xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision dcca6d9d80ebd869fe6029bd05a3aa9faafef49e)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = A * B
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <../src/mat/utils/petscheap.h>
10 #include <petscbt.h>
11 #include <../src/mat/impls/dense/seq/dense.h>
12 
13 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);
14 
15 #undef __FUNCT__
16 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
17 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
18 {
19   PetscErrorCode ierr;
20   const char     *algTypes[6] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed"};
21   PetscInt       alg=0; /* set default algorithm */
22 
23   PetscFunctionBegin;
24   if (scall == MAT_INITIAL_MATRIX) {
25     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
26     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,6,algTypes[0],&alg,NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsEnd();CHKERRQ(ierr);
28     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
29     switch (alg) {
30     case 1:
31       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
32       break;
33     case 2:
34       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
35       break;
36     case 3:
37       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
38       break;
39     case 4:
40       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
41       break;
42     case 5:
43       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
44       break;
45     default:
46       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
47      break;
48     }
49     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
50   }
51 
52   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
53   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
54   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
55   PetscFunctionReturn(0);
56 }
57 
58 #undef __FUNCT__
59 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed"
60 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
61 {
62   PetscErrorCode     ierr;
63   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
64   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
65   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
66   PetscReal          afill;
67   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
68   PetscBT            lnkbt;
69   PetscFreeSpaceList free_space=NULL,current_space=NULL;
70 
71   PetscFunctionBegin;
72   /* Get ci and cj */
73   /*---------------*/
74   /* Allocate ci array, arrays for fill computation and */
75   /* free space for accumulating nonzero column info */
76   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
77   ci[0] = 0;
78 
79   /* create and initialize a linked list */
80   nlnk_max = a->rmax*b->rmax;
81   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
82   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
83 
84   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
85   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
86 
87   current_space = free_space;
88 
89   /* Determine ci and cj */
90   for (i=0; i<am; i++) {
91     anzi = ai[i+1] - ai[i];
92     aj   = a->j + ai[i];
93     for (j=0; j<anzi; j++) {
94       brow = aj[j];
95       bnzj = bi[brow+1] - bi[brow];
96       bj   = b->j + bi[brow];
97       /* add non-zero cols of B into the sorted linked list lnk */
98       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
99     }
100     cnzi = lnk[0];
101 
102     /* If free space is not available, make more free space */
103     /* Double the amount of total space in the list */
104     if (current_space->local_remaining<cnzi) {
105       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
106       ndouble++;
107     }
108 
109     /* Copy data into free space, then initialize lnk */
110     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
111 
112     current_space->array           += cnzi;
113     current_space->local_used      += cnzi;
114     current_space->local_remaining -= cnzi;
115 
116     ci[i+1] = ci[i] + cnzi;
117   }
118 
119   /* Column indices are in the list of free space */
120   /* Allocate space for cj, initialize cj, and */
121   /* destroy list of free space and other temporary array(s) */
122   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
123   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
124   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
125 
126   /* put together the new symbolic matrix */
127   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
128 
129   (*C)->rmap->bs = A->rmap->bs;
130   (*C)->cmap->bs = B->cmap->bs;
131 
132   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
133   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
134   c                         = (Mat_SeqAIJ*)((*C)->data);
135   c->free_a                 = PETSC_FALSE;
136   c->free_ij                = PETSC_TRUE;
137   c->nonew                  = 0;
138   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
139 
140   /* set MatInfo */
141   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
142   if (afill < 1.0) afill = 1.0;
143   c->maxnz                     = ci[am];
144   c->nz                        = ci[am];
145   (*C)->info.mallocs           = ndouble;
146   (*C)->info.fill_ratio_given  = fill;
147   (*C)->info.fill_ratio_needed = afill;
148 
149 #if defined(PETSC_USE_INFO)
150   if (ci[am]) {
151     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
152     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
153   } else {
154     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
155   }
156 #endif
157   PetscFunctionReturn(0);
158 }
159 
160 #undef __FUNCT__
161 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
162 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
163 {
164   PetscErrorCode ierr;
165   PetscLogDouble flops=0.0;
166   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
167   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
168   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
169   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
170   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
171   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
172   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
173   PetscScalar    *ab_dense;
174 
175   PetscFunctionBegin;
176   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
177     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
178     c->a      = ca;
179     c->free_a = PETSC_TRUE;
180   } else {
181     ca        = c->a;
182   }
183   if (!c->matmult_abdense) {
184     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
185     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
186     c->matmult_abdense = ab_dense;
187   } else {
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     MatColoring          coloring;
884     ISColoring           iscoloring;
885     Mat                  Bt_dense,C_dense;
886     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
887     /* inode causes memory problem, don't know why */
888     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
889 
890     ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
891     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
892     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
893     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
894     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
895     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
896     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
897 
898     abt->matcoloring = matcoloring;
899 
900     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
901 
902     /* Create Bt_dense and C_dense = A*Bt_dense */
903     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
904     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
905     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
906     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
907 
908     Bt_dense->assembled = PETSC_TRUE;
909     abt->Bt_den   = Bt_dense;
910 
911     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
912     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
913     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
914     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
915 
916     Bt_dense->assembled = PETSC_TRUE;
917     abt->ABt_den  = C_dense;
918 
919 #if defined(PETSC_USE_INFO)
920     {
921       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
922       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);
923     }
924 #endif
925   }
926   /* clean up */
927   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
928   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
929   PetscFunctionReturn(0);
930 }
931 
932 #undef __FUNCT__
933 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
934 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
935 {
936   PetscErrorCode      ierr;
937   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
938   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
939   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
940   PetscLogDouble      flops=0.0;
941   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
942   Mat_MatMatTransMult *abt = c->abt;
943 
944   PetscFunctionBegin;
945   /* clear old values in C */
946   if (!c->a) {
947     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
948     c->a      = ca;
949     c->free_a = PETSC_TRUE;
950   } else {
951     ca =  c->a;
952   }
953   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
954 
955   if (abt->usecoloring) {
956     MatTransposeColoring matcoloring = abt->matcoloring;
957     Mat                  Bt_dense,C_dense = abt->ABt_den;
958 
959     /* Get Bt_dense by Apply MatTransposeColoring to B */
960     Bt_dense = abt->Bt_den;
961     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
962 
963     /* C_dense = A*Bt_dense */
964     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
965 
966     /* Recover C from C_dense */
967     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
968     PetscFunctionReturn(0);
969   }
970 
971   for (i=0; i<cm; i++) {
972     anzi = ai[i+1] - ai[i];
973     acol = aj + ai[i];
974     aval = aa + ai[i];
975     cnzi = ci[i+1] - ci[i];
976     ccol = cj + ci[i];
977     cval = ca + ci[i];
978     for (j=0; j<cnzi; j++) {
979       brow = ccol[j];
980       bnzj = bi[brow+1] - bi[brow];
981       bcol = bj + bi[brow];
982       bval = ba + bi[brow];
983 
984       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
985       nexta = 0; nextb = 0;
986       while (nexta<anzi && nextb<bnzj) {
987         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
988         if (nexta == anzi) break;
989         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
990         if (nextb == bnzj) break;
991         if (acol[nexta] == bcol[nextb]) {
992           cval[j] += aval[nexta]*bval[nextb];
993           nexta++; nextb++;
994           flops += 2;
995         }
996       }
997     }
998   }
999   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1000   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1001   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1002   PetscFunctionReturn(0);
1003 }
1004 
1005 #undef __FUNCT__
1006 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1007 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1008 {
1009   PetscErrorCode ierr;
1010 
1011   PetscFunctionBegin;
1012   if (scall == MAT_INITIAL_MATRIX) {
1013     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1014     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1015     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1016   }
1017   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1018   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1019   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1020   PetscFunctionReturn(0);
1021 }
1022 
1023 #undef __FUNCT__
1024 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1025 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1026 {
1027   PetscErrorCode ierr;
1028   Mat            At;
1029   PetscInt       *ati,*atj;
1030 
1031   PetscFunctionBegin;
1032   /* create symbolic At */
1033   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1034   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1035 
1036   At->rmap->bs = A->cmap->bs;
1037   At->cmap->bs = B->cmap->bs;
1038 
1039   /* get symbolic C=At*B */
1040   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1041 
1042   /* clean up */
1043   ierr = MatDestroy(&At);CHKERRQ(ierr);
1044   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1045   PetscFunctionReturn(0);
1046 }
1047 
1048 #undef __FUNCT__
1049 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1050 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1051 {
1052   PetscErrorCode ierr;
1053   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1054   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1055   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1056   PetscLogDouble flops=0.0;
1057   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1058 
1059   PetscFunctionBegin;
1060   if (!c->a) {
1061     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1062 
1063     c->a      = ca;
1064     c->free_a = PETSC_TRUE;
1065   } else {
1066     ca = c->a;
1067   }
1068   /* clear old values in C */
1069   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1070 
1071   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1072   for (i=0; i<am; i++) {
1073     bj   = b->j + bi[i];
1074     ba   = b->a + bi[i];
1075     bnzi = bi[i+1] - bi[i];
1076     anzi = ai[i+1] - ai[i];
1077     for (j=0; j<anzi; j++) {
1078       nextb = 0;
1079       crow  = *aj++;
1080       cjj   = cj + ci[crow];
1081       caj   = ca + ci[crow];
1082       /* perform sparse axpy operation.  Note cjj includes bj. */
1083       for (k=0; nextb<bnzi; k++) {
1084         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1085           caj[k] += (*aa)*(*(ba+nextb));
1086           nextb++;
1087         }
1088       }
1089       flops += 2*bnzi;
1090       aa++;
1091     }
1092   }
1093 
1094   /* Assemble the final matrix and clean up */
1095   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1096   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1097   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1098   PetscFunctionReturn(0);
1099 }
1100 
1101 #undef __FUNCT__
1102 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1103 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1104 {
1105   PetscErrorCode ierr;
1106 
1107   PetscFunctionBegin;
1108   if (scall == MAT_INITIAL_MATRIX) {
1109     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1110     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1111     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1112   }
1113   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1114   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1115   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1116   PetscFunctionReturn(0);
1117 }
1118 
1119 #undef __FUNCT__
1120 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1121 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1122 {
1123   PetscErrorCode ierr;
1124 
1125   PetscFunctionBegin;
1126   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1127 
1128   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1129   PetscFunctionReturn(0);
1130 }
1131 
1132 #undef __FUNCT__
1133 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1134 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1135 {
1136   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1137   PetscErrorCode    ierr;
1138   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1139   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1140   const PetscInt    *aj;
1141   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=B->rmap->n,am=A->rmap->n;
1142   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;
1143 
1144   PetscFunctionBegin;
1145   if (!cm || !cn) PetscFunctionReturn(0);
1146   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);
1147   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);
1148   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);
1149   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1150   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1151   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1152   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1153   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1154     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1155       r1 = r2 = r3 = r4 = 0.0;
1156       n  = a->i[i+1] - a->i[i];
1157       aj = a->j + a->i[i];
1158       aa = a->a + a->i[i];
1159       for (j=0; j<n; j++) {
1160         aatmp = aa[j]; ajtmp = aj[j];
1161         r1 += aatmp*b1[ajtmp];
1162         r2 += aatmp*b2[ajtmp];
1163         r3 += aatmp*b3[ajtmp];
1164         r4 += aatmp*b4[ajtmp];
1165       }
1166       c1[i] = r1;
1167       c2[i] = r2;
1168       c3[i] = r3;
1169       c4[i] = r4;
1170     }
1171     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1172     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1173   }
1174   for (; col<cn; col++) {   /* over extra columns of C */
1175     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1176       r1 = 0.0;
1177       n  = a->i[i+1] - a->i[i];
1178       aj = a->j + a->i[i];
1179       aa = a->a + a->i[i];
1180       for (j=0; j<n; j++) {
1181         r1 += aa[j]*b1[aj[j]];
1182       }
1183       c1[i] = r1;
1184     }
1185     b1 += bm;
1186     c1 += am;
1187   }
1188   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1189   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1190   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1191   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1192   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1193   PetscFunctionReturn(0);
1194 }
1195 
1196 /*
1197    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1198 */
1199 #undef __FUNCT__
1200 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1201 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1202 {
1203   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1204   PetscErrorCode ierr;
1205   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1206   MatScalar      *aa;
1207   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1208   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1209 
1210   PetscFunctionBegin;
1211   if (!cm || !cn) PetscFunctionReturn(0);
1212   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1213   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1214   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1215 
1216   if (a->compressedrow.use) { /* use compressed row format */
1217     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1218       colam = col*am;
1219       arm   = a->compressedrow.nrows;
1220       ii    = a->compressedrow.i;
1221       ridx  = a->compressedrow.rindex;
1222       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1223         r1 = r2 = r3 = r4 = 0.0;
1224         n  = ii[i+1] - ii[i];
1225         aj = a->j + ii[i];
1226         aa = a->a + ii[i];
1227         for (j=0; j<n; j++) {
1228           r1 += (*aa)*b1[*aj];
1229           r2 += (*aa)*b2[*aj];
1230           r3 += (*aa)*b3[*aj];
1231           r4 += (*aa++)*b4[*aj++];
1232         }
1233         c[colam       + ridx[i]] += r1;
1234         c[colam + am  + ridx[i]] += r2;
1235         c[colam + am2 + ridx[i]] += r3;
1236         c[colam + am3 + ridx[i]] += r4;
1237       }
1238       b1 += bm4;
1239       b2 += bm4;
1240       b3 += bm4;
1241       b4 += bm4;
1242     }
1243     for (; col<cn; col++) {     /* over extra columns of C */
1244       colam = col*am;
1245       arm   = a->compressedrow.nrows;
1246       ii    = a->compressedrow.i;
1247       ridx  = a->compressedrow.rindex;
1248       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1249         r1 = 0.0;
1250         n  = ii[i+1] - ii[i];
1251         aj = a->j + ii[i];
1252         aa = a->a + ii[i];
1253 
1254         for (j=0; j<n; j++) {
1255           r1 += (*aa++)*b1[*aj++];
1256         }
1257         c[colam + ridx[i]] += r1;
1258       }
1259       b1 += bm;
1260     }
1261   } else {
1262     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1263       colam = col*am;
1264       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1265         r1 = r2 = r3 = r4 = 0.0;
1266         n  = a->i[i+1] - a->i[i];
1267         aj = a->j + a->i[i];
1268         aa = a->a + a->i[i];
1269         for (j=0; j<n; j++) {
1270           r1 += (*aa)*b1[*aj];
1271           r2 += (*aa)*b2[*aj];
1272           r3 += (*aa)*b3[*aj];
1273           r4 += (*aa++)*b4[*aj++];
1274         }
1275         c[colam + i]       += r1;
1276         c[colam + am + i]  += r2;
1277         c[colam + am2 + i] += r3;
1278         c[colam + am3 + i] += r4;
1279       }
1280       b1 += bm4;
1281       b2 += bm4;
1282       b3 += bm4;
1283       b4 += bm4;
1284     }
1285     for (; col<cn; col++) {     /* over extra columns of C */
1286       colam = col*am;
1287       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1288         r1 = 0.0;
1289         n  = a->i[i+1] - a->i[i];
1290         aj = a->j + a->i[i];
1291         aa = a->a + a->i[i];
1292 
1293         for (j=0; j<n; j++) {
1294           r1 += (*aa++)*b1[*aj++];
1295         }
1296         c[colam + i] += r1;
1297       }
1298       b1 += bm;
1299     }
1300   }
1301   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1302   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1303   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1304   PetscFunctionReturn(0);
1305 }
1306 
1307 #undef __FUNCT__
1308 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1309 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1310 {
1311   PetscErrorCode ierr;
1312   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1313   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1314   PetscInt       *bi      = b->i,*bj=b->j;
1315   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1316   MatScalar      *btval,*btval_den,*ba=b->a;
1317   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1318 
1319   PetscFunctionBegin;
1320   btval_den=btdense->v;
1321   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1322   for (k=0; k<ncolors; k++) {
1323     ncolumns = coloring->ncolumns[k];
1324     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1325       col   = *(columns + colorforcol[k] + l);
1326       btcol = bj + bi[col];
1327       btval = ba + bi[col];
1328       anz   = bi[col+1] - bi[col];
1329       for (j=0; j<anz; j++) {
1330         brow            = btcol[j];
1331         btval_den[brow] = btval[j];
1332       }
1333     }
1334     btval_den += m;
1335   }
1336   PetscFunctionReturn(0);
1337 }
1338 
1339 #undef __FUNCT__
1340 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1341 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1342 {
1343   PetscErrorCode ierr;
1344   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1345   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1346   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1347   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1348   PetscInt       nrows,*row,*idx;
1349   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1350 
1351   PetscFunctionBegin;
1352   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1353 
1354   if (brows > 0) {
1355     PetscInt *lstart,row_end,row_start;
1356     lstart = matcoloring->lstart;
1357     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1358 
1359     row_end = brows;
1360     if (row_end > m) row_end = m;
1361     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1362       ca_den_ptr = ca_den;
1363       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1364         nrows = matcoloring->nrows[k];
1365         row   = rows  + colorforrow[k];
1366         idx   = den2sp + colorforrow[k];
1367         for (l=lstart[k]; l<nrows; l++) {
1368           if (row[l] >= row_end) {
1369             lstart[k] = l;
1370             break;
1371           } else {
1372             ca[idx[l]] = ca_den_ptr[row[l]];
1373           }
1374         }
1375         ca_den_ptr += m;
1376       }
1377       row_end += brows;
1378       if (row_end > m) row_end = m;
1379     }
1380   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1381     ca_den_ptr = ca_den;
1382     for (k=0; k<ncolors; k++) {
1383       nrows = matcoloring->nrows[k];
1384       row   = rows  + colorforrow[k];
1385       idx   = den2sp + colorforrow[k];
1386       for (l=0; l<nrows; l++) {
1387         ca[idx[l]] = ca_den_ptr[row[l]];
1388       }
1389       ca_den_ptr += m;
1390     }
1391   }
1392 
1393   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1394 #if defined(PETSC_USE_INFO)
1395   if (matcoloring->brows > 0) {
1396     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1397   } else {
1398     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1399   }
1400 #endif
1401   PetscFunctionReturn(0);
1402 }
1403 
1404 #undef __FUNCT__
1405 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1406 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1407 {
1408   PetscErrorCode ierr;
1409   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1410   const PetscInt *is,*ci,*cj,*row_idx;
1411   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1412   IS             *isa;
1413   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1414   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1415   PetscInt       *colorforcol,*columns,*columns_i,brows;
1416   PetscBool      flg;
1417 
1418   PetscFunctionBegin;
1419   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1420 
1421   /* bs >1 is not being tested yet! */
1422   Nbs       = mat->cmap->N/bs;
1423   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1424   c->N      = Nbs;
1425   c->m      = c->M;
1426   c->rstart = 0;
1427   c->brows  = 100;
1428 
1429   c->ncolors = nis;
1430   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1431   ierr = PetscMalloc((csp->nz+1)*sizeof(PetscInt),&rows);CHKERRQ(ierr);
1432   ierr = PetscMalloc((csp->nz+1)*sizeof(PetscInt),&den2sp);CHKERRQ(ierr);
1433 
1434   brows = c->brows;
1435   ierr = PetscOptionsGetInt(NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1436   if (flg) c->brows = brows;
1437   if (brows > 0) {
1438     ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&c->lstart);CHKERRQ(ierr);
1439   }
1440 
1441   colorforrow[0] = 0;
1442   rows_i         = rows;
1443   den2sp_i       = den2sp;
1444 
1445   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1446   ierr = PetscMalloc((Nbs+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1447 
1448   colorforcol[0] = 0;
1449   columns_i      = columns;
1450 
1451   /* get column-wise storage of mat */
1452   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1453 
1454   cm   = c->m;
1455   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1456   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1457   for (i=0; i<nis; i++) { /* loop over color */
1458     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1459     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1460 
1461     c->ncolumns[i] = n;
1462     if (n) {
1463       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1464     }
1465     colorforcol[i+1] = colorforcol[i] + n;
1466     columns_i       += n;
1467 
1468     /* fast, crude version requires O(N*N) work */
1469     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1470 
1471     for (j=0; j<n; j++) { /* loop over columns*/
1472       col     = is[j];
1473       row_idx = cj + ci[col];
1474       m       = ci[col+1] - ci[col];
1475       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1476         idxhit[*row_idx]   = spidx[ci[col] + k];
1477         rowhit[*row_idx++] = col + 1;
1478       }
1479     }
1480     /* count the number of hits */
1481     nrows = 0;
1482     for (j=0; j<cm; j++) {
1483       if (rowhit[j]) nrows++;
1484     }
1485     c->nrows[i]      = nrows;
1486     colorforrow[i+1] = colorforrow[i] + nrows;
1487 
1488     nrows = 0;
1489     for (j=0; j<cm; j++) { /* loop over rows */
1490       if (rowhit[j]) {
1491         rows_i[nrows]   = j;
1492         den2sp_i[nrows] = idxhit[j];
1493         nrows++;
1494       }
1495     }
1496     den2sp_i += nrows;
1497 
1498     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1499     rows_i += nrows;
1500   }
1501   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1502   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1503   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1504   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1505 
1506   c->colorforrow = colorforrow;
1507   c->rows        = rows;
1508   c->den2sp      = den2sp;
1509   c->colorforcol = colorforcol;
1510   c->columns     = columns;
1511 
1512   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1513   PetscFunctionReturn(0);
1514 }
1515