xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision fce0c873789145caee477924bfa4ad26b4cd6ea4)
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 <../src/mat/impls/dense/seq/dense.h>
12 
13 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);
14 
15 #undef __FUNCT__
16 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
17 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
18 {
19   PetscErrorCode ierr;
20   const char     *algTypes[6] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed"};
21   PetscInt       alg=0; /* set default algorithm */
22 
23   PetscFunctionBegin;
24   if (scall == MAT_INITIAL_MATRIX) {
25     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
26     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,6,algTypes[0],&alg,NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsEnd();CHKERRQ(ierr);
28     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
29     switch (alg) {
30     case 1:
31       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
32       break;
33     case 2:
34       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
35       break;
36     case 3:
37       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
38       break;
39     case 4:
40       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
41       break;
42     case 5:
43       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
44       break;
45     default:
46       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
47      break;
48     }
49     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
50   }
51 
52   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
53   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
54   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
55   PetscFunctionReturn(0);
56 }
57 
58 #undef __FUNCT__
59 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed"
60 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
61 {
62   PetscErrorCode     ierr;
63   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
64   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
65   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
66   PetscReal          afill;
67   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
68   PetscBT            lnkbt;
69   PetscFreeSpaceList free_space=NULL,current_space=NULL;
70 
71   PetscFunctionBegin;
72   /* Get ci and cj */
73   /*---------------*/
74   /* Allocate ci array, arrays for fill computation and */
75   /* free space for accumulating nonzero column info */
76   ierr  = PetscMalloc1(((am+1)+1),&ci);CHKERRQ(ierr);
77   ci[0] = 0;
78 
79   /* create and initialize a linked list */
80   nlnk_max = a->rmax*b->rmax;
81   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
82   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
83 
84   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
85   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
86 
87   current_space = free_space;
88 
89   /* Determine ci and cj */
90   for (i=0; i<am; i++) {
91     anzi = ai[i+1] - ai[i];
92     aj   = a->j + ai[i];
93     for (j=0; j<anzi; j++) {
94       brow = aj[j];
95       bnzj = bi[brow+1] - bi[brow];
96       bj   = b->j + bi[brow];
97       /* add non-zero cols of B into the sorted linked list lnk */
98       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
99     }
100     cnzi = lnk[0];
101 
102     /* If free space is not available, make more free space */
103     /* Double the amount of total space in the list */
104     if (current_space->local_remaining<cnzi) {
105       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
106       ndouble++;
107     }
108 
109     /* Copy data into free space, then initialize lnk */
110     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
111 
112     current_space->array           += cnzi;
113     current_space->local_used      += cnzi;
114     current_space->local_remaining -= cnzi;
115 
116     ci[i+1] = ci[i] + cnzi;
117   }
118 
119   /* Column indices are in the list of free space */
120   /* Allocate space for cj, initialize cj, and */
121   /* destroy list of free space and other temporary array(s) */
122   ierr = PetscMalloc1((ci[am]+1),&cj);CHKERRQ(ierr);
123   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
124   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
125 
126   /* put together the new symbolic matrix */
127   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
128   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
129 
130   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
131   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
132   c                         = (Mat_SeqAIJ*)((*C)->data);
133   c->free_a                 = PETSC_FALSE;
134   c->free_ij                = PETSC_TRUE;
135   c->nonew                  = 0;
136   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
137 
138   /* set MatInfo */
139   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
140   if (afill < 1.0) afill = 1.0;
141   c->maxnz                     = ci[am];
142   c->nz                        = ci[am];
143   (*C)->info.mallocs           = ndouble;
144   (*C)->info.fill_ratio_given  = fill;
145   (*C)->info.fill_ratio_needed = afill;
146 
147 #if defined(PETSC_USE_INFO)
148   if (ci[am]) {
149     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
150     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
151   } else {
152     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
153   }
154 #endif
155   PetscFunctionReturn(0);
156 }
157 
158 #undef __FUNCT__
159 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
160 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
161 {
162   PetscErrorCode ierr;
163   PetscLogDouble flops=0.0;
164   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
165   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
166   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
167   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
168   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
169   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
170   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
171   PetscScalar    *ab_dense;
172 
173   PetscFunctionBegin;
174   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
175     ierr      = PetscMalloc1((ci[cm]+1),&ca);CHKERRQ(ierr);
176     c->a      = ca;
177     c->free_a = PETSC_TRUE;
178   } else {
179     ca        = c->a;
180   }
181   if (!c->matmult_abdense) {
182     ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr);
183     c->matmult_abdense = ab_dense;
184   } else {
185     ab_dense = c->matmult_abdense;
186   }
187 
188   /* clean old values in C */
189   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
190   /* Traverse A row-wise. */
191   /* Build the ith row in C by summing over nonzero columns in A, */
192   /* the rows of B corresponding to nonzeros of A. */
193   for (i=0; i<am; i++) {
194     anzi = ai[i+1] - ai[i];
195     for (j=0; j<anzi; j++) {
196       brow = aj[j];
197       bnzi = bi[brow+1] - bi[brow];
198       bjj  = bj + bi[brow];
199       baj  = ba + bi[brow];
200       /* perform dense axpy */
201       valtmp = aa[j];
202       for (k=0; k<bnzi; k++) {
203         ab_dense[bjj[k]] += valtmp*baj[k];
204       }
205       flops += 2*bnzi;
206     }
207     aj += anzi; aa += anzi;
208 
209     cnzi = ci[i+1] - ci[i];
210     for (k=0; k<cnzi; k++) {
211       ca[k]          += ab_dense[cj[k]];
212       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
213     }
214     flops += cnzi;
215     cj    += cnzi; ca += cnzi;
216   }
217   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
218   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
219   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
220   PetscFunctionReturn(0);
221 }
222 
223 #undef __FUNCT__
224 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
225 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
226 {
227   PetscErrorCode ierr;
228   PetscLogDouble flops=0.0;
229   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
230   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
231   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
232   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
233   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
234   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
235   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
236   PetscInt       nextb;
237 
238   PetscFunctionBegin;
239   /* clean old values in C */
240   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
241   /* Traverse A row-wise. */
242   /* Build the ith row in C by summing over nonzero columns in A, */
243   /* the rows of B corresponding to nonzeros of A. */
244   for (i=0; i<am; i++) {
245     anzi = ai[i+1] - ai[i];
246     cnzi = ci[i+1] - ci[i];
247     for (j=0; j<anzi; j++) {
248       brow = aj[j];
249       bnzi = bi[brow+1] - bi[brow];
250       bjj  = bj + bi[brow];
251       baj  = ba + bi[brow];
252       /* perform sparse axpy */
253       valtmp = aa[j];
254       nextb  = 0;
255       for (k=0; nextb<bnzi; k++) {
256         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
257           ca[k] += valtmp*baj[nextb++];
258         }
259       }
260       flops += 2*bnzi;
261     }
262     aj += anzi; aa += anzi;
263     cj += cnzi; ca += cnzi;
264   }
265 
266   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
267   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
268   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
269   PetscFunctionReturn(0);
270 }
271 
272 #undef __FUNCT__
273 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
274 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
275 {
276   PetscErrorCode     ierr;
277   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
278   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
279   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
280   MatScalar          *ca;
281   PetscReal          afill;
282   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
283   PetscFreeSpaceList free_space=NULL,current_space=NULL;
284 
285   PetscFunctionBegin;
286   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
287   /*-----------------------------------------------------------------------------------------*/
288   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
289   ierr  = PetscMalloc1(((am+1)+1),&ci);CHKERRQ(ierr);
290   ci[0] = 0;
291 
292   /* create and initialize a linked list */
293   nlnk_max = a->rmax*b->rmax;
294   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
295   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
296 
297   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
298   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
299   current_space = free_space;
300 
301   /* Determine ci and cj */
302   for (i=0; i<am; i++) {
303     anzi = ai[i+1] - ai[i];
304     aj   = a->j + ai[i];
305     for (j=0; j<anzi; j++) {
306       brow = aj[j];
307       bnzj = bi[brow+1] - bi[brow];
308       bj   = b->j + bi[brow];
309       /* add non-zero cols of B into the sorted linked list lnk */
310       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
311     }
312     cnzi = lnk[1];
313 
314     /* If free space is not available, make more free space */
315     /* Double the amount of total space in the list */
316     if (current_space->local_remaining<cnzi) {
317       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
318       ndouble++;
319     }
320 
321     /* Copy data into free space, then initialize lnk */
322     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
323 
324     current_space->array           += cnzi;
325     current_space->local_used      += cnzi;
326     current_space->local_remaining -= cnzi;
327 
328     ci[i+1] = ci[i] + cnzi;
329   }
330 
331   /* Column indices are in the list of free space */
332   /* Allocate space for cj, initialize cj, and */
333   /* destroy list of free space and other temporary array(s) */
334   ierr = PetscMalloc1((ci[am]+1),&cj);CHKERRQ(ierr);
335   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
336   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
337 
338   /* Allocate space for ca */
339   ierr = PetscMalloc1((ci[am]+1),&ca);CHKERRQ(ierr);
340   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
341 
342   /* put together the new symbolic matrix */
343   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
344   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
345 
346   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
347   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
348   c          = (Mat_SeqAIJ*)((*C)->data);
349   c->free_a  = PETSC_TRUE;
350   c->free_ij = PETSC_TRUE;
351   c->nonew   = 0;
352 
353   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
354 
355   /* set MatInfo */
356   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
357   if (afill < 1.0) afill = 1.0;
358   c->maxnz                     = ci[am];
359   c->nz                        = ci[am];
360   (*C)->info.mallocs           = ndouble;
361   (*C)->info.fill_ratio_given  = fill;
362   (*C)->info.fill_ratio_needed = afill;
363 
364 #if defined(PETSC_USE_INFO)
365   if (ci[am]) {
366     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
367     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
368   } else {
369     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
370   }
371 #endif
372   PetscFunctionReturn(0);
373 }
374 
375 
376 #undef __FUNCT__
377 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
378 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
379 {
380   PetscErrorCode     ierr;
381   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
382   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
383   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
384   MatScalar          *ca;
385   PetscReal          afill;
386   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
387   PetscFreeSpaceList free_space=NULL,current_space=NULL;
388 
389   PetscFunctionBegin;
390   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
391   /*---------------------------------------------------------------------------------------------*/
392   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
393   ierr  = PetscMalloc1(((am+1)+1),&ci);CHKERRQ(ierr);
394   ci[0] = 0;
395 
396   /* create and initialize a linked list */
397   nlnk_max = a->rmax*b->rmax;
398   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
399   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
400 
401   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
402   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
403   current_space = free_space;
404 
405   /* Determine ci and cj */
406   for (i=0; i<am; i++) {
407     anzi = ai[i+1] - ai[i];
408     aj   = a->j + ai[i];
409     for (j=0; j<anzi; j++) {
410       brow = aj[j];
411       bnzj = bi[brow+1] - bi[brow];
412       bj   = b->j + bi[brow];
413       /* add non-zero cols of B into the sorted linked list lnk */
414       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
415     }
416     cnzi = lnk[0];
417 
418     /* If free space is not available, make more free space */
419     /* Double the amount of total space in the list */
420     if (current_space->local_remaining<cnzi) {
421       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
422       ndouble++;
423     }
424 
425     /* Copy data into free space, then initialize lnk */
426     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
427 
428     current_space->array           += cnzi;
429     current_space->local_used      += cnzi;
430     current_space->local_remaining -= cnzi;
431 
432     ci[i+1] = ci[i] + cnzi;
433   }
434 
435   /* Column indices are in the list of free space */
436   /* Allocate space for cj, initialize cj, and */
437   /* destroy list of free space and other temporary array(s) */
438   ierr = PetscMalloc1((ci[am]+1),&cj);CHKERRQ(ierr);
439   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
440   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
441 
442   /* Allocate space for ca */
443   /*-----------------------*/
444   ierr = PetscMalloc1((ci[am]+1),&ca);CHKERRQ(ierr);
445   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
446 
447   /* put together the new symbolic matrix */
448   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
449   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
450 
451   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
452   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
453   c          = (Mat_SeqAIJ*)((*C)->data);
454   c->free_a  = PETSC_TRUE;
455   c->free_ij = PETSC_TRUE;
456   c->nonew   = 0;
457 
458   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
459 
460   /* set MatInfo */
461   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
462   if (afill < 1.0) afill = 1.0;
463   c->maxnz                     = ci[am];
464   c->nz                        = ci[am];
465   (*C)->info.mallocs           = ndouble;
466   (*C)->info.fill_ratio_given  = fill;
467   (*C)->info.fill_ratio_needed = afill;
468 
469 #if defined(PETSC_USE_INFO)
470   if (ci[am]) {
471     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
472     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
473   } else {
474     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
475   }
476 #endif
477   PetscFunctionReturn(0);
478 }
479 
480 #undef __FUNCT__
481 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
482 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
483 {
484   PetscErrorCode     ierr;
485   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
486   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
487   PetscInt           *ci,*cj,*bb;
488   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
489   PetscReal          afill;
490   PetscInt           i,j,col,ndouble = 0;
491   PetscFreeSpaceList free_space=NULL,current_space=NULL;
492   PetscHeap          h;
493 
494   PetscFunctionBegin;
495   /* Get ci and cj - by merging sorted rows using a heap */
496   /*---------------------------------------------------------------------------------------------*/
497   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
498   ierr  = PetscMalloc1(((am+1)+1),&ci);CHKERRQ(ierr);
499   ci[0] = 0;
500 
501   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
502   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
503   current_space = free_space;
504 
505   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
506   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
507 
508   /* Determine ci and cj */
509   for (i=0; i<am; i++) {
510     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 */
511     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
512     ci[i+1] = ci[i];
513     /* Populate the min heap */
514     for (j=0; j<anzi; j++) {
515       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
516       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
517         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
518       }
519     }
520     /* Pick off the min element, adding it to free space */
521     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
522     while (j >= 0) {
523       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
524         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
525         ndouble++;
526       }
527       *(current_space->array++) = col;
528       current_space->local_used++;
529       current_space->local_remaining--;
530       ci[i+1]++;
531 
532       /* stash if anything else remains in this row of B */
533       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
534       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
535         PetscInt j2,col2;
536         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
537         if (col2 != col) break;
538         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
539         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
540       }
541       /* Put any stashed elements back into the min heap */
542       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
543       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
544     }
545   }
546   ierr = PetscFree(bb);CHKERRQ(ierr);
547   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
548 
549   /* Column indices are in the list of free space */
550   /* Allocate space for cj, initialize cj, and */
551   /* destroy list of free space and other temporary array(s) */
552   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
553   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
554 
555   /* put together the new symbolic matrix */
556   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
557   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
558 
559   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
560   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
561   c          = (Mat_SeqAIJ*)((*C)->data);
562   c->free_a  = PETSC_TRUE;
563   c->free_ij = PETSC_TRUE;
564   c->nonew   = 0;
565 
566   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
567 
568   /* set MatInfo */
569   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
570   if (afill < 1.0) afill = 1.0;
571   c->maxnz                     = ci[am];
572   c->nz                        = ci[am];
573   (*C)->info.mallocs           = ndouble;
574   (*C)->info.fill_ratio_given  = fill;
575   (*C)->info.fill_ratio_needed = afill;
576 
577 #if defined(PETSC_USE_INFO)
578   if (ci[am]) {
579     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
580     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
581   } else {
582     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
583   }
584 #endif
585   PetscFunctionReturn(0);
586 }
587 
588 #undef __FUNCT__
589 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
590 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
591 {
592   PetscErrorCode     ierr;
593   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
594   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
595   PetscInt           *ci,*cj,*bb;
596   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
597   PetscReal          afill;
598   PetscInt           i,j,col,ndouble = 0;
599   PetscFreeSpaceList free_space=NULL,current_space=NULL;
600   PetscHeap          h;
601   PetscBT            bt;
602 
603   PetscFunctionBegin;
604   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
605   /*---------------------------------------------------------------------------------------------*/
606   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
607   ierr  = PetscMalloc1(((am+1)+1),&ci);CHKERRQ(ierr);
608   ci[0] = 0;
609 
610   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
611   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
612 
613   current_space = free_space;
614 
615   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
616   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
617   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
618 
619   /* Determine ci and cj */
620   for (i=0; i<am; i++) {
621     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 */
622     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
623     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
624     ci[i+1] = ci[i];
625     /* Populate the min heap */
626     for (j=0; j<anzi; j++) {
627       PetscInt brow = acol[j];
628       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
629         PetscInt bcol = bj[bb[j]];
630         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
631           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
632           bb[j]++;
633           break;
634         }
635       }
636     }
637     /* Pick off the min element, adding it to free space */
638     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
639     while (j >= 0) {
640       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
641         fptr = NULL;                      /* need PetscBTMemzero */
642         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
643         ndouble++;
644       }
645       *(current_space->array++) = col;
646       current_space->local_used++;
647       current_space->local_remaining--;
648       ci[i+1]++;
649 
650       /* stash if anything else remains in this row of B */
651       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
652         PetscInt bcol = bj[bb[j]];
653         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
654           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
655           bb[j]++;
656           break;
657         }
658       }
659       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
660     }
661     if (fptr) {                 /* Clear the bits for this row */
662       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
663     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
664       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
665     }
666   }
667   ierr = PetscFree(bb);CHKERRQ(ierr);
668   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
669   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
670 
671   /* Column indices are in the list of free space */
672   /* Allocate space for cj, initialize cj, and */
673   /* destroy list of free space and other temporary array(s) */
674   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
675   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
676 
677   /* put together the new symbolic matrix */
678   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
679   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
680 
681   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
682   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
683   c          = (Mat_SeqAIJ*)((*C)->data);
684   c->free_a  = PETSC_TRUE;
685   c->free_ij = PETSC_TRUE;
686   c->nonew   = 0;
687 
688   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
689 
690   /* set MatInfo */
691   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
692   if (afill < 1.0) afill = 1.0;
693   c->maxnz                     = ci[am];
694   c->nz                        = ci[am];
695   (*C)->info.mallocs           = ndouble;
696   (*C)->info.fill_ratio_given  = fill;
697   (*C)->info.fill_ratio_needed = afill;
698 
699 #if defined(PETSC_USE_INFO)
700   if (ci[am]) {
701     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
702     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
703   } else {
704     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
705   }
706 #endif
707   PetscFunctionReturn(0);
708 }
709 
710 #undef __FUNCT__
711 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
712 /* concatenate unique entries and then sort */
713 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
714 {
715   PetscErrorCode     ierr;
716   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
717   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
718   PetscInt           *ci,*cj;
719   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
720   PetscReal          afill;
721   PetscInt           i,j,ndouble = 0;
722   PetscSegBuffer     seg,segrow;
723   char               *seen;
724 
725   PetscFunctionBegin;
726   ierr  = PetscMalloc1((am+1),&ci);CHKERRQ(ierr);
727   ci[0] = 0;
728 
729   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
730   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
731   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
732   ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr);
733   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
734 
735   /* Determine ci and cj */
736   for (i=0; i<am; i++) {
737     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 */
738     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
739     PetscInt packlen = 0,*PETSC_RESTRICT crow;
740     /* Pack segrow */
741     for (j=0; j<anzi; j++) {
742       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
743       for (k=bjstart; k<bjend; k++) {
744         PetscInt bcol = bj[k];
745         if (!seen[bcol]) { /* new entry */
746           PetscInt *PETSC_RESTRICT slot;
747           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
748           *slot = bcol;
749           seen[bcol] = 1;
750           packlen++;
751         }
752       }
753     }
754     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
755     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
756     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
757     ci[i+1] = ci[i] + packlen;
758     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
759   }
760   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
761   ierr = PetscFree(seen);CHKERRQ(ierr);
762 
763   /* Column indices are in the segmented buffer */
764   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
765   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
766 
767   /* put together the new symbolic matrix */
768   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
769   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
770 
771   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
772   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
773   c          = (Mat_SeqAIJ*)((*C)->data);
774   c->free_a  = PETSC_TRUE;
775   c->free_ij = PETSC_TRUE;
776   c->nonew   = 0;
777 
778   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
779 
780   /* set MatInfo */
781   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
782   if (afill < 1.0) afill = 1.0;
783   c->maxnz                     = ci[am];
784   c->nz                        = ci[am];
785   (*C)->info.mallocs           = ndouble;
786   (*C)->info.fill_ratio_given  = fill;
787   (*C)->info.fill_ratio_needed = afill;
788 
789 #if defined(PETSC_USE_INFO)
790   if (ci[am]) {
791     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
792     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
793   } else {
794     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
795   }
796 #endif
797   PetscFunctionReturn(0);
798 }
799 
800 /* This routine is not used. Should be removed! */
801 #undef __FUNCT__
802 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
803 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
804 {
805   PetscErrorCode ierr;
806 
807   PetscFunctionBegin;
808   if (scall == MAT_INITIAL_MATRIX) {
809     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
810     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
811     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
812   }
813   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
814   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
815   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
816   PetscFunctionReturn(0);
817 }
818 
819 #undef __FUNCT__
820 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
821 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
822 {
823   PetscErrorCode      ierr;
824   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
825   Mat_MatMatTransMult *abt=a->abt;
826 
827   PetscFunctionBegin;
828   ierr = (abt->destroy)(A);CHKERRQ(ierr);
829   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
830   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
831   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
832   ierr = PetscFree(abt);CHKERRQ(ierr);
833   PetscFunctionReturn(0);
834 }
835 
836 #undef __FUNCT__
837 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
838 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
839 {
840   PetscErrorCode      ierr;
841   Mat                 Bt;
842   PetscInt            *bti,*btj;
843   Mat_MatMatTransMult *abt;
844   Mat_SeqAIJ          *c;
845 
846   PetscFunctionBegin;
847   /* create symbolic Bt */
848   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
849   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
850   ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
851 
852   /* get symbolic C=A*Bt */
853   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
854 
855   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
856   ierr   = PetscNew(&abt);CHKERRQ(ierr);
857   c      = (Mat_SeqAIJ*)(*C)->data;
858   c->abt = abt;
859 
860   abt->usecoloring = PETSC_FALSE;
861   abt->destroy     = (*C)->ops->destroy;
862   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
863 
864   ierr = PetscOptionsGetBool(NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
865   if (abt->usecoloring) {
866     /* Create MatTransposeColoring from symbolic C=A*B^T */
867     MatTransposeColoring matcoloring;
868     MatColoring          coloring;
869     ISColoring           iscoloring;
870     Mat                  Bt_dense,C_dense;
871     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
872     /* inode causes memory problem, don't know why */
873     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
874 
875     ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
876     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
877     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
878     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
879     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
880     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
881     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
882 
883     abt->matcoloring = matcoloring;
884 
885     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
886 
887     /* Create Bt_dense and C_dense = A*Bt_dense */
888     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
889     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
890     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
891     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
892 
893     Bt_dense->assembled = PETSC_TRUE;
894     abt->Bt_den   = Bt_dense;
895 
896     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
897     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
898     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
899     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
900 
901     Bt_dense->assembled = PETSC_TRUE;
902     abt->ABt_den  = C_dense;
903 
904 #if defined(PETSC_USE_INFO)
905     {
906       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
907       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);
908     }
909 #endif
910   }
911   /* clean up */
912   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
913   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
914   PetscFunctionReturn(0);
915 }
916 
917 #undef __FUNCT__
918 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
919 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
920 {
921   PetscErrorCode      ierr;
922   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
923   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
924   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
925   PetscLogDouble      flops=0.0;
926   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
927   Mat_MatMatTransMult *abt = c->abt;
928 
929   PetscFunctionBegin;
930   /* clear old values in C */
931   if (!c->a) {
932     ierr      = PetscMalloc1((ci[cm]+1),&ca);CHKERRQ(ierr);
933     c->a      = ca;
934     c->free_a = PETSC_TRUE;
935   } else {
936     ca =  c->a;
937   }
938   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
939 
940   if (abt->usecoloring) {
941     MatTransposeColoring matcoloring = abt->matcoloring;
942     Mat                  Bt_dense,C_dense = abt->ABt_den;
943 
944     /* Get Bt_dense by Apply MatTransposeColoring to B */
945     Bt_dense = abt->Bt_den;
946     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
947 
948     /* C_dense = A*Bt_dense */
949     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
950 
951     /* Recover C from C_dense */
952     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
953     PetscFunctionReturn(0);
954   }
955 
956   for (i=0; i<cm; i++) {
957     anzi = ai[i+1] - ai[i];
958     acol = aj + ai[i];
959     aval = aa + ai[i];
960     cnzi = ci[i+1] - ci[i];
961     ccol = cj + ci[i];
962     cval = ca + ci[i];
963     for (j=0; j<cnzi; j++) {
964       brow = ccol[j];
965       bnzj = bi[brow+1] - bi[brow];
966       bcol = bj + bi[brow];
967       bval = ba + bi[brow];
968 
969       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
970       nexta = 0; nextb = 0;
971       while (nexta<anzi && nextb<bnzj) {
972         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
973         if (nexta == anzi) break;
974         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
975         if (nextb == bnzj) break;
976         if (acol[nexta] == bcol[nextb]) {
977           cval[j] += aval[nexta]*bval[nextb];
978           nexta++; nextb++;
979           flops += 2;
980         }
981       }
982     }
983   }
984   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
985   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
986   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
987   PetscFunctionReturn(0);
988 }
989 
990 #undef __FUNCT__
991 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
992 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
993 {
994   PetscErrorCode ierr;
995 
996   PetscFunctionBegin;
997   if (scall == MAT_INITIAL_MATRIX) {
998     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
999     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1000     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1001   }
1002   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1003   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1004   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1005   PetscFunctionReturn(0);
1006 }
1007 
1008 #undef __FUNCT__
1009 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1010 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1011 {
1012   PetscErrorCode ierr;
1013   Mat            At;
1014   PetscInt       *ati,*atj;
1015 
1016   PetscFunctionBegin;
1017   /* create symbolic At */
1018   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1019   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1020   ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1021 
1022   /* get symbolic C=At*B */
1023   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1024 
1025   /* clean up */
1026   ierr = MatDestroy(&At);CHKERRQ(ierr);
1027   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1028   PetscFunctionReturn(0);
1029 }
1030 
1031 #undef __FUNCT__
1032 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1033 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1034 {
1035   PetscErrorCode ierr;
1036   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1037   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1038   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1039   PetscLogDouble flops=0.0;
1040   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1041 
1042   PetscFunctionBegin;
1043   if (!c->a) {
1044     ierr = PetscMalloc1((ci[cm]+1),&ca);CHKERRQ(ierr);
1045 
1046     c->a      = ca;
1047     c->free_a = PETSC_TRUE;
1048   } else {
1049     ca = c->a;
1050   }
1051   /* clear old values in C */
1052   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1053 
1054   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1055   for (i=0; i<am; i++) {
1056     bj   = b->j + bi[i];
1057     ba   = b->a + bi[i];
1058     bnzi = bi[i+1] - bi[i];
1059     anzi = ai[i+1] - ai[i];
1060     for (j=0; j<anzi; j++) {
1061       nextb = 0;
1062       crow  = *aj++;
1063       cjj   = cj + ci[crow];
1064       caj   = ca + ci[crow];
1065       /* perform sparse axpy operation.  Note cjj includes bj. */
1066       for (k=0; nextb<bnzi; k++) {
1067         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1068           caj[k] += (*aa)*(*(ba+nextb));
1069           nextb++;
1070         }
1071       }
1072       flops += 2*bnzi;
1073       aa++;
1074     }
1075   }
1076 
1077   /* Assemble the final matrix and clean up */
1078   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1079   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1080   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1081   PetscFunctionReturn(0);
1082 }
1083 
1084 #undef __FUNCT__
1085 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1086 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1087 {
1088   PetscErrorCode ierr;
1089 
1090   PetscFunctionBegin;
1091   if (scall == MAT_INITIAL_MATRIX) {
1092     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1093     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1094     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1095   }
1096   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1097   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1098   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1099   PetscFunctionReturn(0);
1100 }
1101 
1102 #undef __FUNCT__
1103 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1104 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1105 {
1106   PetscErrorCode ierr;
1107 
1108   PetscFunctionBegin;
1109   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1110 
1111   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1112   PetscFunctionReturn(0);
1113 }
1114 
1115 #undef __FUNCT__
1116 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1117 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1118 {
1119   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1120   PetscErrorCode    ierr;
1121   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1122   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1123   const PetscInt    *aj;
1124   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=B->rmap->n,am=A->rmap->n;
1125   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;
1126 
1127   PetscFunctionBegin;
1128   if (!cm || !cn) PetscFunctionReturn(0);
1129   if (bm != 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,bm);
1130   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);
1131   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);
1132   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1133   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1134   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1135   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1136   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1137     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1138       r1 = r2 = r3 = r4 = 0.0;
1139       n  = a->i[i+1] - a->i[i];
1140       aj = a->j + a->i[i];
1141       aa = a->a + a->i[i];
1142       for (j=0; j<n; j++) {
1143         aatmp = aa[j]; ajtmp = aj[j];
1144         r1 += aatmp*b1[ajtmp];
1145         r2 += aatmp*b2[ajtmp];
1146         r3 += aatmp*b3[ajtmp];
1147         r4 += aatmp*b4[ajtmp];
1148       }
1149       c1[i] = r1;
1150       c2[i] = r2;
1151       c3[i] = r3;
1152       c4[i] = r4;
1153     }
1154     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1155     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1156   }
1157   for (; col<cn; col++) {   /* over extra columns of C */
1158     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1159       r1 = 0.0;
1160       n  = a->i[i+1] - a->i[i];
1161       aj = a->j + a->i[i];
1162       aa = a->a + a->i[i];
1163       for (j=0; j<n; j++) {
1164         r1 += aa[j]*b1[aj[j]];
1165       }
1166       c1[i] = r1;
1167     }
1168     b1 += bm;
1169     c1 += am;
1170   }
1171   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1172   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1173   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1174   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1175   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1176   PetscFunctionReturn(0);
1177 }
1178 
1179 /*
1180    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1181 */
1182 #undef __FUNCT__
1183 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1184 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1185 {
1186   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1187   PetscErrorCode ierr;
1188   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1189   MatScalar      *aa;
1190   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1191   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1192 
1193   PetscFunctionBegin;
1194   if (!cm || !cn) PetscFunctionReturn(0);
1195   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1196   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1197   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1198 
1199   if (a->compressedrow.use) { /* use compressed row format */
1200     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1201       colam = col*am;
1202       arm   = a->compressedrow.nrows;
1203       ii    = a->compressedrow.i;
1204       ridx  = a->compressedrow.rindex;
1205       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1206         r1 = r2 = r3 = r4 = 0.0;
1207         n  = ii[i+1] - ii[i];
1208         aj = a->j + ii[i];
1209         aa = a->a + ii[i];
1210         for (j=0; j<n; j++) {
1211           r1 += (*aa)*b1[*aj];
1212           r2 += (*aa)*b2[*aj];
1213           r3 += (*aa)*b3[*aj];
1214           r4 += (*aa++)*b4[*aj++];
1215         }
1216         c[colam       + ridx[i]] += r1;
1217         c[colam + am  + ridx[i]] += r2;
1218         c[colam + am2 + ridx[i]] += r3;
1219         c[colam + am3 + ridx[i]] += r4;
1220       }
1221       b1 += bm4;
1222       b2 += bm4;
1223       b3 += bm4;
1224       b4 += bm4;
1225     }
1226     for (; col<cn; col++) {     /* over extra columns of C */
1227       colam = col*am;
1228       arm   = a->compressedrow.nrows;
1229       ii    = a->compressedrow.i;
1230       ridx  = a->compressedrow.rindex;
1231       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1232         r1 = 0.0;
1233         n  = ii[i+1] - ii[i];
1234         aj = a->j + ii[i];
1235         aa = a->a + ii[i];
1236 
1237         for (j=0; j<n; j++) {
1238           r1 += (*aa++)*b1[*aj++];
1239         }
1240         c[colam + ridx[i]] += r1;
1241       }
1242       b1 += bm;
1243     }
1244   } else {
1245     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1246       colam = col*am;
1247       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1248         r1 = r2 = r3 = r4 = 0.0;
1249         n  = a->i[i+1] - a->i[i];
1250         aj = a->j + a->i[i];
1251         aa = a->a + a->i[i];
1252         for (j=0; j<n; j++) {
1253           r1 += (*aa)*b1[*aj];
1254           r2 += (*aa)*b2[*aj];
1255           r3 += (*aa)*b3[*aj];
1256           r4 += (*aa++)*b4[*aj++];
1257         }
1258         c[colam + i]       += r1;
1259         c[colam + am + i]  += r2;
1260         c[colam + am2 + i] += r3;
1261         c[colam + am3 + i] += r4;
1262       }
1263       b1 += bm4;
1264       b2 += bm4;
1265       b3 += bm4;
1266       b4 += bm4;
1267     }
1268     for (; col<cn; col++) {     /* over extra columns of C */
1269       colam = col*am;
1270       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1271         r1 = 0.0;
1272         n  = a->i[i+1] - a->i[i];
1273         aj = a->j + a->i[i];
1274         aa = a->a + a->i[i];
1275 
1276         for (j=0; j<n; j++) {
1277           r1 += (*aa++)*b1[*aj++];
1278         }
1279         c[colam + i] += r1;
1280       }
1281       b1 += bm;
1282     }
1283   }
1284   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1285   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1286   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1287   PetscFunctionReturn(0);
1288 }
1289 
1290 #undef __FUNCT__
1291 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1292 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1293 {
1294   PetscErrorCode ierr;
1295   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1296   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1297   PetscInt       *bi      = b->i,*bj=b->j;
1298   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1299   MatScalar      *btval,*btval_den,*ba=b->a;
1300   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1301 
1302   PetscFunctionBegin;
1303   btval_den=btdense->v;
1304   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1305   for (k=0; k<ncolors; k++) {
1306     ncolumns = coloring->ncolumns[k];
1307     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1308       col   = *(columns + colorforcol[k] + l);
1309       btcol = bj + bi[col];
1310       btval = ba + bi[col];
1311       anz   = bi[col+1] - bi[col];
1312       for (j=0; j<anz; j++) {
1313         brow            = btcol[j];
1314         btval_den[brow] = btval[j];
1315       }
1316     }
1317     btval_den += m;
1318   }
1319   PetscFunctionReturn(0);
1320 }
1321 
1322 #undef __FUNCT__
1323 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1324 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1325 {
1326   PetscErrorCode ierr;
1327   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1328   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1329   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1330   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1331   PetscInt       nrows,*row,*idx;
1332   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1333 
1334   PetscFunctionBegin;
1335   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1336 
1337   if (brows > 0) {
1338     PetscInt *lstart,row_end,row_start;
1339     lstart = matcoloring->lstart;
1340     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1341 
1342     row_end = brows;
1343     if (row_end > m) row_end = m;
1344     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1345       ca_den_ptr = ca_den;
1346       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1347         nrows = matcoloring->nrows[k];
1348         row   = rows  + colorforrow[k];
1349         idx   = den2sp + colorforrow[k];
1350         for (l=lstart[k]; l<nrows; l++) {
1351           if (row[l] >= row_end) {
1352             lstart[k] = l;
1353             break;
1354           } else {
1355             ca[idx[l]] = ca_den_ptr[row[l]];
1356           }
1357         }
1358         ca_den_ptr += m;
1359       }
1360       row_end += brows;
1361       if (row_end > m) row_end = m;
1362     }
1363   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1364     ca_den_ptr = ca_den;
1365     for (k=0; k<ncolors; k++) {
1366       nrows = matcoloring->nrows[k];
1367       row   = rows  + colorforrow[k];
1368       idx   = den2sp + colorforrow[k];
1369       for (l=0; l<nrows; l++) {
1370         ca[idx[l]] = ca_den_ptr[row[l]];
1371       }
1372       ca_den_ptr += m;
1373     }
1374   }
1375 
1376   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1377 #if defined(PETSC_USE_INFO)
1378   if (matcoloring->brows > 0) {
1379     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1380   } else {
1381     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1382   }
1383 #endif
1384   PetscFunctionReturn(0);
1385 }
1386 
1387 #undef __FUNCT__
1388 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1389 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1390 {
1391   PetscErrorCode ierr;
1392   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1393   const PetscInt *is,*ci,*cj,*row_idx;
1394   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1395   IS             *isa;
1396   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1397   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1398   PetscInt       *colorforcol,*columns,*columns_i,brows;
1399   PetscBool      flg;
1400 
1401   PetscFunctionBegin;
1402   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1403 
1404   /* bs >1 is not being tested yet! */
1405   Nbs       = mat->cmap->N/bs;
1406   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1407   c->N      = Nbs;
1408   c->m      = c->M;
1409   c->rstart = 0;
1410   c->brows  = 100;
1411 
1412   c->ncolors = nis;
1413   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1414   ierr = PetscMalloc1((csp->nz+1),&rows);CHKERRQ(ierr);
1415   ierr = PetscMalloc1((csp->nz+1),&den2sp);CHKERRQ(ierr);
1416 
1417   brows = c->brows;
1418   ierr = PetscOptionsGetInt(NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1419   if (flg) c->brows = brows;
1420   if (brows > 0) {
1421     ierr = PetscMalloc1((nis+1),&c->lstart);CHKERRQ(ierr);
1422   }
1423 
1424   colorforrow[0] = 0;
1425   rows_i         = rows;
1426   den2sp_i       = den2sp;
1427 
1428   ierr = PetscMalloc1((nis+1),&colorforcol);CHKERRQ(ierr);
1429   ierr = PetscMalloc1((Nbs+1),&columns);CHKERRQ(ierr);
1430 
1431   colorforcol[0] = 0;
1432   columns_i      = columns;
1433 
1434   /* get column-wise storage of mat */
1435   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1436 
1437   cm   = c->m;
1438   ierr = PetscMalloc1((cm+1),&rowhit);CHKERRQ(ierr);
1439   ierr = PetscMalloc1((cm+1),&idxhit);CHKERRQ(ierr);
1440   for (i=0; i<nis; i++) { /* loop over color */
1441     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1442     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1443 
1444     c->ncolumns[i] = n;
1445     if (n) {
1446       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1447     }
1448     colorforcol[i+1] = colorforcol[i] + n;
1449     columns_i       += n;
1450 
1451     /* fast, crude version requires O(N*N) work */
1452     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1453 
1454     for (j=0; j<n; j++) { /* loop over columns*/
1455       col     = is[j];
1456       row_idx = cj + ci[col];
1457       m       = ci[col+1] - ci[col];
1458       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1459         idxhit[*row_idx]   = spidx[ci[col] + k];
1460         rowhit[*row_idx++] = col + 1;
1461       }
1462     }
1463     /* count the number of hits */
1464     nrows = 0;
1465     for (j=0; j<cm; j++) {
1466       if (rowhit[j]) nrows++;
1467     }
1468     c->nrows[i]      = nrows;
1469     colorforrow[i+1] = colorforrow[i] + nrows;
1470 
1471     nrows = 0;
1472     for (j=0; j<cm; j++) { /* loop over rows */
1473       if (rowhit[j]) {
1474         rows_i[nrows]   = j;
1475         den2sp_i[nrows] = idxhit[j];
1476         nrows++;
1477       }
1478     }
1479     den2sp_i += nrows;
1480 
1481     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1482     rows_i += nrows;
1483   }
1484   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1485   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1486   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1487   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1488 
1489   c->colorforrow = colorforrow;
1490   c->rows        = rows;
1491   c->den2sp      = den2sp;
1492   c->colorforcol = colorforcol;
1493   c->columns     = columns;
1494 
1495   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1496   PetscFunctionReturn(0);
1497 }
1498