xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision f2c2a1b97ba623b07d38ea716c110451b7b5ea3c)
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 
20   PetscFunctionBegin;
21   if (scall == MAT_INITIAL_MATRIX){
22     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
23     ierr = PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
24     ierr = PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,PETSC_NULL);CHKERRQ(ierr);
25     ierr = PetscOptionsBool("-matmatmult_heap","Use heap implementation of symbolic factorization C=A*B","",heap,&heap,PETSC_NULL);CHKERRQ(ierr);
26     ierr = PetscOptionsBool("-matmatmult_btheap","Use btheap implementation of symbolic factorization C=A*B","",btheap,&btheap,PETSC_NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsEnd();CHKERRQ(ierr);
28     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
29     if (scalable_fast){
30       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
31     } else if (scalable){
32       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
33     } else if (heap) {
34       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
35     } else if (btheap) {
36       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
37     } else {
38       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
39     }
40     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
41   }
42   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
43   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
44   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
45   PetscFunctionReturn(0);
46 }
47 
48 #undef __FUNCT__
49 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
50 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
51 {
52   PetscErrorCode     ierr;
53   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
54   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
55   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
56   PetscReal          afill;
57   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
58   PetscBT            lnkbt;
59   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
60 
61   PetscFunctionBegin;
62   /* Get ci and cj */
63   /*---------------*/
64   /* Allocate ci array, arrays for fill computation and */
65   /* free space for accumulating nonzero column info */
66   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
67   ci[0] = 0;
68 
69   /* create and initialize a linked list */
70   nlnk_max = a->rmax*b->rmax;
71   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
72   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
73 
74   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
75   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
76   current_space = free_space;
77 
78   /* Determine ci and cj */
79   for (i=0; i<am; i++) {
80     anzi = ai[i+1] - ai[i];
81     aj   = a->j + ai[i];
82     for (j=0; j<anzi; j++){
83       brow = aj[j];
84       bnzj = bi[brow+1] - bi[brow];
85       bj   = b->j + bi[brow];
86       /* add non-zero cols of B into the sorted linked list lnk */
87       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
88     }
89     cnzi = lnk[0];
90 
91     /* If free space is not available, make more free space */
92     /* Double the amount of total space in the list */
93     if (current_space->local_remaining<cnzi) {
94       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
95       ndouble++;
96     }
97 
98     /* Copy data into free space, then initialize lnk */
99     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
100     current_space->array           += cnzi;
101     current_space->local_used      += cnzi;
102     current_space->local_remaining -= cnzi;
103     ci[i+1] = ci[i] + cnzi;
104   }
105 
106   /* Column indices are in the list of free space */
107   /* Allocate space for cj, initialize cj, and */
108   /* destroy list of free space and other temporary array(s) */
109   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
110   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
111   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
112 
113   /* put together the new symbolic matrix */
114   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
115   (*C)->rmap->bs = A->rmap->bs;
116   (*C)->cmap->bs = B->cmap->bs;
117 
118   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
119   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
120   c = (Mat_SeqAIJ *)((*C)->data);
121   c->free_a  = PETSC_FALSE;
122   c->free_ij = PETSC_TRUE;
123   c->nonew   = 0;
124   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
125 
126   /* set MatInfo */
127   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
128   if (afill < 1.0) afill = 1.0;
129   c->maxnz                     = ci[am];
130   c->nz                        = ci[am];
131   (*C)->info.mallocs           = ndouble;
132   (*C)->info.fill_ratio_given  = fill;
133   (*C)->info.fill_ratio_needed = afill;
134 
135 #if defined(PETSC_USE_INFO)
136   if (ci[am]) {
137     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
138     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
139   } else {
140     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
141   }
142 #endif
143   PetscFunctionReturn(0);
144 }
145 
146 #undef __FUNCT__
147 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
148 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
149 {
150   PetscErrorCode ierr;
151   PetscLogDouble flops=0.0;
152   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
153   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
154   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
155   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
156   PetscInt       am=A->rmap->n,cm=C->rmap->n;
157   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
158   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
159   PetscScalar    *ab_dense;
160 
161   PetscFunctionBegin;
162   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
163   if (!c->a){ /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
164     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
165     c->a      = ca;
166     c->free_a = PETSC_TRUE;
167 
168     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
169     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
170     c->matmult_abdense = ab_dense;
171   } else {
172     ca       = c->a;
173     ab_dense = c->matmult_abdense;
174   }
175 
176   /* clean old values in C */
177   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
178   /* Traverse A row-wise. */
179   /* Build the ith row in C by summing over nonzero columns in A, */
180   /* the rows of B corresponding to nonzeros of A. */
181   for (i=0; i<am; i++) {
182     anzi = ai[i+1] - ai[i];
183     for (j=0; j<anzi; j++) {
184       brow = aj[j];
185       bnzi = bi[brow+1] - bi[brow];
186       bjj  = bj + bi[brow];
187       baj  = ba + bi[brow];
188       /* perform dense axpy */
189       valtmp = aa[j];
190       for (k=0; k<bnzi; k++) {
191         ab_dense[bjj[k]] += valtmp*baj[k];
192       }
193       flops += 2*bnzi;
194     }
195     aj += anzi; aa += anzi;
196 
197     cnzi = ci[i+1] - ci[i];
198     for (k=0; k<cnzi; k++) {
199       ca[k]          += ab_dense[cj[k]];
200       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
201     }
202     flops += cnzi;
203     cj += cnzi; ca += cnzi;
204   }
205   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
206   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
207   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
208   PetscFunctionReturn(0);
209 }
210 
211 #undef __FUNCT__
212 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
213 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
214 {
215   PetscErrorCode ierr;
216   PetscLogDouble flops=0.0;
217   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
218   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
219   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
220   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
221   PetscInt       am=A->rmap->N,cm=C->rmap->N;
222   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
223   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
224   PetscInt       nextb;
225 
226   PetscFunctionBegin;
227   /* clean old values in C */
228   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
229   /* Traverse A row-wise. */
230   /* Build the ith row in C by summing over nonzero columns in A, */
231   /* the rows of B corresponding to nonzeros of A. */
232   for (i=0;i<am;i++) {
233     anzi = ai[i+1] - ai[i];
234     cnzi = ci[i+1] - ci[i];
235     for (j=0;j<anzi;j++) {
236       brow = aj[j];
237       bnzi = bi[brow+1] - bi[brow];
238       bjj  = bj + bi[brow];
239       baj  = ba + bi[brow];
240       /* perform sparse axpy */
241       valtmp = aa[j];
242       nextb  = 0;
243       for (k=0; nextb<bnzi; k++) {
244         if (cj[k] == bjj[nextb]){ /* ccol == bcol */
245           ca[k] += valtmp*baj[nextb++];
246         }
247       }
248       flops += 2*bnzi;
249     }
250     aj += anzi; aa += anzi;
251     cj += cnzi; ca += cnzi;
252   }
253 
254   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
255   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
256   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
257   PetscFunctionReturn(0);
258 }
259 
260 #undef __FUNCT__
261 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
262 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
263 {
264   PetscErrorCode     ierr;
265   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
266   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
267   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
268   MatScalar          *ca;
269   PetscReal          afill;
270   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
271   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
272 
273   PetscFunctionBegin;
274   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
275   /*-----------------------------------------------------------------------------------------*/
276   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
277   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
278   ci[0] = 0;
279 
280   /* create and initialize a linked list */
281   nlnk_max = a->rmax*b->rmax;
282   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
283   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
284 
285   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
286   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
287   current_space = free_space;
288 
289   /* Determine ci and cj */
290   for (i=0; i<am; i++) {
291     anzi = ai[i+1] - ai[i];
292     aj   = a->j + ai[i];
293     for (j=0; j<anzi; j++){
294       brow = aj[j];
295       bnzj = bi[brow+1] - bi[brow];
296       bj   = b->j + bi[brow];
297       /* add non-zero cols of B into the sorted linked list lnk */
298       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
299     }
300     cnzi = lnk[1];
301 
302     /* If free space is not available, make more free space */
303     /* Double the amount of total space in the list */
304     if (current_space->local_remaining<cnzi) {
305       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
306       ndouble++;
307     }
308 
309     /* Copy data into free space, then initialize lnk */
310     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
311     current_space->array           += cnzi;
312     current_space->local_used      += cnzi;
313     current_space->local_remaining -= cnzi;
314     ci[i+1] = ci[i] + cnzi;
315   }
316 
317   /* Column indices are in the list of free space */
318   /* Allocate space for cj, initialize cj, and */
319   /* destroy list of free space and other temporary array(s) */
320   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
321   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
322   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
323 
324   /* Allocate space for ca */
325   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
326   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
327 
328   /* put together the new symbolic matrix */
329   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
330   (*C)->rmap->bs = A->rmap->bs;
331   (*C)->cmap->bs = B->cmap->bs;
332 
333   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
334   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
335   c = (Mat_SeqAIJ *)((*C)->data);
336   c->free_a   = PETSC_TRUE;
337   c->free_ij  = PETSC_TRUE;
338   c->nonew    = 0;
339   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
340 
341   /* set MatInfo */
342   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
343   if (afill < 1.0) afill = 1.0;
344   c->maxnz                     = ci[am];
345   c->nz                        = ci[am];
346   (*C)->info.mallocs           = ndouble;
347   (*C)->info.fill_ratio_given  = fill;
348   (*C)->info.fill_ratio_needed = afill;
349 
350 #if defined(PETSC_USE_INFO)
351   if (ci[am]) {
352     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
353     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
354   } else {
355     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
356   }
357 #endif
358   PetscFunctionReturn(0);
359 }
360 
361 
362 #undef __FUNCT__
363 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
364 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
365 {
366   PetscErrorCode     ierr;
367   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
368   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
369   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
370   MatScalar          *ca;
371   PetscReal          afill;
372   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
373   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
374 
375   PetscFunctionBegin;
376   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
377   /*---------------------------------------------------------------------------------------------*/
378   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
379   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
380   ci[0] = 0;
381 
382   /* create and initialize a linked list */
383   nlnk_max = a->rmax*b->rmax;
384   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
385   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
386 
387   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
388   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
389   current_space = free_space;
390 
391   /* Determine ci and cj */
392   for (i=0; i<am; i++) {
393     anzi = ai[i+1] - ai[i];
394     aj   = a->j + ai[i];
395     for (j=0; j<anzi; j++){
396       brow = aj[j];
397       bnzj = bi[brow+1] - bi[brow];
398       bj   = b->j + bi[brow];
399       /* add non-zero cols of B into the sorted linked list lnk */
400       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
401     }
402     cnzi = lnk[0];
403 
404     /* If free space is not available, make more free space */
405     /* Double the amount of total space in the list */
406     if (current_space->local_remaining<cnzi) {
407       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
408       ndouble++;
409     }
410 
411     /* Copy data into free space, then initialize lnk */
412     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
413     current_space->array           += cnzi;
414     current_space->local_used      += cnzi;
415     current_space->local_remaining -= cnzi;
416     ci[i+1] = ci[i] + cnzi;
417   }
418 
419   /* Column indices are in the list of free space */
420   /* Allocate space for cj, initialize cj, and */
421   /* destroy list of free space and other temporary array(s) */
422   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
423   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
424   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
425 
426   /* Allocate space for ca */
427   /*-----------------------*/
428   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
429   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
430 
431   /* put together the new symbolic matrix */
432   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
433   (*C)->rmap->bs = A->rmap->bs;
434   (*C)->cmap->bs = B->cmap->bs;
435 
436   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
437   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
438   c = (Mat_SeqAIJ *)((*C)->data);
439   c->free_a   = PETSC_TRUE;
440   c->free_ij  = PETSC_TRUE;
441   c->nonew    = 0;
442   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
443 
444   /* set MatInfo */
445   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
446   if (afill < 1.0) afill = 1.0;
447   c->maxnz                     = ci[am];
448   c->nz                        = ci[am];
449   (*C)->info.mallocs           = ndouble;
450   (*C)->info.fill_ratio_given  = fill;
451   (*C)->info.fill_ratio_needed = afill;
452 
453 #if defined(PETSC_USE_INFO)
454   if (ci[am]) {
455     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
456     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
457   } else {
458     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
459   }
460 #endif
461   PetscFunctionReturn(0);
462 }
463 
464 #undef __FUNCT__
465 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
466 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
467 {
468   PetscErrorCode     ierr;
469   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
470   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
471   PetscInt           *ci,*cj,*bb;
472   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
473   PetscReal          afill;
474   PetscInt           i,j,col,ndouble = 0;
475   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
476   PetscHeap          h;
477 
478   PetscFunctionBegin;
479   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
480   /*---------------------------------------------------------------------------------------------*/
481   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
482   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
483   ci[0] = 0;
484 
485   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
486   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
487   current_space = free_space;
488 
489   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
490   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
491 
492   /* Determine ci and cj */
493   for (i=0; i<am; i++) {
494     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 */
495     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
496     ci[i+1] = ci[i];
497     /* Populate the min heap */
498     for (j=0; j<anzi; j++) {
499       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
500       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
501         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
502       }
503     }
504     /* Pick off the min element, adding it to free space */
505     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
506     while (j >= 0) {
507       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
508         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
509         ndouble++;
510       }
511       *(current_space->array++) = col;
512       current_space->local_used++;
513       current_space->local_remaining--;
514       ci[i+1]++;
515 
516       /* stash if anything else remains in this row of B */
517       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
518       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
519         PetscInt j2,col2;
520         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
521         if (col2 != col) break;
522         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
523         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
524       }
525       /* Put any stashed elements back into the min heap */
526       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
527       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
528     }
529   }
530   ierr = PetscFree(bb);CHKERRQ(ierr);
531   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
532 
533   /* Column indices are in the list of free space */
534   /* Allocate space for cj, initialize cj, and */
535   /* destroy list of free space and other temporary array(s) */
536   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
537   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
538 
539   /* put together the new symbolic matrix */
540   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
541   (*C)->rmap->bs = A->rmap->bs;
542   (*C)->cmap->bs = B->cmap->bs;
543 
544   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
545   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
546   c = (Mat_SeqAIJ *)((*C)->data);
547   c->free_a   = PETSC_TRUE;
548   c->free_ij  = PETSC_TRUE;
549   c->nonew    = 0;
550   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
551 
552   /* set MatInfo */
553   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
554   if (afill < 1.0) afill = 1.0;
555   c->maxnz                     = ci[am];
556   c->nz                        = ci[am];
557   (*C)->info.mallocs           = ndouble;
558   (*C)->info.fill_ratio_given  = fill;
559   (*C)->info.fill_ratio_needed = afill;
560 
561 #if defined(PETSC_USE_INFO)
562   if (ci[am]) {
563     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
564     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
565   } else {
566     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
567   }
568 #endif
569   PetscFunctionReturn(0);
570 }
571 
572 #undef __FUNCT__
573 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
574 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
575 {
576   PetscErrorCode     ierr;
577   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
578   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
579   PetscInt           *ci,*cj,*bb;
580   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
581   PetscReal          afill;
582   PetscInt           i,j,col,ndouble = 0;
583   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
584   PetscHeap          h;
585   PetscBT            bt;
586 
587   PetscFunctionBegin;
588   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
589   /*---------------------------------------------------------------------------------------------*/
590   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
591   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
592   ci[0] = 0;
593 
594   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
595   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
596   current_space = free_space;
597 
598   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
599   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
600   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
601 
602   /* Determine ci and cj */
603   for (i=0; i<am; i++) {
604     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 */
605     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
606     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
607     ci[i+1] = ci[i];
608     /* Populate the min heap */
609     for (j=0; j<anzi; j++) {
610       PetscInt brow = acol[j];
611       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
612         PetscInt bcol = bj[bb[j]];
613         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
614           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
615           bb[j]++;
616           break;
617         }
618       }
619     }
620     /* Pick off the min element, adding it to free space */
621     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
622     while (j >= 0) {
623       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
624         fptr = PETSC_NULL;                      /* need PetscBTMemzero */
625         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
626         ndouble++;
627       }
628       *(current_space->array++) = col;
629       current_space->local_used++;
630       current_space->local_remaining--;
631       ci[i+1]++;
632 
633       /* stash if anything else remains in this row of B */
634       for ( ; bb[j] < bi[acol[j]+1]; bb[j]++) {
635         PetscInt bcol = bj[bb[j]];
636         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
637           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
638           bb[j]++;
639           break;
640         }
641       }
642       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
643     }
644     if (fptr) {                 /* Clear the bits for this row */
645       for ( ; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
646     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
647       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
648     }
649   }
650   ierr = PetscFree(bb);CHKERRQ(ierr);
651   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
652   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
653 
654   /* Column indices are in the list of free space */
655   /* Allocate space for cj, initialize cj, and */
656   /* destroy list of free space and other temporary array(s) */
657   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
658   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
659 
660   /* put together the new symbolic matrix */
661   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
662   (*C)->rmap->bs = A->rmap->bs;
663   (*C)->cmap->bs = B->cmap->bs;
664 
665   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
666   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
667   c = (Mat_SeqAIJ *)((*C)->data);
668   c->free_a   = PETSC_TRUE;
669   c->free_ij  = PETSC_TRUE;
670   c->nonew    = 0;
671   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
672 
673   /* set MatInfo */
674   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
675   if (afill < 1.0) afill = 1.0;
676   c->maxnz                     = ci[am];
677   c->nz                        = ci[am];
678   (*C)->info.mallocs           = ndouble;
679   (*C)->info.fill_ratio_given  = fill;
680   (*C)->info.fill_ratio_needed = afill;
681 
682 #if defined(PETSC_USE_INFO)
683   if (ci[am]) {
684     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
685     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
686   } else {
687     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
688   }
689 #endif
690   PetscFunctionReturn(0);
691 }
692 
693 /* This routine is not used. Should be removed! */
694 #undef __FUNCT__
695 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
696 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
697 {
698   PetscErrorCode ierr;
699 
700   PetscFunctionBegin;
701   if (scall == MAT_INITIAL_MATRIX){
702     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
703   }
704   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
705   PetscFunctionReturn(0);
706 }
707 
708 #undef __FUNCT__
709 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
710 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
711 {
712   PetscErrorCode      ierr;
713   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
714 
715   PetscFunctionBegin;
716   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
717   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
718   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
719   ierr = PetscFree(multtrans);CHKERRQ(ierr);
720   PetscFunctionReturn(0);
721 }
722 
723 #undef __FUNCT__
724 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
725 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
726 {
727   PetscErrorCode      ierr;
728   PetscContainer      container;
729   Mat_MatMatTransMult *multtrans=PETSC_NULL;
730 
731   PetscFunctionBegin;
732   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
733   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
734   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
735   A->ops->destroy   = multtrans->destroy;
736   if (A->ops->destroy) {
737     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
738   }
739   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
740   PetscFunctionReturn(0);
741 }
742 
743 #undef __FUNCT__
744 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
745 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
746 {
747   PetscErrorCode      ierr;
748   Mat                 Bt;
749   PetscInt            *bti,*btj;
750   Mat_MatMatTransMult *multtrans;
751   PetscContainer      container;
752   PetscLogDouble      t0,tf,etime2=0.0;
753 
754   PetscFunctionBegin;
755   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
756    /* create symbolic Bt */
757   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
758   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
759   Bt->rmap->bs = A->cmap->bs;
760   Bt->cmap->bs = B->cmap->bs;
761 
762   /* get symbolic C=A*Bt */
763   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
764 
765   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
766   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
767 
768   /* attach the supporting struct to C */
769   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
770   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
771   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
772   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
773   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
774 
775   multtrans->usecoloring = PETSC_FALSE;
776   multtrans->destroy = (*C)->ops->destroy;
777   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
778 
779   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
780   etime2 += tf - t0;
781 
782   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
783   if (multtrans->usecoloring){
784     /* Create MatTransposeColoring from symbolic C=A*B^T */
785     MatTransposeColoring matcoloring;
786     ISColoring           iscoloring;
787     Mat                  Bt_dense,C_dense;
788     PetscLogDouble       etime0=0.0,etime01=0.0,etime1=0.0;
789 
790     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
791     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
792     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
793     etime0 += tf - t0;
794 
795     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
796     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
797     multtrans->matcoloring = matcoloring;
798     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
799     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
800     etime01 += tf - t0;
801 
802     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
803     /* Create Bt_dense and C_dense = A*Bt_dense */
804     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
805     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
806     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
807     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
808     Bt_dense->assembled = PETSC_TRUE;
809     multtrans->Bt_den = Bt_dense;
810 
811     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
812     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
813     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
814     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
815     Bt_dense->assembled = PETSC_TRUE;
816     multtrans->ABt_den = C_dense;
817     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
818     etime1 += tf - t0;
819 
820 #if defined(PETSC_USE_INFO)
821     {
822     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
823     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));
824     ierr = PetscInfo5(*C,"Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
825     }
826 #endif
827   }
828   /* clean up */
829   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
830   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
831 
832 
833 
834 #if defined(INEFFICIENT_ALGORITHM)
835   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
836   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
837   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
838   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
839   PetscInt           am=A->rmap->N,bm=B->rmap->N;
840   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
841   MatScalar          *ca;
842   PetscBT            lnkbt;
843   PetscReal          afill;
844 
845   /* Allocate row pointer array ci  */
846   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
847   ci[0] = 0;
848 
849   /* Create and initialize a linked list for C columns */
850   nlnk = bm+1;
851   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
852 
853   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
854   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
855   current_space = free_space;
856 
857   /* Determine symbolic info for each row of the product A*B^T: */
858   for (i=0; i<am; i++) {
859     anzi = ai[i+1] - ai[i];
860     cnzi = 0;
861     acol = aj + ai[i];
862     for (j=0; j<bm; j++){
863       bnzj = bi[j+1] - bi[j];
864       bcol= bj + bi[j];
865       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
866       ka = 0; kb = 0;
867       while (ka < anzi && kb < bnzj){
868         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
869         if (ka == anzi) break;
870         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
871         if (kb == bnzj) break;
872         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
873           index[0] = j;
874           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
875           cnzi++;
876           break;
877         }
878       }
879     }
880 
881     /* If free space is not available, make more free space */
882     /* Double the amount of total space in the list */
883     if (current_space->local_remaining<cnzi) {
884       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
885       nspacedouble++;
886     }
887 
888     /* Copy data into free space, then initialize lnk */
889     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
890     current_space->array           += cnzi;
891     current_space->local_used      += cnzi;
892     current_space->local_remaining -= cnzi;
893 
894     ci[i+1] = ci[i] + cnzi;
895   }
896 
897 
898   /* Column indices are in the list of free space.
899      Allocate array cj, copy column indices to cj, and destroy list of free space */
900   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
901   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
902   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
903 
904   /* Allocate space for ca */
905   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
906   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
907 
908   /* put together the new symbolic matrix */
909   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
910   (*C)->rmap->bs = A->cmap->bs;
911   (*C)->cmap->bs = B->cmap->bs;
912 
913   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
914   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
915   c = (Mat_SeqAIJ *)((*C)->data);
916   c->free_a   = PETSC_TRUE;
917   c->free_ij  = PETSC_TRUE;
918   c->nonew    = 0;
919 
920   /* set MatInfo */
921   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
922   if (afill < 1.0) afill = 1.0;
923   c->maxnz                     = ci[am];
924   c->nz                        = ci[am];
925   (*C)->info.mallocs           = nspacedouble;
926   (*C)->info.fill_ratio_given  = fill;
927   (*C)->info.fill_ratio_needed = afill;
928 
929 #if defined(PETSC_USE_INFO)
930   if (ci[am]) {
931     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
932     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
933   } else {
934     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
935   }
936 #endif
937 #endif
938   PetscFunctionReturn(0);
939 }
940 
941 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
942 #undef __FUNCT__
943 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
944 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
945 {
946   PetscErrorCode ierr;
947   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
948   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
949   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
950   PetscLogDouble flops=0.0;
951   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca,*cval;
952   Mat_MatMatTransMult *multtrans;
953   PetscContainer      container;
954 #if defined(USE_ARRAY)
955   MatScalar      *spdot;
956 #endif
957 
958   PetscFunctionBegin;
959   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
960   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
961   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
962   if (multtrans->usecoloring){
963     MatTransposeColoring  matcoloring = multtrans->matcoloring;
964     Mat                   Bt_dense;
965     PetscInt              m,n;
966     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
967     Mat C_dense = multtrans->ABt_den;
968 
969     Bt_dense = multtrans->Bt_den;
970     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
971 
972     /* Get Bt_dense by Apply MatTransposeColoring to B */
973     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
974     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
975     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
976     etime0 += tf - t0;
977 
978     /* C_dense = A*Bt_dense */
979     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
980     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
981     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
982     etime2 += tf - t0;
983 
984     /* Recover C from C_dense */
985     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
986     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
987     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
988     etime1 += tf - t0;
989 #if defined(PETSC_USE_INFO)
990     ierr = PetscInfo4(C,"Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
991 #endif
992     PetscFunctionReturn(0);
993   }
994 
995 #if defined(USE_ARRAY)
996   /* allocate an array for implementing sparse inner-product */
997   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
998   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
999 #endif
1000 
1001   /* clear old values in C */
1002   if (!c->a){
1003     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1004     c->a      = ca;
1005     c->free_a = PETSC_TRUE;
1006   } else {
1007     ca =  c->a;
1008   }
1009   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1010 
1011   for (i=0; i<cm; i++) {
1012     anzi = ai[i+1] - ai[i];
1013     acol = aj + ai[i];
1014     aval = aa + ai[i];
1015     cnzi = ci[i+1] - ci[i];
1016     ccol = cj + ci[i];
1017     cval = ca + ci[i];
1018     for (j=0; j<cnzi; j++){
1019       brow = ccol[j];
1020       bnzj = bi[brow+1] - bi[brow];
1021       bcol = bj + bi[brow];
1022       bval = ba + bi[brow];
1023 
1024       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1025 #if defined(USE_ARRAY)
1026       /* put ba to spdot array */
1027       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
1028       /* c(i,j)=A[i,:]*B[j,:]^T */
1029       for (nexta=0; nexta<anzi; nexta++){
1030         cval[j] += spdot[acol[nexta]]*aval[nexta];
1031       }
1032       /* zero spdot array */
1033       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1034 #else
1035       nexta = 0; nextb = 0;
1036       while (nexta<anzi && nextb<bnzj){
1037         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
1038         if (nexta == anzi) break;
1039         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
1040         if (nextb == bnzj) break;
1041         if (acol[nexta] == bcol[nextb]){
1042           cval[j] += aval[nexta]*bval[nextb];
1043           nexta++; nextb++;
1044           flops += 2;
1045         }
1046       }
1047 #endif
1048     }
1049   }
1050   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1051   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1052   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1053 #if defined(USE_ARRAY)
1054   ierr = PetscFree(spdot);
1055 #endif
1056   PetscFunctionReturn(0);
1057 }
1058 
1059 #undef __FUNCT__
1060 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1061 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
1062   PetscErrorCode ierr;
1063 
1064   PetscFunctionBegin;
1065   if (scall == MAT_INITIAL_MATRIX){
1066     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1067   }
1068   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1069   PetscFunctionReturn(0);
1070 }
1071 
1072 #undef __FUNCT__
1073 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1074 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1075 {
1076   PetscErrorCode ierr;
1077   Mat            At;
1078   PetscInt       *ati,*atj;
1079 
1080   PetscFunctionBegin;
1081   /* create symbolic At */
1082   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1083   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
1084   At->rmap->bs = A->cmap->bs;
1085   At->cmap->bs = B->cmap->bs;
1086 
1087   /* get symbolic C=At*B */
1088   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1089 
1090   /* clean up */
1091   ierr = MatDestroy(&At);CHKERRQ(ierr);
1092   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1093   PetscFunctionReturn(0);
1094 }
1095 
1096 #undef __FUNCT__
1097 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1098 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1099 {
1100   PetscErrorCode ierr;
1101   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1102   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1103   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1104   PetscLogDouble flops=0.0;
1105   MatScalar      *aa=a->a,*ba,*ca,*caj;
1106 
1107   PetscFunctionBegin;
1108   if (!c->a){
1109     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1110     c->a      = ca;
1111     c->free_a = PETSC_TRUE;
1112   } else {
1113     ca = c->a;
1114   }
1115   /* clear old values in C */
1116   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1117 
1118   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1119   for (i=0;i<am;i++) {
1120     bj   = b->j + bi[i];
1121     ba   = b->a + bi[i];
1122     bnzi = bi[i+1] - bi[i];
1123     anzi = ai[i+1] - ai[i];
1124     for (j=0; j<anzi; j++) {
1125       nextb = 0;
1126       crow  = *aj++;
1127       cjj   = cj + ci[crow];
1128       caj   = ca + ci[crow];
1129       /* perform sparse axpy operation.  Note cjj includes bj. */
1130       for (k=0; nextb<bnzi; k++) {
1131         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1132           caj[k] += (*aa)*(*(ba+nextb));
1133           nextb++;
1134         }
1135       }
1136       flops += 2*bnzi;
1137       aa++;
1138     }
1139   }
1140 
1141   /* Assemble the final matrix and clean up */
1142   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1143   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1144   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1145   PetscFunctionReturn(0);
1146 }
1147 
1148 EXTERN_C_BEGIN
1149 #undef __FUNCT__
1150 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1151 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1152 {
1153   PetscErrorCode ierr;
1154 
1155   PetscFunctionBegin;
1156   if (scall == MAT_INITIAL_MATRIX){
1157     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1158   }
1159   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1160   PetscFunctionReturn(0);
1161 }
1162 EXTERN_C_END
1163 
1164 #undef __FUNCT__
1165 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1166 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1167 {
1168   PetscErrorCode ierr;
1169 
1170   PetscFunctionBegin;
1171   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1172   (*C)->ops->matmult = MatMatMult_SeqAIJ_SeqDense;
1173   PetscFunctionReturn(0);
1174 }
1175 
1176 #undef __FUNCT__
1177 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1178 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1179 {
1180   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1181   PetscErrorCode ierr;
1182   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1183   MatScalar      *aa;
1184   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1185   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1186 
1187   PetscFunctionBegin;
1188   if (!cm || !cn) PetscFunctionReturn(0);
1189   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);
1190   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);
1191   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);
1192   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1193   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1194   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1195   for (col=0; col<cn-4; col += 4){  /* over columns of C */
1196     colam = col*am;
1197     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1198       r1 = r2 = r3 = r4 = 0.0;
1199       n   = a->i[i+1] - a->i[i];
1200       aj  = a->j + a->i[i];
1201       aa  = a->a + a->i[i];
1202       for (j=0; j<n; j++) {
1203         r1 += (*aa)*b1[*aj];
1204         r2 += (*aa)*b2[*aj];
1205         r3 += (*aa)*b3[*aj];
1206         r4 += (*aa++)*b4[*aj++];
1207       }
1208       c[colam + i]       = r1;
1209       c[colam + am + i]  = r2;
1210       c[colam + am2 + i] = r3;
1211       c[colam + am3 + i] = r4;
1212     }
1213     b1 += bm4;
1214     b2 += bm4;
1215     b3 += bm4;
1216     b4 += bm4;
1217   }
1218   for (;col<cn; col++){     /* over extra columns of C */
1219     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1220       r1 = 0.0;
1221       n   = a->i[i+1] - a->i[i];
1222       aj  = a->j + a->i[i];
1223       aa  = a->a + a->i[i];
1224 
1225       for (j=0; j<n; j++) {
1226         r1 += (*aa++)*b1[*aj++];
1227       }
1228       c[col*am + i]     = r1;
1229     }
1230     b1 += bm;
1231   }
1232   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1233   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1234   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1235   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1236   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1237   PetscFunctionReturn(0);
1238 }
1239 
1240 /*
1241    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1242 */
1243 #undef __FUNCT__
1244 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1245 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1246 {
1247   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1248   PetscErrorCode ierr;
1249   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1250   MatScalar      *aa;
1251   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1252   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1253 
1254   PetscFunctionBegin;
1255   if (!cm || !cn) PetscFunctionReturn(0);
1256   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1257   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1258   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1259 
1260   if (a->compressedrow.use){ /* use compressed row format */
1261     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1262       colam = col*am;
1263       arm   = a->compressedrow.nrows;
1264       ii    = a->compressedrow.i;
1265       ridx  = a->compressedrow.rindex;
1266       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1267 	r1 = r2 = r3 = r4 = 0.0;
1268 	n   = ii[i+1] - ii[i];
1269 	aj  = a->j + ii[i];
1270 	aa  = a->a + ii[i];
1271 	for (j=0; j<n; j++) {
1272 	  r1 += (*aa)*b1[*aj];
1273 	  r2 += (*aa)*b2[*aj];
1274 	  r3 += (*aa)*b3[*aj];
1275 	  r4 += (*aa++)*b4[*aj++];
1276 	}
1277 	c[colam       + ridx[i]] += r1;
1278 	c[colam + am  + ridx[i]] += r2;
1279 	c[colam + am2 + ridx[i]] += r3;
1280 	c[colam + am3 + ridx[i]] += r4;
1281       }
1282       b1 += bm4;
1283       b2 += bm4;
1284       b3 += bm4;
1285       b4 += bm4;
1286     }
1287     for (;col<cn; col++){     /* over extra columns of C */
1288       colam = col*am;
1289       arm   = a->compressedrow.nrows;
1290       ii    = a->compressedrow.i;
1291       ridx  = a->compressedrow.rindex;
1292       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1293 	r1 = 0.0;
1294 	n   = ii[i+1] - ii[i];
1295 	aj  = a->j + ii[i];
1296 	aa  = a->a + ii[i];
1297 
1298 	for (j=0; j<n; j++) {
1299 	  r1 += (*aa++)*b1[*aj++];
1300 	}
1301 	c[col*am + ridx[i]] += r1;
1302       }
1303       b1 += bm;
1304     }
1305   } else {
1306     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1307       colam = col*am;
1308       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1309 	r1 = r2 = r3 = r4 = 0.0;
1310 	n   = a->i[i+1] - a->i[i];
1311 	aj  = a->j + a->i[i];
1312 	aa  = a->a + a->i[i];
1313 	for (j=0; j<n; j++) {
1314 	  r1 += (*aa)*b1[*aj];
1315 	  r2 += (*aa)*b2[*aj];
1316 	  r3 += (*aa)*b3[*aj];
1317 	  r4 += (*aa++)*b4[*aj++];
1318 	}
1319 	c[colam + i]       += r1;
1320 	c[colam + am + i]  += r2;
1321 	c[colam + am2 + i] += r3;
1322 	c[colam + am3 + i] += r4;
1323       }
1324       b1 += bm4;
1325       b2 += bm4;
1326       b3 += bm4;
1327       b4 += bm4;
1328     }
1329     for (;col<cn; col++){     /* over extra columns of C */
1330       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1331 	r1 = 0.0;
1332 	n   = a->i[i+1] - a->i[i];
1333 	aj  = a->j + a->i[i];
1334 	aa  = a->a + a->i[i];
1335 
1336 	for (j=0; j<n; j++) {
1337 	  r1 += (*aa++)*b1[*aj++];
1338 	}
1339 	c[col*am + i]     += r1;
1340       }
1341       b1 += bm;
1342     }
1343   }
1344   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1345   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1346   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1347   PetscFunctionReturn(0);
1348 }
1349 
1350 #undef __FUNCT__
1351 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1352 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1353 {
1354   PetscErrorCode ierr;
1355   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
1356   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1357   PetscInt       *bi=b->i,*bj=b->j;
1358   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1359   MatScalar      *btval,*btval_den,*ba=b->a;
1360   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1361 
1362   PetscFunctionBegin;
1363   btval_den=btdense->v;
1364   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1365   for (k=0; k<ncolors; k++) {
1366     ncolumns = coloring->ncolumns[k];
1367     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1368       col   = *(columns + colorforcol[k] + l);
1369       btcol = bj + bi[col];
1370       btval = ba + bi[col];
1371       anz   = bi[col+1] - bi[col];
1372       for (j=0; j<anz; j++){
1373         brow            = btcol[j];
1374         btval_den[brow] = btval[j];
1375       }
1376     }
1377     btval_den += m;
1378   }
1379   PetscFunctionReturn(0);
1380 }
1381 
1382 #undef __FUNCT__
1383 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1384 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1385 {
1386   PetscErrorCode ierr;
1387   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1388   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1389   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1390   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1391 
1392   PetscFunctionBegin;
1393   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1394   ierr = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1395   cp_den = ca_den;
1396   for (k=0; k<ncolors; k++) {
1397     nrows = matcoloring->nrows[k];
1398     row   = rows  + colorforrow[k];
1399     idx   = spidx + colorforrow[k];
1400     for (l=0; l<nrows; l++){
1401       ca[idx[l]] = cp_den[row[l]];
1402     }
1403     cp_den += m;
1404   }
1405   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1406   PetscFunctionReturn(0);
1407 }
1408 
1409 /*
1410  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1411  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1412  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1413  */
1414 #undef __FUNCT__
1415 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1416 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1417 {
1418   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1419   PetscErrorCode ierr;
1420   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1421   PetscInt       nz = a->i[m],row,*jj,mr,col;
1422   PetscInt       *cspidx;
1423 
1424   PetscFunctionBegin;
1425   *nn = n;
1426   if (!ia) PetscFunctionReturn(0);
1427   if (symmetric) {
1428     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1429     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1430   } else {
1431     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1432     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1433     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1434     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1435     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1436     jj = a->j;
1437     for (i=0; i<nz; i++) {
1438       collengths[jj[i]]++;
1439     }
1440     cia[0] = oshift;
1441     for (i=0; i<n; i++) {
1442       cia[i+1] = cia[i] + collengths[i];
1443     }
1444     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1445     jj   = a->j;
1446     for (row=0; row<m; row++) {
1447       mr = a->i[row+1] - a->i[row];
1448       for (i=0; i<mr; i++) {
1449         col = *jj++;
1450         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1451         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
1452       }
1453     }
1454     ierr = PetscFree(collengths);CHKERRQ(ierr);
1455     *ia = cia; *ja = cja;
1456     *spidx = cspidx;
1457   }
1458   PetscFunctionReturn(0);
1459 }
1460 
1461 #undef __FUNCT__
1462 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1463 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1464 {
1465   PetscErrorCode ierr;
1466 
1467   PetscFunctionBegin;
1468   if (!ia) PetscFunctionReturn(0);
1469 
1470   ierr = PetscFree(*ia);CHKERRQ(ierr);
1471   ierr = PetscFree(*ja);CHKERRQ(ierr);
1472   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1473   PetscFunctionReturn(0);
1474 }
1475 
1476 #undef __FUNCT__
1477 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1478 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1479 {
1480   PetscErrorCode ierr;
1481   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
1482   const PetscInt *is,*ci,*cj,*row_idx;
1483   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1484   IS             *isa;
1485   PetscBool      flg1,flg2;
1486   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1487   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1488   PetscInt       *colorforcol,*columns,*columns_i;
1489 
1490   PetscFunctionBegin;
1491   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1492 
1493   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1494   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1495   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1496   if (flg1 || flg2) {
1497     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1498   }
1499 
1500   N         = mat->cmap->N/bs;
1501   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1502   c->N      = mat->cmap->N/bs;
1503   c->m      = mat->rmap->N/bs;
1504   c->rstart = 0;
1505 
1506   c->ncolors = nis;
1507   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1508   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1509   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1510   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1511   colorforrow[0]    = 0;
1512   rows_i            = rows;
1513   columnsforspidx_i = columnsforspidx;
1514 
1515   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1516   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1517   colorforcol[0] = 0;
1518   columns_i      = columns;
1519 
1520   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1521 
1522   cm = c->m;
1523   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1524   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1525   for (i=0; i<nis; i++) {
1526     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1527     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1528     c->ncolumns[i] = n;
1529     if (n) {
1530       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1531     }
1532     colorforcol[i+1] = colorforcol[i] + n;
1533     columns_i       += n;
1534 
1535     /* fast, crude version requires O(N*N) work */
1536     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1537 
1538     /* loop over columns*/
1539     for (j=0; j<n; j++) {
1540       col     = is[j];
1541       row_idx = cj + ci[col];
1542       m       = ci[col+1] - ci[col];
1543       /* loop over columns marking them in rowhit */
1544       for (k=0; k<m; k++) {
1545         idxhit[*row_idx]   = spidx[ci[col] + k];
1546         rowhit[*row_idx++] = col + 1;
1547       }
1548     }
1549     /* count the number of hits */
1550     nrows = 0;
1551     for (j=0; j<cm; j++) {
1552       if (rowhit[j]) nrows++;
1553     }
1554     c->nrows[i]      = nrows;
1555     colorforrow[i+1] = colorforrow[i] + nrows;
1556 
1557     nrows       = 0;
1558     for (j=0; j<cm; j++) {
1559       if (rowhit[j]) {
1560         rows_i[nrows]            = j;
1561         columnsforspidx_i[nrows] = idxhit[j];
1562         nrows++;
1563       }
1564     }
1565     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1566     rows_i += nrows; columnsforspidx_i += nrows;
1567   }
1568   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr);
1569   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1570   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1571 #if defined(PETSC_USE_DEBUG)
1572   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1573 #endif
1574 
1575   c->colorforrow     = colorforrow;
1576   c->rows            = rows;
1577   c->columnsforspidx = columnsforspidx;
1578   c->colorforcol     = colorforcol;
1579   c->columns         = columns;
1580   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1581   PetscFunctionReturn(0);
1582 }
1583