xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 2205254efee3a00a594e5e2a3a70f74dcb40bc03)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = A * B
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <../src/mat/utils/petscheap.h>
10 #include <petscbt.h>
11 #include <../src/mat/impls/dense/seq/dense.h>
12 
13 #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     if (scalable_fast) {
29       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
30     } else if (scalable) {
31       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
32     } else if (heap) {
33       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
34     } else if (btheap) {
35       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
36     } else {
37       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
38     }
39   }
40 
41   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
42   PetscFunctionReturn(0);
43 }
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
47 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
48 {
49   PetscErrorCode     ierr;
50   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
51   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
52   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
53   PetscReal          afill;
54   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
55   PetscBT            lnkbt;
56   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
57 
58   PetscFunctionBegin;
59   /* Get ci and cj */
60   /*---------------*/
61   /* Allocate ci array, arrays for fill computation and */
62   /* free space for accumulating nonzero column info */
63   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
64   ci[0] = 0;
65 
66   /* create and initialize a linked list */
67   nlnk_max = a->rmax*b->rmax;
68   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
69   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
70 
71   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
72   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
73 
74   current_space = free_space;
75 
76   /* Determine ci and cj */
77   for (i=0; i<am; i++) {
78     anzi = ai[i+1] - ai[i];
79     aj   = a->j + ai[i];
80     for (j=0; j<anzi; j++) {
81       brow = aj[j];
82       bnzj = bi[brow+1] - bi[brow];
83       bj   = b->j + bi[brow];
84       /* add non-zero cols of B into the sorted linked list lnk */
85       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
86     }
87     cnzi = lnk[0];
88 
89     /* If free space is not available, make more free space */
90     /* Double the amount of total space in the list */
91     if (current_space->local_remaining<cnzi) {
92       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
93       ndouble++;
94     }
95 
96     /* Copy data into free space, then initialize lnk */
97     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
98 
99     current_space->array           += cnzi;
100     current_space->local_used      += cnzi;
101     current_space->local_remaining -= cnzi;
102 
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 
116   (*C)->rmap->bs = A->rmap->bs;
117   (*C)->cmap->bs = B->cmap->bs;
118 
119   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
120   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
121   c                         = (Mat_SeqAIJ*)((*C)->data);
122   c->free_a                 = PETSC_FALSE;
123   c->free_ij                = PETSC_TRUE;
124   c->nonew                  = 0;
125   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
126 
127   /* set MatInfo */
128   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
129   if (afill < 1.0) afill = 1.0;
130   c->maxnz                     = ci[am];
131   c->nz                        = ci[am];
132   (*C)->info.mallocs           = ndouble;
133   (*C)->info.fill_ratio_given  = fill;
134   (*C)->info.fill_ratio_needed = afill;
135 
136 #if defined(PETSC_USE_INFO)
137   if (ci[am]) {
138     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
139     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
140   } else {
141     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
142   }
143 #endif
144   PetscFunctionReturn(0);
145 }
146 
147 #undef __FUNCT__
148 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
149 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
150 {
151   PetscErrorCode ierr;
152   PetscLogDouble flops=0.0;
153   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
154   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
155   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
156   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
157   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
158   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
159   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
160   PetscScalar    *ab_dense;
161 
162   PetscFunctionBegin;
163   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
164   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
165     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
166     c->a      = ca;
167     c->free_a = PETSC_TRUE;
168 
169     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
170     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
171 
172     c->matmult_abdense = ab_dense;
173   } else {
174     ca       = c->a;
175     ab_dense = c->matmult_abdense;
176   }
177 
178   /* clean old values in C */
179   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
180   /* Traverse A row-wise. */
181   /* Build the ith row in C by summing over nonzero columns in A, */
182   /* the rows of B corresponding to nonzeros of A. */
183   for (i=0; i<am; i++) {
184     anzi = ai[i+1] - ai[i];
185     for (j=0; j<anzi; j++) {
186       brow = aj[j];
187       bnzi = bi[brow+1] - bi[brow];
188       bjj  = bj + bi[brow];
189       baj  = ba + bi[brow];
190       /* perform dense axpy */
191       valtmp = aa[j];
192       for (k=0; k<bnzi; k++) {
193         ab_dense[bjj[k]] += valtmp*baj[k];
194       }
195       flops += 2*bnzi;
196     }
197     aj += anzi; aa += anzi;
198 
199     cnzi = ci[i+1] - ci[i];
200     for (k=0; k<cnzi; k++) {
201       ca[k]          += ab_dense[cj[k]];
202       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
203     }
204     flops += cnzi;
205     cj    += cnzi; ca += cnzi;
206   }
207   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
208   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
209   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
210   PetscFunctionReturn(0);
211 }
212 
213 #undef __FUNCT__
214 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
215 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
216 {
217   PetscErrorCode ierr;
218   PetscLogDouble flops=0.0;
219   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
220   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
221   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
222   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
223   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
224   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
225   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
226   PetscInt       nextb;
227 
228   PetscFunctionBegin;
229   /* clean old values in C */
230   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
231   /* Traverse A row-wise. */
232   /* Build the ith row in C by summing over nonzero columns in A, */
233   /* the rows of B corresponding to nonzeros of A. */
234   for (i=0; i<am; i++) {
235     anzi = ai[i+1] - ai[i];
236     cnzi = ci[i+1] - ci[i];
237     for (j=0; j<anzi; j++) {
238       brow = aj[j];
239       bnzi = bi[brow+1] - bi[brow];
240       bjj  = bj + bi[brow];
241       baj  = ba + bi[brow];
242       /* perform sparse axpy */
243       valtmp = aa[j];
244       nextb  = 0;
245       for (k=0; nextb<bnzi; k++) {
246         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
247           ca[k] += valtmp*baj[nextb++];
248         }
249       }
250       flops += 2*bnzi;
251     }
252     aj += anzi; aa += anzi;
253     cj += cnzi; ca += cnzi;
254   }
255 
256   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
257   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
258   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
259   PetscFunctionReturn(0);
260 }
261 
262 #undef __FUNCT__
263 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
264 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
265 {
266   PetscErrorCode     ierr;
267   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
268   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
269   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
270   MatScalar          *ca;
271   PetscReal          afill;
272   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
273   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
274 
275   PetscFunctionBegin;
276   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
277   /*-----------------------------------------------------------------------------------------*/
278   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
279   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
280   ci[0] = 0;
281 
282   /* create and initialize a linked list */
283   nlnk_max = a->rmax*b->rmax;
284   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
285   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
286 
287   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
288   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
289   current_space = free_space;
290 
291   /* Determine ci and cj */
292   for (i=0; i<am; i++) {
293     anzi = ai[i+1] - ai[i];
294     aj   = a->j + ai[i];
295     for (j=0; j<anzi; j++) {
296       brow = aj[j];
297       bnzj = bi[brow+1] - bi[brow];
298       bj   = b->j + bi[brow];
299       /* add non-zero cols of B into the sorted linked list lnk */
300       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
301     }
302     cnzi = lnk[1];
303 
304     /* If free space is not available, make more free space */
305     /* Double the amount of total space in the list */
306     if (current_space->local_remaining<cnzi) {
307       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
308       ndouble++;
309     }
310 
311     /* Copy data into free space, then initialize lnk */
312     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
313 
314     current_space->array           += cnzi;
315     current_space->local_used      += cnzi;
316     current_space->local_remaining -= cnzi;
317 
318     ci[i+1] = ci[i] + cnzi;
319   }
320 
321   /* Column indices are in the list of free space */
322   /* Allocate space for cj, initialize cj, and */
323   /* destroy list of free space and other temporary array(s) */
324   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
325   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
326   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
327 
328   /* Allocate space for ca */
329   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
330   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
331 
332   /* put together the new symbolic matrix */
333   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
334 
335   (*C)->rmap->bs = A->rmap->bs;
336   (*C)->cmap->bs = B->cmap->bs;
337 
338   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
339   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
340   c          = (Mat_SeqAIJ*)((*C)->data);
341   c->free_a  = PETSC_TRUE;
342   c->free_ij = PETSC_TRUE;
343   c->nonew   = 0;
344 
345   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
346 
347   /* set MatInfo */
348   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
349   if (afill < 1.0) afill = 1.0;
350   c->maxnz                     = ci[am];
351   c->nz                        = ci[am];
352   (*C)->info.mallocs           = ndouble;
353   (*C)->info.fill_ratio_given  = fill;
354   (*C)->info.fill_ratio_needed = afill;
355 
356 #if defined(PETSC_USE_INFO)
357   if (ci[am]) {
358     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
359     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
360   } else {
361     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
362   }
363 #endif
364   PetscFunctionReturn(0);
365 }
366 
367 
368 #undef __FUNCT__
369 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
370 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
371 {
372   PetscErrorCode     ierr;
373   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
374   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
375   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
376   MatScalar          *ca;
377   PetscReal          afill;
378   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
379   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
380 
381   PetscFunctionBegin;
382   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
383   /*---------------------------------------------------------------------------------------------*/
384   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
385   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
386   ci[0] = 0;
387 
388   /* create and initialize a linked list */
389   nlnk_max = a->rmax*b->rmax;
390   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
391   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
392 
393   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
394   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
395   current_space = free_space;
396 
397   /* Determine ci and cj */
398   for (i=0; i<am; i++) {
399     anzi = ai[i+1] - ai[i];
400     aj   = a->j + ai[i];
401     for (j=0; j<anzi; j++) {
402       brow = aj[j];
403       bnzj = bi[brow+1] - bi[brow];
404       bj   = b->j + bi[brow];
405       /* add non-zero cols of B into the sorted linked list lnk */
406       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
407     }
408     cnzi = lnk[0];
409 
410     /* If free space is not available, make more free space */
411     /* Double the amount of total space in the list */
412     if (current_space->local_remaining<cnzi) {
413       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
414       ndouble++;
415     }
416 
417     /* Copy data into free space, then initialize lnk */
418     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
419 
420     current_space->array           += cnzi;
421     current_space->local_used      += cnzi;
422     current_space->local_remaining -= cnzi;
423 
424     ci[i+1] = ci[i] + cnzi;
425   }
426 
427   /* Column indices are in the list of free space */
428   /* Allocate space for cj, initialize cj, and */
429   /* destroy list of free space and other temporary array(s) */
430   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
431   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
432   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
433 
434   /* Allocate space for ca */
435   /*-----------------------*/
436   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
437   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
438 
439   /* put together the new symbolic matrix */
440   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
441 
442   (*C)->rmap->bs = A->rmap->bs;
443   (*C)->cmap->bs = B->cmap->bs;
444 
445   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
446   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
447   c          = (Mat_SeqAIJ*)((*C)->data);
448   c->free_a  = PETSC_TRUE;
449   c->free_ij = PETSC_TRUE;
450   c->nonew   = 0;
451 
452   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
453 
454   /* set MatInfo */
455   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
456   if (afill < 1.0) afill = 1.0;
457   c->maxnz                     = ci[am];
458   c->nz                        = ci[am];
459   (*C)->info.mallocs           = ndouble;
460   (*C)->info.fill_ratio_given  = fill;
461   (*C)->info.fill_ratio_needed = afill;
462 
463 #if defined(PETSC_USE_INFO)
464   if (ci[am]) {
465     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
466     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
467   } else {
468     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
469   }
470 #endif
471   PetscFunctionReturn(0);
472 }
473 
474 #undef __FUNCT__
475 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
476 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
477 {
478   PetscErrorCode     ierr;
479   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
480   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
481   PetscInt           *ci,*cj,*bb;
482   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
483   PetscReal          afill;
484   PetscInt           i,j,col,ndouble = 0;
485   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
486   PetscHeap          h;
487 
488   PetscFunctionBegin;
489   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
490   /*---------------------------------------------------------------------------------------------*/
491   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
492   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
493   ci[0] = 0;
494 
495   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
496   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
497   current_space = free_space;
498 
499   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
500   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
501 
502   /* Determine ci and cj */
503   for (i=0; i<am; i++) {
504     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 */
505     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
506     ci[i+1] = ci[i];
507     /* Populate the min heap */
508     for (j=0; j<anzi; j++) {
509       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
510       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
511         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
512       }
513     }
514     /* Pick off the min element, adding it to free space */
515     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
516     while (j >= 0) {
517       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
518         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
519         ndouble++;
520       }
521       *(current_space->array++) = col;
522       current_space->local_used++;
523       current_space->local_remaining--;
524       ci[i+1]++;
525 
526       /* stash if anything else remains in this row of B */
527       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
528       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
529         PetscInt j2,col2;
530         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
531         if (col2 != col) break;
532         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
533         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
534       }
535       /* Put any stashed elements back into the min heap */
536       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
537       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
538     }
539   }
540   ierr = PetscFree(bb);CHKERRQ(ierr);
541   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
542 
543   /* Column indices are in the list of free space */
544   /* Allocate space for cj, initialize cj, and */
545   /* destroy list of free space and other temporary array(s) */
546   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
547   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
548 
549   /* put together the new symbolic matrix */
550   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
551 
552   (*C)->rmap->bs = A->rmap->bs;
553   (*C)->cmap->bs = B->cmap->bs;
554 
555   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
556   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
557   c          = (Mat_SeqAIJ*)((*C)->data);
558   c->free_a  = PETSC_TRUE;
559   c->free_ij = PETSC_TRUE;
560   c->nonew   = 0;
561   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
562 
563   /* set MatInfo */
564   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
565   if (afill < 1.0) afill = 1.0;
566   c->maxnz                     = ci[am];
567   c->nz                        = ci[am];
568   (*C)->info.mallocs           = ndouble;
569   (*C)->info.fill_ratio_given  = fill;
570   (*C)->info.fill_ratio_needed = afill;
571 
572 #if defined(PETSC_USE_INFO)
573   if (ci[am]) {
574     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
575     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
576   } else {
577     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
578   }
579 #endif
580   PetscFunctionReturn(0);
581 }
582 
583 #undef __FUNCT__
584 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
585 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
586 {
587   PetscErrorCode     ierr;
588   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
589   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
590   PetscInt           *ci,*cj,*bb;
591   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
592   PetscReal          afill;
593   PetscInt           i,j,col,ndouble = 0;
594   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
595   PetscHeap          h;
596   PetscBT            bt;
597 
598   PetscFunctionBegin;
599   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
600   /*---------------------------------------------------------------------------------------------*/
601   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
602   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
603   ci[0] = 0;
604 
605   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
606   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
607 
608   current_space = free_space;
609 
610   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
611   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
612   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
613 
614   /* Determine ci and cj */
615   for (i=0; i<am; i++) {
616     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 */
617     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
618     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
619     ci[i+1] = ci[i];
620     /* Populate the min heap */
621     for (j=0; j<anzi; j++) {
622       PetscInt brow = acol[j];
623       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
624         PetscInt bcol = bj[bb[j]];
625         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
626           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
627           bb[j]++;
628           break;
629         }
630       }
631     }
632     /* Pick off the min element, adding it to free space */
633     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
634     while (j >= 0) {
635       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
636         fptr = PETSC_NULL;                      /* need PetscBTMemzero */
637         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
638         ndouble++;
639       }
640       *(current_space->array++) = col;
641       current_space->local_used++;
642       current_space->local_remaining--;
643       ci[i+1]++;
644 
645       /* stash if anything else remains in this row of B */
646       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
647         PetscInt bcol = bj[bb[j]];
648         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
649           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
650           bb[j]++;
651           break;
652         }
653       }
654       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
655     }
656     if (fptr) {                 /* Clear the bits for this row */
657       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
658     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
659       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
660     }
661   }
662   ierr = PetscFree(bb);CHKERRQ(ierr);
663   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
664   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
665 
666   /* Column indices are in the list of free space */
667   /* Allocate space for cj, initialize cj, and */
668   /* destroy list of free space and other temporary array(s) */
669   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
670   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
671 
672   /* put together the new symbolic matrix */
673   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
674 
675   (*C)->rmap->bs = A->rmap->bs;
676   (*C)->cmap->bs = B->cmap->bs;
677 
678   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
679   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
680   c          = (Mat_SeqAIJ*)((*C)->data);
681   c->free_a  = PETSC_TRUE;
682   c->free_ij = PETSC_TRUE;
683   c->nonew   = 0;
684   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
685 
686   /* set MatInfo */
687   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
688   if (afill < 1.0) afill = 1.0;
689   c->maxnz                     = ci[am];
690   c->nz                        = ci[am];
691   (*C)->info.mallocs           = ndouble;
692   (*C)->info.fill_ratio_given  = fill;
693   (*C)->info.fill_ratio_needed = afill;
694 
695 #if defined(PETSC_USE_INFO)
696   if (ci[am]) {
697     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
698     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
699   } else {
700     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
701   }
702 #endif
703   PetscFunctionReturn(0);
704 }
705 
706 /* This routine is not used. Should be removed! */
707 #undef __FUNCT__
708 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
709 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
710 {
711   PetscErrorCode ierr;
712 
713   PetscFunctionBegin;
714   if (scall == MAT_INITIAL_MATRIX) {
715     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
716   }
717   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
718   PetscFunctionReturn(0);
719 }
720 
721 #undef __FUNCT__
722 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
723 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
724 {
725   PetscErrorCode      ierr;
726   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
727 
728   PetscFunctionBegin;
729   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
730   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
731   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
732   ierr = PetscFree(multtrans);CHKERRQ(ierr);
733   PetscFunctionReturn(0);
734 }
735 
736 #undef __FUNCT__
737 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
738 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
739 {
740   PetscErrorCode      ierr;
741   PetscContainer      container;
742   Mat_MatMatTransMult *multtrans=PETSC_NULL;
743 
744   PetscFunctionBegin;
745   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject*)&container);CHKERRQ(ierr);
746   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
747   ierr = PetscContainerGetPointer(container,(void**)&multtrans);CHKERRQ(ierr);
748 
749   A->ops->destroy = multtrans->destroy;
750   if (A->ops->destroy) {
751     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
752   }
753   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
754   PetscFunctionReturn(0);
755 }
756 
757 #undef __FUNCT__
758 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
759 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
760 {
761   PetscErrorCode      ierr;
762   Mat                 Bt;
763   PetscInt            *bti,*btj;
764   Mat_MatMatTransMult *multtrans;
765   PetscContainer      container;
766 
767   PetscFunctionBegin;
768    /* create symbolic Bt */
769   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
770   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
771 
772   Bt->rmap->bs = A->cmap->bs;
773   Bt->cmap->bs = B->cmap->bs;
774 
775   /* get symbolic C=A*Bt */
776   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
777 
778   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
779   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
780 
781   /* attach the supporting struct to C */
782   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
783   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
784   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
785   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
786   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
787 
788   multtrans->usecoloring = PETSC_FALSE;
789   multtrans->destroy     = (*C)->ops->destroy;
790   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
791 
792   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
793   if (multtrans->usecoloring) {
794     /* Create MatTransposeColoring from symbolic C=A*B^T */
795     MatTransposeColoring matcoloring;
796     ISColoring           iscoloring;
797     Mat                  Bt_dense,C_dense;
798 
799     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
800     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
801 
802     multtrans->matcoloring = matcoloring;
803 
804     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
805 
806     /* Create Bt_dense and C_dense = A*Bt_dense */
807     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
808     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
809     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
810     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
811 
812     Bt_dense->assembled = PETSC_TRUE;
813     multtrans->Bt_den   = Bt_dense;
814 
815     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
816     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
817     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
818     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
819 
820     Bt_dense->assembled = PETSC_TRUE;
821     multtrans->ABt_den  = C_dense;
822 
823 #if defined(PETSC_USE_INFO)
824     {
825       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
826       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));CHKERRQ(ierr);
827     }
828 #endif
829   }
830   /* clean up */
831   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
832   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
833 
834 
835 
836 #if defined(INEFFICIENT_ALGORITHM)
837   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
838   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
839   Mat_SeqAIJ         *a        =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
840   PetscInt           *ai       =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
841   PetscInt           am        =A->rmap->N,bm=B->rmap->N;
842   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
843   MatScalar          *ca;
844   PetscBT            lnkbt;
845   PetscReal          afill;
846 
847   /* Allocate row pointer array ci  */
848   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
849   ci[0] = 0;
850 
851   /* Create and initialize a linked list for C columns */
852   nlnk = bm+1;
853   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
854 
855   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
856   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
857   current_space = free_space;
858 
859   /* Determine symbolic info for each row of the product A*B^T: */
860   for (i=0; i<am; i++) {
861     anzi = ai[i+1] - ai[i];
862     cnzi = 0;
863     acol = aj + ai[i];
864     for (j=0; j<bm; j++) {
865       bnzj = bi[j+1] - bi[j];
866       bcol = bj + bi[j];
867       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
868       ka = 0; kb = 0;
869       while (ka < anzi && kb < bnzj) {
870         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
871         if (ka == anzi) break;
872         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
873         if (kb == bnzj) break;
874         if (acol[ka] == bcol[kb]) { /* add nonzero c(i,j) to lnk */
875           index[0] = j;
876           ierr     = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
877           cnzi++;
878           break;
879         }
880       }
881     }
882 
883     /* If free space is not available, make more free space */
884     /* Double the amount of total space in the list */
885     if (current_space->local_remaining<cnzi) {
886       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
887       nspacedouble++;
888     }
889 
890     /* Copy data into free space, then initialize lnk */
891     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
892 
893     current_space->array           += cnzi;
894     current_space->local_used      += cnzi;
895     current_space->local_remaining -= cnzi;
896 
897     ci[i+1] = ci[i] + cnzi;
898   }
899 
900 
901   /* Column indices are in the list of free space.
902      Allocate array cj, copy column indices to cj, and destroy list of free space */
903   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
904   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
905   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
906 
907   /* Allocate space for ca */
908   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
909   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
910 
911   /* put together the new symbolic matrix */
912   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
913 
914   (*C)->rmap->bs = A->cmap->bs;
915   (*C)->cmap->bs = B->cmap->bs;
916 
917   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
918   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
919   c          = (Mat_SeqAIJ*)((*C)->data);
920   c->free_a  = PETSC_TRUE;
921   c->free_ij = PETSC_TRUE;
922   c->nonew   = 0;
923 
924   /* set MatInfo */
925   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
926   if (afill < 1.0) afill = 1.0;
927   c->maxnz                     = ci[am];
928   c->nz                        = ci[am];
929   (*C)->info.mallocs           = nspacedouble;
930   (*C)->info.fill_ratio_given  = fill;
931   (*C)->info.fill_ratio_needed = afill;
932 
933 #if defined(PETSC_USE_INFO)
934   if (ci[am]) {
935     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
936     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
937   } else {
938     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
939   }
940 #endif
941 #endif
942   PetscFunctionReturn(0);
943 }
944 
945 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
946 #undef __FUNCT__
947 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
948 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
949 {
950   PetscErrorCode      ierr;
951   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
952   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
953   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
954   PetscLogDouble      flops=0.0;
955   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
956   Mat_MatMatTransMult *multtrans;
957   PetscContainer      container;
958 #if defined(USE_ARRAY)
959   MatScalar *spdot;
960 #endif
961 
962   PetscFunctionBegin;
963   /* clear old values in C */
964   if (!c->a) {
965     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
966     c->a      = ca;
967     c->free_a = PETSC_TRUE;
968   } else {
969     ca =  c->a;
970   }
971   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
972 
973   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject*)&container);CHKERRQ(ierr);
974   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
975   ierr = PetscContainerGetPointer(container,(void**)&multtrans);CHKERRQ(ierr);
976   if (multtrans->usecoloring) {
977     MatTransposeColoring matcoloring = multtrans->matcoloring;
978     Mat                  Bt_dense;
979     PetscInt             m,n;
980     Mat                  C_dense = multtrans->ABt_den;
981 
982     Bt_dense = multtrans->Bt_den;
983     ierr     = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
984 
985     /* Get Bt_dense by Apply MatTransposeColoring to B */
986     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
987 
988     /* C_dense = A*Bt_dense */
989     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
990 
991     /* Recover C from C_dense */
992     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
993     PetscFunctionReturn(0);
994   }
995 
996 #if defined(USE_ARRAY)
997   /* allocate an array for implementing sparse inner-product */
998   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
999   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
1000 #endif
1001 
1002   for (i=0; i<cm; i++) {
1003     anzi = ai[i+1] - ai[i];
1004     acol = aj + ai[i];
1005     aval = aa + ai[i];
1006     cnzi = ci[i+1] - ci[i];
1007     ccol = cj + ci[i];
1008     cval = ca + ci[i];
1009     for (j=0; j<cnzi; j++) {
1010       brow = ccol[j];
1011       bnzj = bi[brow+1] - bi[brow];
1012       bcol = bj + bi[brow];
1013       bval = ba + bi[brow];
1014 
1015       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1016 #if defined(USE_ARRAY)
1017       /* put ba to spdot array */
1018       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
1019       /* c(i,j)=A[i,:]*B[j,:]^T */
1020       for (nexta=0; nexta<anzi; nexta++) {
1021         cval[j] += spdot[acol[nexta]]*aval[nexta];
1022       }
1023       /* zero spdot array */
1024       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1025 #else
1026       nexta = 0; nextb = 0;
1027       while (nexta<anzi && nextb<bnzj) {
1028         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
1029         if (nexta == anzi) break;
1030         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
1031         if (nextb == bnzj) break;
1032         if (acol[nexta] == bcol[nextb]) {
1033           cval[j] += aval[nexta]*bval[nextb];
1034           nexta++; nextb++;
1035           flops += 2;
1036         }
1037       }
1038 #endif
1039     }
1040   }
1041   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1042   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1043   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1044 #if defined(USE_ARRAY)
1045   ierr = PetscFree(spdot);
1046 #endif
1047   PetscFunctionReturn(0);
1048 }
1049 
1050 #undef __FUNCT__
1051 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1052 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1053 {
1054   PetscErrorCode ierr;
1055 
1056   PetscFunctionBegin;
1057   if (scall == MAT_INITIAL_MATRIX) {
1058     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1059   }
1060   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1061   PetscFunctionReturn(0);
1062 }
1063 
1064 #undef __FUNCT__
1065 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1066 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1067 {
1068   PetscErrorCode ierr;
1069   Mat            At;
1070   PetscInt       *ati,*atj;
1071 
1072   PetscFunctionBegin;
1073   /* create symbolic At */
1074   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1075   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
1076 
1077   At->rmap->bs = A->cmap->bs;
1078   At->cmap->bs = B->cmap->bs;
1079 
1080   /* get symbolic C=At*B */
1081   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1082 
1083   /* clean up */
1084   ierr = MatDestroy(&At);CHKERRQ(ierr);
1085   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1086   PetscFunctionReturn(0);
1087 }
1088 
1089 #undef __FUNCT__
1090 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1091 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1092 {
1093   PetscErrorCode ierr;
1094   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1095   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1096   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1097   PetscLogDouble flops=0.0;
1098   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1099 
1100   PetscFunctionBegin;
1101   if (!c->a) {
1102     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1103 
1104     c->a      = ca;
1105     c->free_a = PETSC_TRUE;
1106   } else {
1107     ca = c->a;
1108   }
1109   /* clear old values in C */
1110   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1111 
1112   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1113   for (i=0; i<am; i++) {
1114     bj   = b->j + bi[i];
1115     ba   = b->a + bi[i];
1116     bnzi = bi[i+1] - bi[i];
1117     anzi = ai[i+1] - ai[i];
1118     for (j=0; j<anzi; j++) {
1119       nextb = 0;
1120       crow  = *aj++;
1121       cjj   = cj + ci[crow];
1122       caj   = ca + ci[crow];
1123       /* perform sparse axpy operation.  Note cjj includes bj. */
1124       for (k=0; nextb<bnzi; k++) {
1125         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1126           caj[k] += (*aa)*(*(ba+nextb));
1127           nextb++;
1128         }
1129       }
1130       flops += 2*bnzi;
1131       aa++;
1132     }
1133   }
1134 
1135   /* Assemble the final matrix and clean up */
1136   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1137   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1138   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1139   PetscFunctionReturn(0);
1140 }
1141 
1142 EXTERN_C_BEGIN
1143 #undef __FUNCT__
1144 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1145 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1146 {
1147   PetscErrorCode ierr;
1148 
1149   PetscFunctionBegin;
1150   if (scall == MAT_INITIAL_MATRIX) {
1151     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1152   }
1153   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1154   PetscFunctionReturn(0);
1155 }
1156 EXTERN_C_END
1157 
1158 #undef __FUNCT__
1159 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1160 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1161 {
1162   PetscErrorCode ierr;
1163 
1164   PetscFunctionBegin;
1165   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1166 
1167   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1168   PetscFunctionReturn(0);
1169 }
1170 
1171 #undef __FUNCT__
1172 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1173 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1174 {
1175   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1176   PetscErrorCode ierr;
1177   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1178   MatScalar      *aa;
1179   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1180   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1181 
1182   PetscFunctionBegin;
1183   if (!cm || !cn) PetscFunctionReturn(0);
1184   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);
1185   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);
1186   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);
1187   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1188   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1189   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1190   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1191     colam = col*am;
1192     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1193       r1 = r2 = r3 = r4 = 0.0;
1194       n  = a->i[i+1] - a->i[i];
1195       aj = a->j + a->i[i];
1196       aa = a->a + a->i[i];
1197       for (j=0; j<n; j++) {
1198         r1 += (*aa)*b1[*aj];
1199         r2 += (*aa)*b2[*aj];
1200         r3 += (*aa)*b3[*aj];
1201         r4 += (*aa++)*b4[*aj++];
1202       }
1203       c[colam + i]       = r1;
1204       c[colam + am + i]  = r2;
1205       c[colam + am2 + i] = r3;
1206       c[colam + am3 + i] = r4;
1207     }
1208     b1 += bm4;
1209     b2 += bm4;
1210     b3 += bm4;
1211     b4 += bm4;
1212   }
1213   for (; col<cn; col++) {     /* over extra columns of C */
1214     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1215       r1 = 0.0;
1216       n  = a->i[i+1] - a->i[i];
1217       aj = a->j + a->i[i];
1218       aa = a->a + a->i[i];
1219 
1220       for (j=0; j<n; j++) {
1221         r1 += (*aa++)*b1[*aj++];
1222       }
1223       c[col*am + i] = r1;
1224     }
1225     b1 += bm;
1226   }
1227   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1228   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1229   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1230   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1231   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1232   PetscFunctionReturn(0);
1233 }
1234 
1235 /*
1236    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1237 */
1238 #undef __FUNCT__
1239 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1240 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1241 {
1242   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1243   PetscErrorCode ierr;
1244   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1245   MatScalar      *aa;
1246   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1247   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1248 
1249   PetscFunctionBegin;
1250   if (!cm || !cn) PetscFunctionReturn(0);
1251   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1252   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1253   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1254 
1255   if (a->compressedrow.use) { /* use compressed row format */
1256     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1257       colam = col*am;
1258       arm   = a->compressedrow.nrows;
1259       ii    = a->compressedrow.i;
1260       ridx  = a->compressedrow.rindex;
1261       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1262         r1 = r2 = r3 = r4 = 0.0;
1263         n  = ii[i+1] - ii[i];
1264         aj = a->j + ii[i];
1265         aa = a->a + ii[i];
1266         for (j=0; j<n; j++) {
1267           r1 += (*aa)*b1[*aj];
1268           r2 += (*aa)*b2[*aj];
1269           r3 += (*aa)*b3[*aj];
1270           r4 += (*aa++)*b4[*aj++];
1271         }
1272         c[colam       + ridx[i]] += r1;
1273         c[colam + am  + ridx[i]] += r2;
1274         c[colam + am2 + ridx[i]] += r3;
1275         c[colam + am3 + ridx[i]] += r4;
1276       }
1277       b1 += bm4;
1278       b2 += bm4;
1279       b3 += bm4;
1280       b4 += bm4;
1281     }
1282     for (; col<cn; col++) {     /* over extra columns of C */
1283       colam = col*am;
1284       arm   = a->compressedrow.nrows;
1285       ii    = a->compressedrow.i;
1286       ridx  = a->compressedrow.rindex;
1287       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1288         r1 = 0.0;
1289         n  = ii[i+1] - ii[i];
1290         aj = a->j + ii[i];
1291         aa = a->a + ii[i];
1292 
1293         for (j=0; j<n; j++) {
1294           r1 += (*aa++)*b1[*aj++];
1295         }
1296         c[colam + ridx[i]] += r1;
1297       }
1298       b1 += bm;
1299     }
1300   } else {
1301     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1302       colam = col*am;
1303       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1304         r1 = r2 = r3 = r4 = 0.0;
1305         n  = a->i[i+1] - a->i[i];
1306         aj = a->j + a->i[i];
1307         aa = a->a + a->i[i];
1308         for (j=0; j<n; j++) {
1309           r1 += (*aa)*b1[*aj];
1310           r2 += (*aa)*b2[*aj];
1311           r3 += (*aa)*b3[*aj];
1312           r4 += (*aa++)*b4[*aj++];
1313         }
1314         c[colam + i]       += r1;
1315         c[colam + am + i]  += r2;
1316         c[colam + am2 + i] += r3;
1317         c[colam + am3 + i] += r4;
1318       }
1319       b1 += bm4;
1320       b2 += bm4;
1321       b3 += bm4;
1322       b4 += bm4;
1323     }
1324     for (; col<cn; col++) {     /* over extra columns of C */
1325       colam = col*am;
1326       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1327         r1 = 0.0;
1328         n  = a->i[i+1] - a->i[i];
1329         aj = a->j + a->i[i];
1330         aa = a->a + a->i[i];
1331 
1332         for (j=0; j<n; j++) {
1333           r1 += (*aa++)*b1[*aj++];
1334         }
1335         c[colam + i] += r1;
1336       }
1337       b1 += bm;
1338     }
1339   }
1340   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1341   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1342   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1343   PetscFunctionReturn(0);
1344 }
1345 
1346 #undef __FUNCT__
1347 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1348 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1349 {
1350   PetscErrorCode ierr;
1351   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1352   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1353   PetscInt       *bi      = b->i,*bj=b->j;
1354   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1355   MatScalar      *btval,*btval_den,*ba=b->a;
1356   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1357 
1358   PetscFunctionBegin;
1359   btval_den=btdense->v;
1360   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1361   for (k=0; k<ncolors; k++) {
1362     ncolumns = coloring->ncolumns[k];
1363     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1364       col   = *(columns + colorforcol[k] + l);
1365       btcol = bj + bi[col];
1366       btval = ba + bi[col];
1367       anz   = bi[col+1] - bi[col];
1368       for (j=0; j<anz; j++) {
1369         brow            = btcol[j];
1370         btval_den[brow] = btval[j];
1371       }
1372     }
1373     btval_den += m;
1374   }
1375   PetscFunctionReturn(0);
1376 }
1377 
1378 #undef __FUNCT__
1379 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1380 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1381 {
1382   PetscErrorCode ierr;
1383   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1384   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1385   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1386   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1387 
1388   PetscFunctionBegin;
1389   ierr   = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1390   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1391   cp_den = ca_den;
1392   for (k=0; k<ncolors; k++) {
1393     nrows = matcoloring->nrows[k];
1394     row   = rows  + colorforrow[k];
1395     idx   = spidx + colorforrow[k];
1396     for (l=0; l<nrows; l++) {
1397       ca[idx[l]] = cp_den[row[l]];
1398     }
1399     cp_den += m;
1400   }
1401   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1402   PetscFunctionReturn(0);
1403 }
1404 
1405 /*
1406  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1407  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1408  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1409  */
1410 #undef __FUNCT__
1411 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1412 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1413 {
1414   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1415   PetscErrorCode ierr;
1416   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1417   PetscInt       nz = a->i[m],row,*jj,mr,col;
1418   PetscInt       *cspidx;
1419 
1420   PetscFunctionBegin;
1421   *nn = n;
1422   if (!ia) PetscFunctionReturn(0);
1423   if (symmetric) {
1424     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1425     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1426   } else {
1427     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1428     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1429     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1430     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1431     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1432     jj   = a->j;
1433     for (i=0; i<nz; i++) {
1434       collengths[jj[i]]++;
1435     }
1436     cia[0] = oshift;
1437     for (i=0; i<n; i++) {
1438       cia[i+1] = cia[i] + collengths[i];
1439     }
1440     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1441     jj   = a->j;
1442     for (row=0; row<m; row++) {
1443       mr = a->i[row+1] - a->i[row];
1444       for (i=0; i<mr; i++) {
1445         col = *jj++;
1446 
1447         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1448         cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
1449       }
1450     }
1451     ierr   = PetscFree(collengths);CHKERRQ(ierr);
1452     *ia    = cia; *ja = cja;
1453     *spidx = cspidx;
1454   }
1455   PetscFunctionReturn(0);
1456 }
1457 
1458 #undef __FUNCT__
1459 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1460 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1461 {
1462   PetscErrorCode ierr;
1463 
1464   PetscFunctionBegin;
1465   if (!ia) PetscFunctionReturn(0);
1466 
1467   ierr = PetscFree(*ia);CHKERRQ(ierr);
1468   ierr = PetscFree(*ja);CHKERRQ(ierr);
1469   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1470   PetscFunctionReturn(0);
1471 }
1472 
1473 #undef __FUNCT__
1474 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1475 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1476 {
1477   PetscErrorCode ierr;
1478   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
1479   const PetscInt *is,*ci,*cj,*row_idx;
1480   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1481   IS             *isa;
1482   PetscBool      flg1,flg2;
1483   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1484   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1485   PetscInt       *colorforcol,*columns,*columns_i;
1486 
1487   PetscFunctionBegin;
1488   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1489 
1490   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1491   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1492   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1493   if (flg1 || flg2) {
1494     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1495   }
1496 
1497   N         = mat->cmap->N/bs;
1498   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1499   c->N      = mat->cmap->N/bs;
1500   c->m      = mat->rmap->N/bs;
1501   c->rstart = 0;
1502 
1503   c->ncolors = nis;
1504   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1505   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1506   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1507   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1508 
1509   colorforrow[0]    = 0;
1510   rows_i            = rows;
1511   columnsforspidx_i = columnsforspidx;
1512 
1513   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1514   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1515 
1516   colorforcol[0] = 0;
1517   columns_i      = columns;
1518 
1519   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1520 
1521   cm   = c->m;
1522   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1523   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1524   for (i=0; i<nis; i++) {
1525     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1526     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1527 
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 
1581   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1582   PetscFunctionReturn(0);
1583 }
1584