xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision a790c00499656cdc34e95ec8f15f35cf5f4cdcbb)
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 <petscbt.h>
10 #include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/
11 /*
12 #define DEBUG_MATMATMULT
13  */
14 EXTERN_C_BEGIN
15 #undef __FUNCT__
16 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
17 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
18 {
19   PetscErrorCode ierr;
20   PetscBool      scalable=PETSC_FALSE,scalable_fast=PETSC_FALSE;
21 
22   PetscFunctionBegin;
23   if (scall == MAT_INITIAL_MATRIX){
24     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
25     ierr = PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
26     ierr = PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,PETSC_NULL);CHKERRQ(ierr);
27     ierr = 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 {
34       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
35     }
36     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
37   }
38   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
39   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
40   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
41   PetscFunctionReturn(0);
42 }
43 EXTERN_C_END
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   current_space = free_space;
74 
75   /* Determine ci and cj */
76   for (i=0; i<am; i++) {
77     anzi = ai[i+1] - ai[i];
78     aj   = a->j + ai[i];
79     for (j=0; j<anzi; j++){
80       brow = aj[j];
81       bnzj = bi[brow+1] - bi[brow];
82       bj   = b->j + bi[brow];
83       /* add non-zero cols of B into the sorted linked list lnk */
84       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
85     }
86     cnzi = lnk[0];
87 
88     /* If free space is not available, make more free space */
89     /* Double the amount of total space in the list */
90     if (current_space->local_remaining<cnzi) {
91       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
92       ndouble++;
93     }
94 
95     /* Copy data into free space, then initialize lnk */
96     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
97     current_space->array           += cnzi;
98     current_space->local_used      += cnzi;
99     current_space->local_remaining -= cnzi;
100     ci[i+1] = ci[i] + cnzi;
101   }
102 
103   /* Column indices are in the list of free space */
104   /* Allocate space for cj, initialize cj, and */
105   /* destroy list of free space and other temporary array(s) */
106   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
107   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
108   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
109 
110   /* put together the new symbolic matrix */
111   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
112   (*C)->rmap->bs = A->rmap->bs;
113   (*C)->cmap->bs = B->cmap->bs;
114 
115   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
116   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
117   c = (Mat_SeqAIJ *)((*C)->data);
118   c->free_a  = PETSC_FALSE;
119   c->free_ij = PETSC_TRUE;
120   c->nonew   = 0;
121   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
122 
123   /* set MatInfo */
124   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
125   if (afill < 1.0) afill = 1.0;
126   c->maxnz                     = ci[am];
127   c->nz                        = ci[am];
128   (*C)->info.mallocs           = ndouble;
129   (*C)->info.fill_ratio_given  = fill;
130   (*C)->info.fill_ratio_needed = afill;
131 
132 #if defined(PETSC_USE_INFO)
133   if (ci[am]) {
134     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
135     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
136   } else {
137     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
138   }
139 #endif
140   PetscFunctionReturn(0);
141 }
142 
143 #undef __FUNCT__
144 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
145 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
146 {
147   PetscErrorCode ierr;
148   PetscLogDouble flops=0.0;
149   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
150   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
151   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
152   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
153   PetscInt       am=A->rmap->n,cm=C->rmap->n;
154   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
155   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
156   PetscScalar    *ab_dense;
157 
158   PetscFunctionBegin;
159   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
160   if (!c->a){ /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
161     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
162     c->a      = ca;
163     c->free_a = PETSC_TRUE;
164 
165     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
166     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
167     c->matmult_abdense = ab_dense;
168   } else {
169     ca       = c->a;
170     ab_dense = c->matmult_abdense;
171   }
172 
173   /* clean old values in C */
174   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
175   /* Traverse A row-wise. */
176   /* Build the ith row in C by summing over nonzero columns in A, */
177   /* the rows of B corresponding to nonzeros of A. */
178   for (i=0; i<am; i++) {
179     anzi = ai[i+1] - ai[i];
180     for (j=0; j<anzi; j++) {
181       brow = aj[j];
182       bnzi = bi[brow+1] - bi[brow];
183       bjj  = bj + bi[brow];
184       baj  = ba + bi[brow];
185       /* perform dense axpy */
186       valtmp = aa[j];
187       for (k=0; k<bnzi; k++) {
188         ab_dense[bjj[k]] += valtmp*baj[k];
189       }
190       flops += 2*bnzi;
191     }
192     aj += anzi; aa += anzi;
193 
194     cnzi = ci[i+1] - ci[i];
195     for (k=0; k<cnzi; k++) {
196       ca[k]          += ab_dense[cj[k]];
197       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
198     }
199     flops += cnzi;
200     cj += cnzi; ca += cnzi;
201   }
202   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
203   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
204   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
205   PetscFunctionReturn(0);
206 }
207 
208 #undef __FUNCT__
209 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
210 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
211 {
212   PetscErrorCode ierr;
213   PetscLogDouble flops=0.0;
214   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
215   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
216   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
217   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
218   PetscInt       am=A->rmap->N,cm=C->rmap->N;
219   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
220   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
221   PetscInt       nextb;
222 
223   PetscFunctionBegin;
224 #if defined(DEBUG_MATMATMULT)
225   ierr = PetscPrintf(PETSC_COMM_SELF,"MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable...\n");CHKERRQ(ierr);
226 #endif
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 
465 /* This routine is not used. Should be removed! */
466 #undef __FUNCT__
467 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
468 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
469 {
470   PetscErrorCode ierr;
471 
472   PetscFunctionBegin;
473   if (scall == MAT_INITIAL_MATRIX){
474     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
475   }
476   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
477   PetscFunctionReturn(0);
478 }
479 
480 #undef __FUNCT__
481 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
482 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
483 {
484   PetscErrorCode      ierr;
485   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
486 
487   PetscFunctionBegin;
488   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
489   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
490   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
491   ierr = PetscFree(multtrans);CHKERRQ(ierr);
492   PetscFunctionReturn(0);
493 }
494 
495 #undef __FUNCT__
496 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
497 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
498 {
499   PetscErrorCode      ierr;
500   PetscContainer      container;
501   Mat_MatMatTransMult *multtrans=PETSC_NULL;
502 
503   PetscFunctionBegin;
504   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
505   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
506   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
507   A->ops->destroy   = multtrans->destroy;
508   if (A->ops->destroy) {
509     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
510   }
511   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
512   PetscFunctionReturn(0);
513 }
514 
515 #undef __FUNCT__
516 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
517 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
518 {
519   PetscErrorCode      ierr;
520   Mat                 Bt;
521   PetscInt            *bti,*btj;
522   Mat_MatMatTransMult *multtrans;
523   PetscContainer      container;
524   PetscLogDouble      t0,tf,etime2=0.0;
525 
526   PetscFunctionBegin;
527   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
528    /* create symbolic Bt */
529   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
530   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
531   (*C)->rmap->bs = A->cmap->bs;
532   (*C)->cmap->bs = B->cmap->bs;
533 
534   /* get symbolic C=A*Bt */
535   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
536 
537   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
538   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
539 
540   /* attach the supporting struct to C */
541   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
542   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
543   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
544   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
545   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
546 
547   multtrans->usecoloring = PETSC_FALSE;
548   multtrans->destroy = (*C)->ops->destroy;
549   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
550 
551   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
552   etime2 += tf - t0;
553 
554   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
555   if (multtrans->usecoloring){
556     /* Create MatTransposeColoring from symbolic C=A*B^T */
557     MatTransposeColoring matcoloring;
558     ISColoring           iscoloring;
559     Mat                  Bt_dense,C_dense;
560     PetscLogDouble       etime0=0.0,etime01=0.0,etime1=0.0;
561 
562     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
563     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
564     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
565     etime0 += tf - t0;
566 
567     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
568     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
569     multtrans->matcoloring = matcoloring;
570     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
571     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
572     etime01 += tf - t0;
573 
574     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
575     /* Create Bt_dense and C_dense = A*Bt_dense */
576     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
577     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
578     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
579     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
580     Bt_dense->assembled = PETSC_TRUE;
581     multtrans->Bt_den = Bt_dense;
582 
583     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
584     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
585     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
586     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
587     Bt_dense->assembled = PETSC_TRUE;
588     multtrans->ABt_den = C_dense;
589     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
590     etime1 += tf - t0;
591 
592 #if defined(PETSC_USE_INFO)
593     {
594     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
595     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));
596     ierr = PetscInfo5(*C,"Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
597     }
598 #endif
599   }
600   /* clean up */
601   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
602   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
603 
604 
605 
606 #if defined(INEFFICIENT_ALGORITHM)
607   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
608   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
609   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
610   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
611   PetscInt           am=A->rmap->N,bm=B->rmap->N;
612   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
613   MatScalar          *ca;
614   PetscBT            lnkbt;
615   PetscReal          afill;
616 
617   /* Allocate row pointer array ci  */
618   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
619   ci[0] = 0;
620 
621   /* Create and initialize a linked list for C columns */
622   nlnk = bm+1;
623   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
624 
625   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
626   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
627   current_space = free_space;
628 
629   /* Determine symbolic info for each row of the product A*B^T: */
630   for (i=0; i<am; i++) {
631     anzi = ai[i+1] - ai[i];
632     cnzi = 0;
633     acol = aj + ai[i];
634     for (j=0; j<bm; j++){
635       bnzj = bi[j+1] - bi[j];
636       bcol= bj + bi[j];
637       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
638       ka = 0; kb = 0;
639       while (ka < anzi && kb < bnzj){
640         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
641         if (ka == anzi) break;
642         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
643         if (kb == bnzj) break;
644         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
645           index[0] = j;
646           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
647           cnzi++;
648           break;
649         }
650       }
651     }
652 
653     /* If free space is not available, make more free space */
654     /* Double the amount of total space in the list */
655     if (current_space->local_remaining<cnzi) {
656       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
657       nspacedouble++;
658     }
659 
660     /* Copy data into free space, then initialize lnk */
661     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
662     current_space->array           += cnzi;
663     current_space->local_used      += cnzi;
664     current_space->local_remaining -= cnzi;
665 
666     ci[i+1] = ci[i] + cnzi;
667   }
668 
669 
670   /* Column indices are in the list of free space.
671      Allocate array cj, copy column indices to cj, and destroy list of free space */
672   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
673   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
674   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
675 
676   /* Allocate space for ca */
677   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
678   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
679 
680   /* put together the new symbolic matrix */
681   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
682   (*C)->rmap->bs = A->cmap->bs;
683   (*C)->cmap->bs = B->cmap->bs;
684 
685   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
686   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
687   c = (Mat_SeqAIJ *)((*C)->data);
688   c->free_a   = PETSC_TRUE;
689   c->free_ij  = PETSC_TRUE;
690   c->nonew    = 0;
691 
692   /* set MatInfo */
693   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
694   if (afill < 1.0) afill = 1.0;
695   c->maxnz                     = ci[am];
696   c->nz                        = ci[am];
697   (*C)->info.mallocs           = nspacedouble;
698   (*C)->info.fill_ratio_given  = fill;
699   (*C)->info.fill_ratio_needed = afill;
700 
701 #if defined(PETSC_USE_INFO)
702   if (ci[am]) {
703     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
704     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
705   } else {
706     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
707   }
708 #endif
709 #endif
710   PetscFunctionReturn(0);
711 }
712 
713 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
714 #undef __FUNCT__
715 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
716 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
717 {
718   PetscErrorCode ierr;
719   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
720   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
721   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
722   PetscLogDouble flops=0.0;
723   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca,*cval;
724   Mat_MatMatTransMult *multtrans;
725   PetscContainer      container;
726 #if defined(USE_ARRAY)
727   MatScalar      *spdot;
728 #endif
729 
730   PetscFunctionBegin;
731   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
732   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
733   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
734   if (multtrans->usecoloring){
735     MatTransposeColoring  matcoloring = multtrans->matcoloring;
736     Mat                   Bt_dense;
737     PetscInt              m,n;
738     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
739     Mat C_dense = multtrans->ABt_den;
740 
741     Bt_dense = multtrans->Bt_den;
742     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
743 
744     /* Get Bt_dense by Apply MatTransposeColoring to B */
745     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
746     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
747     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
748     etime0 += tf - t0;
749 
750     /* C_dense = A*Bt_dense */
751     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
752     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
753     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
754     etime2 += tf - t0;
755 
756     /* Recover C from C_dense */
757     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
758     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
759     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
760     etime1 += tf - t0;
761 #if defined(PETSC_USE_INFO)
762     ierr = PetscInfo4(C,"Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
763 #endif
764     PetscFunctionReturn(0);
765   }
766 
767 #if defined(USE_ARRAY)
768   /* allocate an array for implementing sparse inner-product */
769   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
770   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
771 #endif
772 
773   /* clear old values in C */
774   if (!c->a){
775     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
776     c->a      = ca;
777     c->free_a = PETSC_TRUE;
778   } else {
779     ca =  c->a;
780   }
781   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
782 
783   for (i=0; i<cm; i++) {
784     anzi = ai[i+1] - ai[i];
785     acol = aj + ai[i];
786     aval = aa + ai[i];
787     cnzi = ci[i+1] - ci[i];
788     ccol = cj + ci[i];
789     cval = ca + ci[i];
790     for (j=0; j<cnzi; j++){
791       brow = ccol[j];
792       bnzj = bi[brow+1] - bi[brow];
793       bcol = bj + bi[brow];
794       bval = ba + bi[brow];
795 
796       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
797 #if defined(USE_ARRAY)
798       /* put ba to spdot array */
799       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
800       /* c(i,j)=A[i,:]*B[j,:]^T */
801       for (nexta=0; nexta<anzi; nexta++){
802         cval[j] += spdot[acol[nexta]]*aval[nexta];
803       }
804       /* zero spdot array */
805       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
806 #else
807       nexta = 0; nextb = 0;
808       while (nexta<anzi && nextb<bnzj){
809         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
810         if (nexta == anzi) break;
811         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
812         if (nextb == bnzj) break;
813         if (acol[nexta] == bcol[nextb]){
814           cval[j] += aval[nexta]*bval[nextb];
815           nexta++; nextb++;
816           flops += 2;
817         }
818       }
819 #endif
820     }
821   }
822   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
823   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
824   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
825 #if defined(USE_ARRAY)
826   ierr = PetscFree(spdot);
827 #endif
828   PetscFunctionReturn(0);
829 }
830 
831 #undef __FUNCT__
832 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
833 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
834   PetscErrorCode ierr;
835 
836   PetscFunctionBegin;
837   if (scall == MAT_INITIAL_MATRIX){
838     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
839   }
840   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
841   PetscFunctionReturn(0);
842 }
843 
844 #undef __FUNCT__
845 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
846 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
847 {
848   PetscErrorCode ierr;
849   Mat            At;
850   PetscInt       *ati,*atj;
851 
852   PetscFunctionBegin;
853   /* create symbolic At */
854   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
855   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
856   At->rmap->bs = A->cmap->bs;
857   At->cmap->bs = B->cmap->bs;
858 
859   /* get symbolic C=At*B */
860   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
861 
862   /* clean up */
863   ierr = MatDestroy(&At);CHKERRQ(ierr);
864   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
865   PetscFunctionReturn(0);
866 }
867 
868 #undef __FUNCT__
869 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
870 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
871 {
872   PetscErrorCode ierr;
873   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
874   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
875   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
876   PetscLogDouble flops=0.0;
877   MatScalar      *aa=a->a,*ba,*ca,*caj;
878 
879   PetscFunctionBegin;
880   if (!c->a){
881     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
882     c->a      = ca;
883     c->free_a = PETSC_TRUE;
884   } else {
885     ca = c->a;
886   }
887   /* clear old values in C */
888   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
889 
890   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
891   for (i=0;i<am;i++) {
892     bj   = b->j + bi[i];
893     ba   = b->a + bi[i];
894     bnzi = bi[i+1] - bi[i];
895     anzi = ai[i+1] - ai[i];
896     for (j=0; j<anzi; j++) {
897       nextb = 0;
898       crow  = *aj++;
899       cjj   = cj + ci[crow];
900       caj   = ca + ci[crow];
901       /* perform sparse axpy operation.  Note cjj includes bj. */
902       for (k=0; nextb<bnzi; k++) {
903         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
904           caj[k] += (*aa)*(*(ba+nextb));
905           nextb++;
906         }
907       }
908       flops += 2*bnzi;
909       aa++;
910     }
911   }
912 
913   /* Assemble the final matrix and clean up */
914   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
915   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
916   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
917   PetscFunctionReturn(0);
918 }
919 
920 EXTERN_C_BEGIN
921 #undef __FUNCT__
922 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
923 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
924 {
925   PetscErrorCode ierr;
926 
927   PetscFunctionBegin;
928   if (scall == MAT_INITIAL_MATRIX){
929     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
930   }
931   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
932   PetscFunctionReturn(0);
933 }
934 EXTERN_C_END
935 
936 #undef __FUNCT__
937 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
938 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
939 {
940   PetscErrorCode ierr;
941 
942   PetscFunctionBegin;
943   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
944   (*C)->ops->matmult = MatMatMult_SeqAIJ_SeqDense;
945   PetscFunctionReturn(0);
946 }
947 
948 #undef __FUNCT__
949 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
950 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
951 {
952   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
953   PetscErrorCode ierr;
954   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
955   MatScalar      *aa;
956   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
957   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
958 
959   PetscFunctionBegin;
960   if (!cm || !cn) PetscFunctionReturn(0);
961   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);
962   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);
963   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);
964   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
965   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
966   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
967   for (col=0; col<cn-4; col += 4){  /* over columns of C */
968     colam = col*am;
969     for (i=0; i<am; i++) {        /* over rows of C in those columns */
970       r1 = r2 = r3 = r4 = 0.0;
971       n   = a->i[i+1] - a->i[i];
972       aj  = a->j + a->i[i];
973       aa  = a->a + a->i[i];
974       for (j=0; j<n; j++) {
975         r1 += (*aa)*b1[*aj];
976         r2 += (*aa)*b2[*aj];
977         r3 += (*aa)*b3[*aj];
978         r4 += (*aa++)*b4[*aj++];
979       }
980       c[colam + i]       = r1;
981       c[colam + am + i]  = r2;
982       c[colam + am2 + i] = r3;
983       c[colam + am3 + i] = r4;
984     }
985     b1 += bm4;
986     b2 += bm4;
987     b3 += bm4;
988     b4 += bm4;
989   }
990   for (;col<cn; col++){     /* over extra columns of C */
991     for (i=0; i<am; i++) {  /* over rows of C in those columns */
992       r1 = 0.0;
993       n   = a->i[i+1] - a->i[i];
994       aj  = a->j + a->i[i];
995       aa  = a->a + a->i[i];
996 
997       for (j=0; j<n; j++) {
998         r1 += (*aa++)*b1[*aj++];
999       }
1000       c[col*am + i]     = r1;
1001     }
1002     b1 += bm;
1003   }
1004   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1005   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1006   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
1007   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1008   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1009   PetscFunctionReturn(0);
1010 }
1011 
1012 /*
1013    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1014 */
1015 #undef __FUNCT__
1016 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1017 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1018 {
1019   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1020   PetscErrorCode ierr;
1021   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1022   MatScalar      *aa;
1023   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1024   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1025 
1026   PetscFunctionBegin;
1027   if (!cm || !cn) PetscFunctionReturn(0);
1028   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1029   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
1030   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1031 
1032   if (a->compressedrow.use){ /* use compressed row format */
1033     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1034       colam = col*am;
1035       arm   = a->compressedrow.nrows;
1036       ii    = a->compressedrow.i;
1037       ridx  = a->compressedrow.rindex;
1038       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1039 	r1 = r2 = r3 = r4 = 0.0;
1040 	n   = ii[i+1] - ii[i];
1041 	aj  = a->j + ii[i];
1042 	aa  = a->a + ii[i];
1043 	for (j=0; j<n; j++) {
1044 	  r1 += (*aa)*b1[*aj];
1045 	  r2 += (*aa)*b2[*aj];
1046 	  r3 += (*aa)*b3[*aj];
1047 	  r4 += (*aa++)*b4[*aj++];
1048 	}
1049 	c[colam       + ridx[i]] += r1;
1050 	c[colam + am  + ridx[i]] += r2;
1051 	c[colam + am2 + ridx[i]] += r3;
1052 	c[colam + am3 + ridx[i]] += r4;
1053       }
1054       b1 += bm4;
1055       b2 += bm4;
1056       b3 += bm4;
1057       b4 += bm4;
1058     }
1059     for (;col<cn; col++){     /* over extra columns of C */
1060       colam = col*am;
1061       arm   = a->compressedrow.nrows;
1062       ii    = a->compressedrow.i;
1063       ridx  = a->compressedrow.rindex;
1064       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1065 	r1 = 0.0;
1066 	n   = ii[i+1] - ii[i];
1067 	aj  = a->j + ii[i];
1068 	aa  = a->a + ii[i];
1069 
1070 	for (j=0; j<n; j++) {
1071 	  r1 += (*aa++)*b1[*aj++];
1072 	}
1073 	c[col*am + ridx[i]] += r1;
1074       }
1075       b1 += bm;
1076     }
1077   } else {
1078     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1079       colam = col*am;
1080       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1081 	r1 = r2 = r3 = r4 = 0.0;
1082 	n   = a->i[i+1] - a->i[i];
1083 	aj  = a->j + a->i[i];
1084 	aa  = a->a + a->i[i];
1085 	for (j=0; j<n; j++) {
1086 	  r1 += (*aa)*b1[*aj];
1087 	  r2 += (*aa)*b2[*aj];
1088 	  r3 += (*aa)*b3[*aj];
1089 	  r4 += (*aa++)*b4[*aj++];
1090 	}
1091 	c[colam + i]       += r1;
1092 	c[colam + am + i]  += r2;
1093 	c[colam + am2 + i] += r3;
1094 	c[colam + am3 + i] += r4;
1095       }
1096       b1 += bm4;
1097       b2 += bm4;
1098       b3 += bm4;
1099       b4 += bm4;
1100     }
1101     for (;col<cn; col++){     /* over extra columns of C */
1102       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1103 	r1 = 0.0;
1104 	n   = a->i[i+1] - a->i[i];
1105 	aj  = a->j + a->i[i];
1106 	aa  = a->a + a->i[i];
1107 
1108 	for (j=0; j<n; j++) {
1109 	  r1 += (*aa++)*b1[*aj++];
1110 	}
1111 	c[col*am + i]     += r1;
1112       }
1113       b1 += bm;
1114     }
1115   }
1116   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1117   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1118   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
1119   PetscFunctionReturn(0);
1120 }
1121 
1122 #undef __FUNCT__
1123 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1124 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1125 {
1126   PetscErrorCode ierr;
1127   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
1128   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1129   PetscInt       *bi=b->i,*bj=b->j;
1130   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1131   MatScalar      *btval,*btval_den,*ba=b->a;
1132   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1133 
1134   PetscFunctionBegin;
1135   btval_den=btdense->v;
1136   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1137   for (k=0; k<ncolors; k++) {
1138     ncolumns = coloring->ncolumns[k];
1139     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1140       col   = *(columns + colorforcol[k] + l);
1141       btcol = bj + bi[col];
1142       btval = ba + bi[col];
1143       anz   = bi[col+1] - bi[col];
1144       for (j=0; j<anz; j++){
1145         brow            = btcol[j];
1146         btval_den[brow] = btval[j];
1147       }
1148     }
1149     btval_den += m;
1150   }
1151   PetscFunctionReturn(0);
1152 }
1153 
1154 #undef __FUNCT__
1155 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1156 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1157 {
1158   PetscErrorCode ierr;
1159   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1160   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1161   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1162   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1163 
1164   PetscFunctionBegin;
1165   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1166   ierr = MatGetArray(Cden,&ca_den);CHKERRQ(ierr);
1167   cp_den = ca_den;
1168   for (k=0; k<ncolors; k++) {
1169     nrows = matcoloring->nrows[k];
1170     row   = rows  + colorforrow[k];
1171     idx   = spidx + colorforrow[k];
1172     for (l=0; l<nrows; l++){
1173       ca[idx[l]] = cp_den[row[l]];
1174     }
1175     cp_den += m;
1176   }
1177   ierr = MatRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1178   PetscFunctionReturn(0);
1179 }
1180 
1181 /*
1182  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1183  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1184  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1185  */
1186 #undef __FUNCT__
1187 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1188 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1189 {
1190   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1191   PetscErrorCode ierr;
1192   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1193   PetscInt       nz = a->i[m],row,*jj,mr,col;
1194   PetscInt       *cspidx;
1195 
1196   PetscFunctionBegin;
1197   *nn = n;
1198   if (!ia) PetscFunctionReturn(0);
1199   if (symmetric) {
1200     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1201     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,ia,ja);CHKERRQ(ierr);
1202   } else {
1203     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1204     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1205     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1206     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1207     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1208     jj = a->j;
1209     for (i=0; i<nz; i++) {
1210       collengths[jj[i]]++;
1211     }
1212     cia[0] = oshift;
1213     for (i=0; i<n; i++) {
1214       cia[i+1] = cia[i] + collengths[i];
1215     }
1216     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1217     jj   = a->j;
1218     for (row=0; row<m; row++) {
1219       mr = a->i[row+1] - a->i[row];
1220       for (i=0; i<mr; i++) {
1221         col = *jj++;
1222         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1223         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
1224       }
1225     }
1226     ierr = PetscFree(collengths);CHKERRQ(ierr);
1227     *ia = cia; *ja = cja;
1228     *spidx = cspidx;
1229   }
1230   PetscFunctionReturn(0);
1231 }
1232 
1233 #undef __FUNCT__
1234 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1235 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1236 {
1237   PetscErrorCode ierr;
1238 
1239   PetscFunctionBegin;
1240   if (!ia) PetscFunctionReturn(0);
1241 
1242   ierr = PetscFree(*ia);CHKERRQ(ierr);
1243   ierr = PetscFree(*ja);CHKERRQ(ierr);
1244   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1245   PetscFunctionReturn(0);
1246 }
1247 
1248 #undef __FUNCT__
1249 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1250 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1251 {
1252   PetscErrorCode ierr;
1253   PetscInt       i,n,nrows,N,j,k,m,*row_idx,*ci,*cj,ncols,col,cm;
1254   const PetscInt *is;
1255   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1256   IS             *isa;
1257   PetscBool      done;
1258   PetscBool      flg1,flg2;
1259   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1260   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1261   PetscInt       *colorforcol,*columns,*columns_i;
1262 
1263   PetscFunctionBegin;
1264   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1265 
1266   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1267   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1268   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1269   if (flg1 || flg2) {
1270     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1271   }
1272 
1273   N         = mat->cmap->N/bs;
1274   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1275   c->N      = mat->cmap->N/bs;
1276   c->m      = mat->rmap->N/bs;
1277   c->rstart = 0;
1278 
1279   c->ncolors = nis;
1280   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1281   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1282   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1283   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1284   colorforrow[0]    = 0;
1285   rows_i            = rows;
1286   columnsforspidx_i = columnsforspidx;
1287 
1288   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1289   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1290   colorforcol[0] = 0;
1291   columns_i      = columns;
1292 
1293   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr); /* column-wise storage of mat */
1294   if (!done) SETERRQ1(((PetscObject)mat)->comm,PETSC_ERR_SUP,"MatGetColumnIJ() not supported for matrix type %s",((PetscObject)mat)->type_name);
1295 
1296   cm = c->m;
1297   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1298   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1299   for (i=0; i<nis; i++) {
1300     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1301     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1302     c->ncolumns[i] = n;
1303     if (n) {
1304       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1305     }
1306     colorforcol[i+1] = colorforcol[i] + n;
1307     columns_i       += n;
1308 
1309     /* fast, crude version requires O(N*N) work */
1310     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1311 
1312     /* loop over columns*/
1313     for (j=0; j<n; j++) {
1314       col     = is[j];
1315       row_idx = cj + ci[col];
1316       m       = ci[col+1] - ci[col];
1317       /* loop over columns marking them in rowhit */
1318       for (k=0; k<m; k++) {
1319         idxhit[*row_idx]   = spidx[ci[col] + k];
1320         rowhit[*row_idx++] = col + 1;
1321       }
1322     }
1323     /* count the number of hits */
1324     nrows = 0;
1325     for (j=0; j<cm; j++) {
1326       if (rowhit[j]) nrows++;
1327     }
1328     c->nrows[i]      = nrows;
1329     colorforrow[i+1] = colorforrow[i] + nrows;
1330 
1331     nrows       = 0;
1332     for (j=0; j<cm; j++) {
1333       if (rowhit[j]) {
1334         rows_i[nrows]            = j;
1335         columnsforspidx_i[nrows] = idxhit[j];
1336         nrows++;
1337       }
1338     }
1339     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1340     rows_i += nrows; columnsforspidx_i += nrows;
1341   }
1342   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr);
1343   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1344   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1345 #if defined(PETSC_USE_DEBUG)
1346   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1347 #endif
1348 
1349   c->colorforrow     = colorforrow;
1350   c->rows            = rows;
1351   c->columnsforspidx = columnsforspidx;
1352   c->colorforcol     = colorforcol;
1353   c->columns         = columns;
1354   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1355   PetscFunctionReturn(0);
1356 }
1357