xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision eff52c0e83802002f81775ce8e94c1333cc52f8e)
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     Mat_SeqAIJ                *c=(Mat_SeqAIJ*)(*C)->data;
273 
274     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
275     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
276     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
277     etime0 += tf - t0;
278 
279     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
280     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
281     multtrans->matcoloring = matcoloring;
282     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
283     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
284     etime01 += tf - t0;
285 
286     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
287     /* Create Bt_dense and C_dense = A*Bt_dense */
288     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
289     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
290     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
291     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
292     Bt_dense->assembled = PETSC_TRUE;
293     multtrans->Bt_den = Bt_dense;
294     printf("\n  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));
295 
296     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
297     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
298     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
299     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
300     Bt_dense->assembled = PETSC_TRUE;
301     multtrans->ABt_den = C_dense;
302     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
303     etime1 += tf - t0;
304     printf("Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
305   }
306   /* clean up */
307   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
308   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
309 
310 #if defined(INEFFICIENT_ALGORITHM)
311   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
312   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
313   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
314   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
315   PetscInt           am=A->rmap->N,bm=B->rmap->N;
316   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
317   MatScalar          *ca;
318   PetscBT            lnkbt;
319   PetscReal          afill;
320 
321   /* Allocate row pointer array ci  */
322   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
323   ci[0] = 0;
324 
325   /* Create and initialize a linked list for C columns */
326   nlnk = bm+1;
327   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
328 
329   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
330   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
331   current_space = free_space;
332 
333   /* Determine symbolic info for each row of the product A*B^T: */
334   for (i=0; i<am; i++) {
335     anzi = ai[i+1] - ai[i];
336     cnzi = 0;
337     acol = aj + ai[i];
338     for (j=0; j<bm; j++){
339       bnzj = bi[j+1] - bi[j];
340       bcol= bj + bi[j];
341       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
342       ka = 0; kb = 0;
343       while (ka < anzi && kb < bnzj){
344         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
345         if (ka == anzi) break;
346         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
347         if (kb == bnzj) break;
348         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
349           index[0] = j;
350           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
351           cnzi++;
352           break;
353         }
354       }
355     }
356 
357     /* If free space is not available, make more free space */
358     /* Double the amount of total space in the list */
359     if (current_space->local_remaining<cnzi) {
360       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
361       nspacedouble++;
362     }
363 
364     /* Copy data into free space, then initialize lnk */
365     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
366     current_space->array           += cnzi;
367     current_space->local_used      += cnzi;
368     current_space->local_remaining -= cnzi;
369 
370     ci[i+1] = ci[i] + cnzi;
371   }
372 
373 
374   /* Column indices are in the list of free space.
375      Allocate array cj, copy column indices to cj, and destroy list of free space */
376   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
377   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
378   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
379 
380   /* Allocate space for ca */
381   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
382   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
383 
384   /* put together the new symbolic matrix */
385   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
386 
387   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
388   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
389   c = (Mat_SeqAIJ *)((*C)->data);
390   c->free_a   = PETSC_TRUE;
391   c->free_ij  = PETSC_TRUE;
392   c->nonew    = 0;
393 
394   /* set MatInfo */
395   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
396   if (afill < 1.0) afill = 1.0;
397   c->maxnz                     = ci[am];
398   c->nz                        = ci[am];
399   (*C)->info.mallocs           = nspacedouble;
400   (*C)->info.fill_ratio_given  = fill;
401   (*C)->info.fill_ratio_needed = afill;
402 
403 #if defined(PETSC_USE_INFO)
404   if (ci[am]) {
405     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
406     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
407   } else {
408     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
409   }
410 #endif
411 #endif
412   PetscFunctionReturn(0);
413 }
414 
415 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
416 #undef __FUNCT__
417 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
418 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
419 {
420   PetscErrorCode ierr;
421   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
422   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
423   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
424   PetscLogDouble flops=0.0;
425   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca=c->a,*cval;
426   Mat_MatMatMultTrans *multtrans;
427   PetscContainer      container;
428 #if defined(USE_ARRAY)
429   MatScalar      *spdot;
430 #endif
431 
432   PetscFunctionBegin;
433   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatMultTrans",(PetscObject *)&container);CHKERRQ(ierr);
434   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
435   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
436   if (multtrans->usecoloring){
437     MatTransposeColoring  matcoloring = multtrans->matcoloring;
438     Mat                   Bt_dense;
439     PetscInt              m,n;
440     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
441     Mat C_dense = multtrans->ABt_den;
442 
443     Bt_dense = multtrans->Bt_den;
444     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
445 
446     /* Get Bt_dense by Apply MatTransposeColoring to B */
447     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
448     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
449     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
450     etime0 += tf - t0;
451 
452     /* C_dense = A*Bt_dense */
453     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
454     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
455     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
456     etime2 += tf - t0;
457 
458     /* Recover C from C_dense */
459     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
460     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
461     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
462     etime1 += tf - t0;
463     printf("Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
464     PetscFunctionReturn(0);
465   }
466 
467 #if defined(USE_ARRAY)
468   /* allocate an array for implementing sparse inner-product */
469   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
470   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
471 #endif
472 
473   /* clear old values in C */
474   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
475 
476   for (i=0; i<cm; i++) {
477     anzi = ai[i+1] - ai[i];
478     acol = aj + ai[i];
479     aval = aa + ai[i];
480     cnzi = ci[i+1] - ci[i];
481     ccol = cj + ci[i];
482     cval = ca + ci[i];
483     for (j=0; j<cnzi; j++){
484       brow = ccol[j];
485       bnzj = bi[brow+1] - bi[brow];
486       bcol = bj + bi[brow];
487       bval = ba + bi[brow];
488 
489       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
490 #if defined(USE_ARRAY)
491       /* put ba to spdot array */
492       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
493       /* c(i,j)=A[i,:]*B[j,:]^T */
494       for (nexta=0; nexta<anzi; nexta++){
495         cval[j] += spdot[acol[nexta]]*aval[nexta];
496       }
497       /* zero spdot array */
498       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
499 #else
500       nexta = 0; nextb = 0;
501       while (nexta<anzi && nextb<bnzj){
502         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
503         if (nexta == anzi) break;
504         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
505         if (nextb == bnzj) break;
506         if (acol[nexta] == bcol[nextb]){
507           cval[j] += aval[nexta]*bval[nextb];
508           nexta++; nextb++;
509           flops += 2;
510         }
511       }
512 #endif
513     }
514   }
515   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
516   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
517   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
518 #if defined(USE_ARRAY)
519   ierr = PetscFree(spdot);
520 #endif
521   PetscFunctionReturn(0);
522 }
523 
524 #undef __FUNCT__
525 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
526 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
527   PetscErrorCode ierr;
528 
529   PetscFunctionBegin;
530   if (scall == MAT_INITIAL_MATRIX){
531     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
532   }
533   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
534   PetscFunctionReturn(0);
535 }
536 
537 #undef __FUNCT__
538 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
539 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
540 {
541   PetscErrorCode ierr;
542   Mat            At;
543   PetscInt       *ati,*atj;
544 
545   PetscFunctionBegin;
546   /* create symbolic At */
547   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
548   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
549 
550   /* get symbolic C=At*B */
551   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
552 
553   /* clean up */
554   ierr = MatDestroy(&At);CHKERRQ(ierr);
555   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
556   PetscFunctionReturn(0);
557 }
558 
559 #undef __FUNCT__
560 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
561 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
562 {
563   PetscErrorCode ierr;
564   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
565   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
566   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
567   PetscLogDouble flops=0.0;
568   MatScalar      *aa=a->a,*ba,*ca=c->a,*caj;
569 
570   PetscFunctionBegin;
571   /* clear old values in C */
572   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
573 
574   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
575   for (i=0;i<am;i++) {
576     bj   = b->j + bi[i];
577     ba   = b->a + bi[i];
578     bnzi = bi[i+1] - bi[i];
579     anzi = ai[i+1] - ai[i];
580     for (j=0; j<anzi; j++) {
581       nextb = 0;
582       crow  = *aj++;
583       cjj   = cj + ci[crow];
584       caj   = ca + ci[crow];
585       /* perform sparse axpy operation.  Note cjj includes bj. */
586       for (k=0; nextb<bnzi; k++) {
587         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
588           caj[k] += (*aa)*(*(ba+nextb));
589           nextb++;
590         }
591       }
592       flops += 2*bnzi;
593       aa++;
594     }
595   }
596 
597   /* Assemble the final matrix and clean up */
598   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
599   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
600   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
601   PetscFunctionReturn(0);
602 }
603 
604 EXTERN_C_BEGIN
605 #undef __FUNCT__
606 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
607 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
608 {
609   PetscErrorCode ierr;
610 
611   PetscFunctionBegin;
612   if (scall == MAT_INITIAL_MATRIX){
613     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
614   }
615   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
616   PetscFunctionReturn(0);
617 }
618 EXTERN_C_END
619 
620 #undef __FUNCT__
621 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
622 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
623 {
624   PetscErrorCode ierr;
625 
626   PetscFunctionBegin;
627   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
628   PetscFunctionReturn(0);
629 }
630 
631 #undef __FUNCT__
632 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
633 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
634 {
635   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
636   PetscErrorCode ierr;
637   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
638   MatScalar      *aa;
639   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
640   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
641 
642   PetscFunctionBegin;
643   if (!cm || !cn) PetscFunctionReturn(0);
644   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);
645   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);
646   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);
647   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
648   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
649   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
650   for (col=0; col<cn-4; col += 4){  /* over columns of C */
651     colam = col*am;
652     for (i=0; i<am; i++) {        /* over rows of C in those columns */
653       r1 = r2 = r3 = r4 = 0.0;
654       n   = a->i[i+1] - a->i[i];
655       aj  = a->j + a->i[i];
656       aa  = a->a + a->i[i];
657       for (j=0; j<n; j++) {
658         r1 += (*aa)*b1[*aj];
659         r2 += (*aa)*b2[*aj];
660         r3 += (*aa)*b3[*aj];
661         r4 += (*aa++)*b4[*aj++];
662       }
663       c[colam + i]       = r1;
664       c[colam + am + i]  = r2;
665       c[colam + am2 + i] = r3;
666       c[colam + am3 + i] = r4;
667     }
668     b1 += bm4;
669     b2 += bm4;
670     b3 += bm4;
671     b4 += bm4;
672   }
673   for (;col<cn; col++){     /* over extra columns of C */
674     for (i=0; i<am; i++) {  /* over rows of C in those columns */
675       r1 = 0.0;
676       n   = a->i[i+1] - a->i[i];
677       aj  = a->j + a->i[i];
678       aa  = a->a + a->i[i];
679 
680       for (j=0; j<n; j++) {
681         r1 += (*aa++)*b1[*aj++];
682       }
683       c[col*am + i]     = r1;
684     }
685     b1 += bm;
686   }
687   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
688   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
689   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
690   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
691   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
692   PetscFunctionReturn(0);
693 }
694 
695 /*
696    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
697 */
698 #undef __FUNCT__
699 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
700 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
701 {
702   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
703   PetscErrorCode ierr;
704   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
705   MatScalar      *aa;
706   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
707   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
708 
709   PetscFunctionBegin;
710   if (!cm || !cn) PetscFunctionReturn(0);
711   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
712   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
713   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
714 
715   if (a->compressedrow.use){ /* use compressed row format */
716     for (col=0; col<cn-4; col += 4){  /* over columns of C */
717       colam = col*am;
718       arm   = a->compressedrow.nrows;
719       ii    = a->compressedrow.i;
720       ridx  = a->compressedrow.rindex;
721       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
722 	r1 = r2 = r3 = r4 = 0.0;
723 	n   = ii[i+1] - ii[i];
724 	aj  = a->j + ii[i];
725 	aa  = a->a + ii[i];
726 	for (j=0; j<n; j++) {
727 	  r1 += (*aa)*b1[*aj];
728 	  r2 += (*aa)*b2[*aj];
729 	  r3 += (*aa)*b3[*aj];
730 	  r4 += (*aa++)*b4[*aj++];
731 	}
732 	c[colam       + ridx[i]] += r1;
733 	c[colam + am  + ridx[i]] += r2;
734 	c[colam + am2 + ridx[i]] += r3;
735 	c[colam + am3 + ridx[i]] += r4;
736       }
737       b1 += bm4;
738       b2 += bm4;
739       b3 += bm4;
740       b4 += bm4;
741     }
742     for (;col<cn; col++){     /* over extra columns of C */
743       colam = col*am;
744       arm   = a->compressedrow.nrows;
745       ii    = a->compressedrow.i;
746       ridx  = a->compressedrow.rindex;
747       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
748 	r1 = 0.0;
749 	n   = ii[i+1] - ii[i];
750 	aj  = a->j + ii[i];
751 	aa  = a->a + ii[i];
752 
753 	for (j=0; j<n; j++) {
754 	  r1 += (*aa++)*b1[*aj++];
755 	}
756 	c[col*am + ridx[i]] += r1;
757       }
758       b1 += bm;
759     }
760   } else {
761     for (col=0; col<cn-4; col += 4){  /* over columns of C */
762       colam = col*am;
763       for (i=0; i<am; i++) {        /* over rows of C in those columns */
764 	r1 = r2 = r3 = r4 = 0.0;
765 	n   = a->i[i+1] - a->i[i];
766 	aj  = a->j + a->i[i];
767 	aa  = a->a + a->i[i];
768 	for (j=0; j<n; j++) {
769 	  r1 += (*aa)*b1[*aj];
770 	  r2 += (*aa)*b2[*aj];
771 	  r3 += (*aa)*b3[*aj];
772 	  r4 += (*aa++)*b4[*aj++];
773 	}
774 	c[colam + i]       += r1;
775 	c[colam + am + i]  += r2;
776 	c[colam + am2 + i] += r3;
777 	c[colam + am3 + i] += r4;
778       }
779       b1 += bm4;
780       b2 += bm4;
781       b3 += bm4;
782       b4 += bm4;
783     }
784     for (;col<cn; col++){     /* over extra columns of C */
785       for (i=0; i<am; i++) {  /* over rows of C in those columns */
786 	r1 = 0.0;
787 	n   = a->i[i+1] - a->i[i];
788 	aj  = a->j + a->i[i];
789 	aa  = a->a + a->i[i];
790 
791 	for (j=0; j<n; j++) {
792 	  r1 += (*aa++)*b1[*aj++];
793 	}
794 	c[col*am + i]     += r1;
795       }
796       b1 += bm;
797     }
798   }
799   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
800   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
801   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
802   PetscFunctionReturn(0);
803 }
804 
805 #undef __FUNCT__
806 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
807 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
808 {
809   PetscErrorCode ierr;
810   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
811   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
812   PetscInt       *bi=b->i,*bj=b->j;
813   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
814   MatScalar      *btval,*btval_den,*ba=b->a;
815   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
816 
817   PetscFunctionBegin;
818   btval_den=btdense->v;
819   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
820   for (k=0; k<ncolors; k++) {
821     ncolumns = coloring->ncolumns[k];
822     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
823       col   = *(columns + colorforcol[k] + l);
824       btcol = bj + bi[col];
825       btval = ba + bi[col];
826       anz   = bi[col+1] - bi[col];
827       for (j=0; j<anz; j++){
828         brow            = btcol[j];
829         btval_den[brow] = btval[j];
830       }
831     }
832     btval_den += m;
833   }
834   PetscFunctionReturn(0);
835 }
836 
837 #undef __FUNCT__
838 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
839 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
840 {
841   PetscErrorCode ierr;
842   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
843   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
844   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
845   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
846 
847   PetscFunctionBegin;
848   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
849   ierr = MatGetArray(Cden,&ca_den);CHKERRQ(ierr);
850   cp_den = ca_den;
851   for (k=0; k<ncolors; k++) {
852     nrows = matcoloring->nrows[k];
853     row   = rows  + colorforrow[k];
854     idx   = spidx + colorforrow[k];
855     for (l=0; l<nrows; l++){
856       ca[idx[l]] = cp_den[row[l]];
857     }
858     cp_den += m;
859   }
860   ierr = MatRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
861   PetscFunctionReturn(0);
862 }
863 
864 /*
865  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
866  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
867  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
868  */
869 #undef __FUNCT__
870 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
871 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
872 {
873   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
874   PetscErrorCode ierr;
875   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
876   PetscInt       nz = a->i[m],row,*jj,mr,col;
877   PetscInt       *cspidx;
878 
879   PetscFunctionBegin;
880   *nn = n;
881   if (!ia) PetscFunctionReturn(0);
882   if (symmetric) {
883     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
884     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,ia,ja);CHKERRQ(ierr);
885   } else {
886     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
887     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
888     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
889     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
890     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
891     jj = a->j;
892     for (i=0; i<nz; i++) {
893       collengths[jj[i]]++;
894     }
895     cia[0] = oshift;
896     for (i=0; i<n; i++) {
897       cia[i+1] = cia[i] + collengths[i];
898     }
899     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
900     jj   = a->j;
901     for (row=0; row<m; row++) {
902       mr = a->i[row+1] - a->i[row];
903       for (i=0; i<mr; i++) {
904         col = *jj++;
905         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
906         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
907       }
908     }
909     ierr = PetscFree(collengths);CHKERRQ(ierr);
910     *ia = cia; *ja = cja;
911     *spidx = cspidx;
912   }
913   PetscFunctionReturn(0);
914 }
915 
916 #undef __FUNCT__
917 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
918 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
919 {
920   PetscErrorCode ierr;
921 
922   PetscFunctionBegin;
923   if (!ia) PetscFunctionReturn(0);
924 
925   ierr = PetscFree(*ia);CHKERRQ(ierr);
926   ierr = PetscFree(*ja);CHKERRQ(ierr);
927   ierr = PetscFree(*spidx);CHKERRQ(ierr);
928   PetscFunctionReturn(0);
929 }
930 
931 #undef __FUNCT__
932 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
933 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
934 {
935   PetscErrorCode ierr;
936   PetscInt       i,n,nrows,N,j,k,m,*row_idx,*ci,*cj,ncols,col,cm;
937   const PetscInt *is;
938   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
939   IS             *isa;
940   PetscBool      done;
941   PetscBool      flg1,flg2;
942   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
943   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
944   PetscInt       *colorforcol,*columns,*columns_i;
945   PetscLogDouble t0,tf,etime_GetIS=0.0,etime_GetColumnIJ=0.0,etime_memzero=0.0,etime_loop=0.0,t00,tf0;
946 
947   PetscFunctionBegin;
948   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
949   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
950   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
951   etime_GetIS += tf - t0;
952 
953   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
954   ierr = PetscTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
955   ierr = PetscTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
956   if (flg1 || flg2) {
957     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
958   }
959 
960   N         = mat->cmap->N/bs;
961   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
962   c->N      = mat->cmap->N/bs;
963   c->m      = mat->rmap->N/bs;
964   c->rstart = 0;
965 
966   c->ncolors = nis;
967   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
968   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
969   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
970   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
971   colorforrow[0]    = 0;
972   rows_i            = rows;
973   columnsforspidx_i = columnsforspidx;
974 
975   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
976   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
977   colorforcol[0] = 0;
978   columns_i      = columns;
979 
980   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
981   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr); /* column-wise storage of mat */
982   if (!done) SETERRQ1(((PetscObject)mat)->comm,PETSC_ERR_SUP,"MatGetColumnIJ() not supported for matrix type %s",((PetscObject)mat)->type_name);
983   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
984   etime_GetColumnIJ += tf - t0;
985 
986   cm = c->m;
987   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
988   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
989   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
990   for (i=0; i<nis; i++) {
991     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
992     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
993     c->ncolumns[i] = n;
994     if (n) {
995       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
996     }
997     colorforcol[i+1] = colorforcol[i] + n;
998     columns_i       += n;
999 
1000     /* fast, crude version requires O(N*N) work */
1001     ierr = PetscGetTime(&t00);CHKERRQ(ierr);
1002     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1003     ierr = PetscGetTime(&tf0);CHKERRQ(ierr);
1004     etime_memzero += tf0 - t00;
1005 
1006     /* loop over columns*/
1007     for (j=0; j<n; j++) {
1008       col     = is[j];
1009       row_idx = cj + ci[col];
1010       m       = ci[col+1] - ci[col];
1011       /* loop over columns marking them in rowhit */
1012       for (k=0; k<m; k++) {
1013         idxhit[*row_idx]   = spidx[ci[col] + k];
1014         rowhit[*row_idx++] = col + 1;
1015       }
1016     }
1017     /* count the number of hits */
1018     nrows = 0;
1019     for (j=0; j<cm; j++) {
1020       if (rowhit[j]) nrows++;
1021     }
1022     c->nrows[i]      = nrows;
1023     colorforrow[i+1] = colorforrow[i] + nrows;
1024 
1025     nrows       = 0;
1026     for (j=0; j<cm; j++) {
1027       if (rowhit[j]) {
1028         rows_i[nrows]            = j;
1029         columnsforspidx_i[nrows] = idxhit[j];
1030         nrows++;
1031       }
1032     }
1033     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1034     rows_i += nrows; columnsforspidx_i += nrows;
1035   }
1036   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
1037   etime_loop += tf - t0;
1038 
1039   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr);
1040   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1041   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1042 #if defined(PETSC_USE_DEBUG)
1043   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1044 #endif
1045 
1046   c->colorforrow     = colorforrow;
1047   c->rows            = rows;
1048   c->columnsforspidx = columnsforspidx;
1049   c->colorforcol     = colorforcol;
1050   c->columns         = columns;
1051   /* printf(" Time for ColoringCreate: IS %g, ColumnIJ: %g, memzero %g, loop %g\n",etime_GetIS,etime_GetColumnIJ,etime_memzero,etime_loop); */
1052   ierr = PetscFree(idxhit);
1053   PetscFunctionReturn(0);
1054 }
1055