xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 2b8d69ca7ea5fe9190df62c1dce3bbd66fce84dd)
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 #undef __FUNCT__
17 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
18 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
19 {
20   PetscErrorCode ierr;
21   const char     *algTypes[6] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed"};
22   PetscInt       alg=0; /* set default algorithm */
23 
24   PetscFunctionBegin;
25   if (scall == MAT_INITIAL_MATRIX) {
26     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
27     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,6,algTypes[0],&alg,NULL);CHKERRQ(ierr);
28     ierr = PetscOptionsEnd();CHKERRQ(ierr);
29     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
30     switch (alg) {
31     case 1:
32       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
33       break;
34     case 2:
35       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
36       break;
37     case 3:
38       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
39       break;
40     case 4:
41       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
42       break;
43     case 5:
44       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
45       break;
46     default:
47       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
48      break;
49     }
50     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
51   }
52 
53   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
54   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
55   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
56   PetscFunctionReturn(0);
57 }
58 
59 #undef __FUNCT__
60 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed"
61 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
62 {
63   PetscErrorCode     ierr;
64   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
65   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
66   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
67   PetscReal          afill;
68   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
69   PetscTable         ta;
70   PetscBT            lnkbt;
71   PetscFreeSpaceList free_space=NULL,current_space=NULL;
72 
73   PetscFunctionBegin;
74   /* Get ci and cj */
75   /*---------------*/
76   /* Allocate ci array, arrays for fill computation and */
77   /* free space for accumulating nonzero column info */
78   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
79   ci[0] = 0;
80 
81   /* create and initialize a linked list */
82   Crmax = 2*(b->rmax + (PetscInt)(1.e-2*bn)); /* expected Crmax */;
83   if (Crmax > bn) Crmax = bn;
84   ierr = PetscTableCreate(Crmax,bn,&ta);CHKERRQ(ierr);
85   MatRowMergeMax_SeqAIJ(b,bn,ta);
86   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
87   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
88 
89   ierr = PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);CHKERRQ(ierr);
90 
91   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
92   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
93 
94   current_space = free_space;
95 
96   /* Determine ci and cj */
97   for (i=0; i<am; i++) {
98     anzi = ai[i+1] - ai[i];
99     aj   = a->j + ai[i];
100     for (j=0; j<anzi; j++) {
101       brow = aj[j];
102       bnzj = bi[brow+1] - bi[brow];
103       bj   = b->j + bi[brow];
104       /* add non-zero cols of B into the sorted linked list lnk */
105       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
106     }
107     cnzi = lnk[0];
108 
109     /* If free space is not available, make more free space */
110     /* Double the amount of total space in the list */
111     if (current_space->local_remaining<cnzi) {
112       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
113       ndouble++;
114     }
115 
116     /* Copy data into free space, then initialize lnk */
117     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
118 
119     current_space->array           += cnzi;
120     current_space->local_used      += cnzi;
121     current_space->local_remaining -= cnzi;
122 
123     ci[i+1] = ci[i] + cnzi;
124   }
125 
126   /* Column indices are in the list of free space */
127   /* Allocate space for cj, initialize cj, and */
128   /* destroy list of free space and other temporary array(s) */
129   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
130   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
131   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
132 
133   /* put together the new symbolic matrix */
134   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
135   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
136 
137   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
138   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
139   c                         = (Mat_SeqAIJ*)((*C)->data);
140   c->free_a                 = PETSC_FALSE;
141   c->free_ij                = PETSC_TRUE;
142   c->nonew                  = 0;
143   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
144 
145   /* set MatInfo */
146   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
147   if (afill < 1.0) afill = 1.0;
148   c->maxnz                     = ci[am];
149   c->nz                        = ci[am];
150   (*C)->info.mallocs           = ndouble;
151   (*C)->info.fill_ratio_given  = fill;
152   (*C)->info.fill_ratio_needed = afill;
153 
154 #if defined(PETSC_USE_INFO)
155   if (ci[am]) {
156     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
157     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
158   } else {
159     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
160   }
161 #endif
162   PetscFunctionReturn(0);
163 }
164 
165 #undef __FUNCT__
166 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
167 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
168 {
169   PetscErrorCode ierr;
170   PetscLogDouble flops=0.0;
171   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
172   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
173   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
174   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
175   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
176   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
177   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
178   PetscScalar    *ab_dense;
179 
180   PetscFunctionBegin;
181   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
182     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
183     c->a      = ca;
184     c->free_a = PETSC_TRUE;
185   } else {
186     ca        = c->a;
187   }
188   if (!c->matmult_abdense) {
189     ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr);
190     c->matmult_abdense = ab_dense;
191   } else {
192     ab_dense = c->matmult_abdense;
193   }
194 
195   /* clean old values in C */
196   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
197   /* Traverse A row-wise. */
198   /* Build the ith row in C by summing over nonzero columns in A, */
199   /* the rows of B corresponding to nonzeros of A. */
200   for (i=0; i<am; i++) {
201     anzi = ai[i+1] - ai[i];
202     for (j=0; j<anzi; j++) {
203       brow = aj[j];
204       bnzi = bi[brow+1] - bi[brow];
205       bjj  = bj + bi[brow];
206       baj  = ba + bi[brow];
207       /* perform dense axpy */
208       valtmp = aa[j];
209       for (k=0; k<bnzi; k++) {
210         ab_dense[bjj[k]] += valtmp*baj[k];
211       }
212       flops += 2*bnzi;
213     }
214     aj += anzi; aa += anzi;
215 
216     cnzi = ci[i+1] - ci[i];
217     for (k=0; k<cnzi; k++) {
218       ca[k]          += ab_dense[cj[k]];
219       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
220     }
221     flops += cnzi;
222     cj    += cnzi; ca += cnzi;
223   }
224   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
225   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
226   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
227   PetscFunctionReturn(0);
228 }
229 
230 #undef __FUNCT__
231 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
232 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
233 {
234   PetscErrorCode ierr;
235   PetscLogDouble flops=0.0;
236   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
237   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
238   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
239   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
240   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
241   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
242   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
243   PetscInt       nextb;
244 
245   PetscFunctionBegin;
246   /* clean old values in C */
247   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
248   /* Traverse A row-wise. */
249   /* Build the ith row in C by summing over nonzero columns in A, */
250   /* the rows of B corresponding to nonzeros of A. */
251   for (i=0; i<am; i++) {
252     anzi = ai[i+1] - ai[i];
253     cnzi = ci[i+1] - ci[i];
254     for (j=0; j<anzi; j++) {
255       brow = aj[j];
256       bnzi = bi[brow+1] - bi[brow];
257       bjj  = bj + bi[brow];
258       baj  = ba + bi[brow];
259       /* perform sparse axpy */
260       valtmp = aa[j];
261       nextb  = 0;
262       for (k=0; nextb<bnzi; k++) {
263         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
264           ca[k] += valtmp*baj[nextb++];
265         }
266       }
267       flops += 2*bnzi;
268     }
269     aj += anzi; aa += anzi;
270     cj += cnzi; ca += cnzi;
271   }
272 
273   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
274   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
275   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
276   PetscFunctionReturn(0);
277 }
278 
279 #undef __FUNCT__
280 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
281 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
282 {
283   PetscErrorCode     ierr;
284   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
285   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
286   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
287   MatScalar          *ca;
288   PetscReal          afill;
289   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
290   PetscTable         ta;
291   PetscFreeSpaceList free_space=NULL,current_space=NULL;
292 
293   PetscFunctionBegin;
294   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
295   /*-----------------------------------------------------------------------------------------*/
296   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
297   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
298   ci[0] = 0;
299 
300   /* create and initialize a linked list */
301   Crmax = 2*(b->rmax + (PetscInt)(1.e-2*bn)); /* expected Crmax */
302   if (Crmax > bn) Crmax = bn;
303   ierr = PetscTableCreate(Crmax,bn,&ta);CHKERRQ(ierr);
304   MatRowMergeMax_SeqAIJ(b,bn,ta);
305   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
306   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
307 
308   ierr = PetscLLCondensedCreate_fast(Crmax,&lnk);CHKERRQ(ierr);
309 
310   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
311   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
312   current_space = free_space;
313 
314   /* Determine ci and cj */
315   for (i=0; i<am; i++) {
316     anzi = ai[i+1] - ai[i];
317     aj   = a->j + ai[i];
318     for (j=0; j<anzi; j++) {
319       brow = aj[j];
320       bnzj = bi[brow+1] - bi[brow];
321       bj   = b->j + bi[brow];
322       /* add non-zero cols of B into the sorted linked list lnk */
323       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
324     }
325     cnzi = lnk[1];
326 
327     /* If free space is not available, make more free space */
328     /* Double the amount of total space in the list */
329     if (current_space->local_remaining<cnzi) {
330       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
331       ndouble++;
332     }
333 
334     /* Copy data into free space, then initialize lnk */
335     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
336 
337     current_space->array           += cnzi;
338     current_space->local_used      += cnzi;
339     current_space->local_remaining -= cnzi;
340 
341     ci[i+1] = ci[i] + cnzi;
342   }
343 
344   /* Column indices are in the list of free space */
345   /* Allocate space for cj, initialize cj, and */
346   /* destroy list of free space and other temporary array(s) */
347   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
348   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
349   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
350 
351   /* Allocate space for ca */
352   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
353   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
354 
355   /* put together the new symbolic matrix */
356   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
357   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
358 
359   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
360   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
361   c          = (Mat_SeqAIJ*)((*C)->data);
362   c->free_a  = PETSC_TRUE;
363   c->free_ij = PETSC_TRUE;
364   c->nonew   = 0;
365 
366   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
367 
368   /* set MatInfo */
369   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
370   if (afill < 1.0) afill = 1.0;
371   c->maxnz                     = ci[am];
372   c->nz                        = ci[am];
373   (*C)->info.mallocs           = ndouble;
374   (*C)->info.fill_ratio_given  = fill;
375   (*C)->info.fill_ratio_needed = afill;
376 
377 #if defined(PETSC_USE_INFO)
378   if (ci[am]) {
379     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
380     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
381   } else {
382     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
383   }
384 #endif
385   PetscFunctionReturn(0);
386 }
387 
388 
389 #undef __FUNCT__
390 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
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   Crmax = 2*(b->rmax  + (PetscInt)(1.e-2*bn)); /* expected Crmax */
412   if (Crmax > bn) Crmax = bn;
413   ierr = PetscTableCreate(Crmax,bn,&ta);CHKERRQ(ierr);
414   MatRowMergeMax_SeqAIJ(b,bn,ta);
415   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
416   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
417 
418   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
419 
420   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
421   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
422   current_space = free_space;
423 
424   /* Determine ci and cj */
425   for (i=0; i<am; i++) {
426     anzi = ai[i+1] - ai[i];
427     aj   = a->j + ai[i];
428     for (j=0; j<anzi; j++) {
429       brow = aj[j];
430       bnzj = bi[brow+1] - bi[brow];
431       bj   = b->j + bi[brow];
432       /* add non-zero cols of B into the sorted linked list lnk */
433       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
434     }
435     cnzi = lnk[0];
436 
437     /* If free space is not available, make more free space */
438     /* Double the amount of total space in the list */
439     if (current_space->local_remaining<cnzi) {
440       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
441       ndouble++;
442     }
443 
444     /* Copy data into free space, then initialize lnk */
445     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
446 
447     current_space->array           += cnzi;
448     current_space->local_used      += cnzi;
449     current_space->local_remaining -= cnzi;
450 
451     ci[i+1] = ci[i] + cnzi;
452   }
453 
454   /* Column indices are in the list of free space */
455   /* Allocate space for cj, initialize cj, and */
456   /* destroy list of free space and other temporary array(s) */
457   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
458   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
459   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
460 
461   /* Allocate space for ca */
462   /*-----------------------*/
463   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
464   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
465 
466   /* put together the new symbolic matrix */
467   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
468   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
469 
470   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
471   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
472   c          = (Mat_SeqAIJ*)((*C)->data);
473   c->free_a  = PETSC_TRUE;
474   c->free_ij = PETSC_TRUE;
475   c->nonew   = 0;
476 
477   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
478 
479   /* set MatInfo */
480   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
481   if (afill < 1.0) afill = 1.0;
482   c->maxnz                     = ci[am];
483   c->nz                        = ci[am];
484   (*C)->info.mallocs           = ndouble;
485   (*C)->info.fill_ratio_given  = fill;
486   (*C)->info.fill_ratio_needed = afill;
487 
488 #if defined(PETSC_USE_INFO)
489   if (ci[am]) {
490     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
491     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
492   } else {
493     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
494   }
495 #endif
496   PetscFunctionReturn(0);
497 }
498 
499 #undef __FUNCT__
500 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
501 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
502 {
503   PetscErrorCode     ierr;
504   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
505   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
506   PetscInt           *ci,*cj,*bb;
507   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
508   PetscReal          afill;
509   PetscInt           i,j,col,ndouble = 0;
510   PetscFreeSpaceList free_space=NULL,current_space=NULL;
511   PetscHeap          h;
512 
513   PetscFunctionBegin;
514   /* Get ci and cj - by merging sorted rows using a heap */
515   /*---------------------------------------------------------------------------------------------*/
516   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
517   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
518   ci[0] = 0;
519 
520   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
521   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
522   current_space = free_space;
523 
524   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
525   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
526 
527   /* Determine ci and cj */
528   for (i=0; i<am; i++) {
529     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 */
530     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
531     ci[i+1] = ci[i];
532     /* Populate the min heap */
533     for (j=0; j<anzi; j++) {
534       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
535       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
536         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
537       }
538     }
539     /* Pick off the min element, adding it to free space */
540     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
541     while (j >= 0) {
542       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
543         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
544         ndouble++;
545       }
546       *(current_space->array++) = col;
547       current_space->local_used++;
548       current_space->local_remaining--;
549       ci[i+1]++;
550 
551       /* stash if anything else remains in this row of B */
552       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
553       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
554         PetscInt j2,col2;
555         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
556         if (col2 != col) break;
557         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
558         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
559       }
560       /* Put any stashed elements back into the min heap */
561       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
562       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
563     }
564   }
565   ierr = PetscFree(bb);CHKERRQ(ierr);
566   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
567 
568   /* Column indices are in the list of free space */
569   /* Allocate space for cj, initialize cj, and */
570   /* destroy list of free space and other temporary array(s) */
571   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
572   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
573 
574   /* put together the new symbolic matrix */
575   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
576   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
577 
578   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
579   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
580   c          = (Mat_SeqAIJ*)((*C)->data);
581   c->free_a  = PETSC_TRUE;
582   c->free_ij = PETSC_TRUE;
583   c->nonew   = 0;
584 
585   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
586 
587   /* set MatInfo */
588   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
589   if (afill < 1.0) afill = 1.0;
590   c->maxnz                     = ci[am];
591   c->nz                        = ci[am];
592   (*C)->info.mallocs           = ndouble;
593   (*C)->info.fill_ratio_given  = fill;
594   (*C)->info.fill_ratio_needed = afill;
595 
596 #if defined(PETSC_USE_INFO)
597   if (ci[am]) {
598     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
599     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
600   } else {
601     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
602   }
603 #endif
604   PetscFunctionReturn(0);
605 }
606 
607 #undef __FUNCT__
608 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
609 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
610 {
611   PetscErrorCode     ierr;
612   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
613   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
614   PetscInt           *ci,*cj,*bb;
615   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
616   PetscReal          afill;
617   PetscInt           i,j,col,ndouble = 0;
618   PetscFreeSpaceList free_space=NULL,current_space=NULL;
619   PetscHeap          h;
620   PetscBT            bt;
621 
622   PetscFunctionBegin;
623   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
624   /*---------------------------------------------------------------------------------------------*/
625   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
626   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
627   ci[0] = 0;
628 
629   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
630   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
631 
632   current_space = free_space;
633 
634   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
635   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
636   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
637 
638   /* Determine ci and cj */
639   for (i=0; i<am; i++) {
640     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 */
641     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
642     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
643     ci[i+1] = ci[i];
644     /* Populate the min heap */
645     for (j=0; j<anzi; j++) {
646       PetscInt brow = acol[j];
647       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
648         PetscInt bcol = bj[bb[j]];
649         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
650           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
651           bb[j]++;
652           break;
653         }
654       }
655     }
656     /* Pick off the min element, adding it to free space */
657     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
658     while (j >= 0) {
659       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
660         fptr = NULL;                      /* need PetscBTMemzero */
661         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
662         ndouble++;
663       }
664       *(current_space->array++) = col;
665       current_space->local_used++;
666       current_space->local_remaining--;
667       ci[i+1]++;
668 
669       /* stash if anything else remains in this row of B */
670       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
671         PetscInt bcol = bj[bb[j]];
672         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
673           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
674           bb[j]++;
675           break;
676         }
677       }
678       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
679     }
680     if (fptr) {                 /* Clear the bits for this row */
681       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
682     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
683       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
684     }
685   }
686   ierr = PetscFree(bb);CHKERRQ(ierr);
687   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
688   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
689 
690   /* Column indices are in the list of free space */
691   /* Allocate space for cj, initialize cj, and */
692   /* destroy list of free space and other temporary array(s) */
693   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
694   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
695 
696   /* put together the new symbolic matrix */
697   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
698   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
699 
700   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
701   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
702   c          = (Mat_SeqAIJ*)((*C)->data);
703   c->free_a  = PETSC_TRUE;
704   c->free_ij = PETSC_TRUE;
705   c->nonew   = 0;
706 
707   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
708 
709   /* set MatInfo */
710   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
711   if (afill < 1.0) afill = 1.0;
712   c->maxnz                     = ci[am];
713   c->nz                        = ci[am];
714   (*C)->info.mallocs           = ndouble;
715   (*C)->info.fill_ratio_given  = fill;
716   (*C)->info.fill_ratio_needed = afill;
717 
718 #if defined(PETSC_USE_INFO)
719   if (ci[am]) {
720     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
721     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
722   } else {
723     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
724   }
725 #endif
726   PetscFunctionReturn(0);
727 }
728 
729 #undef __FUNCT__
730 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
731 /* concatenate unique entries and then sort */
732 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
733 {
734   PetscErrorCode     ierr;
735   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
736   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
737   PetscInt           *ci,*cj;
738   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
739   PetscReal          afill;
740   PetscInt           i,j,ndouble = 0;
741   PetscSegBuffer     seg,segrow;
742   char               *seen;
743 
744   PetscFunctionBegin;
745   ierr  = PetscMalloc1(am+1,&ci);CHKERRQ(ierr);
746   ci[0] = 0;
747 
748   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
749   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
750   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
751   ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr);
752   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
753 
754   /* Determine ci and cj */
755   for (i=0; i<am; i++) {
756     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 */
757     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
758     PetscInt packlen = 0,*PETSC_RESTRICT crow;
759     /* Pack segrow */
760     for (j=0; j<anzi; j++) {
761       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
762       for (k=bjstart; k<bjend; k++) {
763         PetscInt bcol = bj[k];
764         if (!seen[bcol]) { /* new entry */
765           PetscInt *PETSC_RESTRICT slot;
766           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
767           *slot = bcol;
768           seen[bcol] = 1;
769           packlen++;
770         }
771       }
772     }
773     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
774     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
775     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
776     ci[i+1] = ci[i] + packlen;
777     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
778   }
779   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
780   ierr = PetscFree(seen);CHKERRQ(ierr);
781 
782   /* Column indices are in the segmented buffer */
783   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
784   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
785 
786   /* put together the new symbolic matrix */
787   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
788   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
789 
790   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
791   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
792   c          = (Mat_SeqAIJ*)((*C)->data);
793   c->free_a  = PETSC_TRUE;
794   c->free_ij = PETSC_TRUE;
795   c->nonew   = 0;
796 
797   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
798 
799   /* set MatInfo */
800   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
801   if (afill < 1.0) afill = 1.0;
802   c->maxnz                     = ci[am];
803   c->nz                        = ci[am];
804   (*C)->info.mallocs           = ndouble;
805   (*C)->info.fill_ratio_given  = fill;
806   (*C)->info.fill_ratio_needed = afill;
807 
808 #if defined(PETSC_USE_INFO)
809   if (ci[am]) {
810     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
811     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
812   } else {
813     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
814   }
815 #endif
816   PetscFunctionReturn(0);
817 }
818 
819 /* This routine is not used. Should be removed! */
820 #undef __FUNCT__
821 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
822 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
823 {
824   PetscErrorCode ierr;
825 
826   PetscFunctionBegin;
827   if (scall == MAT_INITIAL_MATRIX) {
828     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
829     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
830     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
831   }
832   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
833   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
834   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
835   PetscFunctionReturn(0);
836 }
837 
838 #undef __FUNCT__
839 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
840 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
841 {
842   PetscErrorCode      ierr;
843   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
844   Mat_MatMatTransMult *abt=a->abt;
845 
846   PetscFunctionBegin;
847   ierr = (abt->destroy)(A);CHKERRQ(ierr);
848   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
849   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
850   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
851   ierr = PetscFree(abt);CHKERRQ(ierr);
852   PetscFunctionReturn(0);
853 }
854 
855 #undef __FUNCT__
856 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
857 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
858 {
859   PetscErrorCode      ierr;
860   Mat                 Bt;
861   PetscInt            *bti,*btj;
862   Mat_MatMatTransMult *abt;
863   Mat_SeqAIJ          *c;
864 
865   PetscFunctionBegin;
866   /* create symbolic Bt */
867   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
868   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
869   ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
870 
871   /* get symbolic C=A*Bt */
872   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
873 
874   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
875   ierr   = PetscNew(&abt);CHKERRQ(ierr);
876   c      = (Mat_SeqAIJ*)(*C)->data;
877   c->abt = abt;
878 
879   abt->usecoloring = PETSC_FALSE;
880   abt->destroy     = (*C)->ops->destroy;
881   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
882 
883   ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
884   if (abt->usecoloring) {
885     /* Create MatTransposeColoring from symbolic C=A*B^T */
886     MatTransposeColoring matcoloring;
887     MatColoring          coloring;
888     ISColoring           iscoloring;
889     Mat                  Bt_dense,C_dense;
890     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
891     /* inode causes memory problem, don't know why */
892     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
893 
894     ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
895     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
896     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
897     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
898     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
899     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
900     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
901 
902     abt->matcoloring = matcoloring;
903 
904     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
905 
906     /* Create Bt_dense and C_dense = A*Bt_dense */
907     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
908     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
909     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
910     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
911 
912     Bt_dense->assembled = PETSC_TRUE;
913     abt->Bt_den   = Bt_dense;
914 
915     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
916     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
917     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
918     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
919 
920     Bt_dense->assembled = PETSC_TRUE;
921     abt->ABt_den  = C_dense;
922 
923 #if defined(PETSC_USE_INFO)
924     {
925       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
926       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);
927     }
928 #endif
929   }
930   /* clean up */
931   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
932   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
933   PetscFunctionReturn(0);
934 }
935 
936 #undef __FUNCT__
937 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
938 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
939 {
940   PetscErrorCode      ierr;
941   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
942   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
943   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
944   PetscLogDouble      flops=0.0;
945   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
946   Mat_MatMatTransMult *abt = c->abt;
947 
948   PetscFunctionBegin;
949   /* clear old values in C */
950   if (!c->a) {
951     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
952     c->a      = ca;
953     c->free_a = PETSC_TRUE;
954   } else {
955     ca =  c->a;
956   }
957   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
958 
959   if (abt->usecoloring) {
960     MatTransposeColoring matcoloring = abt->matcoloring;
961     Mat                  Bt_dense,C_dense = abt->ABt_den;
962 
963     /* Get Bt_dense by Apply MatTransposeColoring to B */
964     Bt_dense = abt->Bt_den;
965     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
966 
967     /* C_dense = A*Bt_dense */
968     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
969 
970     /* Recover C from C_dense */
971     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
972     PetscFunctionReturn(0);
973   }
974 
975   for (i=0; i<cm; i++) {
976     anzi = ai[i+1] - ai[i];
977     acol = aj + ai[i];
978     aval = aa + ai[i];
979     cnzi = ci[i+1] - ci[i];
980     ccol = cj + ci[i];
981     cval = ca + ci[i];
982     for (j=0; j<cnzi; j++) {
983       brow = ccol[j];
984       bnzj = bi[brow+1] - bi[brow];
985       bcol = bj + bi[brow];
986       bval = ba + bi[brow];
987 
988       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
989       nexta = 0; nextb = 0;
990       while (nexta<anzi && nextb<bnzj) {
991         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
992         if (nexta == anzi) break;
993         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
994         if (nextb == bnzj) break;
995         if (acol[nexta] == bcol[nextb]) {
996           cval[j] += aval[nexta]*bval[nextb];
997           nexta++; nextb++;
998           flops += 2;
999         }
1000       }
1001     }
1002   }
1003   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1004   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1005   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1006   PetscFunctionReturn(0);
1007 }
1008 
1009 #undef __FUNCT__
1010 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1011 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1012 {
1013   PetscErrorCode ierr;
1014 
1015   PetscFunctionBegin;
1016   if (scall == MAT_INITIAL_MATRIX) {
1017     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1018     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1019     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1020   }
1021   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1022   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1023   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 #undef __FUNCT__
1028 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1029 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1030 {
1031   PetscErrorCode ierr;
1032   Mat            At;
1033   PetscInt       *ati,*atj;
1034 
1035   PetscFunctionBegin;
1036   /* create symbolic At */
1037   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1038   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1039   ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1040 
1041   /* get symbolic C=At*B */
1042   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1043 
1044   /* clean up */
1045   ierr = MatDestroy(&At);CHKERRQ(ierr);
1046   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1047   PetscFunctionReturn(0);
1048 }
1049 
1050 #undef __FUNCT__
1051 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1052 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1053 {
1054   PetscErrorCode ierr;
1055   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1056   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1057   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1058   PetscLogDouble flops=0.0;
1059   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1060 
1061   PetscFunctionBegin;
1062   if (!c->a) {
1063     ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
1064 
1065     c->a      = ca;
1066     c->free_a = PETSC_TRUE;
1067   } else {
1068     ca = c->a;
1069   }
1070   /* clear old values in C */
1071   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1072 
1073   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1074   for (i=0; i<am; i++) {
1075     bj   = b->j + bi[i];
1076     ba   = b->a + bi[i];
1077     bnzi = bi[i+1] - bi[i];
1078     anzi = ai[i+1] - ai[i];
1079     for (j=0; j<anzi; j++) {
1080       nextb = 0;
1081       crow  = *aj++;
1082       cjj   = cj + ci[crow];
1083       caj   = ca + ci[crow];
1084       /* perform sparse axpy operation.  Note cjj includes bj. */
1085       for (k=0; nextb<bnzi; k++) {
1086         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1087           caj[k] += (*aa)*(*(ba+nextb));
1088           nextb++;
1089         }
1090       }
1091       flops += 2*bnzi;
1092       aa++;
1093     }
1094   }
1095 
1096   /* Assemble the final matrix and clean up */
1097   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1098   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1099   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1100   PetscFunctionReturn(0);
1101 }
1102 
1103 #undef __FUNCT__
1104 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1105 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1106 {
1107   PetscErrorCode ierr;
1108 
1109   PetscFunctionBegin;
1110   if (scall == MAT_INITIAL_MATRIX) {
1111     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1112     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1113     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1114   }
1115   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1116   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1117   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1118   PetscFunctionReturn(0);
1119 }
1120 
1121 #undef __FUNCT__
1122 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1123 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1124 {
1125   PetscErrorCode ierr;
1126 
1127   PetscFunctionBegin;
1128   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1129 
1130   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1131   PetscFunctionReturn(0);
1132 }
1133 
1134 #undef __FUNCT__
1135 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1136 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1137 {
1138   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1139   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
1140   PetscErrorCode    ierr;
1141   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1142   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1143   const PetscInt    *aj;
1144   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n;
1145   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;
1146 
1147   PetscFunctionBegin;
1148   if (!cm || !cn) PetscFunctionReturn(0);
1149   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);
1150   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);
1151   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);
1152   b = bd->v;
1153   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1154   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1155   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1156   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1157     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1158       r1 = r2 = r3 = r4 = 0.0;
1159       n  = a->i[i+1] - a->i[i];
1160       aj = a->j + a->i[i];
1161       aa = a->a + a->i[i];
1162       for (j=0; j<n; j++) {
1163         aatmp = aa[j]; ajtmp = aj[j];
1164         r1 += aatmp*b1[ajtmp];
1165         r2 += aatmp*b2[ajtmp];
1166         r3 += aatmp*b3[ajtmp];
1167         r4 += aatmp*b4[ajtmp];
1168       }
1169       c1[i] = r1;
1170       c2[i] = r2;
1171       c3[i] = r3;
1172       c4[i] = r4;
1173     }
1174     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1175     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1176   }
1177   for (; col<cn; col++) {   /* over extra columns of C */
1178     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1179       r1 = 0.0;
1180       n  = a->i[i+1] - a->i[i];
1181       aj = a->j + a->i[i];
1182       aa = a->a + a->i[i];
1183       for (j=0; j<n; j++) {
1184         r1 += aa[j]*b1[aj[j]];
1185       }
1186       c1[i] = r1;
1187     }
1188     b1 += bm;
1189     c1 += am;
1190   }
1191   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1192   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1193   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1194   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1195   PetscFunctionReturn(0);
1196 }
1197 
1198 /*
1199    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1200 */
1201 #undef __FUNCT__
1202 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1203 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1204 {
1205   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1206   Mat_SeqDense   *bd = (Mat_SeqDense*)B->data;
1207   PetscErrorCode ierr;
1208   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1209   MatScalar      *aa;
1210   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1211   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1212 
1213   PetscFunctionBegin;
1214   if (!cm || !cn) PetscFunctionReturn(0);
1215   b = bd->v;
1216   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1217   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1218 
1219   if (a->compressedrow.use) { /* use compressed row format */
1220     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1221       colam = col*am;
1222       arm   = a->compressedrow.nrows;
1223       ii    = a->compressedrow.i;
1224       ridx  = a->compressedrow.rindex;
1225       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1226         r1 = r2 = r3 = r4 = 0.0;
1227         n  = ii[i+1] - ii[i];
1228         aj = a->j + ii[i];
1229         aa = a->a + ii[i];
1230         for (j=0; j<n; j++) {
1231           r1 += (*aa)*b1[*aj];
1232           r2 += (*aa)*b2[*aj];
1233           r3 += (*aa)*b3[*aj];
1234           r4 += (*aa++)*b4[*aj++];
1235         }
1236         c[colam       + ridx[i]] += r1;
1237         c[colam + am  + ridx[i]] += r2;
1238         c[colam + am2 + ridx[i]] += r3;
1239         c[colam + am3 + ridx[i]] += r4;
1240       }
1241       b1 += bm4;
1242       b2 += bm4;
1243       b3 += bm4;
1244       b4 += bm4;
1245     }
1246     for (; col<cn; col++) {     /* over extra columns of C */
1247       colam = col*am;
1248       arm   = a->compressedrow.nrows;
1249       ii    = a->compressedrow.i;
1250       ridx  = a->compressedrow.rindex;
1251       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1252         r1 = 0.0;
1253         n  = ii[i+1] - ii[i];
1254         aj = a->j + ii[i];
1255         aa = a->a + ii[i];
1256 
1257         for (j=0; j<n; j++) {
1258           r1 += (*aa++)*b1[*aj++];
1259         }
1260         c[colam + ridx[i]] += r1;
1261       }
1262       b1 += bm;
1263     }
1264   } else {
1265     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1266       colam = col*am;
1267       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1268         r1 = r2 = r3 = r4 = 0.0;
1269         n  = a->i[i+1] - a->i[i];
1270         aj = a->j + a->i[i];
1271         aa = a->a + a->i[i];
1272         for (j=0; j<n; j++) {
1273           r1 += (*aa)*b1[*aj];
1274           r2 += (*aa)*b2[*aj];
1275           r3 += (*aa)*b3[*aj];
1276           r4 += (*aa++)*b4[*aj++];
1277         }
1278         c[colam + i]       += r1;
1279         c[colam + am + i]  += r2;
1280         c[colam + am2 + i] += r3;
1281         c[colam + am3 + i] += r4;
1282       }
1283       b1 += bm4;
1284       b2 += bm4;
1285       b3 += bm4;
1286       b4 += bm4;
1287     }
1288     for (; col<cn; col++) {     /* over extra columns of C */
1289       colam = col*am;
1290       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1291         r1 = 0.0;
1292         n  = a->i[i+1] - a->i[i];
1293         aj = a->j + a->i[i];
1294         aa = a->a + a->i[i];
1295 
1296         for (j=0; j<n; j++) {
1297           r1 += (*aa++)*b1[*aj++];
1298         }
1299         c[colam + i] += r1;
1300       }
1301       b1 += bm;
1302     }
1303   }
1304   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1305   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1306   PetscFunctionReturn(0);
1307 }
1308 
1309 #undef __FUNCT__
1310 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1311 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1312 {
1313   PetscErrorCode ierr;
1314   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1315   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1316   PetscInt       *bi      = b->i,*bj=b->j;
1317   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1318   MatScalar      *btval,*btval_den,*ba=b->a;
1319   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1320 
1321   PetscFunctionBegin;
1322   btval_den=btdense->v;
1323   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1324   for (k=0; k<ncolors; k++) {
1325     ncolumns = coloring->ncolumns[k];
1326     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1327       col   = *(columns + colorforcol[k] + l);
1328       btcol = bj + bi[col];
1329       btval = ba + bi[col];
1330       anz   = bi[col+1] - bi[col];
1331       for (j=0; j<anz; j++) {
1332         brow            = btcol[j];
1333         btval_den[brow] = btval[j];
1334       }
1335     }
1336     btval_den += m;
1337   }
1338   PetscFunctionReturn(0);
1339 }
1340 
1341 #undef __FUNCT__
1342 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1343 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1344 {
1345   PetscErrorCode ierr;
1346   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1347   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1348   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1349   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1350   PetscInt       nrows,*row,*idx;
1351   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1352 
1353   PetscFunctionBegin;
1354   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1355 
1356   if (brows > 0) {
1357     PetscInt *lstart,row_end,row_start;
1358     lstart = matcoloring->lstart;
1359     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1360 
1361     row_end = brows;
1362     if (row_end > m) row_end = m;
1363     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1364       ca_den_ptr = ca_den;
1365       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1366         nrows = matcoloring->nrows[k];
1367         row   = rows  + colorforrow[k];
1368         idx   = den2sp + colorforrow[k];
1369         for (l=lstart[k]; l<nrows; l++) {
1370           if (row[l] >= row_end) {
1371             lstart[k] = l;
1372             break;
1373           } else {
1374             ca[idx[l]] = ca_den_ptr[row[l]];
1375           }
1376         }
1377         ca_den_ptr += m;
1378       }
1379       row_end += brows;
1380       if (row_end > m) row_end = m;
1381     }
1382   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1383     ca_den_ptr = ca_den;
1384     for (k=0; k<ncolors; k++) {
1385       nrows = matcoloring->nrows[k];
1386       row   = rows  + colorforrow[k];
1387       idx   = den2sp + colorforrow[k];
1388       for (l=0; l<nrows; l++) {
1389         ca[idx[l]] = ca_den_ptr[row[l]];
1390       }
1391       ca_den_ptr += m;
1392     }
1393   }
1394 
1395   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1396 #if defined(PETSC_USE_INFO)
1397   if (matcoloring->brows > 0) {
1398     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1399   } else {
1400     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1401   }
1402 #endif
1403   PetscFunctionReturn(0);
1404 }
1405 
1406 #undef __FUNCT__
1407 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1408 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1409 {
1410   PetscErrorCode ierr;
1411   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1412   const PetscInt *is,*ci,*cj,*row_idx;
1413   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1414   IS             *isa;
1415   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1416   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1417   PetscInt       *colorforcol,*columns,*columns_i,brows;
1418   PetscBool      flg;
1419 
1420   PetscFunctionBegin;
1421   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1422 
1423   /* bs >1 is not being tested yet! */
1424   Nbs       = mat->cmap->N/bs;
1425   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1426   c->N      = Nbs;
1427   c->m      = c->M;
1428   c->rstart = 0;
1429   c->brows  = 100;
1430 
1431   c->ncolors = nis;
1432   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1433   ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr);
1434   ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr);
1435 
1436   brows = c->brows;
1437   ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1438   if (flg) c->brows = brows;
1439   if (brows > 0) {
1440     ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr);
1441   }
1442 
1443   colorforrow[0] = 0;
1444   rows_i         = rows;
1445   den2sp_i       = den2sp;
1446 
1447   ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr);
1448   ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr);
1449 
1450   colorforcol[0] = 0;
1451   columns_i      = columns;
1452 
1453   /* get column-wise storage of mat */
1454   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1455 
1456   cm   = c->m;
1457   ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr);
1458   ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr);
1459   for (i=0; i<nis; i++) { /* loop over color */
1460     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1461     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1462 
1463     c->ncolumns[i] = n;
1464     if (n) {
1465       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1466     }
1467     colorforcol[i+1] = colorforcol[i] + n;
1468     columns_i       += n;
1469 
1470     /* fast, crude version requires O(N*N) work */
1471     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1472 
1473     for (j=0; j<n; j++) { /* loop over columns*/
1474       col     = is[j];
1475       row_idx = cj + ci[col];
1476       m       = ci[col+1] - ci[col];
1477       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1478         idxhit[*row_idx]   = spidx[ci[col] + k];
1479         rowhit[*row_idx++] = col + 1;
1480       }
1481     }
1482     /* count the number of hits */
1483     nrows = 0;
1484     for (j=0; j<cm; j++) {
1485       if (rowhit[j]) nrows++;
1486     }
1487     c->nrows[i]      = nrows;
1488     colorforrow[i+1] = colorforrow[i] + nrows;
1489 
1490     nrows = 0;
1491     for (j=0; j<cm; j++) { /* loop over rows */
1492       if (rowhit[j]) {
1493         rows_i[nrows]   = j;
1494         den2sp_i[nrows] = idxhit[j];
1495         nrows++;
1496       }
1497     }
1498     den2sp_i += nrows;
1499 
1500     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1501     rows_i += nrows;
1502   }
1503   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1504   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1505   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1506   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1507 
1508   c->colorforrow = colorforrow;
1509   c->rows        = rows;
1510   c->den2sp      = den2sp;
1511   c->colorforcol = colorforcol;
1512   c->columns     = columns;
1513 
1514   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1515   PetscFunctionReturn(0);
1516 }
1517