xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 3923b477fd0dced8a2d147b4fb4519fe3af97d3f)
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 #define DEBUG_MATMATMULT
14  */
15 EXTERN_C_BEGIN
16 #undef __FUNCT__
17 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
18 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
19 {
20   PetscErrorCode ierr;
21   PetscBool      scalable=PETSC_FALSE,scalable_fast=PETSC_FALSE,heap = PETSC_FALSE,btheap = PETSC_FALSE;
22 
23   PetscFunctionBegin;
24   if (scall == MAT_INITIAL_MATRIX){
25     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
26     ierr = PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,PETSC_NULL);CHKERRQ(ierr);
28     ierr = PetscOptionsBool("-matmatmult_heap","Use heap implementation of symbolic factorization C=A*B","",heap,&heap,PETSC_NULL);CHKERRQ(ierr);
29     ierr = PetscOptionsBool("-matmatmult_btheap","Use btheap implementation of symbolic factorization C=A*B","",btheap,&btheap,PETSC_NULL);CHKERRQ(ierr);
30     ierr = PetscOptionsEnd();CHKERRQ(ierr);
31     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
32     if (scalable_fast){
33       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
34     } else if (scalable){
35       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
36     } else if (heap) {
37       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
38     } else if (btheap) {
39       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
40     } else {
41       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
42     }
43     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
44   }
45   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
46   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
47   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
48   PetscFunctionReturn(0);
49 }
50 EXTERN_C_END
51 
52 #undef __FUNCT__
53 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
54 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
55 {
56   PetscErrorCode     ierr;
57   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
58   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
59   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
60   PetscReal          afill;
61   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
62   PetscBT            lnkbt;
63   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
64 
65   PetscFunctionBegin;
66   /* Get ci and cj */
67   /*---------------*/
68   /* Allocate ci array, arrays for fill computation and */
69   /* free space for accumulating nonzero column info */
70   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
71   ci[0] = 0;
72 
73   /* create and initialize a linked list */
74   nlnk_max = a->rmax*b->rmax;
75   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
76   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
77 
78   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
79   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
80   current_space = free_space;
81 
82   /* Determine ci and cj */
83   for (i=0; i<am; i++) {
84     anzi = ai[i+1] - ai[i];
85     aj   = a->j + ai[i];
86     for (j=0; j<anzi; j++){
87       brow = aj[j];
88       bnzj = bi[brow+1] - bi[brow];
89       bj   = b->j + bi[brow];
90       /* add non-zero cols of B into the sorted linked list lnk */
91       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
92     }
93     cnzi = lnk[0];
94 
95     /* If free space is not available, make more free space */
96     /* Double the amount of total space in the list */
97     if (current_space->local_remaining<cnzi) {
98       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
99       ndouble++;
100     }
101 
102     /* Copy data into free space, then initialize lnk */
103     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
104     current_space->array           += cnzi;
105     current_space->local_used      += cnzi;
106     current_space->local_remaining -= cnzi;
107     ci[i+1] = ci[i] + cnzi;
108   }
109 
110   /* Column indices are in the list of free space */
111   /* Allocate space for cj, initialize cj, and */
112   /* destroy list of free space and other temporary array(s) */
113   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
114   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
115   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
116 
117   /* put together the new symbolic matrix */
118   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
119   (*C)->rmap->bs = A->rmap->bs;
120   (*C)->cmap->bs = B->cmap->bs;
121 
122   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
123   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
124   c = (Mat_SeqAIJ *)((*C)->data);
125   c->free_a  = PETSC_FALSE;
126   c->free_ij = PETSC_TRUE;
127   c->nonew   = 0;
128   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
129 
130   /* set MatInfo */
131   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
132   if (afill < 1.0) afill = 1.0;
133   c->maxnz                     = ci[am];
134   c->nz                        = ci[am];
135   (*C)->info.mallocs           = ndouble;
136   (*C)->info.fill_ratio_given  = fill;
137   (*C)->info.fill_ratio_needed = afill;
138 
139 #if defined(PETSC_USE_INFO)
140   if (ci[am]) {
141     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
142     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
143   } else {
144     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
145   }
146 #endif
147   PetscFunctionReturn(0);
148 }
149 
150 #undef __FUNCT__
151 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
152 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
153 {
154   PetscErrorCode ierr;
155   PetscLogDouble flops=0.0;
156   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
157   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
158   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
159   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
160   PetscInt       am=A->rmap->n,cm=C->rmap->n;
161   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
162   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
163   PetscScalar    *ab_dense;
164 
165   PetscFunctionBegin;
166   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
167   if (!c->a){ /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
168     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
169     c->a      = ca;
170     c->free_a = PETSC_TRUE;
171 
172     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
173     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
174     c->matmult_abdense = ab_dense;
175   } else {
176     ca       = c->a;
177     ab_dense = c->matmult_abdense;
178   }
179 
180   /* clean old values in C */
181   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
182   /* Traverse A row-wise. */
183   /* Build the ith row in C by summing over nonzero columns in A, */
184   /* the rows of B corresponding to nonzeros of A. */
185   for (i=0; i<am; i++) {
186     anzi = ai[i+1] - ai[i];
187     for (j=0; j<anzi; j++) {
188       brow = aj[j];
189       bnzi = bi[brow+1] - bi[brow];
190       bjj  = bj + bi[brow];
191       baj  = ba + bi[brow];
192       /* perform dense axpy */
193       valtmp = aa[j];
194       for (k=0; k<bnzi; k++) {
195         ab_dense[bjj[k]] += valtmp*baj[k];
196       }
197       flops += 2*bnzi;
198     }
199     aj += anzi; aa += anzi;
200 
201     cnzi = ci[i+1] - ci[i];
202     for (k=0; k<cnzi; k++) {
203       ca[k]          += ab_dense[cj[k]];
204       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
205     }
206     flops += cnzi;
207     cj += cnzi; ca += cnzi;
208   }
209   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
210   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
211   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
212   PetscFunctionReturn(0);
213 }
214 
215 #undef __FUNCT__
216 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
217 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
218 {
219   PetscErrorCode ierr;
220   PetscLogDouble flops=0.0;
221   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
222   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
223   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
224   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
225   PetscInt       am=A->rmap->N,cm=C->rmap->N;
226   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
227   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
228   PetscInt       nextb;
229 
230   PetscFunctionBegin;
231 #if defined(DEBUG_MATMATMULT)
232   ierr = PetscPrintf(PETSC_COMM_SELF,"MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable...\n");CHKERRQ(ierr);
233 #endif
234   /* clean old values in C */
235   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
236   /* Traverse A row-wise. */
237   /* Build the ith row in C by summing over nonzero columns in A, */
238   /* the rows of B corresponding to nonzeros of A. */
239   for (i=0;i<am;i++) {
240     anzi = ai[i+1] - ai[i];
241     cnzi = ci[i+1] - ci[i];
242     for (j=0;j<anzi;j++) {
243       brow = aj[j];
244       bnzi = bi[brow+1] - bi[brow];
245       bjj  = bj + bi[brow];
246       baj  = ba + bi[brow];
247       /* perform sparse axpy */
248       valtmp = aa[j];
249       nextb  = 0;
250       for (k=0; nextb<bnzi; k++) {
251         if (cj[k] == bjj[nextb]){ /* ccol == bcol */
252           ca[k] += valtmp*baj[nextb++];
253         }
254       }
255       flops += 2*bnzi;
256     }
257     aj += anzi; aa += anzi;
258     cj += cnzi; ca += cnzi;
259   }
260 
261   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
262   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
263   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
264   PetscFunctionReturn(0);
265 }
266 
267 #undef __FUNCT__
268 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
269 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
270 {
271   PetscErrorCode     ierr;
272   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
273   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
274   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
275   MatScalar          *ca;
276   PetscReal          afill;
277   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
278   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
279 
280   PetscFunctionBegin;
281   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
282   /*-----------------------------------------------------------------------------------------*/
283   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
284   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
285   ci[0] = 0;
286 
287   /* create and initialize a linked list */
288   nlnk_max = a->rmax*b->rmax;
289   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
290   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
291 
292   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
293   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
294   current_space = free_space;
295 
296   /* Determine ci and cj */
297   for (i=0; i<am; i++) {
298     anzi = ai[i+1] - ai[i];
299     aj   = a->j + ai[i];
300     for (j=0; j<anzi; j++){
301       brow = aj[j];
302       bnzj = bi[brow+1] - bi[brow];
303       bj   = b->j + bi[brow];
304       /* add non-zero cols of B into the sorted linked list lnk */
305       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
306     }
307     cnzi = lnk[1];
308 
309     /* If free space is not available, make more free space */
310     /* Double the amount of total space in the list */
311     if (current_space->local_remaining<cnzi) {
312       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
313       ndouble++;
314     }
315 
316     /* Copy data into free space, then initialize lnk */
317     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
318     current_space->array           += cnzi;
319     current_space->local_used      += cnzi;
320     current_space->local_remaining -= cnzi;
321     ci[i+1] = ci[i] + cnzi;
322   }
323 
324   /* Column indices are in the list of free space */
325   /* Allocate space for cj, initialize cj, and */
326   /* destroy list of free space and other temporary array(s) */
327   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
328   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
329   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
330 
331   /* Allocate space for ca */
332   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
333   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
334 
335   /* put together the new symbolic matrix */
336   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
337   (*C)->rmap->bs = A->rmap->bs;
338   (*C)->cmap->bs = B->cmap->bs;
339 
340   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
341   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
342   c = (Mat_SeqAIJ *)((*C)->data);
343   c->free_a   = PETSC_TRUE;
344   c->free_ij  = PETSC_TRUE;
345   c->nonew    = 0;
346   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
347 
348   /* set MatInfo */
349   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
350   if (afill < 1.0) afill = 1.0;
351   c->maxnz                     = ci[am];
352   c->nz                        = ci[am];
353   (*C)->info.mallocs           = ndouble;
354   (*C)->info.fill_ratio_given  = fill;
355   (*C)->info.fill_ratio_needed = afill;
356 
357 #if defined(PETSC_USE_INFO)
358   if (ci[am]) {
359     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
360     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
361   } else {
362     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
363   }
364 #endif
365   PetscFunctionReturn(0);
366 }
367 
368 
369 #undef __FUNCT__
370 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
371 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
372 {
373   PetscErrorCode     ierr;
374   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
375   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
376   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
377   MatScalar          *ca;
378   PetscReal          afill;
379   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
380   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
381 
382   PetscFunctionBegin;
383   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
384   /*---------------------------------------------------------------------------------------------*/
385   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
386   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
387   ci[0] = 0;
388 
389   /* create and initialize a linked list */
390   nlnk_max = a->rmax*b->rmax;
391   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
392   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
393 
394   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
395   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
396   current_space = free_space;
397 
398   /* Determine ci and cj */
399   for (i=0; i<am; i++) {
400     anzi = ai[i+1] - ai[i];
401     aj   = a->j + ai[i];
402     for (j=0; j<anzi; j++){
403       brow = aj[j];
404       bnzj = bi[brow+1] - bi[brow];
405       bj   = b->j + bi[brow];
406       /* add non-zero cols of B into the sorted linked list lnk */
407       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
408     }
409     cnzi = lnk[0];
410 
411     /* If free space is not available, make more free space */
412     /* Double the amount of total space in the list */
413     if (current_space->local_remaining<cnzi) {
414       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
415       ndouble++;
416     }
417 
418     /* Copy data into free space, then initialize lnk */
419     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
420     current_space->array           += cnzi;
421     current_space->local_used      += cnzi;
422     current_space->local_remaining -= cnzi;
423     ci[i+1] = ci[i] + cnzi;
424   }
425 
426   /* Column indices are in the list of free space */
427   /* Allocate space for cj, initialize cj, and */
428   /* destroy list of free space and other temporary array(s) */
429   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
430   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
431   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
432 
433   /* Allocate space for ca */
434   /*-----------------------*/
435   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
436   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
437 
438   /* put together the new symbolic matrix */
439   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
440   (*C)->rmap->bs = A->rmap->bs;
441   (*C)->cmap->bs = B->cmap->bs;
442 
443   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
444   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
445   c = (Mat_SeqAIJ *)((*C)->data);
446   c->free_a   = PETSC_TRUE;
447   c->free_ij  = PETSC_TRUE;
448   c->nonew    = 0;
449   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
450 
451   /* set MatInfo */
452   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
453   if (afill < 1.0) afill = 1.0;
454   c->maxnz                     = ci[am];
455   c->nz                        = ci[am];
456   (*C)->info.mallocs           = ndouble;
457   (*C)->info.fill_ratio_given  = fill;
458   (*C)->info.fill_ratio_needed = afill;
459 
460 #if defined(PETSC_USE_INFO)
461   if (ci[am]) {
462     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
463     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
464   } else {
465     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
466   }
467 #endif
468   PetscFunctionReturn(0);
469 }
470 
471 #undef __FUNCT__
472 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
473 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
474 {
475   PetscErrorCode     ierr;
476   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
477   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
478   PetscInt           *ci,*cj,*bb;
479   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
480   PetscReal          afill;
481   PetscInt           i,j,col,ndouble = 0;
482   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
483   PetscHeap          h;
484 
485   PetscFunctionBegin;
486   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
487   /*---------------------------------------------------------------------------------------------*/
488   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
489   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
490   ci[0] = 0;
491 
492   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
493   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
494   current_space = free_space;
495 
496   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
497   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
498 
499   /* Determine ci and cj */
500   for (i=0; i<am; i++) {
501     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 */
502     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
503     ci[i+1] = ci[i];
504     /* Populate the min heap */
505     for (j=0; j<anzi; j++) {
506       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
507       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
508         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
509       }
510     }
511     /* Pick off the min element, adding it to free space */
512     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
513     while (j >= 0) {
514       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
515         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
516         ndouble++;
517       }
518       *(current_space->array++) = col;
519       current_space->local_used++;
520       current_space->local_remaining--;
521       ci[i+1]++;
522 
523       /* stash if anything else remains in this row of B */
524       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
525       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
526         PetscInt j2,col2;
527         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
528         if (col2 != col) break;
529         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
530         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
531       }
532       /* Put any stashed elements back into the min heap */
533       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
534       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
535     }
536   }
537   ierr = PetscFree(bb);CHKERRQ(ierr);
538   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
539 
540   /* Column indices are in the list of free space */
541   /* Allocate space for cj, initialize cj, and */
542   /* destroy list of free space and other temporary array(s) */
543   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
544   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
545 
546   /* put together the new symbolic matrix */
547   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
548   (*C)->rmap->bs = A->rmap->bs;
549   (*C)->cmap->bs = B->cmap->bs;
550 
551   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
552   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
553   c = (Mat_SeqAIJ *)((*C)->data);
554   c->free_a   = PETSC_TRUE;
555   c->free_ij  = PETSC_TRUE;
556   c->nonew    = 0;
557   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
558 
559   /* set MatInfo */
560   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
561   if (afill < 1.0) afill = 1.0;
562   c->maxnz                     = ci[am];
563   c->nz                        = ci[am];
564   (*C)->info.mallocs           = ndouble;
565   (*C)->info.fill_ratio_given  = fill;
566   (*C)->info.fill_ratio_needed = afill;
567 
568 #if defined(PETSC_USE_INFO)
569   if (ci[am]) {
570     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
571     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
572   } else {
573     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
574   }
575 #endif
576   PetscFunctionReturn(0);
577 }
578 
579 #undef __FUNCT__
580 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
581 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
582 {
583   PetscErrorCode     ierr;
584   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
585   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
586   PetscInt           *ci,*cj,*bb;
587   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
588   PetscReal          afill;
589   PetscInt           i,j,col,ndouble = 0;
590   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
591   PetscHeap          h;
592   PetscBT            bt;
593 
594   PetscFunctionBegin;
595   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
596   /*---------------------------------------------------------------------------------------------*/
597   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
598   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
599   ci[0] = 0;
600 
601   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
602   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
603   current_space = free_space;
604 
605   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
606   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
607   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
608 
609   /* Determine ci and cj */
610   for (i=0; i<am; i++) {
611     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 */
612     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
613     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
614     ci[i+1] = ci[i];
615     /* Populate the min heap */
616     for (j=0; j<anzi; j++) {
617       PetscInt brow = acol[j];
618       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
619         PetscInt bcol = bj[bb[j]];
620         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
621           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
622           bb[j]++;
623           break;
624         }
625       }
626     }
627     /* Pick off the min element, adding it to free space */
628     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
629     while (j >= 0) {
630       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
631         fptr = PETSC_NULL;                      /* need PetscBTMemzero */
632         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
633         ndouble++;
634       }
635       *(current_space->array++) = col;
636       current_space->local_used++;
637       current_space->local_remaining--;
638       ci[i+1]++;
639 
640       /* stash if anything else remains in this row of B */
641       for ( ; bb[j] < bi[acol[j]+1]; bb[j]++) {
642         PetscInt bcol = bj[bb[j]];
643         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
644           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
645           bb[j]++;
646           break;
647         }
648       }
649       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
650     }
651     if (fptr) {                 /* Clear the bits for this row */
652       for ( ; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
653     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
654       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
655     }
656   }
657   ierr = PetscFree(bb);CHKERRQ(ierr);
658   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
659   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
660 
661   /* Column indices are in the list of free space */
662   /* Allocate space for cj, initialize cj, and */
663   /* destroy list of free space and other temporary array(s) */
664   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
665   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
666 
667   /* put together the new symbolic matrix */
668   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
669   (*C)->rmap->bs = A->rmap->bs;
670   (*C)->cmap->bs = B->cmap->bs;
671 
672   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
673   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
674   c = (Mat_SeqAIJ *)((*C)->data);
675   c->free_a   = PETSC_TRUE;
676   c->free_ij  = PETSC_TRUE;
677   c->nonew    = 0;
678   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
679 
680   /* set MatInfo */
681   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
682   if (afill < 1.0) afill = 1.0;
683   c->maxnz                     = ci[am];
684   c->nz                        = ci[am];
685   (*C)->info.mallocs           = ndouble;
686   (*C)->info.fill_ratio_given  = fill;
687   (*C)->info.fill_ratio_needed = afill;
688 
689 #if defined(PETSC_USE_INFO)
690   if (ci[am]) {
691     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
692     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
693   } else {
694     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
695   }
696 #endif
697   PetscFunctionReturn(0);
698 }
699 
700 /* This routine is not used. Should be removed! */
701 #undef __FUNCT__
702 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
703 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
704 {
705   PetscErrorCode ierr;
706 
707   PetscFunctionBegin;
708   if (scall == MAT_INITIAL_MATRIX){
709     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
710   }
711   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
712   PetscFunctionReturn(0);
713 }
714 
715 #undef __FUNCT__
716 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
717 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
718 {
719   PetscErrorCode      ierr;
720   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
721 
722   PetscFunctionBegin;
723   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
724   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
725   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
726   ierr = PetscFree(multtrans);CHKERRQ(ierr);
727   PetscFunctionReturn(0);
728 }
729 
730 #undef __FUNCT__
731 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
732 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
733 {
734   PetscErrorCode      ierr;
735   PetscContainer      container;
736   Mat_MatMatTransMult *multtrans=PETSC_NULL;
737 
738   PetscFunctionBegin;
739   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
740   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
741   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
742   A->ops->destroy   = multtrans->destroy;
743   if (A->ops->destroy) {
744     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
745   }
746   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
747   PetscFunctionReturn(0);
748 }
749 
750 #undef __FUNCT__
751 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
752 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
753 {
754   PetscErrorCode      ierr;
755   Mat                 Bt;
756   PetscInt            *bti,*btj;
757   Mat_MatMatTransMult *multtrans;
758   PetscContainer      container;
759   PetscLogDouble      t0,tf,etime2=0.0;
760 
761   PetscFunctionBegin;
762   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
763    /* create symbolic Bt */
764   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
765   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
766   Bt->rmap->bs = A->cmap->bs;
767   Bt->cmap->bs = B->cmap->bs;
768 
769   /* get symbolic C=A*Bt */
770   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
771 
772   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
773   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
774 
775   /* attach the supporting struct to C */
776   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
777   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
778   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
779   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
780   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
781 
782   multtrans->usecoloring = PETSC_FALSE;
783   multtrans->destroy = (*C)->ops->destroy;
784   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
785 
786   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
787   etime2 += tf - t0;
788 
789   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
790   if (multtrans->usecoloring){
791     /* Create MatTransposeColoring from symbolic C=A*B^T */
792     MatTransposeColoring matcoloring;
793     ISColoring           iscoloring;
794     Mat                  Bt_dense,C_dense;
795     PetscLogDouble       etime0=0.0,etime01=0.0,etime1=0.0;
796 
797     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
798     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
799     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
800     etime0 += tf - t0;
801 
802     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
803     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
804     multtrans->matcoloring = matcoloring;
805     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
806     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
807     etime01 += tf - t0;
808 
809     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
810     /* Create Bt_dense and C_dense = A*Bt_dense */
811     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
812     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
813     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
814     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
815     Bt_dense->assembled = PETSC_TRUE;
816     multtrans->Bt_den = Bt_dense;
817 
818     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
819     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
820     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
821     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
822     Bt_dense->assembled = PETSC_TRUE;
823     multtrans->ABt_den = C_dense;
824     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
825     etime1 += tf - t0;
826 
827 #if defined(PETSC_USE_INFO)
828     {
829     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
830     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));
831     ierr = PetscInfo5(*C,"Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
832     }
833 #endif
834   }
835   /* clean up */
836   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
837   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
838 
839 
840 
841 #if defined(INEFFICIENT_ALGORITHM)
842   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
843   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
844   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
845   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
846   PetscInt           am=A->rmap->N,bm=B->rmap->N;
847   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
848   MatScalar          *ca;
849   PetscBT            lnkbt;
850   PetscReal          afill;
851 
852   /* Allocate row pointer array ci  */
853   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
854   ci[0] = 0;
855 
856   /* Create and initialize a linked list for C columns */
857   nlnk = bm+1;
858   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
859 
860   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
861   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
862   current_space = free_space;
863 
864   /* Determine symbolic info for each row of the product A*B^T: */
865   for (i=0; i<am; i++) {
866     anzi = ai[i+1] - ai[i];
867     cnzi = 0;
868     acol = aj + ai[i];
869     for (j=0; j<bm; j++){
870       bnzj = bi[j+1] - bi[j];
871       bcol= bj + bi[j];
872       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
873       ka = 0; kb = 0;
874       while (ka < anzi && kb < bnzj){
875         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
876         if (ka == anzi) break;
877         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
878         if (kb == bnzj) break;
879         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
880           index[0] = j;
881           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
882           cnzi++;
883           break;
884         }
885       }
886     }
887 
888     /* If free space is not available, make more free space */
889     /* Double the amount of total space in the list */
890     if (current_space->local_remaining<cnzi) {
891       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
892       nspacedouble++;
893     }
894 
895     /* Copy data into free space, then initialize lnk */
896     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
897     current_space->array           += cnzi;
898     current_space->local_used      += cnzi;
899     current_space->local_remaining -= cnzi;
900 
901     ci[i+1] = ci[i] + cnzi;
902   }
903 
904 
905   /* Column indices are in the list of free space.
906      Allocate array cj, copy column indices to cj, and destroy list of free space */
907   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
908   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
909   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
910 
911   /* Allocate space for ca */
912   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
913   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
914 
915   /* put together the new symbolic matrix */
916   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
917   (*C)->rmap->bs = A->cmap->bs;
918   (*C)->cmap->bs = B->cmap->bs;
919 
920   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
921   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
922   c = (Mat_SeqAIJ *)((*C)->data);
923   c->free_a   = PETSC_TRUE;
924   c->free_ij  = PETSC_TRUE;
925   c->nonew    = 0;
926 
927   /* set MatInfo */
928   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
929   if (afill < 1.0) afill = 1.0;
930   c->maxnz                     = ci[am];
931   c->nz                        = ci[am];
932   (*C)->info.mallocs           = nspacedouble;
933   (*C)->info.fill_ratio_given  = fill;
934   (*C)->info.fill_ratio_needed = afill;
935 
936 #if defined(PETSC_USE_INFO)
937   if (ci[am]) {
938     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
939     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
940   } else {
941     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
942   }
943 #endif
944 #endif
945   PetscFunctionReturn(0);
946 }
947 
948 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
949 #undef __FUNCT__
950 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
951 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
952 {
953   PetscErrorCode ierr;
954   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
955   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
956   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
957   PetscLogDouble flops=0.0;
958   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca,*cval;
959   Mat_MatMatTransMult *multtrans;
960   PetscContainer      container;
961 #if defined(USE_ARRAY)
962   MatScalar      *spdot;
963 #endif
964 
965   PetscFunctionBegin;
966   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
967   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
968   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
969   if (multtrans->usecoloring){
970     MatTransposeColoring  matcoloring = multtrans->matcoloring;
971     Mat                   Bt_dense;
972     PetscInt              m,n;
973     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
974     Mat C_dense = multtrans->ABt_den;
975 
976     Bt_dense = multtrans->Bt_den;
977     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
978 
979     /* Get Bt_dense by Apply MatTransposeColoring to B */
980     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
981     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
982     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
983     etime0 += tf - t0;
984 
985     /* C_dense = A*Bt_dense */
986     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
987     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
988     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
989     etime2 += tf - t0;
990 
991     /* Recover C from C_dense */
992     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
993     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
994     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
995     etime1 += tf - t0;
996 #if defined(PETSC_USE_INFO)
997     ierr = PetscInfo4(C,"Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
998 #endif
999     PetscFunctionReturn(0);
1000   }
1001 
1002 #if defined(USE_ARRAY)
1003   /* allocate an array for implementing sparse inner-product */
1004   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
1005   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
1006 #endif
1007 
1008   /* clear old values in C */
1009   if (!c->a){
1010     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1011     c->a      = ca;
1012     c->free_a = PETSC_TRUE;
1013   } else {
1014     ca =  c->a;
1015   }
1016   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1017 
1018   for (i=0; i<cm; i++) {
1019     anzi = ai[i+1] - ai[i];
1020     acol = aj + ai[i];
1021     aval = aa + ai[i];
1022     cnzi = ci[i+1] - ci[i];
1023     ccol = cj + ci[i];
1024     cval = ca + ci[i];
1025     for (j=0; j<cnzi; j++){
1026       brow = ccol[j];
1027       bnzj = bi[brow+1] - bi[brow];
1028       bcol = bj + bi[brow];
1029       bval = ba + bi[brow];
1030 
1031       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1032 #if defined(USE_ARRAY)
1033       /* put ba to spdot array */
1034       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
1035       /* c(i,j)=A[i,:]*B[j,:]^T */
1036       for (nexta=0; nexta<anzi; nexta++){
1037         cval[j] += spdot[acol[nexta]]*aval[nexta];
1038       }
1039       /* zero spdot array */
1040       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1041 #else
1042       nexta = 0; nextb = 0;
1043       while (nexta<anzi && nextb<bnzj){
1044         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
1045         if (nexta == anzi) break;
1046         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
1047         if (nextb == bnzj) break;
1048         if (acol[nexta] == bcol[nextb]){
1049           cval[j] += aval[nexta]*bval[nextb];
1050           nexta++; nextb++;
1051           flops += 2;
1052         }
1053       }
1054 #endif
1055     }
1056   }
1057   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1058   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1059   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1060 #if defined(USE_ARRAY)
1061   ierr = PetscFree(spdot);
1062 #endif
1063   PetscFunctionReturn(0);
1064 }
1065 
1066 #undef __FUNCT__
1067 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1068 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
1069   PetscErrorCode ierr;
1070 
1071   PetscFunctionBegin;
1072   if (scall == MAT_INITIAL_MATRIX){
1073     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1074   }
1075   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1076   PetscFunctionReturn(0);
1077 }
1078 
1079 #undef __FUNCT__
1080 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1081 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1082 {
1083   PetscErrorCode ierr;
1084   Mat            At;
1085   PetscInt       *ati,*atj;
1086 
1087   PetscFunctionBegin;
1088   /* create symbolic At */
1089   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1090   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
1091   At->rmap->bs = A->cmap->bs;
1092   At->cmap->bs = B->cmap->bs;
1093 
1094   /* get symbolic C=At*B */
1095   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1096 
1097   /* clean up */
1098   ierr = MatDestroy(&At);CHKERRQ(ierr);
1099   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1100   PetscFunctionReturn(0);
1101 }
1102 
1103 #undef __FUNCT__
1104 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1105 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1106 {
1107   PetscErrorCode ierr;
1108   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1109   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1110   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1111   PetscLogDouble flops=0.0;
1112   MatScalar      *aa=a->a,*ba,*ca,*caj;
1113 
1114   PetscFunctionBegin;
1115   if (!c->a){
1116     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1117     c->a      = ca;
1118     c->free_a = PETSC_TRUE;
1119   } else {
1120     ca = c->a;
1121   }
1122   /* clear old values in C */
1123   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1124 
1125   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1126   for (i=0;i<am;i++) {
1127     bj   = b->j + bi[i];
1128     ba   = b->a + bi[i];
1129     bnzi = bi[i+1] - bi[i];
1130     anzi = ai[i+1] - ai[i];
1131     for (j=0; j<anzi; j++) {
1132       nextb = 0;
1133       crow  = *aj++;
1134       cjj   = cj + ci[crow];
1135       caj   = ca + ci[crow];
1136       /* perform sparse axpy operation.  Note cjj includes bj. */
1137       for (k=0; nextb<bnzi; k++) {
1138         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1139           caj[k] += (*aa)*(*(ba+nextb));
1140           nextb++;
1141         }
1142       }
1143       flops += 2*bnzi;
1144       aa++;
1145     }
1146   }
1147 
1148   /* Assemble the final matrix and clean up */
1149   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1150   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1151   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1152   PetscFunctionReturn(0);
1153 }
1154 
1155 EXTERN_C_BEGIN
1156 #undef __FUNCT__
1157 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1158 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1159 {
1160   PetscErrorCode ierr;
1161 
1162   PetscFunctionBegin;
1163   if (scall == MAT_INITIAL_MATRIX){
1164     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1165   }
1166   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1167   PetscFunctionReturn(0);
1168 }
1169 EXTERN_C_END
1170 
1171 #undef __FUNCT__
1172 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1173 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1174 {
1175   PetscErrorCode ierr;
1176 
1177   PetscFunctionBegin;
1178   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1179   (*C)->ops->matmult = MatMatMult_SeqAIJ_SeqDense;
1180   PetscFunctionReturn(0);
1181 }
1182 
1183 #undef __FUNCT__
1184 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1185 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1186 {
1187   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1188   PetscErrorCode ierr;
1189   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1190   MatScalar      *aa;
1191   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1192   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1193 
1194   PetscFunctionBegin;
1195   if (!cm || !cn) PetscFunctionReturn(0);
1196   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);
1197   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);
1198   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);
1199   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1200   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1201   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1202   for (col=0; col<cn-4; col += 4){  /* over columns of C */
1203     colam = col*am;
1204     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1205       r1 = r2 = r3 = r4 = 0.0;
1206       n   = a->i[i+1] - a->i[i];
1207       aj  = a->j + a->i[i];
1208       aa  = a->a + a->i[i];
1209       for (j=0; j<n; j++) {
1210         r1 += (*aa)*b1[*aj];
1211         r2 += (*aa)*b2[*aj];
1212         r3 += (*aa)*b3[*aj];
1213         r4 += (*aa++)*b4[*aj++];
1214       }
1215       c[colam + i]       = r1;
1216       c[colam + am + i]  = r2;
1217       c[colam + am2 + i] = r3;
1218       c[colam + am3 + i] = r4;
1219     }
1220     b1 += bm4;
1221     b2 += bm4;
1222     b3 += bm4;
1223     b4 += bm4;
1224   }
1225   for (;col<cn; col++){     /* over extra columns of C */
1226     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1227       r1 = 0.0;
1228       n   = a->i[i+1] - a->i[i];
1229       aj  = a->j + a->i[i];
1230       aa  = a->a + a->i[i];
1231 
1232       for (j=0; j<n; j++) {
1233         r1 += (*aa++)*b1[*aj++];
1234       }
1235       c[col*am + i]     = r1;
1236     }
1237     b1 += bm;
1238   }
1239   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1240   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1241   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1242   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1243   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1244   PetscFunctionReturn(0);
1245 }
1246 
1247 /*
1248    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1249 */
1250 #undef __FUNCT__
1251 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1252 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1253 {
1254   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1255   PetscErrorCode ierr;
1256   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1257   MatScalar      *aa;
1258   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1259   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1260 
1261   PetscFunctionBegin;
1262   if (!cm || !cn) PetscFunctionReturn(0);
1263   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1264   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1265   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1266 
1267   if (a->compressedrow.use){ /* use compressed row format */
1268     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1269       colam = col*am;
1270       arm   = a->compressedrow.nrows;
1271       ii    = a->compressedrow.i;
1272       ridx  = a->compressedrow.rindex;
1273       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1274 	r1 = r2 = r3 = r4 = 0.0;
1275 	n   = ii[i+1] - ii[i];
1276 	aj  = a->j + ii[i];
1277 	aa  = a->a + ii[i];
1278 	for (j=0; j<n; j++) {
1279 	  r1 += (*aa)*b1[*aj];
1280 	  r2 += (*aa)*b2[*aj];
1281 	  r3 += (*aa)*b3[*aj];
1282 	  r4 += (*aa++)*b4[*aj++];
1283 	}
1284 	c[colam       + ridx[i]] += r1;
1285 	c[colam + am  + ridx[i]] += r2;
1286 	c[colam + am2 + ridx[i]] += r3;
1287 	c[colam + am3 + ridx[i]] += r4;
1288       }
1289       b1 += bm4;
1290       b2 += bm4;
1291       b3 += bm4;
1292       b4 += bm4;
1293     }
1294     for (;col<cn; col++){     /* over extra columns of C */
1295       colam = col*am;
1296       arm   = a->compressedrow.nrows;
1297       ii    = a->compressedrow.i;
1298       ridx  = a->compressedrow.rindex;
1299       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1300 	r1 = 0.0;
1301 	n   = ii[i+1] - ii[i];
1302 	aj  = a->j + ii[i];
1303 	aa  = a->a + ii[i];
1304 
1305 	for (j=0; j<n; j++) {
1306 	  r1 += (*aa++)*b1[*aj++];
1307 	}
1308 	c[col*am + ridx[i]] += r1;
1309       }
1310       b1 += bm;
1311     }
1312   } else {
1313     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1314       colam = col*am;
1315       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1316 	r1 = r2 = r3 = r4 = 0.0;
1317 	n   = a->i[i+1] - a->i[i];
1318 	aj  = a->j + a->i[i];
1319 	aa  = a->a + a->i[i];
1320 	for (j=0; j<n; j++) {
1321 	  r1 += (*aa)*b1[*aj];
1322 	  r2 += (*aa)*b2[*aj];
1323 	  r3 += (*aa)*b3[*aj];
1324 	  r4 += (*aa++)*b4[*aj++];
1325 	}
1326 	c[colam + i]       += r1;
1327 	c[colam + am + i]  += r2;
1328 	c[colam + am2 + i] += r3;
1329 	c[colam + am3 + i] += r4;
1330       }
1331       b1 += bm4;
1332       b2 += bm4;
1333       b3 += bm4;
1334       b4 += bm4;
1335     }
1336     for (;col<cn; col++){     /* over extra columns of C */
1337       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1338 	r1 = 0.0;
1339 	n   = a->i[i+1] - a->i[i];
1340 	aj  = a->j + a->i[i];
1341 	aa  = a->a + a->i[i];
1342 
1343 	for (j=0; j<n; j++) {
1344 	  r1 += (*aa++)*b1[*aj++];
1345 	}
1346 	c[col*am + i]     += r1;
1347       }
1348       b1 += bm;
1349     }
1350   }
1351   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1352   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1353   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1354   PetscFunctionReturn(0);
1355 }
1356 
1357 #undef __FUNCT__
1358 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1359 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1360 {
1361   PetscErrorCode ierr;
1362   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
1363   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1364   PetscInt       *bi=b->i,*bj=b->j;
1365   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1366   MatScalar      *btval,*btval_den,*ba=b->a;
1367   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1368 
1369   PetscFunctionBegin;
1370   btval_den=btdense->v;
1371   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1372   for (k=0; k<ncolors; k++) {
1373     ncolumns = coloring->ncolumns[k];
1374     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1375       col   = *(columns + colorforcol[k] + l);
1376       btcol = bj + bi[col];
1377       btval = ba + bi[col];
1378       anz   = bi[col+1] - bi[col];
1379       for (j=0; j<anz; j++){
1380         brow            = btcol[j];
1381         btval_den[brow] = btval[j];
1382       }
1383     }
1384     btval_den += m;
1385   }
1386   PetscFunctionReturn(0);
1387 }
1388 
1389 #undef __FUNCT__
1390 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1391 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1392 {
1393   PetscErrorCode ierr;
1394   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1395   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1396   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1397   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1398 
1399   PetscFunctionBegin;
1400   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1401   ierr = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1402   cp_den = ca_den;
1403   for (k=0; k<ncolors; k++) {
1404     nrows = matcoloring->nrows[k];
1405     row   = rows  + colorforrow[k];
1406     idx   = spidx + colorforrow[k];
1407     for (l=0; l<nrows; l++){
1408       ca[idx[l]] = cp_den[row[l]];
1409     }
1410     cp_den += m;
1411   }
1412   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1413   PetscFunctionReturn(0);
1414 }
1415 
1416 /*
1417  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1418  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1419  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1420  */
1421 #undef __FUNCT__
1422 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1423 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1424 {
1425   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1426   PetscErrorCode ierr;
1427   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1428   PetscInt       nz = a->i[m],row,*jj,mr,col;
1429   PetscInt       *cspidx;
1430 
1431   PetscFunctionBegin;
1432   *nn = n;
1433   if (!ia) PetscFunctionReturn(0);
1434   if (symmetric) {
1435     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1436     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,ia,ja);CHKERRQ(ierr);
1437   } else {
1438     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1439     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1440     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1441     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1442     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1443     jj = a->j;
1444     for (i=0; i<nz; i++) {
1445       collengths[jj[i]]++;
1446     }
1447     cia[0] = oshift;
1448     for (i=0; i<n; i++) {
1449       cia[i+1] = cia[i] + collengths[i];
1450     }
1451     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1452     jj   = a->j;
1453     for (row=0; row<m; row++) {
1454       mr = a->i[row+1] - a->i[row];
1455       for (i=0; i<mr; i++) {
1456         col = *jj++;
1457         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1458         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
1459       }
1460     }
1461     ierr = PetscFree(collengths);CHKERRQ(ierr);
1462     *ia = cia; *ja = cja;
1463     *spidx = cspidx;
1464   }
1465   PetscFunctionReturn(0);
1466 }
1467 
1468 #undef __FUNCT__
1469 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1470 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1471 {
1472   PetscErrorCode ierr;
1473 
1474   PetscFunctionBegin;
1475   if (!ia) PetscFunctionReturn(0);
1476 
1477   ierr = PetscFree(*ia);CHKERRQ(ierr);
1478   ierr = PetscFree(*ja);CHKERRQ(ierr);
1479   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1480   PetscFunctionReturn(0);
1481 }
1482 
1483 #undef __FUNCT__
1484 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1485 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1486 {
1487   PetscErrorCode ierr;
1488   PetscInt       i,n,nrows,N,j,k,m,*row_idx,*ci,*cj,ncols,col,cm;
1489   const PetscInt *is;
1490   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1491   IS             *isa;
1492   PetscBool      flg1,flg2;
1493   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1494   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1495   PetscInt       *colorforcol,*columns,*columns_i;
1496 
1497   PetscFunctionBegin;
1498   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1499 
1500   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1501   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1502   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1503   if (flg1 || flg2) {
1504     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1505   }
1506 
1507   N         = mat->cmap->N/bs;
1508   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1509   c->N      = mat->cmap->N/bs;
1510   c->m      = mat->rmap->N/bs;
1511   c->rstart = 0;
1512 
1513   c->ncolors = nis;
1514   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1515   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1516   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1517   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1518   colorforrow[0]    = 0;
1519   rows_i            = rows;
1520   columnsforspidx_i = columnsforspidx;
1521 
1522   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1523   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1524   colorforcol[0] = 0;
1525   columns_i      = columns;
1526 
1527   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1528 
1529   cm = c->m;
1530   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1531   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1532   for (i=0; i<nis; i++) {
1533     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1534     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1535     c->ncolumns[i] = n;
1536     if (n) {
1537       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1538     }
1539     colorforcol[i+1] = colorforcol[i] + n;
1540     columns_i       += n;
1541 
1542     /* fast, crude version requires O(N*N) work */
1543     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1544 
1545     /* loop over columns*/
1546     for (j=0; j<n; j++) {
1547       col     = is[j];
1548       row_idx = cj + ci[col];
1549       m       = ci[col+1] - ci[col];
1550       /* loop over columns marking them in rowhit */
1551       for (k=0; k<m; k++) {
1552         idxhit[*row_idx]   = spidx[ci[col] + k];
1553         rowhit[*row_idx++] = col + 1;
1554       }
1555     }
1556     /* count the number of hits */
1557     nrows = 0;
1558     for (j=0; j<cm; j++) {
1559       if (rowhit[j]) nrows++;
1560     }
1561     c->nrows[i]      = nrows;
1562     colorforrow[i+1] = colorforrow[i] + nrows;
1563 
1564     nrows       = 0;
1565     for (j=0; j<cm; j++) {
1566       if (rowhit[j]) {
1567         rows_i[nrows]            = j;
1568         columnsforspidx_i[nrows] = idxhit[j];
1569         nrows++;
1570       }
1571     }
1572     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1573     rows_i += nrows; columnsforspidx_i += nrows;
1574   }
1575   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr);
1576   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1577   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1578 #if defined(PETSC_USE_DEBUG)
1579   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1580 #endif
1581 
1582   c->colorforrow     = colorforrow;
1583   c->rows            = rows;
1584   c->columnsforspidx = columnsforspidx;
1585   c->colorforcol     = colorforcol;
1586   c->columns         = columns;
1587   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1588   PetscFunctionReturn(0);
1589 }
1590