xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision aaf9cf16f7c13493ca75cf610d6a4eecc84850ff)
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_MatMatMultTrans"
194 PetscErrorCode PetscContainerDestroy_Mat_MatMatMultTrans(void *ptr)
195 {
196   PetscErrorCode      ierr;
197   Mat_MatMatMultTrans *multtrans=(Mat_MatMatMultTrans*)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_MatMatMultTrans *multtrans=PETSC_NULL;
214 
215   PetscFunctionBegin;
216   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultTrans",(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_MatMatMultTrans",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_MatMatMultTrans *multtrans;
235   PetscContainer      container;
236 
237   PetscLogDouble      t0,tf,etime2=0.0;
238 
239   PetscFunctionBegin;
240   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
241    /* create symbolic Bt */
242   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
243   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
244 
245   /* get symbolic C=A*Bt */
246   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);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 = PetscGetTime(&tf);CHKERRQ(ierr);
263   etime2 += tf - t0;
264 
265   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmulttrans_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
266   if (multtrans->usecoloring){
267     /* Create MatTransposeColoring from symbolic C=A*B^T */
268     MatTransposeColoring      matcoloring;
269     ISColoring                iscoloring;
270     Mat                       Bt_dense,C_dense;
271     PetscLogDouble            etime0=0.0,etime01=0.0,etime1=0.0;
272 
273     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
274     ierr = MatGetColoring(*C,MATCOLORINGSL,&iscoloring);CHKERRQ(ierr);
275     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
276     etime0 += tf - t0;
277 
278     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
279     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
280     multtrans->matcoloring = matcoloring;
281     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
282     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
283     etime01 += tf - t0;
284 
285     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
286     /* Create Bt_dense and C_dense = A*Bt_dense */
287     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
288     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
289     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
290     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
291     Bt_dense->assembled = PETSC_TRUE;
292     multtrans->Bt_den = Bt_dense;
293 
294     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
295     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
296     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
297     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
298     Bt_dense->assembled = PETSC_TRUE;
299     multtrans->ABt_den = C_dense;
300     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
301     etime1 += tf - t0;
302     printf("Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
303   }
304   /* clean up */
305   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
306   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
307 
308 #if defined(INEFFICIENT_ALGORITHM)
309   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
310   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
311   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
312   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
313   PetscInt           am=A->rmap->N,bm=B->rmap->N;
314   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
315   MatScalar          *ca;
316   PetscBT            lnkbt;
317   PetscReal          afill;
318 
319   /* Allocate row pointer array ci  */
320   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
321   ci[0] = 0;
322 
323   /* Create and initialize a linked list for C columns */
324   nlnk = bm+1;
325   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
326 
327   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
328   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
329   current_space = free_space;
330 
331   /* Determine symbolic info for each row of the product A*B^T: */
332   for (i=0; i<am; i++) {
333     anzi = ai[i+1] - ai[i];
334     cnzi = 0;
335     acol = aj + ai[i];
336     for (j=0; j<bm; j++){
337       bnzj = bi[j+1] - bi[j];
338       bcol= bj + bi[j];
339       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
340       ka = 0; kb = 0;
341       while (ka < anzi && kb < bnzj){
342         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
343         if (ka == anzi) break;
344         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
345         if (kb == bnzj) break;
346         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
347           index[0] = j;
348           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
349           cnzi++;
350           break;
351         }
352       }
353     }
354 
355     /* If free space is not available, make more free space */
356     /* Double the amount of total space in the list */
357     if (current_space->local_remaining<cnzi) {
358       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
359       nspacedouble++;
360     }
361 
362     /* Copy data into free space, then initialize lnk */
363     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
364     current_space->array           += cnzi;
365     current_space->local_used      += cnzi;
366     current_space->local_remaining -= cnzi;
367 
368     ci[i+1] = ci[i] + cnzi;
369   }
370 
371 
372   /* Column indices are in the list of free space.
373      Allocate array cj, copy column indices to cj, and destroy list of free space */
374   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
375   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
376   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
377 
378   /* Allocate space for ca */
379   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
380   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
381 
382   /* put together the new symbolic matrix */
383   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
384 
385   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
386   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
387   c = (Mat_SeqAIJ *)((*C)->data);
388   c->free_a   = PETSC_TRUE;
389   c->free_ij  = PETSC_TRUE;
390   c->nonew    = 0;
391 
392   /* set MatInfo */
393   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
394   if (afill < 1.0) afill = 1.0;
395   c->maxnz                     = ci[am];
396   c->nz                        = ci[am];
397   (*C)->info.mallocs           = nspacedouble;
398   (*C)->info.fill_ratio_given  = fill;
399   (*C)->info.fill_ratio_needed = afill;
400 
401 #if defined(PETSC_USE_INFO)
402   if (ci[am]) {
403     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
404     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
405   } else {
406     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
407   }
408 #endif
409 #endif
410   PetscFunctionReturn(0);
411 }
412 
413 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
414 #undef __FUNCT__
415 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
416 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
417 {
418   PetscErrorCode ierr;
419   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
420   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
421   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
422   PetscLogDouble flops=0.0;
423   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca=c->a,*cval;
424   Mat_MatMatMultTrans *multtrans;
425   PetscContainer      container;
426 #if defined(USE_ARRAY)
427   MatScalar      *spdot;
428 #endif
429 
430   PetscFunctionBegin;
431   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatMultTrans",(PetscObject *)&container);CHKERRQ(ierr);
432   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
433   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
434   if (multtrans->usecoloring){
435     MatTransposeColoring  matcoloring = multtrans->matcoloring;
436     Mat                   Bt_dense;
437     PetscInt              m,n;
438     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
439     Mat C_dense = multtrans->ABt_den;
440 
441     Bt_dense = multtrans->Bt_den;
442     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
443     printf("Bt_dense: %d,%d\n",m,n);
444 
445     /* Get Bt_dense by Apply MatTransposeColoring to B */
446     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
447     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
448     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
449     etime0 += tf - t0;
450 
451     /* C_dense = A*Bt_dense */
452     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
453     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
454     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
455     etime2 += tf - t0;
456 
457     /* Recover C from C_dense */
458     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
459     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
460     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
461     etime1 += tf - t0;
462     printf("Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
463     PetscFunctionReturn(0);
464   }
465 
466 #if defined(USE_ARRAY)
467   /* allocate an array for implementing sparse inner-product */
468   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
469   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
470 #endif
471 
472   /* clear old values in C */
473   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
474 
475   for (i=0; i<cm; i++) {
476     anzi = ai[i+1] - ai[i];
477     acol = aj + ai[i];
478     aval = aa + ai[i];
479     cnzi = ci[i+1] - ci[i];
480     ccol = cj + ci[i];
481     cval = ca + ci[i];
482     for (j=0; j<cnzi; j++){
483       brow = ccol[j];
484       bnzj = bi[brow+1] - bi[brow];
485       bcol = bj + bi[brow];
486       bval = ba + bi[brow];
487 
488       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
489 #if defined(USE_ARRAY)
490       /* put ba to spdot array */
491       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
492       /* c(i,j)=A[i,:]*B[j,:]^T */
493       for (nexta=0; nexta<anzi; nexta++){
494         cval[j] += spdot[acol[nexta]]*aval[nexta];
495       }
496       /* zero spdot array */
497       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
498 #else
499       nexta = 0; nextb = 0;
500       while (nexta<anzi && nextb<bnzj){
501         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
502         if (nexta == anzi) break;
503         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
504         if (nextb == bnzj) break;
505         if (acol[nexta] == bcol[nextb]){
506           cval[j] += aval[nexta]*bval[nextb];
507           nexta++; nextb++;
508           flops += 2;
509         }
510       }
511 #endif
512     }
513   }
514   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
515   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
516   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
517 #if defined(USE_ARRAY)
518   ierr = PetscFree(spdot);
519 #endif
520   PetscFunctionReturn(0);
521 }
522 
523 #undef __FUNCT__
524 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
525 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
526   PetscErrorCode ierr;
527 
528   PetscFunctionBegin;
529   if (scall == MAT_INITIAL_MATRIX){
530     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
531   }
532   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
533   PetscFunctionReturn(0);
534 }
535 
536 #undef __FUNCT__
537 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
538 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
539 {
540   PetscErrorCode ierr;
541   Mat            At;
542   PetscInt       *ati,*atj;
543 
544   PetscFunctionBegin;
545   /* create symbolic At */
546   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
547   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
548 
549   /* get symbolic C=At*B */
550   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
551 
552   /* clean up */
553   ierr = MatDestroy(&At);CHKERRQ(ierr);
554   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
555   PetscFunctionReturn(0);
556 }
557 
558 #undef __FUNCT__
559 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
560 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
561 {
562   PetscErrorCode ierr;
563   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
564   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
565   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
566   PetscLogDouble flops=0.0;
567   MatScalar      *aa=a->a,*ba,*ca=c->a,*caj;
568 
569   PetscFunctionBegin;
570   /* clear old values in C */
571   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
572 
573   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
574   for (i=0;i<am;i++) {
575     bj   = b->j + bi[i];
576     ba   = b->a + bi[i];
577     bnzi = bi[i+1] - bi[i];
578     anzi = ai[i+1] - ai[i];
579     for (j=0; j<anzi; j++) {
580       nextb = 0;
581       crow  = *aj++;
582       cjj   = cj + ci[crow];
583       caj   = ca + ci[crow];
584       /* perform sparse axpy operation.  Note cjj includes bj. */
585       for (k=0; nextb<bnzi; k++) {
586         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
587           caj[k] += (*aa)*(*(ba+nextb));
588           nextb++;
589         }
590       }
591       flops += 2*bnzi;
592       aa++;
593     }
594   }
595 
596   /* Assemble the final matrix and clean up */
597   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
598   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
599   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
600   PetscFunctionReturn(0);
601 }
602 
603 EXTERN_C_BEGIN
604 #undef __FUNCT__
605 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
606 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
607 {
608   PetscErrorCode ierr;
609 
610   PetscFunctionBegin;
611   if (scall == MAT_INITIAL_MATRIX){
612     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
613   }
614   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
615   PetscFunctionReturn(0);
616 }
617 EXTERN_C_END
618 
619 #undef __FUNCT__
620 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
621 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
622 {
623   PetscErrorCode ierr;
624 
625   PetscFunctionBegin;
626   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
627   PetscFunctionReturn(0);
628 }
629 
630 #undef __FUNCT__
631 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
632 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
633 {
634   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
635   PetscErrorCode ierr;
636   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
637   MatScalar      *aa;
638   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
639   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
640 
641   PetscFunctionBegin;
642   if (!cm || !cn) PetscFunctionReturn(0);
643   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);
644   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);
645   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);
646   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
647   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
648   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
649   for (col=0; col<cn-4; col += 4){  /* over columns of C */
650     colam = col*am;
651     for (i=0; i<am; i++) {        /* over rows of C in those columns */
652       r1 = r2 = r3 = r4 = 0.0;
653       n   = a->i[i+1] - a->i[i];
654       aj  = a->j + a->i[i];
655       aa  = a->a + a->i[i];
656       for (j=0; j<n; j++) {
657         r1 += (*aa)*b1[*aj];
658         r2 += (*aa)*b2[*aj];
659         r3 += (*aa)*b3[*aj];
660         r4 += (*aa++)*b4[*aj++];
661       }
662       c[colam + i]       = r1;
663       c[colam + am + i]  = r2;
664       c[colam + am2 + i] = r3;
665       c[colam + am3 + i] = r4;
666     }
667     b1 += bm4;
668     b2 += bm4;
669     b3 += bm4;
670     b4 += bm4;
671   }
672   for (;col<cn; col++){     /* over extra columns of C */
673     for (i=0; i<am; i++) {  /* over rows of C in those columns */
674       r1 = 0.0;
675       n   = a->i[i+1] - a->i[i];
676       aj  = a->j + a->i[i];
677       aa  = a->a + a->i[i];
678 
679       for (j=0; j<n; j++) {
680         r1 += (*aa++)*b1[*aj++];
681       }
682       c[col*am + i]     = r1;
683     }
684     b1 += bm;
685   }
686   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
687   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
688   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
689   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
690   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
691   PetscFunctionReturn(0);
692 }
693 
694 /*
695    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
696 */
697 #undef __FUNCT__
698 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
699 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
700 {
701   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
702   PetscErrorCode ierr;
703   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
704   MatScalar      *aa;
705   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
706   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
707 
708   PetscFunctionBegin;
709   if (!cm || !cn) PetscFunctionReturn(0);
710   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
711   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
712   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
713 
714   if (a->compressedrow.use){ /* use compressed row format */
715     for (col=0; col<cn-4; col += 4){  /* over columns of C */
716       colam = col*am;
717       arm   = a->compressedrow.nrows;
718       ii    = a->compressedrow.i;
719       ridx  = a->compressedrow.rindex;
720       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
721 	r1 = r2 = r3 = r4 = 0.0;
722 	n   = ii[i+1] - ii[i];
723 	aj  = a->j + ii[i];
724 	aa  = a->a + ii[i];
725 	for (j=0; j<n; j++) {
726 	  r1 += (*aa)*b1[*aj];
727 	  r2 += (*aa)*b2[*aj];
728 	  r3 += (*aa)*b3[*aj];
729 	  r4 += (*aa++)*b4[*aj++];
730 	}
731 	c[colam       + ridx[i]] += r1;
732 	c[colam + am  + ridx[i]] += r2;
733 	c[colam + am2 + ridx[i]] += r3;
734 	c[colam + am3 + ridx[i]] += r4;
735       }
736       b1 += bm4;
737       b2 += bm4;
738       b3 += bm4;
739       b4 += bm4;
740     }
741     for (;col<cn; col++){     /* over extra columns of C */
742       colam = col*am;
743       arm   = a->compressedrow.nrows;
744       ii    = a->compressedrow.i;
745       ridx  = a->compressedrow.rindex;
746       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
747 	r1 = 0.0;
748 	n   = ii[i+1] - ii[i];
749 	aj  = a->j + ii[i];
750 	aa  = a->a + ii[i];
751 
752 	for (j=0; j<n; j++) {
753 	  r1 += (*aa++)*b1[*aj++];
754 	}
755 	c[col*am + ridx[i]] += r1;
756       }
757       b1 += bm;
758     }
759   } else {
760     for (col=0; col<cn-4; col += 4){  /* over columns of C */
761       colam = col*am;
762       for (i=0; i<am; i++) {        /* over rows of C in those columns */
763 	r1 = r2 = r3 = r4 = 0.0;
764 	n   = a->i[i+1] - a->i[i];
765 	aj  = a->j + a->i[i];
766 	aa  = a->a + a->i[i];
767 	for (j=0; j<n; j++) {
768 	  r1 += (*aa)*b1[*aj];
769 	  r2 += (*aa)*b2[*aj];
770 	  r3 += (*aa)*b3[*aj];
771 	  r4 += (*aa++)*b4[*aj++];
772 	}
773 	c[colam + i]       += r1;
774 	c[colam + am + i]  += r2;
775 	c[colam + am2 + i] += r3;
776 	c[colam + am3 + i] += r4;
777       }
778       b1 += bm4;
779       b2 += bm4;
780       b3 += bm4;
781       b4 += bm4;
782     }
783     for (;col<cn; col++){     /* over extra columns of C */
784       for (i=0; i<am; i++) {  /* over rows of C in those columns */
785 	r1 = 0.0;
786 	n   = a->i[i+1] - a->i[i];
787 	aj  = a->j + a->i[i];
788 	aa  = a->a + a->i[i];
789 
790 	for (j=0; j<n; j++) {
791 	  r1 += (*aa++)*b1[*aj++];
792 	}
793 	c[col*am + i]     += r1;
794       }
795       b1 += bm;
796     }
797   }
798   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
799   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
800   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
801   PetscFunctionReturn(0);
802 }
803 
804 #undef __FUNCT__
805 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
806 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
807 {
808   PetscErrorCode ierr;
809   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)B->data;
810   Mat_SeqDense   *atdense = (Mat_SeqDense*)Btdense->data;
811   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*atcol,brow;
812   MatScalar      *atval,*bval=atdense->v;
813   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol;
814 
815   PetscFunctionBegin;
816   ierr = PetscMemzero(atdense->v,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
817   for (k=0; k<coloring->ncolors; k++) {
818     for (l=0; l<coloring->ncolumns[k]; l++) { /* insert a row of B to a column of Btdense */
819       col   = *(columns + colorforcol[k] + l);
820       atcol = a->j + a->i[col];
821       atval = a->a + a->i[col];
822       anz   = a->i[col+1] - a->i[col];
823       for (j=0; j<anz; j++){
824         brow  = atcol[j];
825         bval[k*m+brow] = atval[j];
826       }
827     }
828   }
829   PetscFunctionReturn(0);
830 }
831 
832 #undef __FUNCT__
833 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
834 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
835 {
836   PetscErrorCode ierr;
837   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
838   PetscInt       k,l,row,m;
839   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
840   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow,idx;
841 
842   PetscFunctionBegin;
843   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
844   ierr = MatGetArray(Cden,&ca_den);CHKERRQ(ierr);
845   cp_den = ca_den;
846   for (k=0; k<matcoloring->ncolors; k++) {
847     for (l=0; l<matcoloring->nrows[k]; l++){
848       row     = *(rows + colorforrow[k] + l);
849       idx     = *(spidx + colorforrow[k] + l);
850       ca[idx] = cp_den[row];
851     }
852     cp_den += m;
853   }
854   ierr = MatRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
855   PetscFunctionReturn(0);
856 }
857 
858 /*
859  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
860  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
861  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
862  */
863 #undef __FUNCT__
864 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
865 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
866 {
867   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
868   PetscErrorCode ierr;
869   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
870   PetscInt       nz = a->i[m],row,*jj,mr,col;
871   PetscInt       *cspidx;
872 
873   PetscFunctionBegin;
874   *nn = n;
875   if (!ia) PetscFunctionReturn(0);
876   if (symmetric) {
877     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
878     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,ia,ja);CHKERRQ(ierr);
879   } else {
880     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
881     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
882     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
883     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
884     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
885     jj = a->j;
886     for (i=0; i<nz; i++) {
887       collengths[jj[i]]++;
888     }
889     cia[0] = oshift;
890     for (i=0; i<n; i++) {
891       cia[i+1] = cia[i] + collengths[i];
892     }
893     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
894     jj   = a->j;
895     for (row=0; row<m; row++) {
896       mr = a->i[row+1] - a->i[row];
897       for (i=0; i<mr; i++) {
898         col = *jj++;
899         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
900         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
901       }
902     }
903     ierr = PetscFree(collengths);CHKERRQ(ierr);
904     *ia = cia; *ja = cja;
905     *spidx = cspidx;
906   }
907   PetscFunctionReturn(0);
908 }
909 
910 #undef __FUNCT__
911 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
912 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
913 {
914   PetscErrorCode ierr;
915 
916   PetscFunctionBegin;
917   if (!ia) PetscFunctionReturn(0);
918 
919   ierr = PetscFree(*ia);CHKERRQ(ierr);
920   ierr = PetscFree(*ja);CHKERRQ(ierr);
921   ierr = PetscFree(*spidx);CHKERRQ(ierr);
922   PetscFunctionReturn(0);
923 }
924 
925 #undef __FUNCT__
926 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
927 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
928 {
929   PetscErrorCode ierr;
930   PetscInt       i,n,nrows,N,j,k,m,*row_idx,*ci,*cj,ncols,col,cm;
931   const PetscInt *is;
932   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
933   IS             *isa;
934   PetscBool      done;
935   PetscBool      flg1,flg2;
936   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
937   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
938   PetscInt       *colorforcol,*columns,*columns_i;
939   PetscLogDouble t0,tf,etime_GetIS=0.0,etime_GetColumnIJ=0.0,etime_memzero=0.0,etime_loop=0.0,t00,tf0;
940 
941   PetscFunctionBegin;
942   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
943   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
944   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
945   etime_GetIS += tf - t0;
946 
947   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
948   ierr = PetscTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
949   ierr = PetscTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
950   if (flg1 || flg2) {
951     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
952   }
953 
954   N         = mat->cmap->N/bs;
955   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
956   c->N      = mat->cmap->N/bs;
957   c->m      = mat->rmap->N/bs;
958   c->rstart = 0;
959 
960   c->ncolors = nis;
961   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
962   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
963   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
964   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
965   colorforrow[0]    = 0;
966   rows_i            = rows;
967   columnsforspidx_i = columnsforspidx;
968 
969   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
970   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
971   colorforcol[0] = 0;
972   columns_i      = columns;
973 
974   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
975   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr); /* column-wise storage of mat */
976   if (!done) SETERRQ1(((PetscObject)mat)->comm,PETSC_ERR_SUP,"MatGetColumnIJ() not supported for matrix type %s",((PetscObject)mat)->type_name);
977   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
978   etime_GetColumnIJ += tf - t0;
979 
980   cm = c->m;
981   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
982   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
983   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
984   for (i=0; i<nis; i++) {
985     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
986     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
987     c->ncolumns[i] = n;
988     if (n) {
989       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
990     }
991     colorforcol[i+1] = colorforcol[i] + n;
992     columns_i       += n;
993 
994     /* fast, crude version requires O(N*N) work */
995     ierr = PetscGetTime(&t00);CHKERRQ(ierr);
996     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
997     ierr = PetscGetTime(&tf0);CHKERRQ(ierr);
998     etime_memzero += tf0 - t00;
999 
1000     /* loop over columns*/
1001     for (j=0; j<n; j++) {
1002       col     = is[j];
1003       row_idx = cj + ci[col];
1004       m       = ci[col+1] - ci[col];
1005       /* loop over columns marking them in rowhit */
1006       for (k=0; k<m; k++) {
1007         idxhit[*row_idx]   = spidx[ci[col] + k];
1008         rowhit[*row_idx++] = col + 1;
1009       }
1010     }
1011     /* count the number of hits */
1012     nrows = 0;
1013     for (j=0; j<cm; j++) {
1014       if (rowhit[j]) nrows++;
1015     }
1016     c->nrows[i]      = nrows;
1017     colorforrow[i+1] = colorforrow[i] + nrows;
1018 
1019     nrows       = 0;
1020     for (j=0; j<cm; j++) {
1021       if (rowhit[j]) {
1022         rows_i[nrows]            = j;
1023         columnsforspidx_i[nrows] = idxhit[j];
1024         nrows++;
1025       }
1026     }
1027     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1028     rows_i += nrows; columnsforspidx_i += nrows;
1029   }
1030   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
1031   etime_loop += tf - t0;
1032 
1033   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr);
1034   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1035   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1036 #if defined(PETSC_USE_DEBUG)
1037   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1038 #endif
1039 
1040   c->colorforrow     = colorforrow;
1041   c->rows            = rows;
1042   c->columnsforspidx = columnsforspidx;
1043   c->colorforcol     = colorforcol;
1044   c->columns         = columns;
1045   printf(" Time for ColoringCreate: IS %g, ColumnIJ: %g, memzero %g, loop %g\n",etime_GetIS,etime_GetColumnIJ,etime_memzero,etime_loop);
1046   ierr = PetscFree(idxhit);
1047   PetscFunctionReturn(0);
1048 }
1049