xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 3df7fa60a85c59b0989fbd67a4d4b7bd1b76c76c)
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> /*I "petscmat.h" I*/
12 
13 #undef __FUNCT__
14 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
15 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
16 {
17   PetscErrorCode ierr;
18   PetscBool      scalable=PETSC_FALSE,scalable_fast=PETSC_FALSE,heap = PETSC_FALSE,btheap = PETSC_FALSE;
19   PetscLogDouble t0,t1;
20 
21   PetscFunctionBegin;
22   if (scall == MAT_INITIAL_MATRIX){
23     //ierr = MatView(A,PETSC_VIEWER_DRAW_WORLD);
24     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
25     ierr = PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
26     ierr = PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,PETSC_NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsBool("-matmatmult_heap","Use heap implementation of symbolic factorization C=A*B","",heap,&heap,PETSC_NULL);CHKERRQ(ierr);
28     ierr = PetscOptionsBool("-matmatmult_btheap","Use btheap implementation of symbolic factorization C=A*B","",btheap,&btheap,PETSC_NULL);CHKERRQ(ierr);
29     ierr = PetscOptionsEnd();CHKERRQ(ierr);
30     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
31     if (scalable_fast){
32       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
33     } else if (scalable){
34       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
35       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
36       ierr = PetscGetTime(&t1);CHKERRQ(ierr);
37       printf("    Mat %d %d, 2MultSymbolic_SeqAIJ_Scalable time: %g\n",A->rmap->N,A->cmap->N,t1-t0);
38     } else if (heap) {
39       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
40     } else if (btheap) {
41       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
42     } else {
43       ierr = PetscGetTime(&t0);CHKERRQ(ierr);
44       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
45       ierr = PetscGetTime(&t1);CHKERRQ(ierr);
46       printf("    Mat %d %d, 2MultSymbolic_SeqAIJ time: %g\n",A->rmap->N,A->cmap->N,t1-t0);
47     }
48     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
49   }
50   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
51   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
52   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
53   ierr = PetscGetTime(&t1);CHKERRQ(ierr);
54   printf("    2MultNumeric_SeqAIJ time: %g\n",t1-t0);
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"
61 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(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=PETSC_NULL,current_space=PETSC_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   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     current_space->array           += cnzi;
112     current_space->local_used      += cnzi;
113     current_space->local_remaining -= cnzi;
114     ci[i+1] = ci[i] + cnzi;
115   }
116 
117   /* Column indices are in the list of free space */
118   /* Allocate space for cj, initialize cj, and */
119   /* destroy list of free space and other temporary array(s) */
120   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
121   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
122   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
123 
124   /* put together the new symbolic matrix */
125   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
126   (*C)->rmap->bs = A->rmap->bs;
127   (*C)->cmap->bs = B->cmap->bs;
128 
129   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
130   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
131   c = (Mat_SeqAIJ *)((*C)->data);
132   c->free_a  = PETSC_FALSE;
133   c->free_ij = PETSC_TRUE;
134   c->nonew   = 0;
135   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
136 
137   /* set MatInfo */
138   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
139   if (afill < 1.0) afill = 1.0;
140   c->maxnz                     = ci[am];
141   c->nz                        = ci[am];
142   (*C)->info.mallocs           = ndouble;
143   (*C)->info.fill_ratio_given  = fill;
144   (*C)->info.fill_ratio_needed = afill;
145 
146 #if defined(PETSC_USE_INFO)
147   if (ci[am]) {
148     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
149     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
150   } else {
151     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
152   }
153 #endif
154   PetscFunctionReturn(0);
155 }
156 
157 #undef __FUNCT__
158 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
159 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
160 {
161   PetscErrorCode ierr;
162   PetscLogDouble flops=0.0;
163   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
164   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
165   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
166   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
167   PetscInt       am=A->rmap->n,cm=C->rmap->n;
168   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
169   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
170   PetscScalar    *ab_dense;
171 
172   PetscFunctionBegin;
173   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
174   if (!c->a){ /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
175     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
176     c->a      = ca;
177     c->free_a = PETSC_TRUE;
178 
179     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
180     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
181     c->matmult_abdense = ab_dense;
182   } else {
183     ca       = c->a;
184     ab_dense = c->matmult_abdense;
185   }
186 
187   /* clean old values in C */
188   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
189   /* Traverse A row-wise. */
190   /* Build the ith row in C by summing over nonzero columns in A, */
191   /* the rows of B corresponding to nonzeros of A. */
192   for (i=0; i<am; i++) {
193     anzi = ai[i+1] - ai[i];
194     for (j=0; j<anzi; j++) {
195       brow = aj[j];
196       bnzi = bi[brow+1] - bi[brow];
197       bjj  = bj + bi[brow];
198       baj  = ba + bi[brow];
199       /* perform dense axpy */
200       valtmp = aa[j];
201       for (k=0; k<bnzi; k++) {
202         ab_dense[bjj[k]] += valtmp*baj[k];
203       }
204       flops += 2*bnzi;
205     }
206     aj += anzi; aa += anzi;
207 
208     cnzi = ci[i+1] - ci[i];
209     for (k=0; k<cnzi; k++) {
210       ca[k]          += ab_dense[cj[k]];
211       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
212     }
213     flops += cnzi;
214     cj += cnzi; ca += cnzi;
215   }
216   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
217   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
218   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
219   PetscFunctionReturn(0);
220 }
221 
222 #undef __FUNCT__
223 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
224 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
225 {
226   PetscErrorCode ierr;
227   PetscLogDouble flops=0.0;
228   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
229   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
230   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
231   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
232   PetscInt       am=A->rmap->N,cm=C->rmap->N;
233   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
234   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
235   PetscInt       nextb;
236 
237   PetscFunctionBegin;
238   /* clean old values in C */
239   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
240   /* Traverse A row-wise. */
241   /* Build the ith row in C by summing over nonzero columns in A, */
242   /* the rows of B corresponding to nonzeros of A. */
243   for (i=0;i<am;i++) {
244     anzi = ai[i+1] - ai[i];
245     cnzi = ci[i+1] - ci[i];
246     for (j=0;j<anzi;j++) {
247       brow = aj[j];
248       bnzi = bi[brow+1] - bi[brow];
249       bjj  = bj + bi[brow];
250       baj  = ba + bi[brow];
251       /* perform sparse axpy */
252       valtmp = aa[j];
253       nextb  = 0;
254       for (k=0; nextb<bnzi; k++) {
255         if (cj[k] == bjj[nextb]){ /* ccol == bcol */
256           ca[k] += valtmp*baj[nextb++];
257         }
258       }
259       flops += 2*bnzi;
260     }
261     aj += anzi; aa += anzi;
262     cj += cnzi; ca += cnzi;
263   }
264 
265   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
266   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
267   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
268   PetscFunctionReturn(0);
269 }
270 
271 #undef __FUNCT__
272 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
273 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
274 {
275   PetscErrorCode     ierr;
276   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
277   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
278   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
279   MatScalar          *ca;
280   PetscReal          afill;
281   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
282   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
283 
284   PetscFunctionBegin;
285   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
286   /*-----------------------------------------------------------------------------------------*/
287   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
288   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
289   ci[0] = 0;
290 
291   /* create and initialize a linked list */
292   nlnk_max = a->rmax*b->rmax;
293   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
294   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
295 
296   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
297   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
298   current_space = free_space;
299 
300   /* Determine ci and cj */
301   for (i=0; i<am; i++) {
302     anzi = ai[i+1] - ai[i];
303     aj   = a->j + ai[i];
304     for (j=0; j<anzi; j++){
305       brow = aj[j];
306       bnzj = bi[brow+1] - bi[brow];
307       bj   = b->j + bi[brow];
308       /* add non-zero cols of B into the sorted linked list lnk */
309       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
310     }
311     cnzi = lnk[1];
312 
313     /* If free space is not available, make more free space */
314     /* Double the amount of total space in the list */
315     if (current_space->local_remaining<cnzi) {
316       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
317       ndouble++;
318     }
319 
320     /* Copy data into free space, then initialize lnk */
321     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
322     current_space->array           += cnzi;
323     current_space->local_used      += cnzi;
324     current_space->local_remaining -= cnzi;
325     ci[i+1] = ci[i] + cnzi;
326   }
327 
328   /* Column indices are in the list of free space */
329   /* Allocate space for cj, initialize cj, and */
330   /* destroy list of free space and other temporary array(s) */
331   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
332   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
333   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
334 
335   /* Allocate space for ca */
336   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
337   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
338 
339   /* put together the new symbolic matrix */
340   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
341   (*C)->rmap->bs = A->rmap->bs;
342   (*C)->cmap->bs = B->cmap->bs;
343 
344   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
345   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
346   c = (Mat_SeqAIJ *)((*C)->data);
347   c->free_a   = PETSC_TRUE;
348   c->free_ij  = PETSC_TRUE;
349   c->nonew    = 0;
350   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
351 
352   /* set MatInfo */
353   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
354   if (afill < 1.0) afill = 1.0;
355   c->maxnz                     = ci[am];
356   c->nz                        = ci[am];
357   (*C)->info.mallocs           = ndouble;
358   (*C)->info.fill_ratio_given  = fill;
359   (*C)->info.fill_ratio_needed = afill;
360 
361 #if defined(PETSC_USE_INFO)
362   if (ci[am]) {
363     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
364     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
365   } else {
366     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
367   }
368 #endif
369   PetscFunctionReturn(0);
370 }
371 
372 
373 #undef __FUNCT__
374 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
375 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
376 {
377   PetscErrorCode     ierr;
378   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
379   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
380   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
381   MatScalar          *ca;
382   PetscReal          afill;
383   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
384   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
385 
386   PetscFunctionBegin;
387   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
388   /*---------------------------------------------------------------------------------------------*/
389   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
390   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
391   ci[0] = 0;
392 
393   /* create and initialize a linked list */
394   nlnk_max = a->rmax*b->rmax;
395   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
396   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
397 
398   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
399   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
400   current_space = free_space;
401 
402   /* Determine ci and cj */
403   for (i=0; i<am; i++) {
404     anzi = ai[i+1] - ai[i];
405     aj   = a->j + ai[i];
406     for (j=0; j<anzi; j++){
407       brow = aj[j];
408       bnzj = bi[brow+1] - bi[brow];
409       bj   = b->j + bi[brow];
410       /* add non-zero cols of B into the sorted linked list lnk */
411       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
412     }
413     cnzi = lnk[0];
414 
415     /* If free space is not available, make more free space */
416     /* Double the amount of total space in the list */
417     if (current_space->local_remaining<cnzi) {
418       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
419       ndouble++;
420     }
421 
422     /* Copy data into free space, then initialize lnk */
423     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
424     current_space->array           += cnzi;
425     current_space->local_used      += cnzi;
426     current_space->local_remaining -= cnzi;
427     ci[i+1] = ci[i] + cnzi;
428   }
429 
430   /* Column indices are in the list of free space */
431   /* Allocate space for cj, initialize cj, and */
432   /* destroy list of free space and other temporary array(s) */
433   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
434   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
435   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
436 
437   /* Allocate space for ca */
438   /*-----------------------*/
439   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
440   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
441 
442   /* put together the new symbolic matrix */
443   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
444   (*C)->rmap->bs = A->rmap->bs;
445   (*C)->cmap->bs = B->cmap->bs;
446 
447   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
448   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
449   c = (Mat_SeqAIJ *)((*C)->data);
450   c->free_a   = PETSC_TRUE;
451   c->free_ij  = PETSC_TRUE;
452   c->nonew    = 0;
453   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
454 
455   /* set MatInfo */
456   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
457   if (afill < 1.0) afill = 1.0;
458   c->maxnz                     = ci[am];
459   c->nz                        = ci[am];
460   (*C)->info.mallocs           = ndouble;
461   (*C)->info.fill_ratio_given  = fill;
462   (*C)->info.fill_ratio_needed = afill;
463 
464 #if defined(PETSC_USE_INFO)
465   if (ci[am]) {
466     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
467     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
468   } else {
469     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
470   }
471 #endif
472   PetscFunctionReturn(0);
473 }
474 
475 #undef __FUNCT__
476 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
477 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
478 {
479   PetscErrorCode     ierr;
480   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
481   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
482   PetscInt           *ci,*cj,*bb;
483   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
484   PetscReal          afill;
485   PetscInt           i,j,col,ndouble = 0;
486   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
487   PetscHeap          h;
488 
489   PetscFunctionBegin;
490   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
491   /*---------------------------------------------------------------------------------------------*/
492   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
493   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
494   ci[0] = 0;
495 
496   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
497   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
498   current_space = free_space;
499 
500   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
501   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
502 
503   /* Determine ci and cj */
504   for (i=0; i<am; i++) {
505     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 */
506     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
507     ci[i+1] = ci[i];
508     /* Populate the min heap */
509     for (j=0; j<anzi; j++) {
510       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
511       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
512         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
513       }
514     }
515     /* Pick off the min element, adding it to free space */
516     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
517     while (j >= 0) {
518       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
519         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
520         ndouble++;
521       }
522       *(current_space->array++) = col;
523       current_space->local_used++;
524       current_space->local_remaining--;
525       ci[i+1]++;
526 
527       /* stash if anything else remains in this row of B */
528       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
529       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
530         PetscInt j2,col2;
531         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
532         if (col2 != col) break;
533         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
534         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
535       }
536       /* Put any stashed elements back into the min heap */
537       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
538       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
539     }
540   }
541   ierr = PetscFree(bb);CHKERRQ(ierr);
542   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
543 
544   /* Column indices are in the list of free space */
545   /* Allocate space for cj, initialize cj, and */
546   /* destroy list of free space and other temporary array(s) */
547   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
548   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
549 
550   /* put together the new symbolic matrix */
551   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
552   (*C)->rmap->bs = A->rmap->bs;
553   (*C)->cmap->bs = B->cmap->bs;
554 
555   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
556   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
557   c = (Mat_SeqAIJ *)((*C)->data);
558   c->free_a   = PETSC_TRUE;
559   c->free_ij  = PETSC_TRUE;
560   c->nonew    = 0;
561   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
562 
563   /* set MatInfo */
564   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
565   if (afill < 1.0) afill = 1.0;
566   c->maxnz                     = ci[am];
567   c->nz                        = ci[am];
568   (*C)->info.mallocs           = ndouble;
569   (*C)->info.fill_ratio_given  = fill;
570   (*C)->info.fill_ratio_needed = afill;
571 
572 #if defined(PETSC_USE_INFO)
573   if (ci[am]) {
574     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
575     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
576   } else {
577     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
578   }
579 #endif
580   PetscFunctionReturn(0);
581 }
582 
583 #undef __FUNCT__
584 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
585 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
586 {
587   PetscErrorCode     ierr;
588   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
589   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
590   PetscInt           *ci,*cj,*bb;
591   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
592   PetscReal          afill;
593   PetscInt           i,j,col,ndouble = 0;
594   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
595   PetscHeap          h;
596   PetscBT            bt;
597 
598   PetscFunctionBegin;
599   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
600   /*---------------------------------------------------------------------------------------------*/
601   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
602   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
603   ci[0] = 0;
604 
605   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
606   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
607   current_space = free_space;
608 
609   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
610   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
611   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
612 
613   /* Determine ci and cj */
614   for (i=0; i<am; i++) {
615     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 */
616     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
617     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
618     ci[i+1] = ci[i];
619     /* Populate the min heap */
620     for (j=0; j<anzi; j++) {
621       PetscInt brow = acol[j];
622       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
623         PetscInt bcol = bj[bb[j]];
624         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
625           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
626           bb[j]++;
627           break;
628         }
629       }
630     }
631     /* Pick off the min element, adding it to free space */
632     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
633     while (j >= 0) {
634       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
635         fptr = PETSC_NULL;                      /* need PetscBTMemzero */
636         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
637         ndouble++;
638       }
639       *(current_space->array++) = col;
640       current_space->local_used++;
641       current_space->local_remaining--;
642       ci[i+1]++;
643 
644       /* stash if anything else remains in this row of B */
645       for ( ; bb[j] < bi[acol[j]+1]; bb[j]++) {
646         PetscInt bcol = bj[bb[j]];
647         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
648           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
649           bb[j]++;
650           break;
651         }
652       }
653       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
654     }
655     if (fptr) {                 /* Clear the bits for this row */
656       for ( ; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
657     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
658       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
659     }
660   }
661   ierr = PetscFree(bb);CHKERRQ(ierr);
662   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
663   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
664 
665   /* Column indices are in the list of free space */
666   /* Allocate space for cj, initialize cj, and */
667   /* destroy list of free space and other temporary array(s) */
668   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
669   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
670 
671   /* put together the new symbolic matrix */
672   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
673   (*C)->rmap->bs = A->rmap->bs;
674   (*C)->cmap->bs = B->cmap->bs;
675 
676   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
677   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
678   c = (Mat_SeqAIJ *)((*C)->data);
679   c->free_a   = PETSC_TRUE;
680   c->free_ij  = PETSC_TRUE;
681   c->nonew    = 0;
682   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
683 
684   /* set MatInfo */
685   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
686   if (afill < 1.0) afill = 1.0;
687   c->maxnz                     = ci[am];
688   c->nz                        = ci[am];
689   (*C)->info.mallocs           = ndouble;
690   (*C)->info.fill_ratio_given  = fill;
691   (*C)->info.fill_ratio_needed = afill;
692 
693 #if defined(PETSC_USE_INFO)
694   if (ci[am]) {
695     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
696     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
697   } else {
698     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
699   }
700 #endif
701   PetscFunctionReturn(0);
702 }
703 
704 /* This routine is not used. Should be removed! */
705 #undef __FUNCT__
706 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
707 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
708 {
709   PetscErrorCode ierr;
710 
711   PetscFunctionBegin;
712   if (scall == MAT_INITIAL_MATRIX){
713     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
714   }
715   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
716   PetscFunctionReturn(0);
717 }
718 
719 #undef __FUNCT__
720 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
721 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
722 {
723   PetscErrorCode      ierr;
724   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
725 
726   PetscFunctionBegin;
727   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
728   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
729   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
730   ierr = PetscFree(multtrans);CHKERRQ(ierr);
731   PetscFunctionReturn(0);
732 }
733 
734 #undef __FUNCT__
735 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
736 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
737 {
738   PetscErrorCode      ierr;
739   PetscContainer      container;
740   Mat_MatMatTransMult *multtrans=PETSC_NULL;
741 
742   PetscFunctionBegin;
743   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
744   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
745   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
746   A->ops->destroy   = multtrans->destroy;
747   if (A->ops->destroy) {
748     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
749   }
750   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
751   PetscFunctionReturn(0);
752 }
753 
754 #undef __FUNCT__
755 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
756 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
757 {
758   PetscErrorCode      ierr;
759   Mat                 Bt;
760   PetscInt            *bti,*btj;
761   Mat_MatMatTransMult *multtrans;
762   PetscContainer      container;
763   PetscLogDouble      t0,tf,etime2=0.0;
764 
765   PetscFunctionBegin;
766   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
767    /* create symbolic Bt */
768   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
769   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
770   Bt->rmap->bs = A->cmap->bs;
771   Bt->cmap->bs = B->cmap->bs;
772 
773   /* get symbolic C=A*Bt */
774   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
775 
776   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
777   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
778 
779   /* attach the supporting struct to C */
780   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
781   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
782   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
783   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
784   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
785 
786   multtrans->usecoloring = PETSC_FALSE;
787   multtrans->destroy = (*C)->ops->destroy;
788   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
789 
790   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
791   etime2 += tf - t0;
792 
793   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
794   if (multtrans->usecoloring){
795     /* Create MatTransposeColoring from symbolic C=A*B^T */
796     MatTransposeColoring matcoloring;
797     ISColoring           iscoloring;
798     Mat                  Bt_dense,C_dense;
799     PetscLogDouble       etime0=0.0,etime01=0.0,etime1=0.0;
800 
801     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
802     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
803     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
804     etime0 += tf - t0;
805 
806     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
807     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
808     multtrans->matcoloring = matcoloring;
809     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
810     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
811     etime01 += tf - t0;
812 
813     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
814     /* Create Bt_dense and C_dense = A*Bt_dense */
815     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
816     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
817     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
818     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
819     Bt_dense->assembled = PETSC_TRUE;
820     multtrans->Bt_den = Bt_dense;
821 
822     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
823     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
824     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
825     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
826     Bt_dense->assembled = PETSC_TRUE;
827     multtrans->ABt_den = C_dense;
828     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
829     etime1 += tf - t0;
830 
831 #if defined(PETSC_USE_INFO)
832     {
833     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
834     ierr = PetscInfo5(*C,"Bt_dense: %D,%D; Cnz %D / (cm*ncolors %D) = %g\n",A->cmap->n,matcoloring->ncolors,c->nz,A->rmap->n*matcoloring->ncolors,(PetscReal)(c->nz)/(A->rmap->n*matcoloring->ncolors));
835     ierr = PetscInfo5(*C,"Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
836     }
837 #endif
838   }
839   /* clean up */
840   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
841   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
842 
843 
844 
845 #if defined(INEFFICIENT_ALGORITHM)
846   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
847   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
848   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
849   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
850   PetscInt           am=A->rmap->N,bm=B->rmap->N;
851   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
852   MatScalar          *ca;
853   PetscBT            lnkbt;
854   PetscReal          afill;
855 
856   /* Allocate row pointer array ci  */
857   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
858   ci[0] = 0;
859 
860   /* Create and initialize a linked list for C columns */
861   nlnk = bm+1;
862   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
863 
864   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
865   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
866   current_space = free_space;
867 
868   /* Determine symbolic info for each row of the product A*B^T: */
869   for (i=0; i<am; i++) {
870     anzi = ai[i+1] - ai[i];
871     cnzi = 0;
872     acol = aj + ai[i];
873     for (j=0; j<bm; j++){
874       bnzj = bi[j+1] - bi[j];
875       bcol= bj + bi[j];
876       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
877       ka = 0; kb = 0;
878       while (ka < anzi && kb < bnzj){
879         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
880         if (ka == anzi) break;
881         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
882         if (kb == bnzj) break;
883         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
884           index[0] = j;
885           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
886           cnzi++;
887           break;
888         }
889       }
890     }
891 
892     /* If free space is not available, make more free space */
893     /* Double the amount of total space in the list */
894     if (current_space->local_remaining<cnzi) {
895       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
896       nspacedouble++;
897     }
898 
899     /* Copy data into free space, then initialize lnk */
900     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
901     current_space->array           += cnzi;
902     current_space->local_used      += cnzi;
903     current_space->local_remaining -= cnzi;
904 
905     ci[i+1] = ci[i] + cnzi;
906   }
907 
908 
909   /* Column indices are in the list of free space.
910      Allocate array cj, copy column indices to cj, and destroy list of free space */
911   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
912   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
913   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
914 
915   /* Allocate space for ca */
916   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
917   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
918 
919   /* put together the new symbolic matrix */
920   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
921   (*C)->rmap->bs = A->cmap->bs;
922   (*C)->cmap->bs = B->cmap->bs;
923 
924   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
925   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
926   c = (Mat_SeqAIJ *)((*C)->data);
927   c->free_a   = PETSC_TRUE;
928   c->free_ij  = PETSC_TRUE;
929   c->nonew    = 0;
930 
931   /* set MatInfo */
932   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
933   if (afill < 1.0) afill = 1.0;
934   c->maxnz                     = ci[am];
935   c->nz                        = ci[am];
936   (*C)->info.mallocs           = nspacedouble;
937   (*C)->info.fill_ratio_given  = fill;
938   (*C)->info.fill_ratio_needed = afill;
939 
940 #if defined(PETSC_USE_INFO)
941   if (ci[am]) {
942     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
943     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
944   } else {
945     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
946   }
947 #endif
948 #endif
949   PetscFunctionReturn(0);
950 }
951 
952 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
953 #undef __FUNCT__
954 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
955 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
956 {
957   PetscErrorCode ierr;
958   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
959   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
960   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
961   PetscLogDouble flops=0.0;
962   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca,*cval;
963   Mat_MatMatTransMult *multtrans;
964   PetscContainer      container;
965 #if defined(USE_ARRAY)
966   MatScalar      *spdot;
967 #endif
968 
969   PetscFunctionBegin;
970   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
971   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
972   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
973   if (multtrans->usecoloring){
974     MatTransposeColoring  matcoloring = multtrans->matcoloring;
975     Mat                   Bt_dense;
976     PetscInt              m,n;
977     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
978     Mat C_dense = multtrans->ABt_den;
979 
980     Bt_dense = multtrans->Bt_den;
981     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
982 
983     /* Get Bt_dense by Apply MatTransposeColoring to B */
984     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
985     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
986     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
987     etime0 += tf - t0;
988 
989     /* C_dense = A*Bt_dense */
990     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
991     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
992     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
993     etime2 += tf - t0;
994 
995     /* Recover C from C_dense */
996     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
997     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
998     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
999     etime1 += tf - t0;
1000 #if defined(PETSC_USE_INFO)
1001     ierr = PetscInfo4(C,"Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
1002 #endif
1003     PetscFunctionReturn(0);
1004   }
1005 
1006 #if defined(USE_ARRAY)
1007   /* allocate an array for implementing sparse inner-product */
1008   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
1009   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
1010 #endif
1011 
1012   /* clear old values in C */
1013   if (!c->a){
1014     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1015     c->a      = ca;
1016     c->free_a = PETSC_TRUE;
1017   } else {
1018     ca =  c->a;
1019   }
1020   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1021 
1022   for (i=0; i<cm; i++) {
1023     anzi = ai[i+1] - ai[i];
1024     acol = aj + ai[i];
1025     aval = aa + ai[i];
1026     cnzi = ci[i+1] - ci[i];
1027     ccol = cj + ci[i];
1028     cval = ca + ci[i];
1029     for (j=0; j<cnzi; j++){
1030       brow = ccol[j];
1031       bnzj = bi[brow+1] - bi[brow];
1032       bcol = bj + bi[brow];
1033       bval = ba + bi[brow];
1034 
1035       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1036 #if defined(USE_ARRAY)
1037       /* put ba to spdot array */
1038       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
1039       /* c(i,j)=A[i,:]*B[j,:]^T */
1040       for (nexta=0; nexta<anzi; nexta++){
1041         cval[j] += spdot[acol[nexta]]*aval[nexta];
1042       }
1043       /* zero spdot array */
1044       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1045 #else
1046       nexta = 0; nextb = 0;
1047       while (nexta<anzi && nextb<bnzj){
1048         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
1049         if (nexta == anzi) break;
1050         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
1051         if (nextb == bnzj) break;
1052         if (acol[nexta] == bcol[nextb]){
1053           cval[j] += aval[nexta]*bval[nextb];
1054           nexta++; nextb++;
1055           flops += 2;
1056         }
1057       }
1058 #endif
1059     }
1060   }
1061   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1062   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1063   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1064 #if defined(USE_ARRAY)
1065   ierr = PetscFree(spdot);
1066 #endif
1067   PetscFunctionReturn(0);
1068 }
1069 
1070 #undef __FUNCT__
1071 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1072 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
1073   PetscErrorCode ierr;
1074 
1075   PetscFunctionBegin;
1076   if (scall == MAT_INITIAL_MATRIX){
1077     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1078   }
1079   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1080   PetscFunctionReturn(0);
1081 }
1082 
1083 #undef __FUNCT__
1084 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1085 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1086 {
1087   PetscErrorCode ierr;
1088   Mat            At;
1089   PetscInt       *ati,*atj;
1090 
1091   PetscFunctionBegin;
1092   /* create symbolic At */
1093   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1094   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
1095   At->rmap->bs = A->cmap->bs;
1096   At->cmap->bs = B->cmap->bs;
1097 
1098   /* get symbolic C=At*B */
1099   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1100 
1101   /* clean up */
1102   ierr = MatDestroy(&At);CHKERRQ(ierr);
1103   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1104   PetscFunctionReturn(0);
1105 }
1106 
1107 #undef __FUNCT__
1108 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1109 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1110 {
1111   PetscErrorCode ierr;
1112   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1113   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1114   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1115   PetscLogDouble flops=0.0;
1116   MatScalar      *aa=a->a,*ba,*ca,*caj;
1117 
1118   PetscFunctionBegin;
1119   if (!c->a){
1120     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1121     c->a      = ca;
1122     c->free_a = PETSC_TRUE;
1123   } else {
1124     ca = c->a;
1125   }
1126   /* clear old values in C */
1127   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1128 
1129   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1130   for (i=0;i<am;i++) {
1131     bj   = b->j + bi[i];
1132     ba   = b->a + bi[i];
1133     bnzi = bi[i+1] - bi[i];
1134     anzi = ai[i+1] - ai[i];
1135     for (j=0; j<anzi; j++) {
1136       nextb = 0;
1137       crow  = *aj++;
1138       cjj   = cj + ci[crow];
1139       caj   = ca + ci[crow];
1140       /* perform sparse axpy operation.  Note cjj includes bj. */
1141       for (k=0; nextb<bnzi; k++) {
1142         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1143           caj[k] += (*aa)*(*(ba+nextb));
1144           nextb++;
1145         }
1146       }
1147       flops += 2*bnzi;
1148       aa++;
1149     }
1150   }
1151 
1152   /* Assemble the final matrix and clean up */
1153   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1154   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1155   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1156   PetscFunctionReturn(0);
1157 }
1158 
1159 EXTERN_C_BEGIN
1160 #undef __FUNCT__
1161 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1162 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1163 {
1164   PetscErrorCode ierr;
1165 
1166   PetscFunctionBegin;
1167   if (scall == MAT_INITIAL_MATRIX){
1168     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1169   }
1170   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1171   PetscFunctionReturn(0);
1172 }
1173 EXTERN_C_END
1174 
1175 #undef __FUNCT__
1176 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1177 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1178 {
1179   PetscErrorCode ierr;
1180 
1181   PetscFunctionBegin;
1182   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1183   (*C)->ops->matmult = MatMatMult_SeqAIJ_SeqDense;
1184   PetscFunctionReturn(0);
1185 }
1186 
1187 #undef __FUNCT__
1188 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1189 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1190 {
1191   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1192   PetscErrorCode ierr;
1193   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1194   MatScalar      *aa;
1195   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1196   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1197 
1198   PetscFunctionBegin;
1199   if (!cm || !cn) PetscFunctionReturn(0);
1200   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);
1201   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);
1202   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);
1203   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1204   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1205   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1206   for (col=0; col<cn-4; col += 4){  /* over columns of C */
1207     colam = col*am;
1208     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1209       r1 = r2 = r3 = r4 = 0.0;
1210       n   = a->i[i+1] - a->i[i];
1211       aj  = a->j + a->i[i];
1212       aa  = a->a + a->i[i];
1213       for (j=0; j<n; j++) {
1214         r1 += (*aa)*b1[*aj];
1215         r2 += (*aa)*b2[*aj];
1216         r3 += (*aa)*b3[*aj];
1217         r4 += (*aa++)*b4[*aj++];
1218       }
1219       c[colam + i]       = r1;
1220       c[colam + am + i]  = r2;
1221       c[colam + am2 + i] = r3;
1222       c[colam + am3 + i] = r4;
1223     }
1224     b1 += bm4;
1225     b2 += bm4;
1226     b3 += bm4;
1227     b4 += bm4;
1228   }
1229   for (;col<cn; col++){     /* over extra columns of C */
1230     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1231       r1 = 0.0;
1232       n   = a->i[i+1] - a->i[i];
1233       aj  = a->j + a->i[i];
1234       aa  = a->a + a->i[i];
1235 
1236       for (j=0; j<n; j++) {
1237         r1 += (*aa++)*b1[*aj++];
1238       }
1239       c[col*am + i]     = r1;
1240     }
1241     b1 += bm;
1242   }
1243   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1244   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1245   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1246   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1247   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1248   PetscFunctionReturn(0);
1249 }
1250 
1251 /*
1252    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1253 */
1254 #undef __FUNCT__
1255 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1256 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1257 {
1258   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1259   PetscErrorCode ierr;
1260   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1261   MatScalar      *aa;
1262   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1263   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1264 
1265   PetscFunctionBegin;
1266   if (!cm || !cn) PetscFunctionReturn(0);
1267   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1268   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1269   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1270 
1271   if (a->compressedrow.use){ /* use compressed row format */
1272     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1273       colam = col*am;
1274       arm   = a->compressedrow.nrows;
1275       ii    = a->compressedrow.i;
1276       ridx  = a->compressedrow.rindex;
1277       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1278 	r1 = r2 = r3 = r4 = 0.0;
1279 	n   = ii[i+1] - ii[i];
1280 	aj  = a->j + ii[i];
1281 	aa  = a->a + ii[i];
1282 	for (j=0; j<n; j++) {
1283 	  r1 += (*aa)*b1[*aj];
1284 	  r2 += (*aa)*b2[*aj];
1285 	  r3 += (*aa)*b3[*aj];
1286 	  r4 += (*aa++)*b4[*aj++];
1287 	}
1288 	c[colam       + ridx[i]] += r1;
1289 	c[colam + am  + ridx[i]] += r2;
1290 	c[colam + am2 + ridx[i]] += r3;
1291 	c[colam + am3 + ridx[i]] += r4;
1292       }
1293       b1 += bm4;
1294       b2 += bm4;
1295       b3 += bm4;
1296       b4 += bm4;
1297     }
1298     for (;col<cn; col++){     /* over extra columns of C */
1299       colam = col*am;
1300       arm   = a->compressedrow.nrows;
1301       ii    = a->compressedrow.i;
1302       ridx  = a->compressedrow.rindex;
1303       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1304 	r1 = 0.0;
1305 	n   = ii[i+1] - ii[i];
1306 	aj  = a->j + ii[i];
1307 	aa  = a->a + ii[i];
1308 
1309 	for (j=0; j<n; j++) {
1310 	  r1 += (*aa++)*b1[*aj++];
1311 	}
1312 	c[col*am + ridx[i]] += r1;
1313       }
1314       b1 += bm;
1315     }
1316   } else {
1317     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1318       colam = col*am;
1319       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1320 	r1 = r2 = r3 = r4 = 0.0;
1321 	n   = a->i[i+1] - a->i[i];
1322 	aj  = a->j + a->i[i];
1323 	aa  = a->a + a->i[i];
1324 	for (j=0; j<n; j++) {
1325 	  r1 += (*aa)*b1[*aj];
1326 	  r2 += (*aa)*b2[*aj];
1327 	  r3 += (*aa)*b3[*aj];
1328 	  r4 += (*aa++)*b4[*aj++];
1329 	}
1330 	c[colam + i]       += r1;
1331 	c[colam + am + i]  += r2;
1332 	c[colam + am2 + i] += r3;
1333 	c[colam + am3 + i] += r4;
1334       }
1335       b1 += bm4;
1336       b2 += bm4;
1337       b3 += bm4;
1338       b4 += bm4;
1339     }
1340     for (;col<cn; col++){     /* over extra columns of C */
1341       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1342 	r1 = 0.0;
1343 	n   = a->i[i+1] - a->i[i];
1344 	aj  = a->j + a->i[i];
1345 	aa  = a->a + a->i[i];
1346 
1347 	for (j=0; j<n; j++) {
1348 	  r1 += (*aa++)*b1[*aj++];
1349 	}
1350 	c[col*am + i]     += r1;
1351       }
1352       b1 += bm;
1353     }
1354   }
1355   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1356   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1357   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1358   PetscFunctionReturn(0);
1359 }
1360 
1361 #undef __FUNCT__
1362 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1363 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1364 {
1365   PetscErrorCode ierr;
1366   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
1367   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1368   PetscInt       *bi=b->i,*bj=b->j;
1369   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1370   MatScalar      *btval,*btval_den,*ba=b->a;
1371   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1372 
1373   PetscFunctionBegin;
1374   btval_den=btdense->v;
1375   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1376   for (k=0; k<ncolors; k++) {
1377     ncolumns = coloring->ncolumns[k];
1378     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1379       col   = *(columns + colorforcol[k] + l);
1380       btcol = bj + bi[col];
1381       btval = ba + bi[col];
1382       anz   = bi[col+1] - bi[col];
1383       for (j=0; j<anz; j++){
1384         brow            = btcol[j];
1385         btval_den[brow] = btval[j];
1386       }
1387     }
1388     btval_den += m;
1389   }
1390   PetscFunctionReturn(0);
1391 }
1392 
1393 #undef __FUNCT__
1394 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1395 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1396 {
1397   PetscErrorCode ierr;
1398   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1399   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1400   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1401   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1402 
1403   PetscFunctionBegin;
1404   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1405   ierr = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1406   cp_den = ca_den;
1407   for (k=0; k<ncolors; k++) {
1408     nrows = matcoloring->nrows[k];
1409     row   = rows  + colorforrow[k];
1410     idx   = spidx + colorforrow[k];
1411     for (l=0; l<nrows; l++){
1412       ca[idx[l]] = cp_den[row[l]];
1413     }
1414     cp_den += m;
1415   }
1416   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1417   PetscFunctionReturn(0);
1418 }
1419 
1420 /*
1421  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1422  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1423  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1424  */
1425 #undef __FUNCT__
1426 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1427 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1428 {
1429   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1430   PetscErrorCode ierr;
1431   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1432   PetscInt       nz = a->i[m],row,*jj,mr,col;
1433   PetscInt       *cspidx;
1434 
1435   PetscFunctionBegin;
1436   *nn = n;
1437   if (!ia) PetscFunctionReturn(0);
1438   if (symmetric) {
1439     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1440     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1441   } else {
1442     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1443     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1444     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1445     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1446     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1447     jj = a->j;
1448     for (i=0; i<nz; i++) {
1449       collengths[jj[i]]++;
1450     }
1451     cia[0] = oshift;
1452     for (i=0; i<n; i++) {
1453       cia[i+1] = cia[i] + collengths[i];
1454     }
1455     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1456     jj   = a->j;
1457     for (row=0; row<m; row++) {
1458       mr = a->i[row+1] - a->i[row];
1459       for (i=0; i<mr; i++) {
1460         col = *jj++;
1461         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1462         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
1463       }
1464     }
1465     ierr = PetscFree(collengths);CHKERRQ(ierr);
1466     *ia = cia; *ja = cja;
1467     *spidx = cspidx;
1468   }
1469   PetscFunctionReturn(0);
1470 }
1471 
1472 #undef __FUNCT__
1473 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1474 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1475 {
1476   PetscErrorCode ierr;
1477 
1478   PetscFunctionBegin;
1479   if (!ia) PetscFunctionReturn(0);
1480 
1481   ierr = PetscFree(*ia);CHKERRQ(ierr);
1482   ierr = PetscFree(*ja);CHKERRQ(ierr);
1483   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1484   PetscFunctionReturn(0);
1485 }
1486 
1487 #undef __FUNCT__
1488 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1489 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1490 {
1491   PetscErrorCode ierr;
1492   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
1493   const PetscInt *is,*ci,*cj,*row_idx;
1494   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1495   IS             *isa;
1496   PetscBool      flg1,flg2;
1497   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1498   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1499   PetscInt       *colorforcol,*columns,*columns_i;
1500 
1501   PetscFunctionBegin;
1502   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1503 
1504   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1505   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1506   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1507   if (flg1 || flg2) {
1508     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1509   }
1510 
1511   N         = mat->cmap->N/bs;
1512   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1513   c->N      = mat->cmap->N/bs;
1514   c->m      = mat->rmap->N/bs;
1515   c->rstart = 0;
1516 
1517   c->ncolors = nis;
1518   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1519   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1520   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1521   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1522   colorforrow[0]    = 0;
1523   rows_i            = rows;
1524   columnsforspidx_i = columnsforspidx;
1525 
1526   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1527   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1528   colorforcol[0] = 0;
1529   columns_i      = columns;
1530 
1531   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1532 
1533   cm = c->m;
1534   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1535   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1536   for (i=0; i<nis; i++) {
1537     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1538     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1539     c->ncolumns[i] = n;
1540     if (n) {
1541       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1542     }
1543     colorforcol[i+1] = colorforcol[i] + n;
1544     columns_i       += n;
1545 
1546     /* fast, crude version requires O(N*N) work */
1547     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1548 
1549     /* loop over columns*/
1550     for (j=0; j<n; j++) {
1551       col     = is[j];
1552       row_idx = cj + ci[col];
1553       m       = ci[col+1] - ci[col];
1554       /* loop over columns marking them in rowhit */
1555       for (k=0; k<m; k++) {
1556         idxhit[*row_idx]   = spidx[ci[col] + k];
1557         rowhit[*row_idx++] = col + 1;
1558       }
1559     }
1560     /* count the number of hits */
1561     nrows = 0;
1562     for (j=0; j<cm; j++) {
1563       if (rowhit[j]) nrows++;
1564     }
1565     c->nrows[i]      = nrows;
1566     colorforrow[i+1] = colorforrow[i] + nrows;
1567 
1568     nrows       = 0;
1569     for (j=0; j<cm; j++) {
1570       if (rowhit[j]) {
1571         rows_i[nrows]            = j;
1572         columnsforspidx_i[nrows] = idxhit[j];
1573         nrows++;
1574       }
1575     }
1576     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1577     rows_i += nrows; columnsforspidx_i += nrows;
1578   }
1579   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr);
1580   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1581   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1582 #if defined(PETSC_USE_DEBUG)
1583   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1584 #endif
1585 
1586   c->colorforrow     = colorforrow;
1587   c->rows            = rows;
1588   c->columnsforspidx = columnsforspidx;
1589   c->colorforcol     = colorforcol;
1590   c->columns         = columns;
1591   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1592   PetscFunctionReturn(0);
1593 }
1594