xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 3bf036e263fd78807e2931ff42d9ddcd8aae3fd4)
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 
753   PetscFunctionBegin;
754    /* create symbolic Bt */
755   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
756   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
757   Bt->rmap->bs = A->cmap->bs;
758   Bt->cmap->bs = B->cmap->bs;
759 
760   /* get symbolic C=A*Bt */
761   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
762 
763   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
764   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
765 
766   /* attach the supporting struct to C */
767   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
768   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
769   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
770   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
771   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
772 
773   multtrans->usecoloring = PETSC_FALSE;
774   multtrans->destroy = (*C)->ops->destroy;
775   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
776 
777   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
778   if (multtrans->usecoloring){
779     /* Create MatTransposeColoring from symbolic C=A*B^T */
780     MatTransposeColoring matcoloring;
781     ISColoring           iscoloring;
782     Mat                  Bt_dense,C_dense;
783 
784     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
785     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
786     multtrans->matcoloring = matcoloring;
787     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
788 
789     /* Create Bt_dense and C_dense = A*Bt_dense */
790     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
791     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
792     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
793     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
794     Bt_dense->assembled = PETSC_TRUE;
795     multtrans->Bt_den = Bt_dense;
796 
797     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
798     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
799     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
800     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
801     Bt_dense->assembled = PETSC_TRUE;
802     multtrans->ABt_den = C_dense;
803 
804 #if defined(PETSC_USE_INFO)
805     {
806     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
807     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));
808     }
809 #endif
810   }
811   /* clean up */
812   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
813   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
814 
815 
816 
817 #if defined(INEFFICIENT_ALGORITHM)
818   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
819   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
820   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
821   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
822   PetscInt           am=A->rmap->N,bm=B->rmap->N;
823   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
824   MatScalar          *ca;
825   PetscBT            lnkbt;
826   PetscReal          afill;
827 
828   /* Allocate row pointer array ci  */
829   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
830   ci[0] = 0;
831 
832   /* Create and initialize a linked list for C columns */
833   nlnk = bm+1;
834   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
835 
836   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
837   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
838   current_space = free_space;
839 
840   /* Determine symbolic info for each row of the product A*B^T: */
841   for (i=0; i<am; i++) {
842     anzi = ai[i+1] - ai[i];
843     cnzi = 0;
844     acol = aj + ai[i];
845     for (j=0; j<bm; j++){
846       bnzj = bi[j+1] - bi[j];
847       bcol= bj + bi[j];
848       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
849       ka = 0; kb = 0;
850       while (ka < anzi && kb < bnzj){
851         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
852         if (ka == anzi) break;
853         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
854         if (kb == bnzj) break;
855         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
856           index[0] = j;
857           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
858           cnzi++;
859           break;
860         }
861       }
862     }
863 
864     /* If free space is not available, make more free space */
865     /* Double the amount of total space in the list */
866     if (current_space->local_remaining<cnzi) {
867       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
868       nspacedouble++;
869     }
870 
871     /* Copy data into free space, then initialize lnk */
872     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
873     current_space->array           += cnzi;
874     current_space->local_used      += cnzi;
875     current_space->local_remaining -= cnzi;
876 
877     ci[i+1] = ci[i] + cnzi;
878   }
879 
880 
881   /* Column indices are in the list of free space.
882      Allocate array cj, copy column indices to cj, and destroy list of free space */
883   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
884   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
885   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
886 
887   /* Allocate space for ca */
888   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
889   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
890 
891   /* put together the new symbolic matrix */
892   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
893   (*C)->rmap->bs = A->cmap->bs;
894   (*C)->cmap->bs = B->cmap->bs;
895 
896   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
897   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
898   c = (Mat_SeqAIJ *)((*C)->data);
899   c->free_a   = PETSC_TRUE;
900   c->free_ij  = PETSC_TRUE;
901   c->nonew    = 0;
902 
903   /* set MatInfo */
904   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
905   if (afill < 1.0) afill = 1.0;
906   c->maxnz                     = ci[am];
907   c->nz                        = ci[am];
908   (*C)->info.mallocs           = nspacedouble;
909   (*C)->info.fill_ratio_given  = fill;
910   (*C)->info.fill_ratio_needed = afill;
911 
912 #if defined(PETSC_USE_INFO)
913   if (ci[am]) {
914     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
915     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
916   } else {
917     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
918   }
919 #endif
920 #endif
921   PetscFunctionReturn(0);
922 }
923 
924 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
925 #undef __FUNCT__
926 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
927 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
928 {
929   PetscErrorCode ierr;
930   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
931   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
932   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
933   PetscLogDouble flops=0.0;
934   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca,*cval;
935   Mat_MatMatTransMult *multtrans;
936   PetscContainer      container;
937 #if defined(USE_ARRAY)
938   MatScalar      *spdot;
939 #endif
940 
941   PetscFunctionBegin;
942   /* clear old values in C */
943   if (!c->a){
944     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
945     c->a      = ca;
946     c->free_a = PETSC_TRUE;
947   } else {
948     ca =  c->a;
949   }
950   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
951 
952   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
953   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
954   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
955   if (multtrans->usecoloring){
956     MatTransposeColoring  matcoloring = multtrans->matcoloring;
957     Mat                   Bt_dense;
958     PetscInt              m,n;
959     Mat C_dense = multtrans->ABt_den;
960 
961     Bt_dense = multtrans->Bt_den;
962     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
963 
964     /* Get Bt_dense by Apply MatTransposeColoring to B */
965     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
966 
967     /* C_dense = A*Bt_dense */
968     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
969 
970     /* Recover C from C_dense */
971     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
972     PetscFunctionReturn(0);
973   }
974 
975 #if defined(USE_ARRAY)
976   /* allocate an array for implementing sparse inner-product */
977   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
978   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
979 #endif
980 
981   for (i=0; i<cm; i++) {
982     anzi = ai[i+1] - ai[i];
983     acol = aj + ai[i];
984     aval = aa + ai[i];
985     cnzi = ci[i+1] - ci[i];
986     ccol = cj + ci[i];
987     cval = ca + ci[i];
988     for (j=0; j<cnzi; j++){
989       brow = ccol[j];
990       bnzj = bi[brow+1] - bi[brow];
991       bcol = bj + bi[brow];
992       bval = ba + bi[brow];
993 
994       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
995 #if defined(USE_ARRAY)
996       /* put ba to spdot array */
997       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
998       /* c(i,j)=A[i,:]*B[j,:]^T */
999       for (nexta=0; nexta<anzi; nexta++){
1000         cval[j] += spdot[acol[nexta]]*aval[nexta];
1001       }
1002       /* zero spdot array */
1003       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1004 #else
1005       nexta = 0; nextb = 0;
1006       while (nexta<anzi && nextb<bnzj){
1007         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
1008         if (nexta == anzi) break;
1009         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
1010         if (nextb == bnzj) break;
1011         if (acol[nexta] == bcol[nextb]){
1012           cval[j] += aval[nexta]*bval[nextb];
1013           nexta++; nextb++;
1014           flops += 2;
1015         }
1016       }
1017 #endif
1018     }
1019   }
1020   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1021   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1022   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1023 #if defined(USE_ARRAY)
1024   ierr = PetscFree(spdot);
1025 #endif
1026   PetscFunctionReturn(0);
1027 }
1028 
1029 #undef __FUNCT__
1030 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1031 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
1032   PetscErrorCode ierr;
1033 
1034   PetscFunctionBegin;
1035   if (scall == MAT_INITIAL_MATRIX){
1036     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1037   }
1038   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1039   PetscFunctionReturn(0);
1040 }
1041 
1042 #undef __FUNCT__
1043 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1044 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1045 {
1046   PetscErrorCode ierr;
1047   Mat            At;
1048   PetscInt       *ati,*atj;
1049 
1050   PetscFunctionBegin;
1051   /* create symbolic At */
1052   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1053   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
1054   At->rmap->bs = A->cmap->bs;
1055   At->cmap->bs = B->cmap->bs;
1056 
1057   /* get symbolic C=At*B */
1058   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1059 
1060   /* clean up */
1061   ierr = MatDestroy(&At);CHKERRQ(ierr);
1062   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1063   PetscFunctionReturn(0);
1064 }
1065 
1066 #undef __FUNCT__
1067 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1068 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1069 {
1070   PetscErrorCode ierr;
1071   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1072   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1073   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1074   PetscLogDouble flops=0.0;
1075   MatScalar      *aa=a->a,*ba,*ca,*caj;
1076 
1077   PetscFunctionBegin;
1078   if (!c->a){
1079     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1080     c->a      = ca;
1081     c->free_a = PETSC_TRUE;
1082   } else {
1083     ca = c->a;
1084   }
1085   /* clear old values in C */
1086   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1087 
1088   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1089   for (i=0;i<am;i++) {
1090     bj   = b->j + bi[i];
1091     ba   = b->a + bi[i];
1092     bnzi = bi[i+1] - bi[i];
1093     anzi = ai[i+1] - ai[i];
1094     for (j=0; j<anzi; j++) {
1095       nextb = 0;
1096       crow  = *aj++;
1097       cjj   = cj + ci[crow];
1098       caj   = ca + ci[crow];
1099       /* perform sparse axpy operation.  Note cjj includes bj. */
1100       for (k=0; nextb<bnzi; k++) {
1101         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1102           caj[k] += (*aa)*(*(ba+nextb));
1103           nextb++;
1104         }
1105       }
1106       flops += 2*bnzi;
1107       aa++;
1108     }
1109   }
1110 
1111   /* Assemble the final matrix and clean up */
1112   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1113   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1114   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1115   PetscFunctionReturn(0);
1116 }
1117 
1118 EXTERN_C_BEGIN
1119 #undef __FUNCT__
1120 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1121 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1122 {
1123   PetscErrorCode ierr;
1124 
1125   PetscFunctionBegin;
1126   if (scall == MAT_INITIAL_MATRIX){
1127     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1128   }
1129   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1130   PetscFunctionReturn(0);
1131 }
1132 EXTERN_C_END
1133 
1134 #undef __FUNCT__
1135 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1136 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1137 {
1138   PetscErrorCode ierr;
1139 
1140   PetscFunctionBegin;
1141   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1142   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1143   PetscFunctionReturn(0);
1144 }
1145 
1146 #undef __FUNCT__
1147 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1148 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1149 {
1150   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1151   PetscErrorCode ierr;
1152   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1153   MatScalar      *aa;
1154   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1155   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1156 
1157   PetscFunctionBegin;
1158   if (!cm || !cn) PetscFunctionReturn(0);
1159   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);
1160   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);
1161   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);
1162   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1163   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1164   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1165   for (col=0; col<cn-4; col += 4){  /* over columns of C */
1166     colam = col*am;
1167     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1168       r1 = r2 = r3 = r4 = 0.0;
1169       n   = a->i[i+1] - a->i[i];
1170       aj  = a->j + a->i[i];
1171       aa  = a->a + a->i[i];
1172       for (j=0; j<n; j++) {
1173         r1 += (*aa)*b1[*aj];
1174         r2 += (*aa)*b2[*aj];
1175         r3 += (*aa)*b3[*aj];
1176         r4 += (*aa++)*b4[*aj++];
1177       }
1178       c[colam + i]       = r1;
1179       c[colam + am + i]  = r2;
1180       c[colam + am2 + i] = r3;
1181       c[colam + am3 + i] = r4;
1182     }
1183     b1 += bm4;
1184     b2 += bm4;
1185     b3 += bm4;
1186     b4 += bm4;
1187   }
1188   for (;col<cn; col++){     /* over extra columns of C */
1189     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1190       r1 = 0.0;
1191       n   = a->i[i+1] - a->i[i];
1192       aj  = a->j + a->i[i];
1193       aa  = a->a + a->i[i];
1194 
1195       for (j=0; j<n; j++) {
1196         r1 += (*aa++)*b1[*aj++];
1197       }
1198       c[col*am + i]     = r1;
1199     }
1200     b1 += bm;
1201   }
1202   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1203   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1204   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1205   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1206   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1207   PetscFunctionReturn(0);
1208 }
1209 
1210 /*
1211    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1212 */
1213 #undef __FUNCT__
1214 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1215 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1216 {
1217   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1218   PetscErrorCode ierr;
1219   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1220   MatScalar      *aa;
1221   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1222   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1223 
1224   PetscFunctionBegin;
1225   if (!cm || !cn) PetscFunctionReturn(0);
1226   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1227   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1228   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1229 
1230   if (a->compressedrow.use){ /* use compressed row format */
1231     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1232       colam = col*am;
1233       arm   = a->compressedrow.nrows;
1234       ii    = a->compressedrow.i;
1235       ridx  = a->compressedrow.rindex;
1236       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1237 	r1 = r2 = r3 = r4 = 0.0;
1238 	n   = ii[i+1] - ii[i];
1239 	aj  = a->j + ii[i];
1240 	aa  = a->a + ii[i];
1241 	for (j=0; j<n; j++) {
1242 	  r1 += (*aa)*b1[*aj];
1243 	  r2 += (*aa)*b2[*aj];
1244 	  r3 += (*aa)*b3[*aj];
1245 	  r4 += (*aa++)*b4[*aj++];
1246 	}
1247 	c[colam       + ridx[i]] += r1;
1248 	c[colam + am  + ridx[i]] += r2;
1249 	c[colam + am2 + ridx[i]] += r3;
1250 	c[colam + am3 + ridx[i]] += r4;
1251       }
1252       b1 += bm4;
1253       b2 += bm4;
1254       b3 += bm4;
1255       b4 += bm4;
1256     }
1257     for (;col<cn; col++){     /* over extra columns of C */
1258       colam = col*am;
1259       arm   = a->compressedrow.nrows;
1260       ii    = a->compressedrow.i;
1261       ridx  = a->compressedrow.rindex;
1262       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1263 	r1 = 0.0;
1264 	n   = ii[i+1] - ii[i];
1265 	aj  = a->j + ii[i];
1266 	aa  = a->a + ii[i];
1267 
1268 	for (j=0; j<n; j++) {
1269 	  r1 += (*aa++)*b1[*aj++];
1270 	}
1271 	c[colam + ridx[i]] += r1;
1272       }
1273       b1 += bm;
1274     }
1275   } else {
1276     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1277       colam = col*am;
1278       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1279 	r1 = r2 = r3 = r4 = 0.0;
1280 	n   = a->i[i+1] - a->i[i];
1281 	aj  = a->j + a->i[i];
1282 	aa  = a->a + a->i[i];
1283 	for (j=0; j<n; j++) {
1284 	  r1 += (*aa)*b1[*aj];
1285 	  r2 += (*aa)*b2[*aj];
1286 	  r3 += (*aa)*b3[*aj];
1287 	  r4 += (*aa++)*b4[*aj++];
1288 	}
1289 	c[colam + i]       += r1;
1290 	c[colam + am + i]  += r2;
1291 	c[colam + am2 + i] += r3;
1292 	c[colam + am3 + i] += r4;
1293       }
1294       b1 += bm4;
1295       b2 += bm4;
1296       b3 += bm4;
1297       b4 += bm4;
1298     }
1299     for (;col<cn; col++){     /* over extra columns of C */
1300       colam = col*am;
1301       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1302 	r1 = 0.0;
1303 	n   = a->i[i+1] - a->i[i];
1304 	aj  = a->j + a->i[i];
1305 	aa  = a->a + a->i[i];
1306 
1307 	for (j=0; j<n; j++) {
1308 	  r1 += (*aa++)*b1[*aj++];
1309 	}
1310 	c[colam + i]     += r1;
1311       }
1312       b1 += bm;
1313     }
1314   }
1315   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1316   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1317   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1318   PetscFunctionReturn(0);
1319 }
1320 
1321 #undef __FUNCT__
1322 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1323 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1324 {
1325   PetscErrorCode ierr;
1326   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
1327   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1328   PetscInt       *bi=b->i,*bj=b->j;
1329   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1330   MatScalar      *btval,*btval_den,*ba=b->a;
1331   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1332 
1333   PetscFunctionBegin;
1334   btval_den=btdense->v;
1335   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1336   for (k=0; k<ncolors; k++) {
1337     ncolumns = coloring->ncolumns[k];
1338     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1339       col   = *(columns + colorforcol[k] + l);
1340       btcol = bj + bi[col];
1341       btval = ba + bi[col];
1342       anz   = bi[col+1] - bi[col];
1343       for (j=0; j<anz; j++){
1344         brow            = btcol[j];
1345         btval_den[brow] = btval[j];
1346       }
1347     }
1348     btval_den += m;
1349   }
1350   PetscFunctionReturn(0);
1351 }
1352 
1353 #undef __FUNCT__
1354 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1355 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1356 {
1357   PetscErrorCode ierr;
1358   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1359   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1360   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1361   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1362 
1363   PetscFunctionBegin;
1364   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1365   ierr = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1366   cp_den = ca_den;
1367   for (k=0; k<ncolors; k++) {
1368     nrows = matcoloring->nrows[k];
1369     row   = rows  + colorforrow[k];
1370     idx   = spidx + colorforrow[k];
1371     for (l=0; l<nrows; l++){
1372       ca[idx[l]] = cp_den[row[l]];
1373     }
1374     cp_den += m;
1375   }
1376   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 /*
1381  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1382  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1383  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1384  */
1385 #undef __FUNCT__
1386 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1387 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1388 {
1389   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1390   PetscErrorCode ierr;
1391   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1392   PetscInt       nz = a->i[m],row,*jj,mr,col;
1393   PetscInt       *cspidx;
1394 
1395   PetscFunctionBegin;
1396   *nn = n;
1397   if (!ia) PetscFunctionReturn(0);
1398   if (symmetric) {
1399     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1400     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1401   } else {
1402     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1403     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1404     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1405     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1406     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1407     jj = a->j;
1408     for (i=0; i<nz; i++) {
1409       collengths[jj[i]]++;
1410     }
1411     cia[0] = oshift;
1412     for (i=0; i<n; i++) {
1413       cia[i+1] = cia[i] + collengths[i];
1414     }
1415     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1416     jj   = a->j;
1417     for (row=0; row<m; row++) {
1418       mr = a->i[row+1] - a->i[row];
1419       for (i=0; i<mr; i++) {
1420         col = *jj++;
1421         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1422         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
1423       }
1424     }
1425     ierr = PetscFree(collengths);CHKERRQ(ierr);
1426     *ia = cia; *ja = cja;
1427     *spidx = cspidx;
1428   }
1429   PetscFunctionReturn(0);
1430 }
1431 
1432 #undef __FUNCT__
1433 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1434 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1435 {
1436   PetscErrorCode ierr;
1437 
1438   PetscFunctionBegin;
1439   if (!ia) PetscFunctionReturn(0);
1440 
1441   ierr = PetscFree(*ia);CHKERRQ(ierr);
1442   ierr = PetscFree(*ja);CHKERRQ(ierr);
1443   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1444   PetscFunctionReturn(0);
1445 }
1446 
1447 #undef __FUNCT__
1448 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1449 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1450 {
1451   PetscErrorCode ierr;
1452   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
1453   const PetscInt *is,*ci,*cj,*row_idx;
1454   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1455   IS             *isa;
1456   PetscBool      flg1,flg2;
1457   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1458   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1459   PetscInt       *colorforcol,*columns,*columns_i;
1460 
1461   PetscFunctionBegin;
1462   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1463 
1464   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1465   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1466   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1467   if (flg1 || flg2) {
1468     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1469   }
1470 
1471   N         = mat->cmap->N/bs;
1472   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1473   c->N      = mat->cmap->N/bs;
1474   c->m      = mat->rmap->N/bs;
1475   c->rstart = 0;
1476 
1477   c->ncolors = nis;
1478   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1479   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1480   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1481   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1482   colorforrow[0]    = 0;
1483   rows_i            = rows;
1484   columnsforspidx_i = columnsforspidx;
1485 
1486   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1487   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1488   colorforcol[0] = 0;
1489   columns_i      = columns;
1490 
1491   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1492 
1493   cm = c->m;
1494   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1495   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1496   for (i=0; i<nis; i++) {
1497     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1498     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1499     c->ncolumns[i] = n;
1500     if (n) {
1501       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1502     }
1503     colorforcol[i+1] = colorforcol[i] + n;
1504     columns_i       += n;
1505 
1506     /* fast, crude version requires O(N*N) work */
1507     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1508 
1509     /* loop over columns*/
1510     for (j=0; j<n; j++) {
1511       col     = is[j];
1512       row_idx = cj + ci[col];
1513       m       = ci[col+1] - ci[col];
1514       /* loop over columns marking them in rowhit */
1515       for (k=0; k<m; k++) {
1516         idxhit[*row_idx]   = spidx[ci[col] + k];
1517         rowhit[*row_idx++] = col + 1;
1518       }
1519     }
1520     /* count the number of hits */
1521     nrows = 0;
1522     for (j=0; j<cm; j++) {
1523       if (rowhit[j]) nrows++;
1524     }
1525     c->nrows[i]      = nrows;
1526     colorforrow[i+1] = colorforrow[i] + nrows;
1527 
1528     nrows       = 0;
1529     for (j=0; j<cm; j++) {
1530       if (rowhit[j]) {
1531         rows_i[nrows]            = j;
1532         columnsforspidx_i[nrows] = idxhit[j];
1533         nrows++;
1534       }
1535     }
1536     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1537     rows_i += nrows; columnsforspidx_i += nrows;
1538   }
1539   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr);
1540   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1541   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1542 #if defined(PETSC_USE_DEBUG)
1543   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1544 #endif
1545 
1546   c->colorforrow     = colorforrow;
1547   c->rows            = rows;
1548   c->columnsforspidx = columnsforspidx;
1549   c->colorforcol     = colorforcol;
1550   c->columns         = columns;
1551   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1552   PetscFunctionReturn(0);
1553 }
1554