xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision cc46b9d1a836b7d5113f0c696af451865df2bbc8)
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 EXTERN_C_BEGIN
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 
19   PetscFunctionBegin;
20   if (scall == MAT_INITIAL_MATRIX){
21     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
22   }
23   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
24   PetscFunctionReturn(0);
25 }
26 EXTERN_C_END
27 
28 #undef __FUNCT__
29 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
30 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
31 {
32   PetscErrorCode     ierr;
33   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
34   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
35   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci,*cj;
36   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
37   PetscInt           i,j,anzi,brow,bnzj,cnzi,nlnk,*lnk,nspacedouble=0;
38   MatScalar          *ca;
39   PetscBT            lnkbt;
40   PetscReal          afill;
41 
42   PetscFunctionBegin;
43   /* Allocate ci array, arrays for fill computation and */
44   /* free space for accumulating nonzero column info */
45   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
46   ci[0] = 0;
47 
48   /* create and initialize a linked list */
49   nlnk = bn+1;
50   ierr = PetscLLCreate(bn,bn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
51 
52   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
53   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
54   current_space = free_space;
55 
56   /* Determine symbolic info for each row of the product: */
57   for (i=0;i<am;i++) {
58     anzi = ai[i+1] - ai[i];
59     cnzi = 0;
60     j    = anzi;
61     aj   = a->j + ai[i];
62     while (j){/* assume cols are almost in increasing order, starting from its end saves computation */
63       j--;
64       brow = *(aj + j);
65       bnzj = bi[brow+1] - bi[brow];
66       bjj  = bj + bi[brow];
67       /* add non-zero cols of B into the sorted linked list lnk */
68       ierr = PetscLLAdd(bnzj,bjj,bn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
69       cnzi += nlnk;
70     }
71 
72     /* If free space is not available, make more free space */
73     /* Double the amount of total space in the list */
74     if (current_space->local_remaining<cnzi) {
75       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
76       nspacedouble++;
77     }
78 
79     /* Copy data into free space, then initialize lnk */
80     ierr = PetscLLClean(bn,bn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
81     current_space->array           += cnzi;
82     current_space->local_used      += cnzi;
83     current_space->local_remaining -= cnzi;
84 
85     ci[i+1] = ci[i] + cnzi;
86   }
87 
88   /* Column indices are in the list of free space */
89   /* Allocate space for cj, initialize cj, and */
90   /* destroy list of free space and other temporary array(s) */
91   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
92   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
93   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
94 
95   /* Allocate space for ca */
96   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
97   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
98 
99   /* put together the new symbolic matrix */
100   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
101 
102   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
103   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
104   c = (Mat_SeqAIJ *)((*C)->data);
105   c->free_a   = PETSC_TRUE;
106   c->free_ij  = PETSC_TRUE;
107   c->nonew    = 0;
108 
109   /* set MatInfo */
110   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
111   if (afill < 1.0) afill = 1.0;
112   c->maxnz                     = ci[am];
113   c->nz                        = ci[am];
114   (*C)->info.mallocs           = nspacedouble;
115   (*C)->info.fill_ratio_given  = fill;
116   (*C)->info.fill_ratio_needed = afill;
117 
118 #if defined(PETSC_USE_INFO)
119   if (ci[am]) {
120     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
121     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
122   } else {
123     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
124   }
125 #endif
126   PetscFunctionReturn(0);
127 }
128 
129 
130 #undef __FUNCT__
131 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
132 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
133 {
134   PetscErrorCode ierr;
135   PetscLogDouble flops=0.0;
136   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
137   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
138   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
139   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
140   PetscInt       am=A->rmap->N,cm=C->rmap->N;
141   PetscInt       i,j,k,anzi,bnzi,cnzi,brow,nextb;
142   MatScalar      *aa=a->a,*ba=b->a,*baj,*ca=c->a;
143 
144   PetscFunctionBegin;
145   /* clean old values in C */
146   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
147   /* Traverse A row-wise. */
148   /* Build the ith row in C by summing over nonzero columns in A, */
149   /* the rows of B corresponding to nonzeros of A. */
150   for (i=0;i<am;i++) {
151     anzi = ai[i+1] - ai[i];
152     for (j=0;j<anzi;j++) {
153       brow = *aj++;
154       bnzi = bi[brow+1] - bi[brow];
155       bjj  = bj + bi[brow];
156       baj  = ba + bi[brow];
157       nextb = 0;
158       for (k=0; nextb<bnzi; k++) {
159         if (cj[k] == bjj[nextb]){ /* ccol == bcol */
160           ca[k] += (*aa)*baj[nextb++];
161         }
162       }
163       flops += 2*bnzi;
164       aa++;
165     }
166     cnzi = ci[i+1] - ci[i];
167     ca += cnzi;
168     cj += cnzi;
169   }
170   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
171   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
172 
173   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
174   PetscFunctionReturn(0);
175 }
176 
177 #undef __FUNCT__
178 #define __FUNCT__ "MatMatMultTranspose_SeqAIJ_SeqAIJ"
179 PetscErrorCode MatMatMultTranspose_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
180 {
181   PetscErrorCode ierr;
182 
183   PetscFunctionBegin;
184   if (scall == MAT_INITIAL_MATRIX){
185     ierr = MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
186   }
187   ierr = MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
188   PetscFunctionReturn(0);
189 }
190 
191 #undef __FUNCT__
192 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatMultTrans"
193 PetscErrorCode PetscContainerDestroy_Mat_MatMatMultTrans(void *ptr)
194 {
195   PetscErrorCode      ierr;
196   Mat_MatMatMultTrans *multtrans=(Mat_MatMatMultTrans*)ptr;
197 
198   PetscFunctionBegin;
199   ierr = MatMultTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
200   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
201   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
202   ierr = PetscFree(multtrans);CHKERRQ(ierr);
203   PetscFunctionReturn(0);
204 }
205 
206 #undef __FUNCT__
207 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
208 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
209 {
210   PetscErrorCode      ierr;
211   PetscContainer      container;
212   Mat_MatMatMultTrans *multtrans=PETSC_NULL;
213 
214   PetscFunctionBegin;
215   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultTrans",(PetscObject *)&container);CHKERRQ(ierr);
216   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
217   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
218   A->ops->destroy   = multtrans->destroy;
219   if (A->ops->destroy) {
220     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
221   }
222   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatMultTrans",0);CHKERRQ(ierr);
223   PetscFunctionReturn(0);
224 }
225 
226 #undef __FUNCT__
227 #define __FUNCT__ "MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ"
228 PetscErrorCode MatMatMultTransposeSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
229 {
230   PetscErrorCode      ierr;
231   Mat                 Bt;
232   PetscInt            *bti,*btj;
233   Mat_MatMatMultTrans *multtrans;
234   PetscContainer      container;
235 
236   PetscFunctionBegin;
237    /* create symbolic Bt */
238   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
239   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
240 
241   /* get symbolic C=A*Bt */
242   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
243 
244   /* clean up */
245   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
246   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
247 
248   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
249   ierr = PetscNew(Mat_MatMatMultTrans,&multtrans);CHKERRQ(ierr);
250 
251   /* attach the supporting struct to C */
252   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
253   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
254   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatMultTrans);CHKERRQ(ierr);
255   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatMultTrans",(PetscObject)container);CHKERRQ(ierr);
256   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
257 
258   multtrans->usecoloring = PETSC_FALSE;
259   multtrans->destroy = (*C)->ops->destroy;
260   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
261 
262   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmulttrans_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
263   if (multtrans->usecoloring){
264     /* Create MatMultTransposeColoring from symbolic C=A*B^T */
265     MatMultTransposeColoring  matcoloring;
266     ISColoring                iscoloring;
267     Mat                       Bt_dense,C_dense;
268     printf("Create MatMultTransposeColoring ...\n");
269     ierr = MatGetColoring(*C,MATCOLORINGSL,&iscoloring);CHKERRQ(ierr);
270     ierr = MatMultTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
271     multtrans->matcoloring = matcoloring;
272     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
273     printf("Create MatMultTransposeColoring is done \n");
274 
275     /* Create Bt_dense and C_dense = A*Bt_dense */
276     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
277     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
278     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
279     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
280     Bt_dense->assembled = PETSC_TRUE;
281     multtrans->Bt_den = Bt_dense;
282 
283     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
284     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
285     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
286     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
287     Bt_dense->assembled = PETSC_TRUE;
288     multtrans->ABt_den = C_dense;
289   }
290 
291 #if defined(INEFFICIENT_ALGORITHM)
292   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
293   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
294   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
295   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
296   PetscInt           am=A->rmap->N,bm=B->rmap->N;
297   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
298   MatScalar          *ca;
299   PetscBT            lnkbt;
300   PetscReal          afill;
301 
302   /* Allocate row pointer array ci  */
303   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
304   ci[0] = 0;
305 
306   /* Create and initialize a linked list for C columns */
307   nlnk = bm+1;
308   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
309 
310   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
311   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
312   current_space = free_space;
313 
314   /* Determine symbolic info for each row of the product A*B^T: */
315   for (i=0; i<am; i++) {
316     anzi = ai[i+1] - ai[i];
317     cnzi = 0;
318     acol = aj + ai[i];
319     for (j=0; j<bm; j++){
320       bnzj = bi[j+1] - bi[j];
321       bcol= bj + bi[j];
322       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
323       ka = 0; kb = 0;
324       while (ka < anzi && kb < bnzj){
325         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
326         if (ka == anzi) break;
327         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
328         if (kb == bnzj) break;
329         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
330           index[0] = j;
331           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
332           cnzi++;
333           break;
334         }
335       }
336     }
337 
338     /* If free space is not available, make more free space */
339     /* Double the amount of total space in the list */
340     if (current_space->local_remaining<cnzi) {
341       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
342       nspacedouble++;
343     }
344 
345     /* Copy data into free space, then initialize lnk */
346     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
347     current_space->array           += cnzi;
348     current_space->local_used      += cnzi;
349     current_space->local_remaining -= cnzi;
350 
351     ci[i+1] = ci[i] + cnzi;
352   }
353 
354 
355   /* Column indices are in the list of free space.
356      Allocate array cj, copy column indices to cj, and destroy list of free space */
357   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
358   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
359   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
360 
361   /* Allocate space for ca */
362   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
363   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
364 
365   /* put together the new symbolic matrix */
366   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
367 
368   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
369   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
370   c = (Mat_SeqAIJ *)((*C)->data);
371   c->free_a   = PETSC_TRUE;
372   c->free_ij  = PETSC_TRUE;
373   c->nonew    = 0;
374 
375   /* set MatInfo */
376   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
377   if (afill < 1.0) afill = 1.0;
378   c->maxnz                     = ci[am];
379   c->nz                        = ci[am];
380   (*C)->info.mallocs           = nspacedouble;
381   (*C)->info.fill_ratio_given  = fill;
382   (*C)->info.fill_ratio_needed = afill;
383 
384 #if defined(PETSC_USE_INFO)
385   if (ci[am]) {
386     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
387     ierr = PetscInfo1((*C),"Use MatMatMultTranspose(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
388   } else {
389     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
390   }
391 #endif
392 #endif
393   PetscFunctionReturn(0);
394 }
395 
396 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
397 #undef __FUNCT__
398 #define __FUNCT__ "MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ"
399 PetscErrorCode MatMatMultTransposeNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
400 {
401   PetscErrorCode ierr;
402   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
403   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
404   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
405   PetscLogDouble flops=0.0;
406   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca=c->a,*cval;
407   Mat_MatMatMultTrans *multtrans;
408   PetscContainer      container;
409 #if defined(USE_ARRAY)
410   MatScalar      *spdot;
411 #endif
412 
413   PetscFunctionBegin;
414   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatMultTrans",(PetscObject *)&container);CHKERRQ(ierr);
415   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
416   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
417   if (multtrans->usecoloring){
418     MatMultTransposeColoring  matcoloring = multtrans->matcoloring;
419     Mat      Bt_dense;
420     PetscInt m,n;
421     PetscLogDouble t0,tf,etime1=0.0,etime2=0.0;
422     Mat C_dense = multtrans->ABt_den;
423 
424     Bt_dense = multtrans->Bt_den;
425     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
426     printf("Bt_dense: %d,%d\n",m,n);
427 
428     /* Get Bt_dense by Apply MatMultTransposeColoring to B */
429     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
430     ierr = MatMultTransposeColoringApply(B,Bt_dense,matcoloring);CHKERRQ(ierr);
431     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
432     etime1 += tf - t0;
433 
434     /* C_dense = A*Bt_dense */
435     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
436     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
437     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
438     etime2 += tf - t0;
439 
440     /* Recover C from C_dense */
441     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
442     ierr = MatMultTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
443     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
444     etime1 += tf - t0;
445     printf("etime ColoringApply: %g; MatMatMultNumeric_sp_dense: %g\n",etime1,etime2);
446     PetscFunctionReturn(0);
447   }
448 
449 #if defined(USE_ARRAY)
450   /* allocate an array for implementing sparse inner-product */
451   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
452   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
453 #endif
454 
455   /* clear old values in C */
456   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
457 
458   for (i=0; i<cm; i++) {
459     anzi = ai[i+1] - ai[i];
460     acol = aj + ai[i];
461     aval = aa + ai[i];
462     cnzi = ci[i+1] - ci[i];
463     ccol = cj + ci[i];
464     cval = ca + ci[i];
465     for (j=0; j<cnzi; j++){
466       brow = ccol[j];
467       bnzj = bi[brow+1] - bi[brow];
468       bcol = bj + bi[brow];
469       bval = ba + bi[brow];
470 
471       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
472 #if defined(USE_ARRAY)
473       /* put ba to spdot array */
474       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
475       /* c(i,j)=A[i,:]*B[j,:]^T */
476       for (nexta=0; nexta<anzi; nexta++){
477         cval[j] += spdot[acol[nexta]]*aval[nexta];
478       }
479       /* zero spdot array */
480       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
481 #else
482       nexta = 0; nextb = 0;
483       while (nexta<anzi && nextb<bnzj){
484         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
485         if (nexta == anzi) break;
486         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
487         if (nextb == bnzj) break;
488         if (acol[nexta] == bcol[nextb]){
489           cval[j] += aval[nexta]*bval[nextb];
490           nexta++; nextb++;
491           flops += 2;
492         }
493       }
494 #endif
495     }
496   }
497   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
498   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
499   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
500 #if defined(USE_ARRAY)
501   ierr = PetscFree(spdot);
502 #endif
503   PetscFunctionReturn(0);
504 }
505 
506 #undef __FUNCT__
507 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
508 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
509   PetscErrorCode ierr;
510 
511   PetscFunctionBegin;
512   if (scall == MAT_INITIAL_MATRIX){
513     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
514   }
515   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
516   PetscFunctionReturn(0);
517 }
518 
519 #undef __FUNCT__
520 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
521 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
522 {
523   PetscErrorCode ierr;
524   Mat            At;
525   PetscInt       *ati,*atj;
526 
527   PetscFunctionBegin;
528   /* create symbolic At */
529   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
530   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
531 
532   /* get symbolic C=At*B */
533   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
534 
535   /* clean up */
536   ierr = MatDestroy(&At);CHKERRQ(ierr);
537   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
538   PetscFunctionReturn(0);
539 }
540 
541 #undef __FUNCT__
542 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
543 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
544 {
545   PetscErrorCode ierr;
546   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
547   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
548   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
549   PetscLogDouble flops=0.0;
550   MatScalar      *aa=a->a,*ba,*ca=c->a,*caj;
551 
552   PetscFunctionBegin;
553   /* clear old values in C */
554   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
555 
556   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
557   for (i=0;i<am;i++) {
558     bj   = b->j + bi[i];
559     ba   = b->a + bi[i];
560     bnzi = bi[i+1] - bi[i];
561     anzi = ai[i+1] - ai[i];
562     for (j=0; j<anzi; j++) {
563       nextb = 0;
564       crow  = *aj++;
565       cjj   = cj + ci[crow];
566       caj   = ca + ci[crow];
567       /* perform sparse axpy operation.  Note cjj includes bj. */
568       for (k=0; nextb<bnzi; k++) {
569         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
570           caj[k] += (*aa)*(*(ba+nextb));
571           nextb++;
572         }
573       }
574       flops += 2*bnzi;
575       aa++;
576     }
577   }
578 
579   /* Assemble the final matrix and clean up */
580   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
581   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
582   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
583   PetscFunctionReturn(0);
584 }
585 
586 EXTERN_C_BEGIN
587 #undef __FUNCT__
588 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
589 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
590 {
591   PetscErrorCode ierr;
592 
593   PetscFunctionBegin;
594   if (scall == MAT_INITIAL_MATRIX){
595     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
596   }
597   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
598   PetscFunctionReturn(0);
599 }
600 EXTERN_C_END
601 
602 #undef __FUNCT__
603 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
604 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
605 {
606   PetscErrorCode ierr;
607 
608   PetscFunctionBegin;
609   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
610   PetscFunctionReturn(0);
611 }
612 
613 #undef __FUNCT__
614 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
615 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
616 {
617   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
618   PetscErrorCode ierr;
619   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
620   MatScalar      *aa;
621   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
622   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
623 
624   PetscFunctionBegin;
625   if (!cm || !cn) PetscFunctionReturn(0);
626   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);
627   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);
628   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);
629   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
630   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
631   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
632   for (col=0; col<cn-4; col += 4){  /* over columns of C */
633     colam = col*am;
634     for (i=0; i<am; i++) {        /* over rows of C in those columns */
635       r1 = r2 = r3 = r4 = 0.0;
636       n   = a->i[i+1] - a->i[i];
637       aj  = a->j + a->i[i];
638       aa  = a->a + a->i[i];
639       for (j=0; j<n; j++) {
640         r1 += (*aa)*b1[*aj];
641         r2 += (*aa)*b2[*aj];
642         r3 += (*aa)*b3[*aj];
643         r4 += (*aa++)*b4[*aj++];
644       }
645       c[colam + i]       = r1;
646       c[colam + am + i]  = r2;
647       c[colam + am2 + i] = r3;
648       c[colam + am3 + i] = r4;
649     }
650     b1 += bm4;
651     b2 += bm4;
652     b3 += bm4;
653     b4 += bm4;
654   }
655   for (;col<cn; col++){     /* over extra columns of C */
656     for (i=0; i<am; i++) {  /* over rows of C in those columns */
657       r1 = 0.0;
658       n   = a->i[i+1] - a->i[i];
659       aj  = a->j + a->i[i];
660       aa  = a->a + a->i[i];
661 
662       for (j=0; j<n; j++) {
663         r1 += (*aa++)*b1[*aj++];
664       }
665       c[col*am + i]     = r1;
666     }
667     b1 += bm;
668   }
669   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
670   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
671   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
672   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
673   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
674   PetscFunctionReturn(0);
675 }
676 
677 /*
678    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
679 */
680 #undef __FUNCT__
681 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
682 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
683 {
684   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
685   PetscErrorCode ierr;
686   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
687   MatScalar      *aa;
688   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
689   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
690 
691   PetscFunctionBegin;
692   if (!cm || !cn) PetscFunctionReturn(0);
693   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
694   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
695   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
696 
697   if (a->compressedrow.use){ /* use compressed row format */
698     for (col=0; col<cn-4; col += 4){  /* over columns of C */
699       colam = col*am;
700       arm   = a->compressedrow.nrows;
701       ii    = a->compressedrow.i;
702       ridx  = a->compressedrow.rindex;
703       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
704 	r1 = r2 = r3 = r4 = 0.0;
705 	n   = ii[i+1] - ii[i];
706 	aj  = a->j + ii[i];
707 	aa  = a->a + ii[i];
708 	for (j=0; j<n; j++) {
709 	  r1 += (*aa)*b1[*aj];
710 	  r2 += (*aa)*b2[*aj];
711 	  r3 += (*aa)*b3[*aj];
712 	  r4 += (*aa++)*b4[*aj++];
713 	}
714 	c[colam       + ridx[i]] += r1;
715 	c[colam + am  + ridx[i]] += r2;
716 	c[colam + am2 + ridx[i]] += r3;
717 	c[colam + am3 + ridx[i]] += r4;
718       }
719       b1 += bm4;
720       b2 += bm4;
721       b3 += bm4;
722       b4 += bm4;
723     }
724     for (;col<cn; col++){     /* over extra columns of C */
725       colam = col*am;
726       arm   = a->compressedrow.nrows;
727       ii    = a->compressedrow.i;
728       ridx  = a->compressedrow.rindex;
729       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
730 	r1 = 0.0;
731 	n   = ii[i+1] - ii[i];
732 	aj  = a->j + ii[i];
733 	aa  = a->a + ii[i];
734 
735 	for (j=0; j<n; j++) {
736 	  r1 += (*aa++)*b1[*aj++];
737 	}
738 	c[col*am + ridx[i]] += r1;
739       }
740       b1 += bm;
741     }
742   } else {
743     for (col=0; col<cn-4; col += 4){  /* over columns of C */
744       colam = col*am;
745       for (i=0; i<am; i++) {        /* over rows of C in those columns */
746 	r1 = r2 = r3 = r4 = 0.0;
747 	n   = a->i[i+1] - a->i[i];
748 	aj  = a->j + a->i[i];
749 	aa  = a->a + a->i[i];
750 	for (j=0; j<n; j++) {
751 	  r1 += (*aa)*b1[*aj];
752 	  r2 += (*aa)*b2[*aj];
753 	  r3 += (*aa)*b3[*aj];
754 	  r4 += (*aa++)*b4[*aj++];
755 	}
756 	c[colam + i]       += r1;
757 	c[colam + am + i]  += r2;
758 	c[colam + am2 + i] += r3;
759 	c[colam + am3 + i] += r4;
760       }
761       b1 += bm4;
762       b2 += bm4;
763       b3 += bm4;
764       b4 += bm4;
765     }
766     for (;col<cn; col++){     /* over extra columns of C */
767       for (i=0; i<am; i++) {  /* over rows of C in those columns */
768 	r1 = 0.0;
769 	n   = a->i[i+1] - a->i[i];
770 	aj  = a->j + a->i[i];
771 	aa  = a->a + a->i[i];
772 
773 	for (j=0; j<n; j++) {
774 	  r1 += (*aa++)*b1[*aj++];
775 	}
776 	c[col*am + i]     += r1;
777       }
778       b1 += bm;
779     }
780   }
781   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
782   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
783   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
784   PetscFunctionReturn(0);
785 }
786 
787 #undef __FUNCT__
788 #define __FUNCT__ "MatMultTransposeColoringApply_SeqAIJ"
789 PetscErrorCode  MatMultTransposeColoringApply_SeqAIJ(Mat B,Mat Btdense,MatMultTransposeColoring coloring)
790 {
791   PetscErrorCode ierr;
792   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)B->data;
793   Mat_SeqDense   *atdense = (Mat_SeqDense*)Btdense->data;
794   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*atcol,brow,bcol;
795   MatScalar      *atval,*bval;
796 
797   PetscFunctionBegin;
798   ierr = PetscMemzero(atdense->v,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
799   for (k=0; k<coloring->ncolors; k++) {
800     for (l=0; l<coloring->ncolumns[k]; l++) { /* insert a row of B to a column of Btdense */
801       col = coloring->columns[k][l];   /* =row of B */
802       anz = a->i[col+1] - a->i[col];
803       for (j=0; j<anz; j++){
804         atcol = a->j + a->i[col];
805         atval = a->a + a->i[col];
806         bval  = atdense->v;
807         brow  = atcol[j];
808         bcol  = k;
809         bval[bcol*m+brow] = atval[j];
810       }
811     }
812   }
813   PetscFunctionReturn(0);
814 }
815 
816 #undef __FUNCT__
817 #define __FUNCT__ "MatMultTransColoringApplyDenToSp_SeqAIJ"
818 PetscErrorCode MatMultTransColoringApplyDenToSp_SeqAIJ(MatMultTransposeColoring matcoloring,Mat Cden,Mat Csp)
819 {
820   PetscErrorCode ierr;
821   PetscInt       k,l,row,col,m;
822   PetscScalar    *ca,*cval;
823 
824   PetscFunctionBegin;
825   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
826   ierr = MatGetArray(Cden,&ca);CHKERRQ(ierr);
827   cval = ca;
828   for (k=0; k<matcoloring->ncolors; k++) {
829     for (l=0; l<matcoloring->nrows[k]; l++){
830       row  = matcoloring->rows[k][l];             /* local row index */
831       col  = matcoloring->columnsforrow[k][l];    /* global column index */
832       ierr = MatSetValues(Csp,1,&row,1,&col,cval+row,INSERT_VALUES);CHKERRQ(ierr);
833     }
834     cval += m;
835   }
836   ierr = MatRestoreArray(Cden,&ca);CHKERRQ(ierr);
837   ierr = MatAssemblyBegin(Csp,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
838   ierr = MatAssemblyEnd(Csp,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
839   PetscFunctionReturn(0);
840 }
841 
842 #undef __FUNCT__
843 #define __FUNCT__ "MatMultTransposeColoringCreate_SeqAIJ"
844 PetscErrorCode MatMultTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatMultTransposeColoring c)
845 {
846   PetscErrorCode ierr;
847   PetscInt       i,n,nrows,N,j,k,m,*rows,*ci,*cj,ncols,col;
848   const PetscInt *is;
849   PetscInt       nis = iscoloring->n,*rowhit,*columnsforrow,bs = 1;
850   IS             *isa;
851   PetscBool      done;
852   PetscBool      flg1,flg2;
853 
854   PetscFunctionBegin;
855   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix must be assembled by calls to MatAssemblyBegin/End();");
856 
857   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
858   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
859   ierr = PetscTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
860   ierr = PetscTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
861   if (flg1 || flg2) {
862     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
863   }
864 
865   N          = mat->cmap->N/bs;
866   c->M       = mat->rmap->N/bs;  /* set total rows, columns and local rows */
867   c->N       = mat->cmap->N/bs;
868   c->m       = mat->rmap->N/bs;
869   c->rstart  = 0;
870 
871   c->ncolors = nis;
872   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
873   ierr       = PetscMalloc(nis*sizeof(PetscInt*),&c->columns);CHKERRQ(ierr);
874   ierr       = PetscMalloc(c->m*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
875   ierr       = PetscMalloc(c->m*sizeof(PetscInt*),&c->rows);CHKERRQ(ierr);
876   ierr       = PetscMalloc(c->m*sizeof(PetscInt*),&c->columnsforrow);CHKERRQ(ierr);
877 
878   ierr = MatGetColumnIJ(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&done);CHKERRQ(ierr);
879   if (!done) SETERRQ1(((PetscObject)mat)->comm,PETSC_ERR_SUP,"MatGetColumnIJ() not supported for matrix type %s",((PetscObject)mat)->type_name);
880 
881   ierr = PetscMalloc((c->m+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
882   ierr = PetscMalloc((c->m+1)*sizeof(PetscInt),&columnsforrow);CHKERRQ(ierr);
883 
884   for (i=0; i<nis; i++) {
885     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
886     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
887     c->ncolumns[i] = n;
888     if (n) {
889       ierr = PetscMalloc(n*sizeof(PetscInt),&c->columns[i]);CHKERRQ(ierr);
890       ierr = PetscMemcpy(c->columns[i],is,n*sizeof(PetscInt));CHKERRQ(ierr);
891     } else {
892       c->columns[i]  = 0;
893     }
894 
895     /* fast, crude version requires O(N*N) work */
896     ierr = PetscMemzero(rowhit,c->m*sizeof(PetscInt));CHKERRQ(ierr);
897     /* loop over columns*/
898     for (j=0; j<n; j++) {
899       col  = is[j];
900       rows = cj + ci[col];
901       m    = ci[col+1] - ci[col];
902       /* loop over columns marking them in rowhit */
903       for (k=0; k<m; k++) {
904         rowhit[*rows++] = col + 1;
905       }
906     }
907       /* count the number of hits */
908       nrows = 0;
909       for (j=0; j<c->m; j++) {
910         if (rowhit[j]) nrows++;
911       }
912       c->nrows[i] = nrows;
913       ierr        = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->rows[i]);CHKERRQ(ierr);
914       ierr        = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->columnsforrow[i]);CHKERRQ(ierr);
915       nrows       = 0;
916       for (j=0; j<c->m; j++) {
917         if (rowhit[j]) {
918           c->rows[i][nrows]          = j;
919           c->columnsforrow[i][nrows] = rowhit[j] - 1;
920           nrows++;
921         }
922       }
923     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
924   }
925   ierr = MatRestoreColumnIJ(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&done);CHKERRQ(ierr);
926 
927   ierr = PetscFree(rowhit);CHKERRQ(ierr);
928   ierr = PetscFree(columnsforrow);CHKERRQ(ierr);
929   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
930   PetscFunctionReturn(0);
931 }
932