xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision e6e75211d226c622f451867f53ce5d558649ff4f)
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 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,nlnk_max,*lnk,ndouble=0;
69   PetscBT            lnkbt;
70   PetscFreeSpaceList free_space=NULL,current_space=NULL;
71 
72   PetscFunctionBegin;
73   /* Get ci and cj */
74   /*---------------*/
75   /* Allocate ci array, arrays for fill computation and */
76   /* free space for accumulating nonzero column info */
77   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
78   ci[0] = 0;
79 
80   /* create and initialize a linked list */
81   nlnk_max = a->rmax*b->rmax;
82   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
83   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
84 
85   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
86   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
87 
88   current_space = free_space;
89 
90   /* Determine ci and cj */
91   for (i=0; i<am; i++) {
92     anzi = ai[i+1] - ai[i];
93     aj   = a->j + ai[i];
94     for (j=0; j<anzi; j++) {
95       brow = aj[j];
96       bnzj = bi[brow+1] - bi[brow];
97       bj   = b->j + bi[brow];
98       /* add non-zero cols of B into the sorted linked list lnk */
99       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
100     }
101     cnzi = lnk[0];
102 
103     /* If free space is not available, make more free space */
104     /* Double the amount of total space in the list */
105     if (current_space->local_remaining<cnzi) {
106       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
107       ndouble++;
108     }
109 
110     /* Copy data into free space, then initialize lnk */
111     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
112 
113     current_space->array           += cnzi;
114     current_space->local_used      += cnzi;
115     current_space->local_remaining -= cnzi;
116 
117     ci[i+1] = ci[i] + cnzi;
118   }
119 
120   /* Column indices are in the list of free space */
121   /* Allocate space for cj, initialize cj, and */
122   /* destroy list of free space and other temporary array(s) */
123   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
124   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
125   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
126 
127   /* put together the new symbolic matrix */
128   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
129   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
130 
131   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
132   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
133   c                         = (Mat_SeqAIJ*)((*C)->data);
134   c->free_a                 = PETSC_FALSE;
135   c->free_ij                = PETSC_TRUE;
136   c->nonew                  = 0;
137   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
138 
139   /* set MatInfo */
140   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
141   if (afill < 1.0) afill = 1.0;
142   c->maxnz                     = ci[am];
143   c->nz                        = ci[am];
144   (*C)->info.mallocs           = ndouble;
145   (*C)->info.fill_ratio_given  = fill;
146   (*C)->info.fill_ratio_needed = afill;
147 
148 #if defined(PETSC_USE_INFO)
149   if (ci[am]) {
150     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
151     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
152   } else {
153     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
154   }
155 #endif
156   PetscFunctionReturn(0);
157 }
158 
159 #undef __FUNCT__
160 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
161 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
162 {
163   PetscErrorCode ierr;
164   PetscLogDouble flops=0.0;
165   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
166   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
167   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
168   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
169   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
170   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
171   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
172   PetscScalar    *ab_dense;
173 
174   PetscFunctionBegin;
175   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
176     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
177     c->a      = ca;
178     c->free_a = PETSC_TRUE;
179   } else {
180     ca        = c->a;
181   }
182   if (!c->matmult_abdense) {
183     ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr);
184     c->matmult_abdense = ab_dense;
185   } else {
186     ab_dense = c->matmult_abdense;
187   }
188 
189   /* clean old values in C */
190   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
191   /* Traverse A row-wise. */
192   /* Build the ith row in C by summing over nonzero columns in A, */
193   /* the rows of B corresponding to nonzeros of A. */
194   for (i=0; i<am; i++) {
195     anzi = ai[i+1] - ai[i];
196     for (j=0; j<anzi; j++) {
197       brow = aj[j];
198       bnzi = bi[brow+1] - bi[brow];
199       bjj  = bj + bi[brow];
200       baj  = ba + bi[brow];
201       /* perform dense axpy */
202       valtmp = aa[j];
203       for (k=0; k<bnzi; k++) {
204         ab_dense[bjj[k]] += valtmp*baj[k];
205       }
206       flops += 2*bnzi;
207     }
208     aj += anzi; aa += anzi;
209 
210     cnzi = ci[i+1] - ci[i];
211     for (k=0; k<cnzi; k++) {
212       ca[k]          += ab_dense[cj[k]];
213       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
214     }
215     flops += cnzi;
216     cj    += cnzi; ca += cnzi;
217   }
218   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
219   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
220   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
221   PetscFunctionReturn(0);
222 }
223 
224 #undef __FUNCT__
225 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
226 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
227 {
228   PetscErrorCode ierr;
229   PetscLogDouble flops=0.0;
230   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
231   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
232   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
233   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
234   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
235   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
236   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
237   PetscInt       nextb;
238 
239   PetscFunctionBegin;
240   /* clean old values in C */
241   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
242   /* Traverse A row-wise. */
243   /* Build the ith row in C by summing over nonzero columns in A, */
244   /* the rows of B corresponding to nonzeros of A. */
245   for (i=0; i<am; i++) {
246     anzi = ai[i+1] - ai[i];
247     cnzi = ci[i+1] - ci[i];
248     for (j=0; j<anzi; j++) {
249       brow = aj[j];
250       bnzi = bi[brow+1] - bi[brow];
251       bjj  = bj + bi[brow];
252       baj  = ba + bi[brow];
253       /* perform sparse axpy */
254       valtmp = aa[j];
255       nextb  = 0;
256       for (k=0; nextb<bnzi; k++) {
257         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
258           ca[k] += valtmp*baj[nextb++];
259         }
260       }
261       flops += 2*bnzi;
262     }
263     aj += anzi; aa += anzi;
264     cj += cnzi; ca += cnzi;
265   }
266 
267   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
268   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
269   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
270   PetscFunctionReturn(0);
271 }
272 
273 #undef __FUNCT__
274 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
275 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
276 {
277   PetscErrorCode     ierr;
278   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
279   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
280   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
281   MatScalar          *ca;
282   PetscReal          afill;
283   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
284   PetscFreeSpaceList free_space=NULL,current_space=NULL;
285 
286   PetscFunctionBegin;
287   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
288   /*-----------------------------------------------------------------------------------------*/
289   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
290   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
291   ci[0] = 0;
292 
293   /* create and initialize a linked list */
294   nlnk_max = a->rmax*b->rmax;
295   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
296   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
297 
298   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
299   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
300   current_space = free_space;
301 
302   /* Determine ci and cj */
303   for (i=0; i<am; i++) {
304     anzi = ai[i+1] - ai[i];
305     aj   = a->j + ai[i];
306     for (j=0; j<anzi; j++) {
307       brow = aj[j];
308       bnzj = bi[brow+1] - bi[brow];
309       bj   = b->j + bi[brow];
310       /* add non-zero cols of B into the sorted linked list lnk */
311       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
312     }
313     cnzi = lnk[1];
314 
315     /* If free space is not available, make more free space */
316     /* Double the amount of total space in the list */
317     if (current_space->local_remaining<cnzi) {
318       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
319       ndouble++;
320     }
321 
322     /* Copy data into free space, then initialize lnk */
323     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
324 
325     current_space->array           += cnzi;
326     current_space->local_used      += cnzi;
327     current_space->local_remaining -= cnzi;
328 
329     ci[i+1] = ci[i] + cnzi;
330   }
331 
332   /* Column indices are in the list of free space */
333   /* Allocate space for cj, initialize cj, and */
334   /* destroy list of free space and other temporary array(s) */
335   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
336   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
337   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
338 
339   /* Allocate space for ca */
340   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
341   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
342 
343   /* put together the new symbolic matrix */
344   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
345   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
346 
347   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
348   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
349   c          = (Mat_SeqAIJ*)((*C)->data);
350   c->free_a  = PETSC_TRUE;
351   c->free_ij = PETSC_TRUE;
352   c->nonew   = 0;
353 
354   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
355 
356   /* set MatInfo */
357   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
358   if (afill < 1.0) afill = 1.0;
359   c->maxnz                     = ci[am];
360   c->nz                        = ci[am];
361   (*C)->info.mallocs           = ndouble;
362   (*C)->info.fill_ratio_given  = fill;
363   (*C)->info.fill_ratio_needed = afill;
364 
365 #if defined(PETSC_USE_INFO)
366   if (ci[am]) {
367     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
368     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
369   } else {
370     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
371   }
372 #endif
373   PetscFunctionReturn(0);
374 }
375 
376 
377 #undef __FUNCT__
378 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
379 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
380 {
381   PetscErrorCode     ierr;
382   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
383   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
384   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
385   MatScalar          *ca;
386   PetscReal          afill;
387   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
388   PetscFreeSpaceList free_space=NULL,current_space=NULL;
389 
390   PetscFunctionBegin;
391   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
392   /*---------------------------------------------------------------------------------------------*/
393   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
394   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
395   ci[0] = 0;
396 
397   /* create and initialize a linked list */
398   nlnk_max = a->rmax*b->rmax;
399   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
400   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
401 
402   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
403   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
404   current_space = free_space;
405 
406   /* Determine ci and cj */
407   for (i=0; i<am; i++) {
408     anzi = ai[i+1] - ai[i];
409     aj   = a->j + ai[i];
410     for (j=0; j<anzi; j++) {
411       brow = aj[j];
412       bnzj = bi[brow+1] - bi[brow];
413       bj   = b->j + bi[brow];
414       /* add non-zero cols of B into the sorted linked list lnk */
415       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
416     }
417     cnzi = lnk[0];
418 
419     /* If free space is not available, make more free space */
420     /* Double the amount of total space in the list */
421     if (current_space->local_remaining<cnzi) {
422       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
423       ndouble++;
424     }
425 
426     /* Copy data into free space, then initialize lnk */
427     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
428 
429     current_space->array           += cnzi;
430     current_space->local_used      += cnzi;
431     current_space->local_remaining -= cnzi;
432 
433     ci[i+1] = ci[i] + cnzi;
434   }
435 
436   /* Column indices are in the list of free space */
437   /* Allocate space for cj, initialize cj, and */
438   /* destroy list of free space and other temporary array(s) */
439   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
440   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
441   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
442 
443   /* Allocate space for ca */
444   /*-----------------------*/
445   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
446   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
447 
448   /* put together the new symbolic matrix */
449   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
450   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
451 
452   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
453   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
454   c          = (Mat_SeqAIJ*)((*C)->data);
455   c->free_a  = PETSC_TRUE;
456   c->free_ij = PETSC_TRUE;
457   c->nonew   = 0;
458 
459   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
460 
461   /* set MatInfo */
462   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
463   if (afill < 1.0) afill = 1.0;
464   c->maxnz                     = ci[am];
465   c->nz                        = ci[am];
466   (*C)->info.mallocs           = ndouble;
467   (*C)->info.fill_ratio_given  = fill;
468   (*C)->info.fill_ratio_needed = afill;
469 
470 #if defined(PETSC_USE_INFO)
471   if (ci[am]) {
472     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
473     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
474   } else {
475     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
476   }
477 #endif
478   PetscFunctionReturn(0);
479 }
480 
481 #undef __FUNCT__
482 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
483 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
484 {
485   PetscErrorCode     ierr;
486   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
487   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
488   PetscInt           *ci,*cj,*bb;
489   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
490   PetscReal          afill;
491   PetscInt           i,j,col,ndouble = 0;
492   PetscFreeSpaceList free_space=NULL,current_space=NULL;
493   PetscHeap          h;
494 
495   PetscFunctionBegin;
496   /* Get ci and cj - by merging sorted rows using a heap */
497   /*---------------------------------------------------------------------------------------------*/
498   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
499   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
500   ci[0] = 0;
501 
502   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
503   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
504   current_space = free_space;
505 
506   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
507   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
508 
509   /* Determine ci and cj */
510   for (i=0; i<am; i++) {
511     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 */
512     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
513     ci[i+1] = ci[i];
514     /* Populate the min heap */
515     for (j=0; j<anzi; j++) {
516       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
517       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
518         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
519       }
520     }
521     /* Pick off the min element, adding it to free space */
522     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
523     while (j >= 0) {
524       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
525         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
526         ndouble++;
527       }
528       *(current_space->array++) = col;
529       current_space->local_used++;
530       current_space->local_remaining--;
531       ci[i+1]++;
532 
533       /* stash if anything else remains in this row of B */
534       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
535       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
536         PetscInt j2,col2;
537         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
538         if (col2 != col) break;
539         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
540         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
541       }
542       /* Put any stashed elements back into the min heap */
543       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
544       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
545     }
546   }
547   ierr = PetscFree(bb);CHKERRQ(ierr);
548   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
549 
550   /* Column indices are in the list of free space */
551   /* Allocate space for cj, initialize cj, and */
552   /* destroy list of free space and other temporary array(s) */
553   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
554   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
555 
556   /* put together the new symbolic matrix */
557   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
558   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
559 
560   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
561   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
562   c          = (Mat_SeqAIJ*)((*C)->data);
563   c->free_a  = PETSC_TRUE;
564   c->free_ij = PETSC_TRUE;
565   c->nonew   = 0;
566 
567   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
568 
569   /* set MatInfo */
570   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
571   if (afill < 1.0) afill = 1.0;
572   c->maxnz                     = ci[am];
573   c->nz                        = ci[am];
574   (*C)->info.mallocs           = ndouble;
575   (*C)->info.fill_ratio_given  = fill;
576   (*C)->info.fill_ratio_needed = afill;
577 
578 #if defined(PETSC_USE_INFO)
579   if (ci[am]) {
580     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
581     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
582   } else {
583     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
584   }
585 #endif
586   PetscFunctionReturn(0);
587 }
588 
589 #undef __FUNCT__
590 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
591 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
592 {
593   PetscErrorCode     ierr;
594   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
595   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
596   PetscInt           *ci,*cj,*bb;
597   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
598   PetscReal          afill;
599   PetscInt           i,j,col,ndouble = 0;
600   PetscFreeSpaceList free_space=NULL,current_space=NULL;
601   PetscHeap          h;
602   PetscBT            bt;
603 
604   PetscFunctionBegin;
605   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
606   /*---------------------------------------------------------------------------------------------*/
607   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
608   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
609   ci[0] = 0;
610 
611   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
612   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
613 
614   current_space = free_space;
615 
616   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
617   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
618   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
619 
620   /* Determine ci and cj */
621   for (i=0; i<am; i++) {
622     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 */
623     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
624     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
625     ci[i+1] = ci[i];
626     /* Populate the min heap */
627     for (j=0; j<anzi; j++) {
628       PetscInt brow = acol[j];
629       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
630         PetscInt bcol = bj[bb[j]];
631         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
632           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
633           bb[j]++;
634           break;
635         }
636       }
637     }
638     /* Pick off the min element, adding it to free space */
639     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
640     while (j >= 0) {
641       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
642         fptr = NULL;                      /* need PetscBTMemzero */
643         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
644         ndouble++;
645       }
646       *(current_space->array++) = col;
647       current_space->local_used++;
648       current_space->local_remaining--;
649       ci[i+1]++;
650 
651       /* stash if anything else remains in this row of B */
652       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
653         PetscInt bcol = bj[bb[j]];
654         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
655           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
656           bb[j]++;
657           break;
658         }
659       }
660       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
661     }
662     if (fptr) {                 /* Clear the bits for this row */
663       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
664     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
665       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
666     }
667   }
668   ierr = PetscFree(bb);CHKERRQ(ierr);
669   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
670   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
671 
672   /* Column indices are in the list of free space */
673   /* Allocate space for cj, initialize cj, and */
674   /* destroy list of free space and other temporary array(s) */
675   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
676   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
677 
678   /* put together the new symbolic matrix */
679   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
680   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
681 
682   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
683   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
684   c          = (Mat_SeqAIJ*)((*C)->data);
685   c->free_a  = PETSC_TRUE;
686   c->free_ij = PETSC_TRUE;
687   c->nonew   = 0;
688 
689   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
690 
691   /* set MatInfo */
692   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
693   if (afill < 1.0) afill = 1.0;
694   c->maxnz                     = ci[am];
695   c->nz                        = ci[am];
696   (*C)->info.mallocs           = ndouble;
697   (*C)->info.fill_ratio_given  = fill;
698   (*C)->info.fill_ratio_needed = afill;
699 
700 #if defined(PETSC_USE_INFO)
701   if (ci[am]) {
702     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
703     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
704   } else {
705     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
706   }
707 #endif
708   PetscFunctionReturn(0);
709 }
710 
711 #undef __FUNCT__
712 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
713 /* concatenate unique entries and then sort */
714 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
715 {
716   PetscErrorCode     ierr;
717   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
718   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
719   PetscInt           *ci,*cj;
720   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
721   PetscReal          afill;
722   PetscInt           i,j,ndouble = 0;
723   PetscSegBuffer     seg,segrow;
724   char               *seen;
725 
726   PetscFunctionBegin;
727   ierr  = PetscMalloc1(am+1,&ci);CHKERRQ(ierr);
728   ci[0] = 0;
729 
730   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
731   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
732   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
733   ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr);
734   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
735 
736   /* Determine ci and cj */
737   for (i=0; i<am; i++) {
738     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 */
739     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
740     PetscInt packlen = 0,*PETSC_RESTRICT crow;
741     /* Pack segrow */
742     for (j=0; j<anzi; j++) {
743       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
744       for (k=bjstart; k<bjend; k++) {
745         PetscInt bcol = bj[k];
746         if (!seen[bcol]) { /* new entry */
747           PetscInt *PETSC_RESTRICT slot;
748           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
749           *slot = bcol;
750           seen[bcol] = 1;
751           packlen++;
752         }
753       }
754     }
755     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
756     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
757     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
758     ci[i+1] = ci[i] + packlen;
759     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
760   }
761   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
762   ierr = PetscFree(seen);CHKERRQ(ierr);
763 
764   /* Column indices are in the segmented buffer */
765   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
766   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
767 
768   /* put together the new symbolic matrix */
769   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
770   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
771 
772   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
773   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
774   c          = (Mat_SeqAIJ*)((*C)->data);
775   c->free_a  = PETSC_TRUE;
776   c->free_ij = PETSC_TRUE;
777   c->nonew   = 0;
778 
779   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
780 
781   /* set MatInfo */
782   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
783   if (afill < 1.0) afill = 1.0;
784   c->maxnz                     = ci[am];
785   c->nz                        = ci[am];
786   (*C)->info.mallocs           = ndouble;
787   (*C)->info.fill_ratio_given  = fill;
788   (*C)->info.fill_ratio_needed = afill;
789 
790 #if defined(PETSC_USE_INFO)
791   if (ci[am]) {
792     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
793     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
794   } else {
795     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
796   }
797 #endif
798   PetscFunctionReturn(0);
799 }
800 
801 /* This routine is not used. Should be removed! */
802 #undef __FUNCT__
803 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
804 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
805 {
806   PetscErrorCode ierr;
807 
808   PetscFunctionBegin;
809   if (scall == MAT_INITIAL_MATRIX) {
810     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
811     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
812     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
813   }
814   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
815   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
816   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
817   PetscFunctionReturn(0);
818 }
819 
820 #undef __FUNCT__
821 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
822 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
823 {
824   PetscErrorCode      ierr;
825   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
826   Mat_MatMatTransMult *abt=a->abt;
827 
828   PetscFunctionBegin;
829   ierr = (abt->destroy)(A);CHKERRQ(ierr);
830   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
831   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
832   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
833   ierr = PetscFree(abt);CHKERRQ(ierr);
834   PetscFunctionReturn(0);
835 }
836 
837 #undef __FUNCT__
838 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
839 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
840 {
841   PetscErrorCode      ierr;
842   Mat                 Bt;
843   PetscInt            *bti,*btj;
844   Mat_MatMatTransMult *abt;
845   Mat_SeqAIJ          *c;
846 
847   PetscFunctionBegin;
848   /* create symbolic Bt */
849   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
850   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
851   ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
852 
853   /* get symbolic C=A*Bt */
854   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
855 
856   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
857   ierr   = PetscNew(&abt);CHKERRQ(ierr);
858   c      = (Mat_SeqAIJ*)(*C)->data;
859   c->abt = abt;
860 
861   abt->usecoloring = PETSC_FALSE;
862   abt->destroy     = (*C)->ops->destroy;
863   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
864 
865   ierr = PetscOptionsGetBool(NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
866   if (abt->usecoloring) {
867     /* Create MatTransposeColoring from symbolic C=A*B^T */
868     MatTransposeColoring matcoloring;
869     MatColoring          coloring;
870     ISColoring           iscoloring;
871     Mat                  Bt_dense,C_dense;
872     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
873     /* inode causes memory problem, don't know why */
874     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
875 
876     ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
877     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
878     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
879     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
880     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
881     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
882     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
883 
884     abt->matcoloring = matcoloring;
885 
886     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
887 
888     /* Create Bt_dense and C_dense = A*Bt_dense */
889     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
890     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
891     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
892     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
893 
894     Bt_dense->assembled = PETSC_TRUE;
895     abt->Bt_den   = Bt_dense;
896 
897     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
898     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
899     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
900     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
901 
902     Bt_dense->assembled = PETSC_TRUE;
903     abt->ABt_den  = C_dense;
904 
905 #if defined(PETSC_USE_INFO)
906     {
907       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
908       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);
909     }
910 #endif
911   }
912   /* clean up */
913   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
914   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
915   PetscFunctionReturn(0);
916 }
917 
918 #undef __FUNCT__
919 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
920 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
921 {
922   PetscErrorCode      ierr;
923   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
924   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
925   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
926   PetscLogDouble      flops=0.0;
927   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
928   Mat_MatMatTransMult *abt = c->abt;
929 
930   PetscFunctionBegin;
931   /* clear old values in C */
932   if (!c->a) {
933     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
934     c->a      = ca;
935     c->free_a = PETSC_TRUE;
936   } else {
937     ca =  c->a;
938   }
939   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
940 
941   if (abt->usecoloring) {
942     MatTransposeColoring matcoloring = abt->matcoloring;
943     Mat                  Bt_dense,C_dense = abt->ABt_den;
944 
945     /* Get Bt_dense by Apply MatTransposeColoring to B */
946     Bt_dense = abt->Bt_den;
947     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
948 
949     /* C_dense = A*Bt_dense */
950     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
951 
952     /* Recover C from C_dense */
953     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
954     PetscFunctionReturn(0);
955   }
956 
957   for (i=0; i<cm; i++) {
958     anzi = ai[i+1] - ai[i];
959     acol = aj + ai[i];
960     aval = aa + ai[i];
961     cnzi = ci[i+1] - ci[i];
962     ccol = cj + ci[i];
963     cval = ca + ci[i];
964     for (j=0; j<cnzi; j++) {
965       brow = ccol[j];
966       bnzj = bi[brow+1] - bi[brow];
967       bcol = bj + bi[brow];
968       bval = ba + bi[brow];
969 
970       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
971       nexta = 0; nextb = 0;
972       while (nexta<anzi && nextb<bnzj) {
973         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
974         if (nexta == anzi) break;
975         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
976         if (nextb == bnzj) break;
977         if (acol[nexta] == bcol[nextb]) {
978           cval[j] += aval[nexta]*bval[nextb];
979           nexta++; nextb++;
980           flops += 2;
981         }
982       }
983     }
984   }
985   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
986   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
987   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
988   PetscFunctionReturn(0);
989 }
990 
991 #undef __FUNCT__
992 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
993 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
994 {
995   PetscErrorCode ierr;
996 
997   PetscFunctionBegin;
998   if (scall == MAT_INITIAL_MATRIX) {
999     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1000     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1001     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1002   }
1003   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1004   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1005   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1006   PetscFunctionReturn(0);
1007 }
1008 
1009 #undef __FUNCT__
1010 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1011 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1012 {
1013   PetscErrorCode ierr;
1014   Mat            At;
1015   PetscInt       *ati,*atj;
1016 
1017   PetscFunctionBegin;
1018   /* create symbolic At */
1019   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1020   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1021   ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1022 
1023   /* get symbolic C=At*B */
1024   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1025 
1026   /* clean up */
1027   ierr = MatDestroy(&At);CHKERRQ(ierr);
1028   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1029   PetscFunctionReturn(0);
1030 }
1031 
1032 #undef __FUNCT__
1033 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1034 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1035 {
1036   PetscErrorCode ierr;
1037   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1038   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1039   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1040   PetscLogDouble flops=0.0;
1041   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1042 
1043   PetscFunctionBegin;
1044   if (!c->a) {
1045     ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
1046 
1047     c->a      = ca;
1048     c->free_a = PETSC_TRUE;
1049   } else {
1050     ca = c->a;
1051   }
1052   /* clear old values in C */
1053   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1054 
1055   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1056   for (i=0; i<am; i++) {
1057     bj   = b->j + bi[i];
1058     ba   = b->a + bi[i];
1059     bnzi = bi[i+1] - bi[i];
1060     anzi = ai[i+1] - ai[i];
1061     for (j=0; j<anzi; j++) {
1062       nextb = 0;
1063       crow  = *aj++;
1064       cjj   = cj + ci[crow];
1065       caj   = ca + ci[crow];
1066       /* perform sparse axpy operation.  Note cjj includes bj. */
1067       for (k=0; nextb<bnzi; k++) {
1068         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1069           caj[k] += (*aa)*(*(ba+nextb));
1070           nextb++;
1071         }
1072       }
1073       flops += 2*bnzi;
1074       aa++;
1075     }
1076   }
1077 
1078   /* Assemble the final matrix and clean up */
1079   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1080   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1081   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1082   PetscFunctionReturn(0);
1083 }
1084 
1085 #undef __FUNCT__
1086 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1087 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1088 {
1089   PetscErrorCode ierr;
1090 
1091   PetscFunctionBegin;
1092   if (scall == MAT_INITIAL_MATRIX) {
1093     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1094     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1095     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1096   }
1097   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1098   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1099   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1100   PetscFunctionReturn(0);
1101 }
1102 
1103 #undef __FUNCT__
1104 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1105 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1106 {
1107   PetscErrorCode ierr;
1108 
1109   PetscFunctionBegin;
1110   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1111 
1112   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1113   PetscFunctionReturn(0);
1114 }
1115 
1116 #undef __FUNCT__
1117 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1118 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1119 {
1120   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1121   PetscErrorCode    ierr;
1122   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1123   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1124   const PetscInt    *aj;
1125   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=B->rmap->n,am=A->rmap->n;
1126   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;
1127 
1128   PetscFunctionBegin;
1129   if (!cm || !cn) PetscFunctionReturn(0);
1130   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);
1131   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);
1132   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);
1133   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1134   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1135   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1136   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1137   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1138     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1139       r1 = r2 = r3 = r4 = 0.0;
1140       n  = a->i[i+1] - a->i[i];
1141       aj = a->j + a->i[i];
1142       aa = a->a + a->i[i];
1143       for (j=0; j<n; j++) {
1144         aatmp = aa[j]; ajtmp = aj[j];
1145         r1 += aatmp*b1[ajtmp];
1146         r2 += aatmp*b2[ajtmp];
1147         r3 += aatmp*b3[ajtmp];
1148         r4 += aatmp*b4[ajtmp];
1149       }
1150       c1[i] = r1;
1151       c2[i] = r2;
1152       c3[i] = r3;
1153       c4[i] = r4;
1154     }
1155     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1156     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1157   }
1158   for (; col<cn; col++) {   /* over extra columns of C */
1159     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1160       r1 = 0.0;
1161       n  = a->i[i+1] - a->i[i];
1162       aj = a->j + a->i[i];
1163       aa = a->a + a->i[i];
1164       for (j=0; j<n; j++) {
1165         r1 += aa[j]*b1[aj[j]];
1166       }
1167       c1[i] = r1;
1168     }
1169     b1 += bm;
1170     c1 += am;
1171   }
1172   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1173   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1174   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1175   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1176   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 /*
1181    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1182 */
1183 #undef __FUNCT__
1184 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1185 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1186 {
1187   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1188   PetscErrorCode ierr;
1189   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1190   MatScalar      *aa;
1191   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1192   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1193 
1194   PetscFunctionBegin;
1195   if (!cm || !cn) PetscFunctionReturn(0);
1196   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1197   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1198   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1199 
1200   if (a->compressedrow.use) { /* use compressed row format */
1201     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1202       colam = col*am;
1203       arm   = a->compressedrow.nrows;
1204       ii    = a->compressedrow.i;
1205       ridx  = a->compressedrow.rindex;
1206       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1207         r1 = r2 = r3 = r4 = 0.0;
1208         n  = ii[i+1] - ii[i];
1209         aj = a->j + ii[i];
1210         aa = a->a + ii[i];
1211         for (j=0; j<n; j++) {
1212           r1 += (*aa)*b1[*aj];
1213           r2 += (*aa)*b2[*aj];
1214           r3 += (*aa)*b3[*aj];
1215           r4 += (*aa++)*b4[*aj++];
1216         }
1217         c[colam       + ridx[i]] += r1;
1218         c[colam + am  + ridx[i]] += r2;
1219         c[colam + am2 + ridx[i]] += r3;
1220         c[colam + am3 + ridx[i]] += r4;
1221       }
1222       b1 += bm4;
1223       b2 += bm4;
1224       b3 += bm4;
1225       b4 += bm4;
1226     }
1227     for (; col<cn; col++) {     /* over extra columns of C */
1228       colam = col*am;
1229       arm   = a->compressedrow.nrows;
1230       ii    = a->compressedrow.i;
1231       ridx  = a->compressedrow.rindex;
1232       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1233         r1 = 0.0;
1234         n  = ii[i+1] - ii[i];
1235         aj = a->j + ii[i];
1236         aa = a->a + ii[i];
1237 
1238         for (j=0; j<n; j++) {
1239           r1 += (*aa++)*b1[*aj++];
1240         }
1241         c[colam + ridx[i]] += r1;
1242       }
1243       b1 += bm;
1244     }
1245   } else {
1246     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1247       colam = col*am;
1248       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1249         r1 = r2 = r3 = r4 = 0.0;
1250         n  = a->i[i+1] - a->i[i];
1251         aj = a->j + a->i[i];
1252         aa = a->a + a->i[i];
1253         for (j=0; j<n; j++) {
1254           r1 += (*aa)*b1[*aj];
1255           r2 += (*aa)*b2[*aj];
1256           r3 += (*aa)*b3[*aj];
1257           r4 += (*aa++)*b4[*aj++];
1258         }
1259         c[colam + i]       += r1;
1260         c[colam + am + i]  += r2;
1261         c[colam + am2 + i] += r3;
1262         c[colam + am3 + i] += r4;
1263       }
1264       b1 += bm4;
1265       b2 += bm4;
1266       b3 += bm4;
1267       b4 += bm4;
1268     }
1269     for (; col<cn; col++) {     /* over extra columns of C */
1270       colam = col*am;
1271       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1272         r1 = 0.0;
1273         n  = a->i[i+1] - a->i[i];
1274         aj = a->j + a->i[i];
1275         aa = a->a + a->i[i];
1276 
1277         for (j=0; j<n; j++) {
1278           r1 += (*aa++)*b1[*aj++];
1279         }
1280         c[colam + i] += r1;
1281       }
1282       b1 += bm;
1283     }
1284   }
1285   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1286   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1287   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1288   PetscFunctionReturn(0);
1289 }
1290 
1291 #undef __FUNCT__
1292 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1293 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1294 {
1295   PetscErrorCode ierr;
1296   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1297   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1298   PetscInt       *bi      = b->i,*bj=b->j;
1299   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1300   MatScalar      *btval,*btval_den,*ba=b->a;
1301   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1302 
1303   PetscFunctionBegin;
1304   btval_den=btdense->v;
1305   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1306   for (k=0; k<ncolors; k++) {
1307     ncolumns = coloring->ncolumns[k];
1308     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1309       col   = *(columns + colorforcol[k] + l);
1310       btcol = bj + bi[col];
1311       btval = ba + bi[col];
1312       anz   = bi[col+1] - bi[col];
1313       for (j=0; j<anz; j++) {
1314         brow            = btcol[j];
1315         btval_den[brow] = btval[j];
1316       }
1317     }
1318     btval_den += m;
1319   }
1320   PetscFunctionReturn(0);
1321 }
1322 
1323 #undef __FUNCT__
1324 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1325 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1326 {
1327   PetscErrorCode ierr;
1328   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1329   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1330   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1331   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1332   PetscInt       nrows,*row,*idx;
1333   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1334 
1335   PetscFunctionBegin;
1336   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1337 
1338   if (brows > 0) {
1339     PetscInt *lstart,row_end,row_start;
1340     lstart = matcoloring->lstart;
1341     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1342 
1343     row_end = brows;
1344     if (row_end > m) row_end = m;
1345     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1346       ca_den_ptr = ca_den;
1347       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1348         nrows = matcoloring->nrows[k];
1349         row   = rows  + colorforrow[k];
1350         idx   = den2sp + colorforrow[k];
1351         for (l=lstart[k]; l<nrows; l++) {
1352           if (row[l] >= row_end) {
1353             lstart[k] = l;
1354             break;
1355           } else {
1356             ca[idx[l]] = ca_den_ptr[row[l]];
1357           }
1358         }
1359         ca_den_ptr += m;
1360       }
1361       row_end += brows;
1362       if (row_end > m) row_end = m;
1363     }
1364   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1365     ca_den_ptr = ca_den;
1366     for (k=0; k<ncolors; k++) {
1367       nrows = matcoloring->nrows[k];
1368       row   = rows  + colorforrow[k];
1369       idx   = den2sp + colorforrow[k];
1370       for (l=0; l<nrows; l++) {
1371         ca[idx[l]] = ca_den_ptr[row[l]];
1372       }
1373       ca_den_ptr += m;
1374     }
1375   }
1376 
1377   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1378 #if defined(PETSC_USE_INFO)
1379   if (matcoloring->brows > 0) {
1380     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1381   } else {
1382     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1383   }
1384 #endif
1385   PetscFunctionReturn(0);
1386 }
1387 
1388 #undef __FUNCT__
1389 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1390 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1391 {
1392   PetscErrorCode ierr;
1393   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1394   const PetscInt *is,*ci,*cj,*row_idx;
1395   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1396   IS             *isa;
1397   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1398   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1399   PetscInt       *colorforcol,*columns,*columns_i,brows;
1400   PetscBool      flg;
1401 
1402   PetscFunctionBegin;
1403   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1404 
1405   /* bs >1 is not being tested yet! */
1406   Nbs       = mat->cmap->N/bs;
1407   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1408   c->N      = Nbs;
1409   c->m      = c->M;
1410   c->rstart = 0;
1411   c->brows  = 100;
1412 
1413   c->ncolors = nis;
1414   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1415   ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr);
1416   ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr);
1417 
1418   brows = c->brows;
1419   ierr = PetscOptionsGetInt(NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1420   if (flg) c->brows = brows;
1421   if (brows > 0) {
1422     ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr);
1423   }
1424 
1425   colorforrow[0] = 0;
1426   rows_i         = rows;
1427   den2sp_i       = den2sp;
1428 
1429   ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr);
1430   ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr);
1431 
1432   colorforcol[0] = 0;
1433   columns_i      = columns;
1434 
1435   /* get column-wise storage of mat */
1436   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1437 
1438   cm   = c->m;
1439   ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr);
1440   ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr);
1441   for (i=0; i<nis; i++) { /* loop over color */
1442     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1443     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1444 
1445     c->ncolumns[i] = n;
1446     if (n) {
1447       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1448     }
1449     colorforcol[i+1] = colorforcol[i] + n;
1450     columns_i       += n;
1451 
1452     /* fast, crude version requires O(N*N) work */
1453     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1454 
1455     for (j=0; j<n; j++) { /* loop over columns*/
1456       col     = is[j];
1457       row_idx = cj + ci[col];
1458       m       = ci[col+1] - ci[col];
1459       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1460         idxhit[*row_idx]   = spidx[ci[col] + k];
1461         rowhit[*row_idx++] = col + 1;
1462       }
1463     }
1464     /* count the number of hits */
1465     nrows = 0;
1466     for (j=0; j<cm; j++) {
1467       if (rowhit[j]) nrows++;
1468     }
1469     c->nrows[i]      = nrows;
1470     colorforrow[i+1] = colorforrow[i] + nrows;
1471 
1472     nrows = 0;
1473     for (j=0; j<cm; j++) { /* loop over rows */
1474       if (rowhit[j]) {
1475         rows_i[nrows]   = j;
1476         den2sp_i[nrows] = idxhit[j];
1477         nrows++;
1478       }
1479     }
1480     den2sp_i += nrows;
1481 
1482     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1483     rows_i += nrows;
1484   }
1485   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1486   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1487   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1488   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1489 
1490   c->colorforrow = colorforrow;
1491   c->rows        = rows;
1492   c->den2sp      = den2sp;
1493   c->colorforcol = colorforcol;
1494   c->columns     = columns;
1495 
1496   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1497   PetscFunctionReturn(0);
1498 }
1499