xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 4fc747eaadbeca11629f314a99edccbc2ed7b3d3)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = A * B
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <../src/mat/utils/petscheap.h>
10 #include <petscbt.h>
11 #include <petsc/private/isimpl.h>
12 #include <../src/mat/impls/dense/seq/dense.h>
13 
14 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);
15 
16 #undef __FUNCT__
17 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
18 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
19 {
20   PetscErrorCode ierr;
21   const char     *algTypes[6] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed"};
22   PetscInt       alg=0; /* set default algorithm */
23 
24   PetscFunctionBegin;
25   if (scall == MAT_INITIAL_MATRIX) {
26     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
27     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,6,algTypes[0],&alg,NULL);CHKERRQ(ierr);
28     ierr = PetscOptionsEnd();CHKERRQ(ierr);
29     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
30     switch (alg) {
31     case 1:
32       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
33       break;
34     case 2:
35       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
36       break;
37     case 3:
38       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
39       break;
40     case 4:
41       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
42       break;
43     case 5:
44       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
45       break;
46     default:
47       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
48      break;
49     }
50     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
51   }
52 
53   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
54   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
55   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
56   PetscFunctionReturn(0);
57 }
58 
59 #undef __FUNCT__
60 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed"
61 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
62 {
63   PetscErrorCode     ierr;
64   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
65   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
66   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
67   PetscReal          afill;
68   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
69   PetscTable         ta;
70   PetscBT            lnkbt;
71   PetscFreeSpaceList free_space=NULL,current_space=NULL;
72 
73   PetscFunctionBegin;
74   /* Get ci and cj */
75   /*---------------*/
76   /* Allocate ci array, arrays for fill computation and */
77   /* free space for accumulating nonzero column info */
78   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
79   ci[0] = 0;
80 
81   /* create and initialize a linked list */
82   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
83   MatRowMergeMax_SeqAIJ(b,bm,ta);
84   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
85   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
86 
87   ierr = PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);CHKERRQ(ierr);
88 
89   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
90   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
91 
92   current_space = free_space;
93 
94   /* Determine ci and cj */
95   for (i=0; i<am; i++) {
96     anzi = ai[i+1] - ai[i];
97     aj   = a->j + ai[i];
98     for (j=0; j<anzi; j++) {
99       brow = aj[j];
100       bnzj = bi[brow+1] - bi[brow];
101       bj   = b->j + bi[brow];
102       /* add non-zero cols of B into the sorted linked list lnk */
103       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
104     }
105     cnzi = lnk[0];
106 
107     /* If free space is not available, make more free space */
108     /* Double the amount of total space in the list */
109     if (current_space->local_remaining<cnzi) {
110       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
111       ndouble++;
112     }
113 
114     /* Copy data into free space, then initialize lnk */
115     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
116 
117     current_space->array           += cnzi;
118     current_space->local_used      += cnzi;
119     current_space->local_remaining -= cnzi;
120 
121     ci[i+1] = ci[i] + cnzi;
122   }
123 
124   /* Column indices are in the list of free space */
125   /* Allocate space for cj, initialize cj, and */
126   /* destroy list of free space and other temporary array(s) */
127   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
128   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
129   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
130 
131   /* put together the new symbolic matrix */
132   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
133   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
134 
135   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
136   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
137   c                         = (Mat_SeqAIJ*)((*C)->data);
138   c->free_a                 = PETSC_FALSE;
139   c->free_ij                = PETSC_TRUE;
140   c->nonew                  = 0;
141   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
142 
143   /* set MatInfo */
144   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
145   if (afill < 1.0) afill = 1.0;
146   c->maxnz                     = ci[am];
147   c->nz                        = ci[am];
148   (*C)->info.mallocs           = ndouble;
149   (*C)->info.fill_ratio_given  = fill;
150   (*C)->info.fill_ratio_needed = afill;
151 
152 #if defined(PETSC_USE_INFO)
153   if (ci[am]) {
154     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
155     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
156   } else {
157     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
158   }
159 #endif
160   PetscFunctionReturn(0);
161 }
162 
163 #undef __FUNCT__
164 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
165 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
166 {
167   PetscErrorCode ierr;
168   PetscLogDouble flops=0.0;
169   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
170   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
171   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
172   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
173   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
174   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
175   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
176   PetscScalar    *ab_dense;
177 
178   PetscFunctionBegin;
179   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
180     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
181     c->a      = ca;
182     c->free_a = PETSC_TRUE;
183   } else {
184     ca        = c->a;
185   }
186   if (!c->matmult_abdense) {
187     ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr);
188     c->matmult_abdense = ab_dense;
189   } else {
190     ab_dense = c->matmult_abdense;
191   }
192 
193   /* clean old values in C */
194   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
195   /* Traverse A row-wise. */
196   /* Build the ith row in C by summing over nonzero columns in A, */
197   /* the rows of B corresponding to nonzeros of A. */
198   for (i=0; i<am; i++) {
199     anzi = ai[i+1] - ai[i];
200     for (j=0; j<anzi; j++) {
201       brow = aj[j];
202       bnzi = bi[brow+1] - bi[brow];
203       bjj  = bj + bi[brow];
204       baj  = ba + bi[brow];
205       /* perform dense axpy */
206       valtmp = aa[j];
207       for (k=0; k<bnzi; k++) {
208         ab_dense[bjj[k]] += valtmp*baj[k];
209       }
210       flops += 2*bnzi;
211     }
212     aj += anzi; aa += anzi;
213 
214     cnzi = ci[i+1] - ci[i];
215     for (k=0; k<cnzi; k++) {
216       ca[k]          += ab_dense[cj[k]];
217       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
218     }
219     flops += cnzi;
220     cj    += cnzi; ca += cnzi;
221   }
222   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
223   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
224   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
225   PetscFunctionReturn(0);
226 }
227 
228 #undef __FUNCT__
229 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
230 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
231 {
232   PetscErrorCode ierr;
233   PetscLogDouble flops=0.0;
234   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
235   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
236   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
237   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
238   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
239   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
240   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
241   PetscInt       nextb;
242 
243   PetscFunctionBegin;
244   /* clean old values in C */
245   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
246   /* Traverse A row-wise. */
247   /* Build the ith row in C by summing over nonzero columns in A, */
248   /* the rows of B corresponding to nonzeros of A. */
249   for (i=0; i<am; i++) {
250     anzi = ai[i+1] - ai[i];
251     cnzi = ci[i+1] - ci[i];
252     for (j=0; j<anzi; j++) {
253       brow = aj[j];
254       bnzi = bi[brow+1] - bi[brow];
255       bjj  = bj + bi[brow];
256       baj  = ba + bi[brow];
257       /* perform sparse axpy */
258       valtmp = aa[j];
259       nextb  = 0;
260       for (k=0; nextb<bnzi; k++) {
261         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
262           ca[k] += valtmp*baj[nextb++];
263         }
264       }
265       flops += 2*bnzi;
266     }
267     aj += anzi; aa += anzi;
268     cj += cnzi; ca += cnzi;
269   }
270 
271   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
272   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
273   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
274   PetscFunctionReturn(0);
275 }
276 
277 #undef __FUNCT__
278 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
279 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
280 {
281   PetscErrorCode     ierr;
282   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
283   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
284   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
285   MatScalar          *ca;
286   PetscReal          afill;
287   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
288   PetscTable         ta;
289   PetscFreeSpaceList free_space=NULL,current_space=NULL;
290 
291   PetscFunctionBegin;
292   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
293   /*-----------------------------------------------------------------------------------------*/
294   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
295   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
296   ci[0] = 0;
297 
298   /* create and initialize a linked list */
299   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
300   MatRowMergeMax_SeqAIJ(b,bm,ta);
301   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
302   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
303 
304   ierr = PetscLLCondensedCreate_fast(Crmax,&lnk);CHKERRQ(ierr);
305 
306   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
307   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
308   current_space = free_space;
309 
310   /* Determine ci and cj */
311   for (i=0; i<am; i++) {
312     anzi = ai[i+1] - ai[i];
313     aj   = a->j + ai[i];
314     for (j=0; j<anzi; j++) {
315       brow = aj[j];
316       bnzj = bi[brow+1] - bi[brow];
317       bj   = b->j + bi[brow];
318       /* add non-zero cols of B into the sorted linked list lnk */
319       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
320     }
321     cnzi = lnk[1];
322 
323     /* If free space is not available, make more free space */
324     /* Double the amount of total space in the list */
325     if (current_space->local_remaining<cnzi) {
326       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
327       ndouble++;
328     }
329 
330     /* Copy data into free space, then initialize lnk */
331     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
332 
333     current_space->array           += cnzi;
334     current_space->local_used      += cnzi;
335     current_space->local_remaining -= cnzi;
336 
337     ci[i+1] = ci[i] + cnzi;
338   }
339 
340   /* Column indices are in the list of free space */
341   /* Allocate space for cj, initialize cj, and */
342   /* destroy list of free space and other temporary array(s) */
343   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
344   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
345   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
346 
347   /* Allocate space for ca */
348   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
349   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
350 
351   /* put together the new symbolic matrix */
352   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
353   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
354 
355   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
356   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
357   c          = (Mat_SeqAIJ*)((*C)->data);
358   c->free_a  = PETSC_TRUE;
359   c->free_ij = PETSC_TRUE;
360   c->nonew   = 0;
361 
362   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
363 
364   /* set MatInfo */
365   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
366   if (afill < 1.0) afill = 1.0;
367   c->maxnz                     = ci[am];
368   c->nz                        = ci[am];
369   (*C)->info.mallocs           = ndouble;
370   (*C)->info.fill_ratio_given  = fill;
371   (*C)->info.fill_ratio_needed = afill;
372 
373 #if defined(PETSC_USE_INFO)
374   if (ci[am]) {
375     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
376     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
377   } else {
378     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
379   }
380 #endif
381   PetscFunctionReturn(0);
382 }
383 
384 
385 #undef __FUNCT__
386 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
387 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
388 {
389   PetscErrorCode     ierr;
390   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
391   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
392   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
393   MatScalar          *ca;
394   PetscReal          afill;
395   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
396   PetscTable         ta;
397   PetscFreeSpaceList free_space=NULL,current_space=NULL;
398 
399   PetscFunctionBegin;
400   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
401   /*---------------------------------------------------------------------------------------------*/
402   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
403   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
404   ci[0] = 0;
405 
406   /* create and initialize a linked list */
407   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
408   MatRowMergeMax_SeqAIJ(b,bm,ta);
409   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
410   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
411   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
412 
413   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
414   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
415   current_space = free_space;
416 
417   /* Determine ci and cj */
418   for (i=0; i<am; i++) {
419     anzi = ai[i+1] - ai[i];
420     aj   = a->j + ai[i];
421     for (j=0; j<anzi; j++) {
422       brow = aj[j];
423       bnzj = bi[brow+1] - bi[brow];
424       bj   = b->j + bi[brow];
425       /* add non-zero cols of B into the sorted linked list lnk */
426       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
427     }
428     cnzi = lnk[0];
429 
430     /* If free space is not available, make more free space */
431     /* Double the amount of total space in the list */
432     if (current_space->local_remaining<cnzi) {
433       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
434       ndouble++;
435     }
436 
437     /* Copy data into free space, then initialize lnk */
438     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
439 
440     current_space->array           += cnzi;
441     current_space->local_used      += cnzi;
442     current_space->local_remaining -= cnzi;
443 
444     ci[i+1] = ci[i] + cnzi;
445   }
446 
447   /* Column indices are in the list of free space */
448   /* Allocate space for cj, initialize cj, and */
449   /* destroy list of free space and other temporary array(s) */
450   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
451   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
452   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
453 
454   /* Allocate space for ca */
455   /*-----------------------*/
456   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
457   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
458 
459   /* put together the new symbolic matrix */
460   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
461   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
462 
463   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
464   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
465   c          = (Mat_SeqAIJ*)((*C)->data);
466   c->free_a  = PETSC_TRUE;
467   c->free_ij = PETSC_TRUE;
468   c->nonew   = 0;
469 
470   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
471 
472   /* set MatInfo */
473   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
474   if (afill < 1.0) afill = 1.0;
475   c->maxnz                     = ci[am];
476   c->nz                        = ci[am];
477   (*C)->info.mallocs           = ndouble;
478   (*C)->info.fill_ratio_given  = fill;
479   (*C)->info.fill_ratio_needed = afill;
480 
481 #if defined(PETSC_USE_INFO)
482   if (ci[am]) {
483     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
484     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
485   } else {
486     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
487   }
488 #endif
489   PetscFunctionReturn(0);
490 }
491 
492 #undef __FUNCT__
493 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
494 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
495 {
496   PetscErrorCode     ierr;
497   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
498   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
499   PetscInt           *ci,*cj,*bb;
500   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
501   PetscReal          afill;
502   PetscInt           i,j,col,ndouble = 0;
503   PetscFreeSpaceList free_space=NULL,current_space=NULL;
504   PetscHeap          h;
505 
506   PetscFunctionBegin;
507   /* Get ci and cj - by merging sorted rows using a heap */
508   /*---------------------------------------------------------------------------------------------*/
509   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
510   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
511   ci[0] = 0;
512 
513   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
514   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
515   current_space = free_space;
516 
517   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
518   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
519 
520   /* Determine ci and cj */
521   for (i=0; i<am; i++) {
522     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 */
523     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
524     ci[i+1] = ci[i];
525     /* Populate the min heap */
526     for (j=0; j<anzi; j++) {
527       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
528       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
529         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
530       }
531     }
532     /* Pick off the min element, adding it to free space */
533     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
534     while (j >= 0) {
535       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
536         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
537         ndouble++;
538       }
539       *(current_space->array++) = col;
540       current_space->local_used++;
541       current_space->local_remaining--;
542       ci[i+1]++;
543 
544       /* stash if anything else remains in this row of B */
545       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
546       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
547         PetscInt j2,col2;
548         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
549         if (col2 != col) break;
550         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
551         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
552       }
553       /* Put any stashed elements back into the min heap */
554       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
555       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
556     }
557   }
558   ierr = PetscFree(bb);CHKERRQ(ierr);
559   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
560 
561   /* Column indices are in the list of free space */
562   /* Allocate space for cj, initialize cj, and */
563   /* destroy list of free space and other temporary array(s) */
564   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
565   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
566 
567   /* put together the new symbolic matrix */
568   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
569   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
570 
571   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
572   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
573   c          = (Mat_SeqAIJ*)((*C)->data);
574   c->free_a  = PETSC_TRUE;
575   c->free_ij = PETSC_TRUE;
576   c->nonew   = 0;
577 
578   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
579 
580   /* set MatInfo */
581   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
582   if (afill < 1.0) afill = 1.0;
583   c->maxnz                     = ci[am];
584   c->nz                        = ci[am];
585   (*C)->info.mallocs           = ndouble;
586   (*C)->info.fill_ratio_given  = fill;
587   (*C)->info.fill_ratio_needed = afill;
588 
589 #if defined(PETSC_USE_INFO)
590   if (ci[am]) {
591     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
592     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
593   } else {
594     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
595   }
596 #endif
597   PetscFunctionReturn(0);
598 }
599 
600 #undef __FUNCT__
601 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
602 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
603 {
604   PetscErrorCode     ierr;
605   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
606   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
607   PetscInt           *ci,*cj,*bb;
608   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
609   PetscReal          afill;
610   PetscInt           i,j,col,ndouble = 0;
611   PetscFreeSpaceList free_space=NULL,current_space=NULL;
612   PetscHeap          h;
613   PetscBT            bt;
614 
615   PetscFunctionBegin;
616   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
617   /*---------------------------------------------------------------------------------------------*/
618   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
619   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
620   ci[0] = 0;
621 
622   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
623   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
624 
625   current_space = free_space;
626 
627   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
628   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
629   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
630 
631   /* Determine ci and cj */
632   for (i=0; i<am; i++) {
633     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
634     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
635     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
636     ci[i+1] = ci[i];
637     /* Populate the min heap */
638     for (j=0; j<anzi; j++) {
639       PetscInt brow = acol[j];
640       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
641         PetscInt bcol = bj[bb[j]];
642         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
643           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
644           bb[j]++;
645           break;
646         }
647       }
648     }
649     /* Pick off the min element, adding it to free space */
650     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
651     while (j >= 0) {
652       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
653         fptr = NULL;                      /* need PetscBTMemzero */
654         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
655         ndouble++;
656       }
657       *(current_space->array++) = col;
658       current_space->local_used++;
659       current_space->local_remaining--;
660       ci[i+1]++;
661 
662       /* stash if anything else remains in this row of B */
663       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
664         PetscInt bcol = bj[bb[j]];
665         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
666           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
667           bb[j]++;
668           break;
669         }
670       }
671       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
672     }
673     if (fptr) {                 /* Clear the bits for this row */
674       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
675     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
676       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
677     }
678   }
679   ierr = PetscFree(bb);CHKERRQ(ierr);
680   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
681   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
682 
683   /* Column indices are in the list of free space */
684   /* Allocate space for cj, initialize cj, and */
685   /* destroy list of free space and other temporary array(s) */
686   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
687   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
688 
689   /* put together the new symbolic matrix */
690   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
691   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
692 
693   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
694   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
695   c          = (Mat_SeqAIJ*)((*C)->data);
696   c->free_a  = PETSC_TRUE;
697   c->free_ij = PETSC_TRUE;
698   c->nonew   = 0;
699 
700   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
701 
702   /* set MatInfo */
703   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
704   if (afill < 1.0) afill = 1.0;
705   c->maxnz                     = ci[am];
706   c->nz                        = ci[am];
707   (*C)->info.mallocs           = ndouble;
708   (*C)->info.fill_ratio_given  = fill;
709   (*C)->info.fill_ratio_needed = afill;
710 
711 #if defined(PETSC_USE_INFO)
712   if (ci[am]) {
713     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
714     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
715   } else {
716     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
717   }
718 #endif
719   PetscFunctionReturn(0);
720 }
721 
722 #undef __FUNCT__
723 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
724 /* concatenate unique entries and then sort */
725 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
726 {
727   PetscErrorCode     ierr;
728   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
729   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
730   PetscInt           *ci,*cj;
731   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
732   PetscReal          afill;
733   PetscInt           i,j,ndouble = 0;
734   PetscSegBuffer     seg,segrow;
735   char               *seen;
736 
737   PetscFunctionBegin;
738   ierr  = PetscMalloc1(am+1,&ci);CHKERRQ(ierr);
739   ci[0] = 0;
740 
741   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
742   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
743   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
744   ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr);
745   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
746 
747   /* Determine ci and cj */
748   for (i=0; i<am; i++) {
749     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 */
750     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
751     PetscInt packlen = 0,*PETSC_RESTRICT crow;
752     /* Pack segrow */
753     for (j=0; j<anzi; j++) {
754       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
755       for (k=bjstart; k<bjend; k++) {
756         PetscInt bcol = bj[k];
757         if (!seen[bcol]) { /* new entry */
758           PetscInt *PETSC_RESTRICT slot;
759           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
760           *slot = bcol;
761           seen[bcol] = 1;
762           packlen++;
763         }
764       }
765     }
766     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
767     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
768     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
769     ci[i+1] = ci[i] + packlen;
770     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
771   }
772   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
773   ierr = PetscFree(seen);CHKERRQ(ierr);
774 
775   /* Column indices are in the segmented buffer */
776   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
777   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
778 
779   /* put together the new symbolic matrix */
780   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
781   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
782 
783   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
784   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
785   c          = (Mat_SeqAIJ*)((*C)->data);
786   c->free_a  = PETSC_TRUE;
787   c->free_ij = PETSC_TRUE;
788   c->nonew   = 0;
789 
790   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
791 
792   /* set MatInfo */
793   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
794   if (afill < 1.0) afill = 1.0;
795   c->maxnz                     = ci[am];
796   c->nz                        = ci[am];
797   (*C)->info.mallocs           = ndouble;
798   (*C)->info.fill_ratio_given  = fill;
799   (*C)->info.fill_ratio_needed = afill;
800 
801 #if defined(PETSC_USE_INFO)
802   if (ci[am]) {
803     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
804     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
805   } else {
806     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
807   }
808 #endif
809   PetscFunctionReturn(0);
810 }
811 
812 /* This routine is not used. Should be removed! */
813 #undef __FUNCT__
814 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
815 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
816 {
817   PetscErrorCode ierr;
818 
819   PetscFunctionBegin;
820   if (scall == MAT_INITIAL_MATRIX) {
821     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
822     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
823     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
824   }
825   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
826   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
827   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
828   PetscFunctionReturn(0);
829 }
830 
831 #undef __FUNCT__
832 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
833 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
834 {
835   PetscErrorCode      ierr;
836   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
837   Mat_MatMatTransMult *abt=a->abt;
838 
839   PetscFunctionBegin;
840   ierr = (abt->destroy)(A);CHKERRQ(ierr);
841   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
842   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
843   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
844   ierr = PetscFree(abt);CHKERRQ(ierr);
845   PetscFunctionReturn(0);
846 }
847 
848 #undef __FUNCT__
849 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
850 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
851 {
852   PetscErrorCode      ierr;
853   Mat                 Bt;
854   PetscInt            *bti,*btj;
855   Mat_MatMatTransMult *abt;
856   Mat_SeqAIJ          *c;
857 
858   PetscFunctionBegin;
859   /* create symbolic Bt */
860   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
861   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
862   ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
863 
864   /* get symbolic C=A*Bt */
865   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
866 
867   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
868   ierr   = PetscNew(&abt);CHKERRQ(ierr);
869   c      = (Mat_SeqAIJ*)(*C)->data;
870   c->abt = abt;
871 
872   abt->usecoloring = PETSC_FALSE;
873   abt->destroy     = (*C)->ops->destroy;
874   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
875 
876   ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
877   if (abt->usecoloring) {
878     /* Create MatTransposeColoring from symbolic C=A*B^T */
879     MatTransposeColoring matcoloring;
880     MatColoring          coloring;
881     ISColoring           iscoloring;
882     Mat                  Bt_dense,C_dense;
883     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
884     /* inode causes memory problem, don't know why */
885     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
886 
887     ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
888     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
889     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
890     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
891     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
892     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
893     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
894 
895     abt->matcoloring = matcoloring;
896 
897     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
898 
899     /* Create Bt_dense and C_dense = A*Bt_dense */
900     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
901     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
902     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
903     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
904 
905     Bt_dense->assembled = PETSC_TRUE;
906     abt->Bt_den   = Bt_dense;
907 
908     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
909     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
910     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
911     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
912 
913     Bt_dense->assembled = PETSC_TRUE;
914     abt->ABt_den  = C_dense;
915 
916 #if defined(PETSC_USE_INFO)
917     {
918       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
919       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);
920     }
921 #endif
922   }
923   /* clean up */
924   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
925   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
926   PetscFunctionReturn(0);
927 }
928 
929 #undef __FUNCT__
930 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
931 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
932 {
933   PetscErrorCode      ierr;
934   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
935   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
936   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
937   PetscLogDouble      flops=0.0;
938   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
939   Mat_MatMatTransMult *abt = c->abt;
940 
941   PetscFunctionBegin;
942   /* clear old values in C */
943   if (!c->a) {
944     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
945     c->a      = ca;
946     c->free_a = PETSC_TRUE;
947   } else {
948     ca =  c->a;
949   }
950   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
951 
952   if (abt->usecoloring) {
953     MatTransposeColoring matcoloring = abt->matcoloring;
954     Mat                  Bt_dense,C_dense = abt->ABt_den;
955 
956     /* Get Bt_dense by Apply MatTransposeColoring to B */
957     Bt_dense = abt->Bt_den;
958     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
959 
960     /* C_dense = A*Bt_dense */
961     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
962 
963     /* Recover C from C_dense */
964     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
965     PetscFunctionReturn(0);
966   }
967 
968   for (i=0; i<cm; i++) {
969     anzi = ai[i+1] - ai[i];
970     acol = aj + ai[i];
971     aval = aa + ai[i];
972     cnzi = ci[i+1] - ci[i];
973     ccol = cj + ci[i];
974     cval = ca + ci[i];
975     for (j=0; j<cnzi; j++) {
976       brow = ccol[j];
977       bnzj = bi[brow+1] - bi[brow];
978       bcol = bj + bi[brow];
979       bval = ba + bi[brow];
980 
981       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
982       nexta = 0; nextb = 0;
983       while (nexta<anzi && nextb<bnzj) {
984         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
985         if (nexta == anzi) break;
986         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
987         if (nextb == bnzj) break;
988         if (acol[nexta] == bcol[nextb]) {
989           cval[j] += aval[nexta]*bval[nextb];
990           nexta++; nextb++;
991           flops += 2;
992         }
993       }
994     }
995   }
996   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
997   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
998   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
999   PetscFunctionReturn(0);
1000 }
1001 
1002 #undef __FUNCT__
1003 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1004 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1005 {
1006   PetscErrorCode ierr;
1007 
1008   PetscFunctionBegin;
1009   if (scall == MAT_INITIAL_MATRIX) {
1010     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1011     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1012     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1013   }
1014   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1015   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1016   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1017   PetscFunctionReturn(0);
1018 }
1019 
1020 #undef __FUNCT__
1021 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1022 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1023 {
1024   PetscErrorCode ierr;
1025   Mat            At;
1026   PetscInt       *ati,*atj;
1027 
1028   PetscFunctionBegin;
1029   /* create symbolic At */
1030   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1031   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1032   ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1033 
1034   /* get symbolic C=At*B */
1035   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1036 
1037   /* clean up */
1038   ierr = MatDestroy(&At);CHKERRQ(ierr);
1039   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1040   PetscFunctionReturn(0);
1041 }
1042 
1043 #undef __FUNCT__
1044 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1045 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1046 {
1047   PetscErrorCode ierr;
1048   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1049   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1050   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1051   PetscLogDouble flops=0.0;
1052   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1053 
1054   PetscFunctionBegin;
1055   if (!c->a) {
1056     ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
1057 
1058     c->a      = ca;
1059     c->free_a = PETSC_TRUE;
1060   } else {
1061     ca = c->a;
1062   }
1063   /* clear old values in C */
1064   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1065 
1066   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1067   for (i=0; i<am; i++) {
1068     bj   = b->j + bi[i];
1069     ba   = b->a + bi[i];
1070     bnzi = bi[i+1] - bi[i];
1071     anzi = ai[i+1] - ai[i];
1072     for (j=0; j<anzi; j++) {
1073       nextb = 0;
1074       crow  = *aj++;
1075       cjj   = cj + ci[crow];
1076       caj   = ca + ci[crow];
1077       /* perform sparse axpy operation.  Note cjj includes bj. */
1078       for (k=0; nextb<bnzi; k++) {
1079         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1080           caj[k] += (*aa)*(*(ba+nextb));
1081           nextb++;
1082         }
1083       }
1084       flops += 2*bnzi;
1085       aa++;
1086     }
1087   }
1088 
1089   /* Assemble the final matrix and clean up */
1090   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1091   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1092   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1093   PetscFunctionReturn(0);
1094 }
1095 
1096 #undef __FUNCT__
1097 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1098 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1099 {
1100   PetscErrorCode ierr;
1101 
1102   PetscFunctionBegin;
1103   if (scall == MAT_INITIAL_MATRIX) {
1104     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1105     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1106     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1107   }
1108   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1109   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1110   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1111   PetscFunctionReturn(0);
1112 }
1113 
1114 #undef __FUNCT__
1115 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1116 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1117 {
1118   PetscErrorCode ierr;
1119 
1120   PetscFunctionBegin;
1121   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1122 
1123   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1124   PetscFunctionReturn(0);
1125 }
1126 
1127 #undef __FUNCT__
1128 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1129 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1130 {
1131   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1132   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
1133   PetscErrorCode    ierr;
1134   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1135   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1136   const PetscInt    *aj;
1137   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n;
1138   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;
1139 
1140   PetscFunctionBegin;
1141   if (!cm || !cn) PetscFunctionReturn(0);
1142   if (B->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,B->rmap->n);
1143   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);
1144   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);
1145   b = bd->v;
1146   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1147   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1148   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1149   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1150     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1151       r1 = r2 = r3 = r4 = 0.0;
1152       n  = a->i[i+1] - a->i[i];
1153       aj = a->j + a->i[i];
1154       aa = a->a + a->i[i];
1155       for (j=0; j<n; j++) {
1156         aatmp = aa[j]; ajtmp = aj[j];
1157         r1 += aatmp*b1[ajtmp];
1158         r2 += aatmp*b2[ajtmp];
1159         r3 += aatmp*b3[ajtmp];
1160         r4 += aatmp*b4[ajtmp];
1161       }
1162       c1[i] = r1;
1163       c2[i] = r2;
1164       c3[i] = r3;
1165       c4[i] = r4;
1166     }
1167     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1168     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1169   }
1170   for (; col<cn; col++) {   /* over extra columns of C */
1171     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1172       r1 = 0.0;
1173       n  = a->i[i+1] - a->i[i];
1174       aj = a->j + a->i[i];
1175       aa = a->a + a->i[i];
1176       for (j=0; j<n; j++) {
1177         r1 += aa[j]*b1[aj[j]];
1178       }
1179       c1[i] = r1;
1180     }
1181     b1 += bm;
1182     c1 += am;
1183   }
1184   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1185   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1186   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1187   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1188   PetscFunctionReturn(0);
1189 }
1190 
1191 /*
1192    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1193 */
1194 #undef __FUNCT__
1195 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1196 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1197 {
1198   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1199   Mat_SeqDense   *bd = (Mat_SeqDense*)B->data;
1200   PetscErrorCode ierr;
1201   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1202   MatScalar      *aa;
1203   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1204   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1205 
1206   PetscFunctionBegin;
1207   if (!cm || !cn) PetscFunctionReturn(0);
1208   b = bd->v;
1209   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1210   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1211 
1212   if (a->compressedrow.use) { /* use compressed row format */
1213     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1214       colam = col*am;
1215       arm   = a->compressedrow.nrows;
1216       ii    = a->compressedrow.i;
1217       ridx  = a->compressedrow.rindex;
1218       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1219         r1 = r2 = r3 = r4 = 0.0;
1220         n  = ii[i+1] - ii[i];
1221         aj = a->j + ii[i];
1222         aa = a->a + ii[i];
1223         for (j=0; j<n; j++) {
1224           r1 += (*aa)*b1[*aj];
1225           r2 += (*aa)*b2[*aj];
1226           r3 += (*aa)*b3[*aj];
1227           r4 += (*aa++)*b4[*aj++];
1228         }
1229         c[colam       + ridx[i]] += r1;
1230         c[colam + am  + ridx[i]] += r2;
1231         c[colam + am2 + ridx[i]] += r3;
1232         c[colam + am3 + ridx[i]] += r4;
1233       }
1234       b1 += bm4;
1235       b2 += bm4;
1236       b3 += bm4;
1237       b4 += bm4;
1238     }
1239     for (; col<cn; col++) {     /* over extra columns of C */
1240       colam = col*am;
1241       arm   = a->compressedrow.nrows;
1242       ii    = a->compressedrow.i;
1243       ridx  = a->compressedrow.rindex;
1244       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1245         r1 = 0.0;
1246         n  = ii[i+1] - ii[i];
1247         aj = a->j + ii[i];
1248         aa = a->a + ii[i];
1249 
1250         for (j=0; j<n; j++) {
1251           r1 += (*aa++)*b1[*aj++];
1252         }
1253         c[colam + ridx[i]] += r1;
1254       }
1255       b1 += bm;
1256     }
1257   } else {
1258     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1259       colam = col*am;
1260       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1261         r1 = r2 = r3 = r4 = 0.0;
1262         n  = a->i[i+1] - a->i[i];
1263         aj = a->j + a->i[i];
1264         aa = a->a + a->i[i];
1265         for (j=0; j<n; j++) {
1266           r1 += (*aa)*b1[*aj];
1267           r2 += (*aa)*b2[*aj];
1268           r3 += (*aa)*b3[*aj];
1269           r4 += (*aa++)*b4[*aj++];
1270         }
1271         c[colam + i]       += r1;
1272         c[colam + am + i]  += r2;
1273         c[colam + am2 + i] += r3;
1274         c[colam + am3 + i] += r4;
1275       }
1276       b1 += bm4;
1277       b2 += bm4;
1278       b3 += bm4;
1279       b4 += bm4;
1280     }
1281     for (; col<cn; col++) {     /* over extra columns of C */
1282       colam = col*am;
1283       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1284         r1 = 0.0;
1285         n  = a->i[i+1] - a->i[i];
1286         aj = a->j + a->i[i];
1287         aa = a->a + a->i[i];
1288 
1289         for (j=0; j<n; j++) {
1290           r1 += (*aa++)*b1[*aj++];
1291         }
1292         c[colam + i] += r1;
1293       }
1294       b1 += bm;
1295     }
1296   }
1297   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1298   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1299   PetscFunctionReturn(0);
1300 }
1301 
1302 #undef __FUNCT__
1303 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1304 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1305 {
1306   PetscErrorCode ierr;
1307   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1308   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1309   PetscInt       *bi      = b->i,*bj=b->j;
1310   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1311   MatScalar      *btval,*btval_den,*ba=b->a;
1312   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1313 
1314   PetscFunctionBegin;
1315   btval_den=btdense->v;
1316   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1317   for (k=0; k<ncolors; k++) {
1318     ncolumns = coloring->ncolumns[k];
1319     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1320       col   = *(columns + colorforcol[k] + l);
1321       btcol = bj + bi[col];
1322       btval = ba + bi[col];
1323       anz   = bi[col+1] - bi[col];
1324       for (j=0; j<anz; j++) {
1325         brow            = btcol[j];
1326         btval_den[brow] = btval[j];
1327       }
1328     }
1329     btval_den += m;
1330   }
1331   PetscFunctionReturn(0);
1332 }
1333 
1334 #undef __FUNCT__
1335 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1336 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1337 {
1338   PetscErrorCode ierr;
1339   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1340   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1341   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1342   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1343   PetscInt       nrows,*row,*idx;
1344   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1345 
1346   PetscFunctionBegin;
1347   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1348 
1349   if (brows > 0) {
1350     PetscInt *lstart,row_end,row_start;
1351     lstart = matcoloring->lstart;
1352     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1353 
1354     row_end = brows;
1355     if (row_end > m) row_end = m;
1356     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1357       ca_den_ptr = ca_den;
1358       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1359         nrows = matcoloring->nrows[k];
1360         row   = rows  + colorforrow[k];
1361         idx   = den2sp + colorforrow[k];
1362         for (l=lstart[k]; l<nrows; l++) {
1363           if (row[l] >= row_end) {
1364             lstart[k] = l;
1365             break;
1366           } else {
1367             ca[idx[l]] = ca_den_ptr[row[l]];
1368           }
1369         }
1370         ca_den_ptr += m;
1371       }
1372       row_end += brows;
1373       if (row_end > m) row_end = m;
1374     }
1375   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1376     ca_den_ptr = ca_den;
1377     for (k=0; k<ncolors; k++) {
1378       nrows = matcoloring->nrows[k];
1379       row   = rows  + colorforrow[k];
1380       idx   = den2sp + colorforrow[k];
1381       for (l=0; l<nrows; l++) {
1382         ca[idx[l]] = ca_den_ptr[row[l]];
1383       }
1384       ca_den_ptr += m;
1385     }
1386   }
1387 
1388   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1389 #if defined(PETSC_USE_INFO)
1390   if (matcoloring->brows > 0) {
1391     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1392   } else {
1393     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1394   }
1395 #endif
1396   PetscFunctionReturn(0);
1397 }
1398 
1399 #undef __FUNCT__
1400 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1401 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1402 {
1403   PetscErrorCode ierr;
1404   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1405   const PetscInt *is,*ci,*cj,*row_idx;
1406   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1407   IS             *isa;
1408   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1409   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1410   PetscInt       *colorforcol,*columns,*columns_i,brows;
1411   PetscBool      flg;
1412 
1413   PetscFunctionBegin;
1414   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1415 
1416   /* bs >1 is not being tested yet! */
1417   Nbs       = mat->cmap->N/bs;
1418   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1419   c->N      = Nbs;
1420   c->m      = c->M;
1421   c->rstart = 0;
1422   c->brows  = 100;
1423 
1424   c->ncolors = nis;
1425   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1426   ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr);
1427   ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr);
1428 
1429   brows = c->brows;
1430   ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1431   if (flg) c->brows = brows;
1432   if (brows > 0) {
1433     ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr);
1434   }
1435 
1436   colorforrow[0] = 0;
1437   rows_i         = rows;
1438   den2sp_i       = den2sp;
1439 
1440   ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr);
1441   ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr);
1442 
1443   colorforcol[0] = 0;
1444   columns_i      = columns;
1445 
1446   /* get column-wise storage of mat */
1447   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1448 
1449   cm   = c->m;
1450   ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr);
1451   ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr);
1452   for (i=0; i<nis; i++) { /* loop over color */
1453     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1454     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1455 
1456     c->ncolumns[i] = n;
1457     if (n) {
1458       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1459     }
1460     colorforcol[i+1] = colorforcol[i] + n;
1461     columns_i       += n;
1462 
1463     /* fast, crude version requires O(N*N) work */
1464     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1465 
1466     for (j=0; j<n; j++) { /* loop over columns*/
1467       col     = is[j];
1468       row_idx = cj + ci[col];
1469       m       = ci[col+1] - ci[col];
1470       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1471         idxhit[*row_idx]   = spidx[ci[col] + k];
1472         rowhit[*row_idx++] = col + 1;
1473       }
1474     }
1475     /* count the number of hits */
1476     nrows = 0;
1477     for (j=0; j<cm; j++) {
1478       if (rowhit[j]) nrows++;
1479     }
1480     c->nrows[i]      = nrows;
1481     colorforrow[i+1] = colorforrow[i] + nrows;
1482 
1483     nrows = 0;
1484     for (j=0; j<cm; j++) { /* loop over rows */
1485       if (rowhit[j]) {
1486         rows_i[nrows]   = j;
1487         den2sp_i[nrows] = idxhit[j];
1488         nrows++;
1489       }
1490     }
1491     den2sp_i += nrows;
1492 
1493     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1494     rows_i += nrows;
1495   }
1496   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1497   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1498   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1499   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1500 
1501   c->colorforrow = colorforrow;
1502   c->rows        = rows;
1503   c->den2sp      = den2sp;
1504   c->colorforcol = colorforcol;
1505   c->columns     = columns;
1506 
1507   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1508   PetscFunctionReturn(0);
1509 }
1510