xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision be7a6d03210faab0df8c3f3b720c976929326be8)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = A * B
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <../src/mat/utils/petscheap.h>
10 #include <petscbt.h>
11 #include <../src/mat/impls/dense/seq/dense.h>
12 #include <petsctime.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  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&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 = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&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 
130   (*C)->rmap->bs = A->rmap->bs;
131   (*C)->cmap->bs = B->cmap->bs;
132 
133   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
134   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
135   c                         = (Mat_SeqAIJ*)((*C)->data);
136   c->free_a                 = PETSC_FALSE;
137   c->free_ij                = PETSC_TRUE;
138   c->nonew                  = 0;
139   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
140 
141   /* set MatInfo */
142   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
143   if (afill < 1.0) afill = 1.0;
144   c->maxnz                     = ci[am];
145   c->nz                        = ci[am];
146   (*C)->info.mallocs           = ndouble;
147   (*C)->info.fill_ratio_given  = fill;
148   (*C)->info.fill_ratio_needed = afill;
149 
150 #if defined(PETSC_USE_INFO)
151   if (ci[am]) {
152     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
153     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
154   } else {
155     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
156   }
157 #endif
158   PetscFunctionReturn(0);
159 }
160 
161 #undef __FUNCT__
162 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
163 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
164 {
165   PetscErrorCode ierr;
166   PetscLogDouble flops=0.0;
167   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
168   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
169   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
170   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
171   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
172   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
173   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
174   PetscScalar    *ab_dense;
175 
176   PetscFunctionBegin;
177   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
178     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
179     c->a      = ca;
180     c->free_a = PETSC_TRUE;
181 
182     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
183     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
184 
185     c->matmult_abdense = ab_dense;
186   } else {
187     ca       = c->a;
188     ab_dense = c->matmult_abdense;
189   }
190 
191   /* clean old values in C */
192   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
193   /* Traverse A row-wise. */
194   /* Build the ith row in C by summing over nonzero columns in A, */
195   /* the rows of B corresponding to nonzeros of A. */
196   for (i=0; i<am; i++) {
197     anzi = ai[i+1] - ai[i];
198     for (j=0; j<anzi; j++) {
199       brow = aj[j];
200       bnzi = bi[brow+1] - bi[brow];
201       bjj  = bj + bi[brow];
202       baj  = ba + bi[brow];
203       /* perform dense axpy */
204       valtmp = aa[j];
205       for (k=0; k<bnzi; k++) {
206         ab_dense[bjj[k]] += valtmp*baj[k];
207       }
208       flops += 2*bnzi;
209     }
210     aj += anzi; aa += anzi;
211 
212     cnzi = ci[i+1] - ci[i];
213     for (k=0; k<cnzi; k++) {
214       ca[k]          += ab_dense[cj[k]];
215       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
216     }
217     flops += cnzi;
218     cj    += cnzi; ca += cnzi;
219   }
220   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
221   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
222   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
223   PetscFunctionReturn(0);
224 }
225 
226 #undef __FUNCT__
227 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
228 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
229 {
230   PetscErrorCode ierr;
231   PetscLogDouble flops=0.0;
232   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
233   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
234   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
235   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
236   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
237   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
238   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
239   PetscInt       nextb;
240 
241   PetscFunctionBegin;
242   /* clean old values in C */
243   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
244   /* Traverse A row-wise. */
245   /* Build the ith row in C by summing over nonzero columns in A, */
246   /* the rows of B corresponding to nonzeros of A. */
247   for (i=0; i<am; i++) {
248     anzi = ai[i+1] - ai[i];
249     cnzi = ci[i+1] - ci[i];
250     for (j=0; j<anzi; j++) {
251       brow = aj[j];
252       bnzi = bi[brow+1] - bi[brow];
253       bjj  = bj + bi[brow];
254       baj  = ba + bi[brow];
255       /* perform sparse axpy */
256       valtmp = aa[j];
257       nextb  = 0;
258       for (k=0; nextb<bnzi; k++) {
259         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
260           ca[k] += valtmp*baj[nextb++];
261         }
262       }
263       flops += 2*bnzi;
264     }
265     aj += anzi; aa += anzi;
266     cj += cnzi; ca += cnzi;
267   }
268 
269   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
270   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
271   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
272   PetscFunctionReturn(0);
273 }
274 
275 #undef __FUNCT__
276 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
277 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
278 {
279   PetscErrorCode     ierr;
280   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
281   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
282   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
283   MatScalar          *ca;
284   PetscReal          afill;
285   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
286   PetscFreeSpaceList free_space=NULL,current_space=NULL;
287 
288   PetscFunctionBegin;
289   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
290   /*-----------------------------------------------------------------------------------------*/
291   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
292   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
293   ci[0] = 0;
294 
295   /* create and initialize a linked list */
296   nlnk_max = a->rmax*b->rmax;
297   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
298   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
299 
300   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
301   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
302   current_space = free_space;
303 
304   /* Determine ci and cj */
305   for (i=0; i<am; i++) {
306     anzi = ai[i+1] - ai[i];
307     aj   = a->j + ai[i];
308     for (j=0; j<anzi; j++) {
309       brow = aj[j];
310       bnzj = bi[brow+1] - bi[brow];
311       bj   = b->j + bi[brow];
312       /* add non-zero cols of B into the sorted linked list lnk */
313       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
314     }
315     cnzi = lnk[1];
316 
317     /* If free space is not available, make more free space */
318     /* Double the amount of total space in the list */
319     if (current_space->local_remaining<cnzi) {
320       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
321       ndouble++;
322     }
323 
324     /* Copy data into free space, then initialize lnk */
325     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
326 
327     current_space->array           += cnzi;
328     current_space->local_used      += cnzi;
329     current_space->local_remaining -= cnzi;
330 
331     ci[i+1] = ci[i] + cnzi;
332   }
333 
334   /* Column indices are in the list of free space */
335   /* Allocate space for cj, initialize cj, and */
336   /* destroy list of free space and other temporary array(s) */
337   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
338   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
339   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
340 
341   /* Allocate space for ca */
342   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
343   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
344 
345   /* put together the new symbolic matrix */
346   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
347 
348   (*C)->rmap->bs = A->rmap->bs;
349   (*C)->cmap->bs = B->cmap->bs;
350 
351   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
352   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
353   c          = (Mat_SeqAIJ*)((*C)->data);
354   c->free_a  = PETSC_TRUE;
355   c->free_ij = PETSC_TRUE;
356   c->nonew   = 0;
357 
358   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
359 
360   /* set MatInfo */
361   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
362   if (afill < 1.0) afill = 1.0;
363   c->maxnz                     = ci[am];
364   c->nz                        = ci[am];
365   (*C)->info.mallocs           = ndouble;
366   (*C)->info.fill_ratio_given  = fill;
367   (*C)->info.fill_ratio_needed = afill;
368 
369 #if defined(PETSC_USE_INFO)
370   if (ci[am]) {
371     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
372     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
373   } else {
374     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
375   }
376 #endif
377   PetscFunctionReturn(0);
378 }
379 
380 
381 #undef __FUNCT__
382 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
383 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
384 {
385   PetscErrorCode     ierr;
386   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
387   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
388   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
389   MatScalar          *ca;
390   PetscReal          afill;
391   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
392   PetscFreeSpaceList free_space=NULL,current_space=NULL;
393 
394   PetscFunctionBegin;
395   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
396   /*---------------------------------------------------------------------------------------------*/
397   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
398   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
399   ci[0] = 0;
400 
401   /* create and initialize a linked list */
402   nlnk_max = a->rmax*b->rmax;
403   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
404   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
405 
406   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
407   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
408   current_space = free_space;
409 
410   /* Determine ci and cj */
411   for (i=0; i<am; i++) {
412     anzi = ai[i+1] - ai[i];
413     aj   = a->j + ai[i];
414     for (j=0; j<anzi; j++) {
415       brow = aj[j];
416       bnzj = bi[brow+1] - bi[brow];
417       bj   = b->j + bi[brow];
418       /* add non-zero cols of B into the sorted linked list lnk */
419       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
420     }
421     cnzi = lnk[0];
422 
423     /* If free space is not available, make more free space */
424     /* Double the amount of total space in the list */
425     if (current_space->local_remaining<cnzi) {
426       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
427       ndouble++;
428     }
429 
430     /* Copy data into free space, then initialize lnk */
431     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
432 
433     current_space->array           += cnzi;
434     current_space->local_used      += cnzi;
435     current_space->local_remaining -= cnzi;
436 
437     ci[i+1] = ci[i] + cnzi;
438   }
439 
440   /* Column indices are in the list of free space */
441   /* Allocate space for cj, initialize cj, and */
442   /* destroy list of free space and other temporary array(s) */
443   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
444   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
445   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
446 
447   /* Allocate space for ca */
448   /*-----------------------*/
449   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
450   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
451 
452   /* put together the new symbolic matrix */
453   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
454 
455   (*C)->rmap->bs = A->rmap->bs;
456   (*C)->cmap->bs = B->cmap->bs;
457 
458   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
459   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
460   c          = (Mat_SeqAIJ*)((*C)->data);
461   c->free_a  = PETSC_TRUE;
462   c->free_ij = PETSC_TRUE;
463   c->nonew   = 0;
464 
465   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
466 
467   /* set MatInfo */
468   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
469   if (afill < 1.0) afill = 1.0;
470   c->maxnz                     = ci[am];
471   c->nz                        = ci[am];
472   (*C)->info.mallocs           = ndouble;
473   (*C)->info.fill_ratio_given  = fill;
474   (*C)->info.fill_ratio_needed = afill;
475 
476 #if defined(PETSC_USE_INFO)
477   if (ci[am]) {
478     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
479     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
480   } else {
481     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
482   }
483 #endif
484   PetscFunctionReturn(0);
485 }
486 
487 #undef __FUNCT__
488 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
489 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
490 {
491   PetscErrorCode     ierr;
492   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
493   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
494   PetscInt           *ci,*cj,*bb;
495   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
496   PetscReal          afill;
497   PetscInt           i,j,col,ndouble = 0;
498   PetscFreeSpaceList free_space=NULL,current_space=NULL;
499   PetscHeap          h;
500 
501   PetscFunctionBegin;
502   /* Get ci and cj - by merging sorted rows using a heap */
503   /*---------------------------------------------------------------------------------------------*/
504   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
505   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
506   ci[0] = 0;
507 
508   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
509   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
510   current_space = free_space;
511 
512   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
513   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
514 
515   /* Determine ci and cj */
516   for (i=0; i<am; i++) {
517     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 */
518     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
519     ci[i+1] = ci[i];
520     /* Populate the min heap */
521     for (j=0; j<anzi; j++) {
522       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
523       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
524         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
525       }
526     }
527     /* Pick off the min element, adding it to free space */
528     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
529     while (j >= 0) {
530       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
531         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
532         ndouble++;
533       }
534       *(current_space->array++) = col;
535       current_space->local_used++;
536       current_space->local_remaining--;
537       ci[i+1]++;
538 
539       /* stash if anything else remains in this row of B */
540       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
541       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
542         PetscInt j2,col2;
543         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
544         if (col2 != col) break;
545         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
546         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
547       }
548       /* Put any stashed elements back into the min heap */
549       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
550       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
551     }
552   }
553   ierr = PetscFree(bb);CHKERRQ(ierr);
554   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
555 
556   /* Column indices are in the list of free space */
557   /* Allocate space for cj, initialize cj, and */
558   /* destroy list of free space and other temporary array(s) */
559   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
560   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
561 
562   /* put together the new symbolic matrix */
563   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
564 
565   (*C)->rmap->bs = A->rmap->bs;
566   (*C)->cmap->bs = B->cmap->bs;
567 
568   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
569   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
570   c          = (Mat_SeqAIJ*)((*C)->data);
571   c->free_a  = PETSC_TRUE;
572   c->free_ij = PETSC_TRUE;
573   c->nonew   = 0;
574 
575   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
576 
577   /* set MatInfo */
578   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
579   if (afill < 1.0) afill = 1.0;
580   c->maxnz                     = ci[am];
581   c->nz                        = ci[am];
582   (*C)->info.mallocs           = ndouble;
583   (*C)->info.fill_ratio_given  = fill;
584   (*C)->info.fill_ratio_needed = afill;
585 
586 #if defined(PETSC_USE_INFO)
587   if (ci[am]) {
588     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
589     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
590   } else {
591     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
592   }
593 #endif
594   PetscFunctionReturn(0);
595 }
596 
597 #undef __FUNCT__
598 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
599 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
600 {
601   PetscErrorCode     ierr;
602   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
603   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
604   PetscInt           *ci,*cj,*bb;
605   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
606   PetscReal          afill;
607   PetscInt           i,j,col,ndouble = 0;
608   PetscFreeSpaceList free_space=NULL,current_space=NULL;
609   PetscHeap          h;
610   PetscBT            bt;
611 
612   PetscFunctionBegin;
613   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
614   /*---------------------------------------------------------------------------------------------*/
615   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
616   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
617   ci[0] = 0;
618 
619   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
620   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
621 
622   current_space = free_space;
623 
624   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
625   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
626   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
627 
628   /* Determine ci and cj */
629   for (i=0; i<am; i++) {
630     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 */
631     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
632     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
633     ci[i+1] = ci[i];
634     /* Populate the min heap */
635     for (j=0; j<anzi; j++) {
636       PetscInt brow = acol[j];
637       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
638         PetscInt bcol = bj[bb[j]];
639         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
640           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
641           bb[j]++;
642           break;
643         }
644       }
645     }
646     /* Pick off the min element, adding it to free space */
647     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
648     while (j >= 0) {
649       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
650         fptr = NULL;                      /* need PetscBTMemzero */
651         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
652         ndouble++;
653       }
654       *(current_space->array++) = col;
655       current_space->local_used++;
656       current_space->local_remaining--;
657       ci[i+1]++;
658 
659       /* stash if anything else remains in this row of B */
660       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
661         PetscInt bcol = bj[bb[j]];
662         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
663           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
664           bb[j]++;
665           break;
666         }
667       }
668       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
669     }
670     if (fptr) {                 /* Clear the bits for this row */
671       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
672     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
673       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
674     }
675   }
676   ierr = PetscFree(bb);CHKERRQ(ierr);
677   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
678   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
679 
680   /* Column indices are in the list of free space */
681   /* Allocate space for cj, initialize cj, and */
682   /* destroy list of free space and other temporary array(s) */
683   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
684   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
685 
686   /* put together the new symbolic matrix */
687   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
688 
689   (*C)->rmap->bs = A->rmap->bs;
690   (*C)->cmap->bs = B->cmap->bs;
691 
692   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
693   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
694   c          = (Mat_SeqAIJ*)((*C)->data);
695   c->free_a  = PETSC_TRUE;
696   c->free_ij = PETSC_TRUE;
697   c->nonew   = 0;
698 
699   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
700 
701   /* set MatInfo */
702   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
703   if (afill < 1.0) afill = 1.0;
704   c->maxnz                     = ci[am];
705   c->nz                        = ci[am];
706   (*C)->info.mallocs           = ndouble;
707   (*C)->info.fill_ratio_given  = fill;
708   (*C)->info.fill_ratio_needed = afill;
709 
710 #if defined(PETSC_USE_INFO)
711   if (ci[am]) {
712     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
713     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
714   } else {
715     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
716   }
717 #endif
718   PetscFunctionReturn(0);
719 }
720 
721 #undef __FUNCT__
722 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
723 /* concatenate unique entries and then sort */
724 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
725 {
726   PetscErrorCode     ierr;
727   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
728   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
729   PetscInt           *ci,*cj;
730   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
731   PetscReal          afill;
732   PetscInt           i,j,ndouble = 0;
733   PetscSegBuffer     seg,segrow;
734   char               *seen;
735 
736   PetscFunctionBegin;
737   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
738   ci[0] = 0;
739 
740   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
741   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
742   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
743   ierr = PetscMalloc(bn*sizeof(char),&seen);CHKERRQ(ierr);
744   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
745 
746   /* Determine ci and cj */
747   for (i=0; i<am; i++) {
748     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
749     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
750     PetscInt packlen = 0,*PETSC_RESTRICT crow;
751     /* Pack segrow */
752     for (j=0; j<anzi; j++) {
753       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
754       for (k=bjstart; k<bjend; k++) {
755         PetscInt bcol = bj[k];
756         if (!seen[bcol]) { /* new entry */
757           PetscInt *PETSC_RESTRICT slot;
758           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
759           *slot = bcol;
760           seen[bcol] = 1;
761           packlen++;
762         }
763       }
764     }
765     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
766     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
767     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
768     ci[i+1] = ci[i] + packlen;
769     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
770   }
771   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
772   ierr = PetscFree(seen);CHKERRQ(ierr);
773 
774   /* Column indices are in the segmented buffer */
775   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
776   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
777 
778   /* put together the new symbolic matrix */
779   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
780 
781   (*C)->rmap->bs = A->rmap->bs;
782   (*C)->cmap->bs = B->cmap->bs;
783 
784   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
785   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
786   c          = (Mat_SeqAIJ*)((*C)->data);
787   c->free_a  = PETSC_TRUE;
788   c->free_ij = PETSC_TRUE;
789   c->nonew   = 0;
790 
791   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
792 
793   /* set MatInfo */
794   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
795   if (afill < 1.0) afill = 1.0;
796   c->maxnz                     = ci[am];
797   c->nz                        = ci[am];
798   (*C)->info.mallocs           = ndouble;
799   (*C)->info.fill_ratio_given  = fill;
800   (*C)->info.fill_ratio_needed = afill;
801 
802 #if defined(PETSC_USE_INFO)
803   if (ci[am]) {
804     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
805     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
806   } else {
807     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
808   }
809 #endif
810   PetscFunctionReturn(0);
811 }
812 
813 /* This routine is not used. Should be removed! */
814 #undef __FUNCT__
815 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
816 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
817 {
818   PetscErrorCode ierr;
819 
820   PetscFunctionBegin;
821   if (scall == MAT_INITIAL_MATRIX) {
822     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
823     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
824     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
825   }
826   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
827   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
828   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
829   PetscFunctionReturn(0);
830 }
831 
832 #undef __FUNCT__
833 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
834 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
835 {
836   PetscErrorCode      ierr;
837   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
838   Mat_MatMatTransMult *abt=a->abt;
839 
840   PetscFunctionBegin;
841   ierr = (abt->destroy)(A);CHKERRQ(ierr);
842   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
843   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
844   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
845   ierr = PetscFree(abt);CHKERRQ(ierr);
846   PetscFunctionReturn(0);
847 }
848 
849 #undef __FUNCT__
850 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
851 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
852 {
853   PetscErrorCode      ierr;
854   Mat                 Bt;
855   PetscInt            *bti,*btj;
856   Mat_MatMatTransMult *abt;
857   Mat_SeqAIJ          *c;
858 
859   PetscFunctionBegin;
860   /* create symbolic Bt */
861   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
862   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
863 
864   Bt->rmap->bs = A->cmap->bs;
865   Bt->cmap->bs = B->cmap->bs;
866 
867   /* get symbolic C=A*Bt */
868   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
869 
870   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
871   ierr   = PetscNew(Mat_MatMatTransMult,&abt);CHKERRQ(ierr);
872   c      = (Mat_SeqAIJ*)(*C)->data;
873   c->abt = abt;
874 
875   abt->usecoloring = PETSC_FALSE;
876   abt->destroy     = (*C)->ops->destroy;
877   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
878 
879   ierr = PetscOptionsGetBool(NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
880   if (abt->usecoloring) {
881     /* Create MatTransposeColoring from symbolic C=A*B^T */
882     MatTransposeColoring matcoloring;
883     ISColoring           iscoloring;
884     Mat                  Bt_dense,C_dense;
885     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
886     /* inode causes memory problem, don't know why */
887     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
888 
889     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
890     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
891 
892     abt->matcoloring = matcoloring;
893 
894     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
895 
896     /* Create Bt_dense and C_dense = A*Bt_dense */
897     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
898     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
899     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
900     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
901 
902     Bt_dense->assembled = PETSC_TRUE;
903     abt->Bt_den   = Bt_dense;
904 
905     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
906     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
907     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
908     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
909 
910     Bt_dense->assembled = PETSC_TRUE;
911     abt->ABt_den  = C_dense;
912 
913 #if defined(PETSC_USE_INFO)
914     {
915       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
916       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);
917     }
918 #endif
919   }
920   /* clean up */
921   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
922   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
923   PetscFunctionReturn(0);
924 }
925 
926 #undef __FUNCT__
927 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
928 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
929 {
930   PetscErrorCode      ierr;
931   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
932   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
933   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
934   PetscLogDouble      flops=0.0;
935   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
936   Mat_MatMatTransMult *abt = c->abt;
937 
938   PetscFunctionBegin;
939   /* clear old values in C */
940   if (!c->a) {
941     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
942     c->a      = ca;
943     c->free_a = PETSC_TRUE;
944   } else {
945     ca =  c->a;
946   }
947   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
948 
949   if (abt->usecoloring) {
950     MatTransposeColoring matcoloring = abt->matcoloring;
951     Mat                  Bt_dense,C_dense = abt->ABt_den;
952 
953     /* Get Bt_dense by Apply MatTransposeColoring to B */
954     Bt_dense = abt->Bt_den;
955     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
956 
957     /* C_dense = A*Bt_dense */
958     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
959 
960     /* Recover C from C_dense */
961     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
962     PetscFunctionReturn(0);
963   }
964 
965   for (i=0; i<cm; i++) {
966     anzi = ai[i+1] - ai[i];
967     acol = aj + ai[i];
968     aval = aa + ai[i];
969     cnzi = ci[i+1] - ci[i];
970     ccol = cj + ci[i];
971     cval = ca + ci[i];
972     for (j=0; j<cnzi; j++) {
973       brow = ccol[j];
974       bnzj = bi[brow+1] - bi[brow];
975       bcol = bj + bi[brow];
976       bval = ba + bi[brow];
977 
978       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
979       nexta = 0; nextb = 0;
980       while (nexta<anzi && nextb<bnzj) {
981         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
982         if (nexta == anzi) break;
983         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
984         if (nextb == bnzj) break;
985         if (acol[nexta] == bcol[nextb]) {
986           cval[j] += aval[nexta]*bval[nextb];
987           nexta++; nextb++;
988           flops += 2;
989         }
990       }
991     }
992   }
993   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
994   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
995   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
996   PetscFunctionReturn(0);
997 }
998 
999 #undef __FUNCT__
1000 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1001 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1002 {
1003   PetscErrorCode ierr;
1004 
1005   PetscFunctionBegin;
1006   if (scall == MAT_INITIAL_MATRIX) {
1007     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1008     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1009     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1010   }
1011   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1012   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1013   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1014   PetscFunctionReturn(0);
1015 }
1016 
1017 #undef __FUNCT__
1018 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1019 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1020 {
1021   PetscErrorCode ierr;
1022   Mat            At;
1023   PetscInt       *ati,*atj;
1024 
1025   PetscFunctionBegin;
1026   /* create symbolic At */
1027   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1028   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1029 
1030   At->rmap->bs = A->cmap->bs;
1031   At->cmap->bs = B->cmap->bs;
1032 
1033   /* get symbolic C=At*B */
1034   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1035 
1036   /* clean up */
1037   ierr = MatDestroy(&At);CHKERRQ(ierr);
1038   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1039   PetscFunctionReturn(0);
1040 }
1041 
1042 #undef __FUNCT__
1043 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1044 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1045 {
1046   PetscErrorCode ierr;
1047   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1048   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1049   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1050   PetscLogDouble flops=0.0;
1051   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1052 
1053   PetscFunctionBegin;
1054   if (!c->a) {
1055     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1056 
1057     c->a      = ca;
1058     c->free_a = PETSC_TRUE;
1059   } else {
1060     ca = c->a;
1061   }
1062   /* clear old values in C */
1063   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1064 
1065   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1066   for (i=0; i<am; i++) {
1067     bj   = b->j + bi[i];
1068     ba   = b->a + bi[i];
1069     bnzi = bi[i+1] - bi[i];
1070     anzi = ai[i+1] - ai[i];
1071     for (j=0; j<anzi; j++) {
1072       nextb = 0;
1073       crow  = *aj++;
1074       cjj   = cj + ci[crow];
1075       caj   = ca + ci[crow];
1076       /* perform sparse axpy operation.  Note cjj includes bj. */
1077       for (k=0; nextb<bnzi; k++) {
1078         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1079           caj[k] += (*aa)*(*(ba+nextb));
1080           nextb++;
1081         }
1082       }
1083       flops += 2*bnzi;
1084       aa++;
1085     }
1086   }
1087 
1088   /* Assemble the final matrix and clean up */
1089   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1090   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1091   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1092   PetscFunctionReturn(0);
1093 }
1094 
1095 #undef __FUNCT__
1096 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1097 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1098 {
1099   PetscErrorCode ierr;
1100 
1101   PetscFunctionBegin;
1102   if (scall == MAT_INITIAL_MATRIX) {
1103     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1104     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1105     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1106   }
1107   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1108   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1109   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1110   PetscFunctionReturn(0);
1111 }
1112 
1113 #undef __FUNCT__
1114 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1115 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1116 {
1117   PetscErrorCode ierr;
1118 
1119   PetscFunctionBegin;
1120   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1121 
1122   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1123   PetscFunctionReturn(0);
1124 }
1125 
1126 #undef __FUNCT__
1127 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1128 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1129 {
1130   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1131   PetscErrorCode ierr;
1132   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1133   MatScalar      *aa;
1134   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1135   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1136 
1137   PetscFunctionBegin;
1138   if (!cm || !cn) PetscFunctionReturn(0);
1139   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);
1140   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);
1141   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);
1142   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1143   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1144   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1145   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1146     colam = col*am;
1147     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1148       r1 = r2 = r3 = r4 = 0.0;
1149       n  = a->i[i+1] - a->i[i];
1150       aj = a->j + a->i[i];
1151       aa = a->a + a->i[i];
1152       for (j=0; j<n; j++) {
1153         r1 += (*aa)*b1[*aj];
1154         r2 += (*aa)*b2[*aj];
1155         r3 += (*aa)*b3[*aj];
1156         r4 += (*aa++)*b4[*aj++];
1157       }
1158       c[colam + i]       = r1;
1159       c[colam + am + i]  = r2;
1160       c[colam + am2 + i] = r3;
1161       c[colam + am3 + i] = r4;
1162     }
1163     b1 += bm4;
1164     b2 += bm4;
1165     b3 += bm4;
1166     b4 += bm4;
1167   }
1168   for (; col<cn; col++) {     /* over extra columns of C */
1169     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1170       r1 = 0.0;
1171       n  = a->i[i+1] - a->i[i];
1172       aj = a->j + a->i[i];
1173       aa = a->a + a->i[i];
1174 
1175       for (j=0; j<n; j++) {
1176         r1 += (*aa++)*b1[*aj++];
1177       }
1178       c[col*am + i] = r1;
1179     }
1180     b1 += bm;
1181   }
1182   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1183   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1184   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1185   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1186   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1187   PetscFunctionReturn(0);
1188 }
1189 
1190 /*
1191    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1192 */
1193 #undef __FUNCT__
1194 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1195 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1196 {
1197   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1198   PetscErrorCode ierr;
1199   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1200   MatScalar      *aa;
1201   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1202   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1203 
1204   PetscFunctionBegin;
1205   if (!cm || !cn) PetscFunctionReturn(0);
1206   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1207   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1208   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1209 
1210   if (a->compressedrow.use) { /* use compressed row format */
1211     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1212       colam = col*am;
1213       arm   = a->compressedrow.nrows;
1214       ii    = a->compressedrow.i;
1215       ridx  = a->compressedrow.rindex;
1216       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1217         r1 = r2 = r3 = r4 = 0.0;
1218         n  = ii[i+1] - ii[i];
1219         aj = a->j + ii[i];
1220         aa = a->a + ii[i];
1221         for (j=0; j<n; j++) {
1222           r1 += (*aa)*b1[*aj];
1223           r2 += (*aa)*b2[*aj];
1224           r3 += (*aa)*b3[*aj];
1225           r4 += (*aa++)*b4[*aj++];
1226         }
1227         c[colam       + ridx[i]] += r1;
1228         c[colam + am  + ridx[i]] += r2;
1229         c[colam + am2 + ridx[i]] += r3;
1230         c[colam + am3 + ridx[i]] += r4;
1231       }
1232       b1 += bm4;
1233       b2 += bm4;
1234       b3 += bm4;
1235       b4 += bm4;
1236     }
1237     for (; col<cn; col++) {     /* over extra columns of C */
1238       colam = col*am;
1239       arm   = a->compressedrow.nrows;
1240       ii    = a->compressedrow.i;
1241       ridx  = a->compressedrow.rindex;
1242       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1243         r1 = 0.0;
1244         n  = ii[i+1] - ii[i];
1245         aj = a->j + ii[i];
1246         aa = a->a + ii[i];
1247 
1248         for (j=0; j<n; j++) {
1249           r1 += (*aa++)*b1[*aj++];
1250         }
1251         c[colam + ridx[i]] += r1;
1252       }
1253       b1 += bm;
1254     }
1255   } else {
1256     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1257       colam = col*am;
1258       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1259         r1 = r2 = r3 = r4 = 0.0;
1260         n  = a->i[i+1] - a->i[i];
1261         aj = a->j + a->i[i];
1262         aa = a->a + a->i[i];
1263         for (j=0; j<n; j++) {
1264           r1 += (*aa)*b1[*aj];
1265           r2 += (*aa)*b2[*aj];
1266           r3 += (*aa)*b3[*aj];
1267           r4 += (*aa++)*b4[*aj++];
1268         }
1269         c[colam + i]       += r1;
1270         c[colam + am + i]  += r2;
1271         c[colam + am2 + i] += r3;
1272         c[colam + am3 + i] += r4;
1273       }
1274       b1 += bm4;
1275       b2 += bm4;
1276       b3 += bm4;
1277       b4 += bm4;
1278     }
1279     for (; col<cn; col++) {     /* over extra columns of C */
1280       colam = col*am;
1281       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1282         r1 = 0.0;
1283         n  = a->i[i+1] - a->i[i];
1284         aj = a->j + a->i[i];
1285         aa = a->a + a->i[i];
1286 
1287         for (j=0; j<n; j++) {
1288           r1 += (*aa++)*b1[*aj++];
1289         }
1290         c[colam + i] += r1;
1291       }
1292       b1 += bm;
1293     }
1294   }
1295   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1296   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1297   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1298   PetscFunctionReturn(0);
1299 }
1300 
1301 #undef __FUNCT__
1302 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1303 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1304 {
1305   PetscErrorCode ierr;
1306   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1307   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1308   PetscInt       *bi      = b->i,*bj=b->j;
1309   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1310   MatScalar      *btval,*btval_den,*ba=b->a;
1311   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1312 
1313   PetscFunctionBegin;
1314   btval_den=btdense->v;
1315   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1316   for (k=0; k<ncolors; k++) {
1317     ncolumns = coloring->ncolumns[k];
1318     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1319       col   = *(columns + colorforcol[k] + l);
1320       btcol = bj + bi[col];
1321       btval = ba + bi[col];
1322       anz   = bi[col+1] - bi[col];
1323       for (j=0; j<anz; j++) {
1324         brow            = btcol[j];
1325         btval_den[brow] = btval[j];
1326       }
1327     }
1328     btval_den += m;
1329   }
1330   PetscFunctionReturn(0);
1331 }
1332 
1333 #undef __FUNCT__
1334 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1335 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1336 {
1337   PetscErrorCode ierr;
1338   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1339   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1340   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1341   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1342   PetscInt       nrows,*row,*idx;
1343   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1344 
1345   PetscFunctionBegin;
1346   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1347 
1348   if (brows > 0) {
1349     PetscInt *lstart,row_end,row_start;
1350     lstart = matcoloring->lstart;
1351     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1352 
1353     row_end = brows;
1354     if (row_end > m) row_end = m;
1355     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1356       ca_den_ptr = ca_den;
1357       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1358         nrows = matcoloring->nrows[k];
1359         row   = rows  + colorforrow[k];
1360         idx   = den2sp + colorforrow[k];
1361         for (l=lstart[k]; l<nrows; l++) {
1362           if (row[l] >= row_end) {
1363             lstart[k] = l;
1364             break;
1365           } else {
1366             ca[idx[l]] = ca_den_ptr[row[l]];
1367           }
1368         }
1369         ca_den_ptr += m;
1370       }
1371       row_end += brows;
1372       if (row_end > m) row_end = m;
1373     }
1374   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1375     ca_den_ptr = ca_den;
1376     for (k=0; k<ncolors; k++) {
1377       nrows = matcoloring->nrows[k];
1378       row   = rows  + colorforrow[k];
1379       idx   = den2sp + colorforrow[k];
1380       for (l=0; l<nrows; l++) {
1381         ca[idx[l]] = ca_den_ptr[row[l]];
1382       }
1383       ca_den_ptr += m;
1384     }
1385   }
1386 
1387   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1388 #if defined(PETSC_USE_INFO)
1389   if (matcoloring->brows > 0) {
1390     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1391   } else {
1392     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1393   }
1394 #endif
1395   PetscFunctionReturn(0);
1396 }
1397 
1398 /*
1399  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1400  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1401  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ().
1402  */
1403 #undef __FUNCT__
1404 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1405 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1406 {
1407   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1408   PetscErrorCode ierr;
1409   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1410   PetscInt       nz = a->i[m],row,*jj,mr,col;
1411   PetscInt       *cspidx;
1412 
1413   PetscFunctionBegin;
1414   *nn = n;
1415   if (!ia) PetscFunctionReturn(0);
1416   if (symmetric) {
1417     SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1418     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1419   } else {
1420     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1421     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1422     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1423     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1424     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1425     jj   = a->j;
1426     for (i=0; i<nz; i++) {
1427       collengths[jj[i]]++;
1428     }
1429     cia[0] = oshift;
1430     for (i=0; i<n; i++) {
1431       cia[i+1] = cia[i] + collengths[i];
1432     }
1433     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1434     jj   = a->j;
1435     for (row=0; row<m; row++) {
1436       mr = a->i[row+1] - a->i[row];
1437       for (i=0; i<mr; i++) {
1438         col = *jj++;
1439 
1440         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1441         cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
1442       }
1443     }
1444     ierr   = PetscFree(collengths);CHKERRQ(ierr);
1445     *ia    = cia; *ja = cja;
1446     *spidx = cspidx;
1447   }
1448   PetscFunctionReturn(0);
1449 }
1450 
1451 #undef __FUNCT__
1452 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1453 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1454 {
1455   PetscErrorCode ierr;
1456 
1457   PetscFunctionBegin;
1458   if (!ia) PetscFunctionReturn(0);
1459 
1460   ierr = PetscFree(*ia);CHKERRQ(ierr);
1461   ierr = PetscFree(*ja);CHKERRQ(ierr);
1462   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1463   PetscFunctionReturn(0);
1464 }
1465 
1466 #undef __FUNCT__
1467 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1468 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1469 {
1470   PetscErrorCode ierr;
1471   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1472   const PetscInt *is,*ci,*cj,*row_idx;
1473   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1474   IS             *isa;
1475   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1476   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1477   PetscInt       *colorforcol,*columns,*columns_i,brows;
1478   PetscBool      flg;
1479 
1480   PetscFunctionBegin;
1481   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1482 
1483   /* bs >1 is not being tested yet! */
1484   Nbs       = mat->cmap->N/bs;
1485   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1486   c->N      = Nbs;
1487   c->m      = c->M;
1488   c->rstart = 0;
1489   c->brows  = 100;
1490 
1491   c->ncolors = nis;
1492   ierr = PetscMalloc3(nis,PetscInt,&c->ncolumns,nis,PetscInt,&c->nrows,nis+1,PetscInt,&colorforrow);CHKERRQ(ierr);
1493   ierr = PetscMalloc((csp->nz+1)*sizeof(PetscInt),&rows);CHKERRQ(ierr);
1494   ierr = PetscMalloc((csp->nz+1)*sizeof(PetscInt),&den2sp);CHKERRQ(ierr);
1495 
1496   brows = c->brows;
1497   ierr = PetscOptionsGetInt(NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1498   if (flg) c->brows = brows;
1499   if (brows > 0) {
1500     ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&c->lstart);CHKERRQ(ierr);
1501   }
1502 
1503   colorforrow[0] = 0;
1504   rows_i         = rows;
1505   den2sp_i       = den2sp;
1506 
1507   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1508   ierr = PetscMalloc((Nbs+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1509 
1510   colorforcol[0] = 0;
1511   columns_i      = columns;
1512 
1513   /* get column-wise storage of mat */
1514   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1515 
1516   cm   = c->m;
1517   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1518   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1519   for (i=0; i<nis; i++) { /* loop over color */
1520     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1521     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1522 
1523     c->ncolumns[i] = n;
1524     if (n) {
1525       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1526     }
1527     colorforcol[i+1] = colorforcol[i] + n;
1528     columns_i       += n;
1529 
1530     /* fast, crude version requires O(N*N) work */
1531     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1532 
1533     /* loop over columns*/
1534     for (j=0; j<n; j++) {
1535       col     = is[j];
1536       row_idx = cj + ci[col];
1537       m       = ci[col+1] - ci[col];
1538       /* loop over columns marking them in rowhit */
1539       for (k=0; k<m; k++) {
1540         idxhit[*row_idx]   = spidx[ci[col] + k];
1541         rowhit[*row_idx++] = col + 1;
1542       }
1543     }
1544     /* count the number of hits */
1545     nrows = 0;
1546     for (j=0; j<cm; j++) {
1547       if (rowhit[j]) nrows++;
1548     }
1549     c->nrows[i]      = nrows;
1550     colorforrow[i+1] = colorforrow[i] + nrows;
1551 
1552     nrows = 0;
1553     for (j=0; j<cm; j++) {
1554       if (rowhit[j]) {
1555         rows_i[nrows]   = j;
1556         den2sp_i[nrows] = idxhit[j];
1557         nrows++;
1558       }
1559     }
1560     den2sp_i += nrows;
1561 
1562     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1563     rows_i += nrows;
1564   }
1565   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1566   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1567   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1568   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1569 
1570   c->colorforrow = colorforrow;
1571   c->rows        = rows;
1572   c->den2sp      = den2sp;
1573   c->colorforcol = colorforcol;
1574   c->columns     = columns;
1575 
1576   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1577   PetscFunctionReturn(0);
1578 }
1579