       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1430     }
1431     colorforcol[i+1] = colorforcol[i] + n;
1432     columns_i       += n;
1433 
1434     /* fast, crude version requires O(N*N) work */
1435     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1436 
1437     for (j=0; j<n; j++) { /* loop over columns*/
1438       col     = is[j];
1439       row_idx = cj + ci[col];
1440       m       = ci[col+1] - ci[col];
1441       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1442         idxhit[*row_idx]   = spidx[ci[col] + k];
1443         rowhit[*row_idx++] = col + 1;
1444       }
1445     }
1446     /* count the number of hits */
1447     nrows = 0;
1448     for (j=0; j<cm; j++) {
1449       if (rowhit[j]) nrows++;
1450     }
1451     c->nrows[i]      = nrows;
1452     colorforrow[i+1] = colorforrow[i] + nrows;
1453 
1454     nrows = 0;
1455     for (j=0; j<cm; j++) { /* loop over rows */
1456       if (rowhit[j]) {
1457         rows_i[nrows]   = j;
1458         den2sp_i[nrows] = idxhit[j];
1459         nrows++;
1460       }
1461     }
1462     den2sp_i += nrows;
1463 
1464     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1465     rows_i += nrows;
1466   }
1467   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1468   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1469   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1470   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1471 
1472   c->colorforrow = colorforrow;
1473   c->rows        = rows;
1474   c->den2sp      = den2sp;
1475   c->colorforcol = colorforcol;
1476   c->columns     = columns;
1477 
1478   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1479   PetscFunctionReturn(0);
1480 }
1481