xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 9ff76d2c1165698255fb7c007af3c9986d2cdf39)
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 /* This routine is not used. Should be removed! */
178 #undef __FUNCT__
179 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
180 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
181 {
182   PetscErrorCode ierr;
183 
184   PetscFunctionBegin;
185   if (scall == MAT_INITIAL_MATRIX){
186     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
187   }
188   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
189   PetscFunctionReturn(0);
190 }
191 
192 #undef __FUNCT__
193 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
194 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
195 {
196   PetscErrorCode      ierr;
197   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
198 
199   PetscFunctionBegin;
200   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
201   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
202   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
203   ierr = PetscFree(multtrans);CHKERRQ(ierr);
204   PetscFunctionReturn(0);
205 }
206 
207 #undef __FUNCT__
208 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
209 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
210 {
211   PetscErrorCode      ierr;
212   PetscContainer      container;
213   Mat_MatMatTransMult *multtrans=PETSC_NULL;
214 
215   PetscFunctionBegin;
216   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
217   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
218   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
219   A->ops->destroy   = multtrans->destroy;
220   if (A->ops->destroy) {
221     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
222   }
223   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
224   PetscFunctionReturn(0);
225 }
226 
227 #undef __FUNCT__
228 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
229 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
230 {
231   PetscErrorCode      ierr;
232   Mat                 Bt;
233   PetscInt            *bti,*btj;
234   Mat_MatMatTransMult *multtrans;
235   PetscContainer      container;
236   PetscLogDouble      t0,tf,etime2=0.0;
237 
238   PetscFunctionBegin;
239   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
240    /* create symbolic Bt */
241   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
242   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
243 
244   /* get symbolic C=A*Bt */
245   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
246 
247   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
248   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
249 
250   /* attach the supporting struct to C */
251   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
252   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
253   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
254   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
255   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
256 
257   multtrans->usecoloring = PETSC_FALSE;
258   multtrans->destroy = (*C)->ops->destroy;
259   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
260 
261   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
262   etime2 += tf - t0;
263 
264   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
265   if (multtrans->usecoloring){
266     /* Create MatTransposeColoring from symbolic C=A*B^T */
267     MatTransposeColoring matcoloring;
268     ISColoring           iscoloring;
269     Mat                  Bt_dense,C_dense;
270     PetscLogDouble       etime0=0.0,etime01=0.0,etime1=0.0;
271 
272     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
273     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
274     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
275     etime0 += tf - t0;
276 
277     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
278     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
279     multtrans->matcoloring = matcoloring;
280     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
281     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
282     etime01 += tf - t0;
283 
284     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
285     /* Create Bt_dense and C_dense = A*Bt_dense */
286     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
287     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
288     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
289     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
290     Bt_dense->assembled = PETSC_TRUE;
291     multtrans->Bt_den = Bt_dense;
292 
293     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
294     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
295     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
296     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
297     Bt_dense->assembled = PETSC_TRUE;
298     multtrans->ABt_den = C_dense;
299     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
300     etime1 += tf - t0;
301 
302 #if defined(PETSC_USE_INFO)
303     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
304     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));
305     ierr = PetscInfo5(*C,"Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
306 #endif
307   }
308   /* clean up */
309   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
310   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
311 
312 
313 
314 #if defined(INEFFICIENT_ALGORITHM)
315   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
316   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
317   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
318   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
319   PetscInt           am=A->rmap->N,bm=B->rmap->N;
320   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
321   MatScalar          *ca;
322   PetscBT            lnkbt;
323   PetscReal          afill;
324 
325   /* Allocate row pointer array ci  */
326   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
327   ci[0] = 0;
328 
329   /* Create and initialize a linked list for C columns */
330   nlnk = bm+1;
331   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
332 
333   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
334   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
335   current_space = free_space;
336 
337   /* Determine symbolic info for each row of the product A*B^T: */
338   for (i=0; i<am; i++) {
339     anzi = ai[i+1] - ai[i];
340     cnzi = 0;
341     acol = aj + ai[i];
342     for (j=0; j<bm; j++){
343       bnzj = bi[j+1] - bi[j];
344       bcol= bj + bi[j];
345       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
346       ka = 0; kb = 0;
347       while (ka < anzi && kb < bnzj){
348         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
349         if (ka == anzi) break;
350         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
351         if (kb == bnzj) break;
352         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
353           index[0] = j;
354           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
355           cnzi++;
356           break;
357         }
358       }
359     }
360 
361     /* If free space is not available, make more free space */
362     /* Double the amount of total space in the list */
363     if (current_space->local_remaining<cnzi) {
364       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
365       nspacedouble++;
366     }
367 
368     /* Copy data into free space, then initialize lnk */
369     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
370     current_space->array           += cnzi;
371     current_space->local_used      += cnzi;
372     current_space->local_remaining -= cnzi;
373 
374     ci[i+1] = ci[i] + cnzi;
375   }
376 
377 
378   /* Column indices are in the list of free space.
379      Allocate array cj, copy column indices to cj, and destroy list of free space */
380   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
381   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
382   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
383 
384   /* Allocate space for ca */
385   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
386   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
387 
388   /* put together the new symbolic matrix */
389   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
390 
391   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
392   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
393   c = (Mat_SeqAIJ *)((*C)->data);
394   c->free_a   = PETSC_TRUE;
395   c->free_ij  = PETSC_TRUE;
396   c->nonew    = 0;
397 
398   /* set MatInfo */
399   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
400   if (afill < 1.0) afill = 1.0;
401   c->maxnz                     = ci[am];
402   c->nz                        = ci[am];
403   (*C)->info.mallocs           = nspacedouble;
404   (*C)->info.fill_ratio_given  = fill;
405   (*C)->info.fill_ratio_needed = afill;
406 
407 #if defined(PETSC_USE_INFO)
408   if (ci[am]) {
409     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
410     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
411   } else {
412     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
413   }
414 #endif
415 #endif
416   PetscFunctionReturn(0);
417 }
418 
419 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
420 #undef __FUNCT__
421 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
422 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
423 {
424   PetscErrorCode ierr;
425   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
426   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
427   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
428   PetscLogDouble flops=0.0;
429   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca=c->a,*cval;
430   Mat_MatMatTransMult *multtrans;
431   PetscContainer      container;
432 #if defined(USE_ARRAY)
433   MatScalar      *spdot;
434 #endif
435 
436   PetscFunctionBegin;
437   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
438   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
439   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
440   if (multtrans->usecoloring){
441     MatTransposeColoring  matcoloring = multtrans->matcoloring;
442     Mat                   Bt_dense;
443     PetscInt              m,n;
444     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
445     Mat C_dense = multtrans->ABt_den;
446 
447     Bt_dense = multtrans->Bt_den;
448     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
449 
450     /* Get Bt_dense by Apply MatTransposeColoring to B */
451     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
452     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
453     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
454     etime0 += tf - t0;
455 
456     /* C_dense = A*Bt_dense */
457     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
458     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
459     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
460     etime2 += tf - t0;
461 
462     /* Recover C from C_dense */
463     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
464     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
465     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
466     etime1 += tf - t0;
467 #if defined(PETSC_USE_INFO)
468     ierr = PetscInfo4(C,"Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
469 #endif
470     PetscFunctionReturn(0);
471   }
472 
473 #if defined(USE_ARRAY)
474   /* allocate an array for implementing sparse inner-product */
475   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
476   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
477 #endif
478 
479   /* clear old values in C */
480   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
481 
482   for (i=0; i<cm; i++) {
483     anzi = ai[i+1] - ai[i];
484     acol = aj + ai[i];
485     aval = aa + ai[i];
486     cnzi = ci[i+1] - ci[i];
487     ccol = cj + ci[i];
488     cval = ca + ci[i];
489     for (j=0; j<cnzi; j++){
490       brow = ccol[j];
491       bnzj = bi[brow+1] - bi[brow];
492       bcol = bj + bi[brow];
493       bval = ba + bi[brow];
494 
495       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
496 #if defined(USE_ARRAY)
497       /* put ba to spdot array */
498       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
499       /* c(i,j)=A[i,:]*B[j,:]^T */
500       for (nexta=0; nexta<anzi; nexta++){
501         cval[j] += spdot[acol[nexta]]*aval[nexta];
502       }
503       /* zero spdot array */
504       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
505 #else
506       nexta = 0; nextb = 0;
507       while (nexta<anzi && nextb<bnzj){
508         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
509         if (nexta == anzi) break;
510         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
511         if (nextb == bnzj) break;
512         if (acol[nexta] == bcol[nextb]){
513           cval[j] += aval[nexta]*bval[nextb];
514           nexta++; nextb++;
515           flops += 2;
516         }
517       }
518 #endif
519     }
520   }
521   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
522   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
523   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
524 #if defined(USE_ARRAY)
525   ierr = PetscFree(spdot);
526 #endif
527   PetscFunctionReturn(0);
528 }
529 
530 #undef __FUNCT__
531 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
532 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
533   PetscErrorCode ierr;
534 
535   PetscFunctionBegin;
536   if (scall == MAT_INITIAL_MATRIX){
537     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
538   }
539   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
540   PetscFunctionReturn(0);
541 }
542 
543 #undef __FUNCT__
544 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
545 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
546 {
547   PetscErrorCode ierr;
548   Mat            At;
549   PetscInt       *ati,*atj;
550 
551   PetscFunctionBegin;
552   /* create symbolic At */
553   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
554   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
555 
556   /* get symbolic C=At*B */
557   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
558 
559   /* clean up */
560   ierr = MatDestroy(&At);CHKERRQ(ierr);
561   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
562   PetscFunctionReturn(0);
563 }
564 
565 #undef __FUNCT__
566 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
567 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
568 {
569   PetscErrorCode ierr;
570   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
571   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
572   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
573   PetscLogDouble flops=0.0;
574   MatScalar      *aa=a->a,*ba,*ca=c->a,*caj;
575 
576   PetscFunctionBegin;
577   /* clear old values in C */
578   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
579 
580   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
581   for (i=0;i<am;i++) {
582     bj   = b->j + bi[i];
583     ba   = b->a + bi[i];
584     bnzi = bi[i+1] - bi[i];
585     anzi = ai[i+1] - ai[i];
586     for (j=0; j<anzi; j++) {
587       nextb = 0;
588       crow  = *aj++;
589       cjj   = cj + ci[crow];
590       caj   = ca + ci[crow];
591       /* perform sparse axpy operation.  Note cjj includes bj. */
592       for (k=0; nextb<bnzi; k++) {
593         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
594           caj[k] += (*aa)*(*(ba+nextb));
595           nextb++;
596         }
597       }
598       flops += 2*bnzi;
599       aa++;
600     }
601   }
602 
603   /* Assemble the final matrix and clean up */
604   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
605   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
606   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
607   PetscFunctionReturn(0);
608 }
609 
610 EXTERN_C_BEGIN
611 #undef __FUNCT__
612 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
613 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
614 {
615   PetscErrorCode ierr;
616 
617   PetscFunctionBegin;
618   if (scall == MAT_INITIAL_MATRIX){
619     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
620   }
621   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
622   PetscFunctionReturn(0);
623 }
624 EXTERN_C_END
625 
626 #undef __FUNCT__
627 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
628 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
629 {
630   PetscErrorCode ierr;
631 
632   PetscFunctionBegin;
633   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
634   PetscFunctionReturn(0);
635 }
636 
637 #undef __FUNCT__
638 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
639 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
640 {
641   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
642   PetscErrorCode ierr;
643   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
644   MatScalar      *aa;
645   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
646   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
647 
648   PetscFunctionBegin;
649   if (!cm || !cn) PetscFunctionReturn(0);
650   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);
651   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);
652   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);
653   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
654   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
655   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
656   for (col=0; col<cn-4; col += 4){  /* over columns of C */
657     colam = col*am;
658     for (i=0; i<am; i++) {        /* over rows of C in those columns */
659       r1 = r2 = r3 = r4 = 0.0;
660       n   = a->i[i+1] - a->i[i];
661       aj  = a->j + a->i[i];
662       aa  = a->a + a->i[i];
663       for (j=0; j<n; j++) {
664         r1 += (*aa)*b1[*aj];
665         r2 += (*aa)*b2[*aj];
666         r3 += (*aa)*b3[*aj];
667         r4 += (*aa++)*b4[*aj++];
668       }
669       c[colam + i]       = r1;
670       c[colam + am + i]  = r2;
671       c[colam + am2 + i] = r3;
672       c[colam + am3 + i] = r4;
673     }
674     b1 += bm4;
675     b2 += bm4;
676     b3 += bm4;
677     b4 += bm4;
678   }
679   for (;col<cn; col++){     /* over extra columns of C */
680     for (i=0; i<am; i++) {  /* over rows of C in those columns */
681       r1 = 0.0;
682       n   = a->i[i+1] - a->i[i];
683       aj  = a->j + a->i[i];
684       aa  = a->a + a->i[i];
685 
686       for (j=0; j<n; j++) {
687         r1 += (*aa++)*b1[*aj++];
688       }
689       c[col*am + i]     = r1;
690     }
691     b1 += bm;
692   }
693   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
694   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
695   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
696   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
697   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
698   PetscFunctionReturn(0);
699 }
700 
701 /*
702    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
703 */
704 #undef __FUNCT__
705 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
706 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
707 {
708   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
709   PetscErrorCode ierr;
710   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
711   MatScalar      *aa;
712   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
713   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
714 
715   PetscFunctionBegin;
716   if (!cm || !cn) PetscFunctionReturn(0);
717   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
718   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
719   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
720 
721   if (a->compressedrow.use){ /* use compressed row format */
722     for (col=0; col<cn-4; col += 4){  /* over columns of C */
723       colam = col*am;
724       arm   = a->compressedrow.nrows;
725       ii    = a->compressedrow.i;
726       ridx  = a->compressedrow.rindex;
727       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
728 	r1 = r2 = r3 = r4 = 0.0;
729 	n   = ii[i+1] - ii[i];
730 	aj  = a->j + ii[i];
731 	aa  = a->a + ii[i];
732 	for (j=0; j<n; j++) {
733 	  r1 += (*aa)*b1[*aj];
734 	  r2 += (*aa)*b2[*aj];
735 	  r3 += (*aa)*b3[*aj];
736 	  r4 += (*aa++)*b4[*aj++];
737 	}
738 	c[colam       + ridx[i]] += r1;
739 	c[colam + am  + ridx[i]] += r2;
740 	c[colam + am2 + ridx[i]] += r3;
741 	c[colam + am3 + ridx[i]] += r4;
742       }
743       b1 += bm4;
744       b2 += bm4;
745       b3 += bm4;
746       b4 += bm4;
747     }
748     for (;col<cn; col++){     /* over extra columns of C */
749       colam = col*am;
750       arm   = a->compressedrow.nrows;
751       ii    = a->compressedrow.i;
752       ridx  = a->compressedrow.rindex;
753       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
754 	r1 = 0.0;
755 	n   = ii[i+1] - ii[i];
756 	aj  = a->j + ii[i];
757 	aa  = a->a + ii[i];
758 
759 	for (j=0; j<n; j++) {
760 	  r1 += (*aa++)*b1[*aj++];
761 	}
762 	c[col*am + ridx[i]] += r1;
763       }
764       b1 += bm;
765     }
766   } else {
767     for (col=0; col<cn-4; col += 4){  /* over columns of C */
768       colam = col*am;
769       for (i=0; i<am; i++) {        /* over rows of C in those columns */
770 	r1 = r2 = r3 = r4 = 0.0;
771 	n   = a->i[i+1] - a->i[i];
772 	aj  = a->j + a->i[i];
773 	aa  = a->a + a->i[i];
774 	for (j=0; j<n; j++) {
775 	  r1 += (*aa)*b1[*aj];
776 	  r2 += (*aa)*b2[*aj];
777 	  r3 += (*aa)*b3[*aj];
778 	  r4 += (*aa++)*b4[*aj++];
779 	}
780 	c[colam + i]       += r1;
781 	c[colam + am + i]  += r2;
782 	c[colam + am2 + i] += r3;
783 	c[colam + am3 + i] += r4;
784       }
785       b1 += bm4;
786       b2 += bm4;
787       b3 += bm4;
788       b4 += bm4;
789     }
790     for (;col<cn; col++){     /* over extra columns of C */
791       for (i=0; i<am; i++) {  /* over rows of C in those columns */
792 	r1 = 0.0;
793 	n   = a->i[i+1] - a->i[i];
794 	aj  = a->j + a->i[i];
795 	aa  = a->a + a->i[i];
796 
797 	for (j=0; j<n; j++) {
798 	  r1 += (*aa++)*b1[*aj++];
799 	}
800 	c[col*am + i]     += r1;
801       }
802       b1 += bm;
803     }
804   }
805   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
806   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
807   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
808   PetscFunctionReturn(0);
809 }
810 
811 #undef __FUNCT__
812 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
813 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
814 {
815   PetscErrorCode ierr;
816   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
817   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
818   PetscInt       *bi=b->i,*bj=b->j;
819   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
820   MatScalar      *btval,*btval_den,*ba=b->a;
821   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
822 
823   PetscFunctionBegin;
824   btval_den=btdense->v;
825   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
826   for (k=0; k<ncolors; k++) {
827     ncolumns = coloring->ncolumns[k];
828     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
829       col   = *(columns + colorforcol[k] + l);
830       btcol = bj + bi[col];
831       btval = ba + bi[col];
832       anz   = bi[col+1] - bi[col];
833       for (j=0; j<anz; j++){
834         brow            = btcol[j];
835         btval_den[brow] = btval[j];
836       }
837     }
838     btval_den += m;
839   }
840   PetscFunctionReturn(0);
841 }
842 
843 #undef __FUNCT__
844 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
845 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
846 {
847   PetscErrorCode ierr;
848   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
849   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
850   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
851   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
852 
853   PetscFunctionBegin;
854   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
855   ierr = MatGetArray(Cden,&ca_den);CHKERRQ(ierr);
856   cp_den = ca_den;
857   for (k=0; k<ncolors; k++) {
858     nrows = matcoloring->nrows[k];
859     row   = rows  + colorforrow[k];
860     idx   = spidx + colorforrow[k];
861     for (l=0; l<nrows; l++){
862       ca[idx[l]] = cp_den[row[l]];
863     }
864     cp_den += m;
865   }
866   ierr = MatRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
867   PetscFunctionReturn(0);
868 }
869 
870 /*
871  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
872  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
873  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
874  */
875 #undef __FUNCT__
876 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
877 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
878 {
879   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
880   PetscErrorCode ierr;
881   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
882   PetscInt       nz = a->i[m],row,*jj,mr,col;
883   PetscInt       *cspidx;
884 
885   PetscFunctionBegin;
886   *nn = n;
887   if (!ia) PetscFunctionReturn(0);
888   if (symmetric) {
889     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
890     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,ia,ja);CHKERRQ(ierr);
891   } else {
892     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
893     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
894     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
895     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
896     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
897     jj = a->j;
898     for (i=0; i<nz; i++) {
899       collengths[jj[i]]++;
900     }
901     cia[0] = oshift;
902     for (i=0; i<n; i++) {
903       cia[i+1] = cia[i] + collengths[i];
904     }
905     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
906     jj   = a->j;
907     for (row=0; row<m; row++) {
908       mr = a->i[row+1] - a->i[row];
909       for (i=0; i<mr; i++) {
910         col = *jj++;
911         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
912         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
913       }
914     }
915     ierr = PetscFree(collengths);CHKERRQ(ierr);
916     *ia = cia; *ja = cja;
917     *spidx = cspidx;
918   }
919   PetscFunctionReturn(0);
920 }
921 
922 #undef __FUNCT__
923 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
924 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
925 {
926   PetscErrorCode ierr;
927 
928   PetscFunctionBegin;
929   if (!ia) PetscFunctionReturn(0);
930 
931   ierr = PetscFree(*ia);CHKERRQ(ierr);
932   ierr = PetscFree(*ja);CHKERRQ(ierr);
933   ierr = PetscFree(*spidx);CHKERRQ(ierr);
934   PetscFunctionReturn(0);
935 }
936 
937 #undef __FUNCT__
938 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
939 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
940 {
941   PetscErrorCode ierr;
942   PetscInt       i,n,nrows,N,j,k,m,*row_idx,*ci,*cj,ncols,col,cm;
943   const PetscInt *is;
944   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
945   IS             *isa;
946   PetscBool      done;
947   PetscBool      flg1,flg2;
948   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
949   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
950   PetscInt       *colorforcol,*columns,*columns_i;
951 
952   PetscFunctionBegin;
953   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
954 
955   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
956   ierr = PetscTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
957   ierr = PetscTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
958   if (flg1 || flg2) {
959     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
960   }
961 
962   N         = mat->cmap->N/bs;
963   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
964   c->N      = mat->cmap->N/bs;
965   c->m      = mat->rmap->N/bs;
966   c->rstart = 0;
967 
968   c->ncolors = nis;
969   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
970   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
971   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
972   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
973   colorforrow[0]    = 0;
974   rows_i            = rows;
975   columnsforspidx_i = columnsforspidx;
976 
977   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
978   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
979   colorforcol[0] = 0;
980   columns_i      = columns;
981 
982   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr); /* column-wise storage of mat */
983   if (!done) SETERRQ1(((PetscObject)mat)->comm,PETSC_ERR_SUP,"MatGetColumnIJ() not supported for matrix type %s",((PetscObject)mat)->type_name);
984 
985   cm = c->m;
986   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
987   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
988   for (i=0; i<nis; i++) {
989     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
990     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
991     c->ncolumns[i] = n;
992     if (n) {
993       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
994     }
995     colorforcol[i+1] = colorforcol[i] + n;
996     columns_i       += n;
997 
998     /* fast, crude version requires O(N*N) work */
999     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1000 
1001     /* loop over columns*/
1002     for (j=0; j<n; j++) {
1003       col     = is[j];
1004       row_idx = cj + ci[col];
1005       m       = ci[col+1] - ci[col];
1006       /* loop over columns marking them in rowhit */
1007       for (k=0; k<m; k++) {
1008         idxhit[*row_idx]   = spidx[ci[col] + k];
1009         rowhit[*row_idx++] = col + 1;
1010       }
1011     }
1012     /* count the number of hits */
1013     nrows = 0;
1014     for (j=0; j<cm; j++) {
1015       if (rowhit[j]) nrows++;
1016     }
1017     c->nrows[i]      = nrows;
1018     colorforrow[i+1] = colorforrow[i] + nrows;
1019 
1020     nrows       = 0;
1021     for (j=0; j<cm; j++) {
1022       if (rowhit[j]) {
1023         rows_i[nrows]            = j;
1024         columnsforspidx_i[nrows] = idxhit[j];
1025         nrows++;
1026       }
1027     }
1028     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1029     rows_i += nrows; columnsforspidx_i += nrows;
1030   }
1031   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr);
1032   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1033   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1034 #if defined(PETSC_USE_DEBUG)
1035   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1036 #endif
1037 
1038   c->colorforrow     = colorforrow;
1039   c->rows            = rows;
1040   c->columnsforspidx = columnsforspidx;
1041   c->colorforcol     = colorforcol;
1042   c->columns         = columns;
1043   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1044   PetscFunctionReturn(0);
1045 }
1046