xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision ea5d4fccf296dd2bbd0f9c3a3343651cb1066da7)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = A * B
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <petscbt.h>
10 #include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/
11 /*
12 #define DEBUG_MATMATMULT
13  */
14 EXTERN_C_BEGIN
15 #undef __FUNCT__
16 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
17 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
18 {
19   PetscErrorCode ierr;
20   PetscBool      scalable=PETSC_FALSE,scalable_fast=PETSC_FALSE;
21 
22   PetscFunctionBegin;
23   if (scall == MAT_INITIAL_MATRIX){
24     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
25     ierr = PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
26     ierr = PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,PETSC_NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsEnd();CHKERRQ(ierr);
28     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
29     if (scalable_fast){
30       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
31     } else if (scalable){
32       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
33     } else {
34       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
35     }
36     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
37   }
38   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
39   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
40   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
41   PetscFunctionReturn(0);
42 }
43 EXTERN_C_END
44 
45 #undef __FUNCT__
46 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
47 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
48 {
49   PetscErrorCode     ierr;
50   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
51   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
52   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
53   PetscReal          afill;
54   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
55   PetscBT            lnkbt;
56   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
57 
58   PetscFunctionBegin;
59   /* Get ci and cj */
60   /*---------------*/
61   /* Allocate ci array, arrays for fill computation and */
62   /* free space for accumulating nonzero column info */
63   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
64   ci[0] = 0;
65 
66   /* create and initialize a linked list */
67   nlnk_max = a->rmax*b->rmax;
68   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
69   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
70 
71   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
72   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
73   current_space = free_space;
74 
75   /* Determine ci and cj */
76   for (i=0; i<am; i++) {
77     anzi = ai[i+1] - ai[i];
78     aj   = a->j + ai[i];
79     for (j=0; j<anzi; j++){
80       brow = aj[j];
81       bnzj = bi[brow+1] - bi[brow];
82       bj   = b->j + bi[brow];
83       /* add non-zero cols of B into the sorted linked list lnk */
84       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
85     }
86     cnzi = lnk[0];
87 
88     /* If free space is not available, make more free space */
89     /* Double the amount of total space in the list */
90     if (current_space->local_remaining<cnzi) {
91       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
92       ndouble++;
93     }
94 
95     /* Copy data into free space, then initialize lnk */
96     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
97     current_space->array           += cnzi;
98     current_space->local_used      += cnzi;
99     current_space->local_remaining -= cnzi;
100     ci[i+1] = ci[i] + cnzi;
101   }
102 
103   /* Column indices are in the list of free space */
104   /* Allocate space for cj, initialize cj, and */
105   /* destroy list of free space and other temporary array(s) */
106   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
107   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
108   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
109 
110   /* put together the new symbolic matrix */
111   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
112 
113   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
114   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
115   c = (Mat_SeqAIJ *)((*C)->data);
116   c->free_a  = PETSC_FALSE;
117   c->free_ij = PETSC_TRUE;
118   c->nonew   = 0;
119   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
120 
121   /* set MatInfo */
122   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
123   if (afill < 1.0) afill = 1.0;
124   c->maxnz                     = ci[am];
125   c->nz                        = ci[am];
126   (*C)->info.mallocs           = ndouble;
127   (*C)->info.fill_ratio_given  = fill;
128   (*C)->info.fill_ratio_needed = afill;
129 
130 #if defined(PETSC_USE_INFO)
131   if (ci[am]) {
132     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
133     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
134   } else {
135     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
136   }
137 #endif
138   PetscFunctionReturn(0);
139 }
140 
141 #undef __FUNCT__
142 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
143 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
144 {
145   PetscErrorCode ierr;
146   PetscLogDouble flops=0.0;
147   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
148   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
149   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
150   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
151   PetscInt       am=A->rmap->n,cm=C->rmap->n;
152   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
153   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
154   PetscScalar    *ab_dense;
155 
156   PetscFunctionBegin;
157   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
158   if (!c->a){ /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
159     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
160     c->a      = ca;
161     c->free_a = PETSC_TRUE;
162 
163     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
164     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
165     c->matmult_abdense = ab_dense;
166   } else {
167     ca       = c->a;
168     ab_dense = c->matmult_abdense;
169   }
170 
171   /* clean old values in C */
172   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
173   /* Traverse A row-wise. */
174   /* Build the ith row in C by summing over nonzero columns in A, */
175   /* the rows of B corresponding to nonzeros of A. */
176   for (i=0; i<am; i++) {
177     anzi = ai[i+1] - ai[i];
178     for (j=0; j<anzi; j++) {
179       brow = aj[j];
180       bnzi = bi[brow+1] - bi[brow];
181       bjj  = bj + bi[brow];
182       baj  = ba + bi[brow];
183       /* perform dense axpy */
184       valtmp = aa[j];
185       for (k=0; k<bnzi; k++) {
186         ab_dense[bjj[k]] += valtmp*baj[k];
187       }
188       flops += 2*bnzi;
189     }
190     aj += anzi; aa += anzi;
191 
192     cnzi = ci[i+1] - ci[i];
193     for (k=0; k<cnzi; k++) {
194       ca[k]          += ab_dense[cj[k]];
195       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
196     }
197     flops += cnzi;
198     cj += cnzi; ca += cnzi;
199   }
200   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
201   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
202   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
203   PetscFunctionReturn(0);
204 }
205 
206 #undef __FUNCT__
207 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
208 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
209 {
210   PetscErrorCode ierr;
211   PetscLogDouble flops=0.0;
212   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
213   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
214   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
215   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
216   PetscInt       am=A->rmap->N,cm=C->rmap->N;
217   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
218   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
219   PetscInt       nextb;
220 
221   PetscFunctionBegin;
222 #if defined(DEBUG_MATMATMULT)
223   ierr = PetscPrintf(PETSC_COMM_SELF,"MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable...\n");CHKERRQ(ierr);
224 #endif
225   /* clean old values in C */
226   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
227   /* Traverse A row-wise. */
228   /* Build the ith row in C by summing over nonzero columns in A, */
229   /* the rows of B corresponding to nonzeros of A. */
230   for (i=0;i<am;i++) {
231     anzi = ai[i+1] - ai[i];
232     cnzi = ci[i+1] - ci[i];
233     for (j=0;j<anzi;j++) {
234       brow = aj[j];
235       bnzi = bi[brow+1] - bi[brow];
236       bjj  = bj + bi[brow];
237       baj  = ba + bi[brow];
238       /* perform sparse axpy */
239       valtmp = aa[j];
240       nextb  = 0;
241       for (k=0; nextb<bnzi; k++) {
242         if (cj[k] == bjj[nextb]){ /* ccol == bcol */
243           ca[k] += valtmp*baj[nextb++];
244         }
245       }
246       flops += 2*bnzi;
247     }
248     aj += anzi; aa += anzi;
249     cj += cnzi; ca += cnzi;
250   }
251 
252   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
253   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
254   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
255   PetscFunctionReturn(0);
256 }
257 
258 #undef __FUNCT__
259 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
260 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
261 {
262   PetscErrorCode     ierr;
263   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
264   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
265   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
266   MatScalar          *ca;
267   PetscReal          afill;
268   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
269   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
270 
271   PetscFunctionBegin;
272   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
273   /*-----------------------------------------------------------------------------------------*/
274   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
275   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
276   ci[0] = 0;
277 
278   /* create and initialize a linked list */
279   nlnk_max = a->rmax*b->rmax;
280   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
281   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
282 
283   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
284   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
285   current_space = free_space;
286 
287   /* Determine ci and cj */
288   for (i=0; i<am; i++) {
289     anzi = ai[i+1] - ai[i];
290     aj   = a->j + ai[i];
291     for (j=0; j<anzi; j++){
292       brow = aj[j];
293       bnzj = bi[brow+1] - bi[brow];
294       bj   = b->j + bi[brow];
295       /* add non-zero cols of B into the sorted linked list lnk */
296       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
297     }
298     cnzi = lnk[1];
299 
300     /* If free space is not available, make more free space */
301     /* Double the amount of total space in the list */
302     if (current_space->local_remaining<cnzi) {
303       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
304       ndouble++;
305     }
306 
307     /* Copy data into free space, then initialize lnk */
308     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
309     current_space->array           += cnzi;
310     current_space->local_used      += cnzi;
311     current_space->local_remaining -= cnzi;
312     ci[i+1] = ci[i] + cnzi;
313   }
314 
315   /* Column indices are in the list of free space */
316   /* Allocate space for cj, initialize cj, and */
317   /* destroy list of free space and other temporary array(s) */
318   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
319   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
320   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
321 
322   /* Allocate space for ca */
323   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
324   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
325 
326   /* put together the new symbolic matrix */
327   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
328 
329   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
330   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
331   c = (Mat_SeqAIJ *)((*C)->data);
332   c->free_a   = PETSC_TRUE;
333   c->free_ij  = PETSC_TRUE;
334   c->nonew    = 0;
335   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
336 
337   /* set MatInfo */
338   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
339   if (afill < 1.0) afill = 1.0;
340   c->maxnz                     = ci[am];
341   c->nz                        = ci[am];
342   (*C)->info.mallocs           = ndouble;
343   (*C)->info.fill_ratio_given  = fill;
344   (*C)->info.fill_ratio_needed = afill;
345 
346 #if defined(PETSC_USE_INFO)
347   if (ci[am]) {
348     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
349     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
350   } else {
351     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
352   }
353 #endif
354   PetscFunctionReturn(0);
355 }
356 
357 
358 #undef __FUNCT__
359 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
360 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
361 {
362   PetscErrorCode     ierr;
363   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
364   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
365   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
366   MatScalar          *ca;
367   PetscReal          afill;
368   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
369   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
370 
371   PetscFunctionBegin;
372   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
373   /*---------------------------------------------------------------------------------------------*/
374   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
375   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
376   ci[0] = 0;
377 
378   /* create and initialize a linked list */
379   nlnk_max = a->rmax*b->rmax;
380   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
381   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
382 
383   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
384   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
385   current_space = free_space;
386 
387   /* Determine ci and cj */
388   for (i=0; i<am; i++) {
389     anzi = ai[i+1] - ai[i];
390     aj   = a->j + ai[i];
391     for (j=0; j<anzi; j++){
392       brow = aj[j];
393       bnzj = bi[brow+1] - bi[brow];
394       bj   = b->j + bi[brow];
395       /* add non-zero cols of B into the sorted linked list lnk */
396       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
397     }
398     cnzi = lnk[0];
399 
400     /* If free space is not available, make more free space */
401     /* Double the amount of total space in the list */
402     if (current_space->local_remaining<cnzi) {
403       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
404       ndouble++;
405     }
406 
407     /* Copy data into free space, then initialize lnk */
408     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
409     current_space->array           += cnzi;
410     current_space->local_used      += cnzi;
411     current_space->local_remaining -= cnzi;
412     ci[i+1] = ci[i] + cnzi;
413   }
414 
415   /* Column indices are in the list of free space */
416   /* Allocate space for cj, initialize cj, and */
417   /* destroy list of free space and other temporary array(s) */
418   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
419   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
420   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
421 
422   /* Allocate space for ca */
423   /*-----------------------*/
424   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
425   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
426 
427   /* put together the new symbolic matrix */
428   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
429 
430   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
431   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
432   c = (Mat_SeqAIJ *)((*C)->data);
433   c->free_a   = PETSC_TRUE;
434   c->free_ij  = PETSC_TRUE;
435   c->nonew    = 0;
436   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
437 
438   /* set MatInfo */
439   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
440   if (afill < 1.0) afill = 1.0;
441   c->maxnz                     = ci[am];
442   c->nz                        = ci[am];
443   (*C)->info.mallocs           = ndouble;
444   (*C)->info.fill_ratio_given  = fill;
445   (*C)->info.fill_ratio_needed = afill;
446 
447 #if defined(PETSC_USE_INFO)
448   if (ci[am]) {
449     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
450     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
451   } else {
452     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
453   }
454 #endif
455   PetscFunctionReturn(0);
456 }
457 
458 
459 /* This routine is not used. Should be removed! */
460 #undef __FUNCT__
461 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
462 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
463 {
464   PetscErrorCode ierr;
465 
466   PetscFunctionBegin;
467   if (scall == MAT_INITIAL_MATRIX){
468     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
469   }
470   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
471   PetscFunctionReturn(0);
472 }
473 
474 #undef __FUNCT__
475 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
476 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
477 {
478   PetscErrorCode      ierr;
479   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
480 
481   PetscFunctionBegin;
482   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
483   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
484   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
485   ierr = PetscFree(multtrans);CHKERRQ(ierr);
486   PetscFunctionReturn(0);
487 }
488 
489 #undef __FUNCT__
490 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
491 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
492 {
493   PetscErrorCode      ierr;
494   PetscContainer      container;
495   Mat_MatMatTransMult *multtrans=PETSC_NULL;
496 
497   PetscFunctionBegin;
498   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
499   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
500   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
501   A->ops->destroy   = multtrans->destroy;
502   if (A->ops->destroy) {
503     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
504   }
505   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
506   PetscFunctionReturn(0);
507 }
508 
509 #undef __FUNCT__
510 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
511 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
512 {
513   PetscErrorCode      ierr;
514   Mat                 Bt;
515   PetscInt            *bti,*btj;
516   Mat_MatMatTransMult *multtrans;
517   PetscContainer      container;
518   PetscLogDouble      t0,tf,etime2=0.0;
519 
520   PetscFunctionBegin;
521   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
522    /* create symbolic Bt */
523   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
524   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
525 
526   /* get symbolic C=A*Bt */
527   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
528 
529   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
530   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
531 
532   /* attach the supporting struct to C */
533   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
534   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
535   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
536   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
537   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
538 
539   multtrans->usecoloring = PETSC_FALSE;
540   multtrans->destroy = (*C)->ops->destroy;
541   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
542 
543   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
544   etime2 += tf - t0;
545 
546   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
547   if (multtrans->usecoloring){
548     /* Create MatTransposeColoring from symbolic C=A*B^T */
549     MatTransposeColoring matcoloring;
550     ISColoring           iscoloring;
551     Mat                  Bt_dense,C_dense;
552     PetscLogDouble       etime0=0.0,etime01=0.0,etime1=0.0;
553 
554     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
555     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
556     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
557     etime0 += tf - t0;
558 
559     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
560     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
561     multtrans->matcoloring = matcoloring;
562     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
563     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
564     etime01 += tf - t0;
565 
566     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
567     /* Create Bt_dense and C_dense = A*Bt_dense */
568     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
569     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
570     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
571     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
572     Bt_dense->assembled = PETSC_TRUE;
573     multtrans->Bt_den = Bt_dense;
574 
575     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
576     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
577     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
578     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
579     Bt_dense->assembled = PETSC_TRUE;
580     multtrans->ABt_den = C_dense;
581     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
582     etime1 += tf - t0;
583 
584 #if defined(PETSC_USE_INFO)
585     {
586     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
587     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));
588     ierr = PetscInfo5(*C,"Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
589     }
590 #endif
591   }
592   /* clean up */
593   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
594   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
595 
596 
597 
598 #if defined(INEFFICIENT_ALGORITHM)
599   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
600   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
601   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
602   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
603   PetscInt           am=A->rmap->N,bm=B->rmap->N;
604   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
605   MatScalar          *ca;
606   PetscBT            lnkbt;
607   PetscReal          afill;
608 
609   /* Allocate row pointer array ci  */
610   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
611   ci[0] = 0;
612 
613   /* Create and initialize a linked list for C columns */
614   nlnk = bm+1;
615   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
616 
617   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
618   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
619   current_space = free_space;
620 
621   /* Determine symbolic info for each row of the product A*B^T: */
622   for (i=0; i<am; i++) {
623     anzi = ai[i+1] - ai[i];
624     cnzi = 0;
625     acol = aj + ai[i];
626     for (j=0; j<bm; j++){
627       bnzj = bi[j+1] - bi[j];
628       bcol= bj + bi[j];
629       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
630       ka = 0; kb = 0;
631       while (ka < anzi && kb < bnzj){
632         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
633         if (ka == anzi) break;
634         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
635         if (kb == bnzj) break;
636         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
637           index[0] = j;
638           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
639           cnzi++;
640           break;
641         }
642       }
643     }
644 
645     /* If free space is not available, make more free space */
646     /* Double the amount of total space in the list */
647     if (current_space->local_remaining<cnzi) {
648       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
649       nspacedouble++;
650     }
651 
652     /* Copy data into free space, then initialize lnk */
653     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
654     current_space->array           += cnzi;
655     current_space->local_used      += cnzi;
656     current_space->local_remaining -= cnzi;
657 
658     ci[i+1] = ci[i] + cnzi;
659   }
660 
661 
662   /* Column indices are in the list of free space.
663      Allocate array cj, copy column indices to cj, and destroy list of free space */
664   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
665   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
666   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
667 
668   /* Allocate space for ca */
669   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
670   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
671 
672   /* put together the new symbolic matrix */
673   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
674 
675   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
676   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
677   c = (Mat_SeqAIJ *)((*C)->data);
678   c->free_a   = PETSC_TRUE;
679   c->free_ij  = PETSC_TRUE;
680   c->nonew    = 0;
681 
682   /* set MatInfo */
683   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
684   if (afill < 1.0) afill = 1.0;
685   c->maxnz                     = ci[am];
686   c->nz                        = ci[am];
687   (*C)->info.mallocs           = nspacedouble;
688   (*C)->info.fill_ratio_given  = fill;
689   (*C)->info.fill_ratio_needed = afill;
690 
691 #if defined(PETSC_USE_INFO)
692   if (ci[am]) {
693     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
694     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
695   } else {
696     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
697   }
698 #endif
699 #endif
700   PetscFunctionReturn(0);
701 }
702 
703 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
704 #undef __FUNCT__
705 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
706 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
707 {
708   PetscErrorCode ierr;
709   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
710   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
711   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
712   PetscLogDouble flops=0.0;
713   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca,*cval;
714   Mat_MatMatTransMult *multtrans;
715   PetscContainer      container;
716 #if defined(USE_ARRAY)
717   MatScalar      *spdot;
718 #endif
719 
720   PetscFunctionBegin;
721   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
722   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
723   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
724   if (multtrans->usecoloring){
725     MatTransposeColoring  matcoloring = multtrans->matcoloring;
726     Mat                   Bt_dense;
727     PetscInt              m,n;
728     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
729     Mat C_dense = multtrans->ABt_den;
730 
731     Bt_dense = multtrans->Bt_den;
732     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
733 
734     /* Get Bt_dense by Apply MatTransposeColoring to B */
735     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
736     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
737     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
738     etime0 += tf - t0;
739 
740     /* C_dense = A*Bt_dense */
741     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
742     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
743     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
744     etime2 += tf - t0;
745 
746     /* Recover C from C_dense */
747     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
748     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
749     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
750     etime1 += tf - t0;
751 #if defined(PETSC_USE_INFO)
752     ierr = PetscInfo4(C,"Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
753 #endif
754     PetscFunctionReturn(0);
755   }
756 
757 #if defined(USE_ARRAY)
758   /* allocate an array for implementing sparse inner-product */
759   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
760   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
761 #endif
762 
763   /* clear old values in C */
764   if (!c->a){
765     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
766     c->a      = ca;
767     c->free_a = PETSC_TRUE;
768   } else {
769     ca =  c->a;
770   }
771   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
772 
773   for (i=0; i<cm; i++) {
774     anzi = ai[i+1] - ai[i];
775     acol = aj + ai[i];
776     aval = aa + ai[i];
777     cnzi = ci[i+1] - ci[i];
778     ccol = cj + ci[i];
779     cval = ca + ci[i];
780     for (j=0; j<cnzi; j++){
781       brow = ccol[j];
782       bnzj = bi[brow+1] - bi[brow];
783       bcol = bj + bi[brow];
784       bval = ba + bi[brow];
785 
786       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
787 #if defined(USE_ARRAY)
788       /* put ba to spdot array */
789       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
790       /* c(i,j)=A[i,:]*B[j,:]^T */
791       for (nexta=0; nexta<anzi; nexta++){
792         cval[j] += spdot[acol[nexta]]*aval[nexta];
793       }
794       /* zero spdot array */
795       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
796 #else
797       nexta = 0; nextb = 0;
798       while (nexta<anzi && nextb<bnzj){
799         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
800         if (nexta == anzi) break;
801         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
802         if (nextb == bnzj) break;
803         if (acol[nexta] == bcol[nextb]){
804           cval[j] += aval[nexta]*bval[nextb];
805           nexta++; nextb++;
806           flops += 2;
807         }
808       }
809 #endif
810     }
811   }
812   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
813   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
814   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
815 #if defined(USE_ARRAY)
816   ierr = PetscFree(spdot);
817 #endif
818   PetscFunctionReturn(0);
819 }
820 
821 #undef __FUNCT__
822 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
823 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
824   PetscErrorCode ierr;
825 
826   PetscFunctionBegin;
827   if (scall == MAT_INITIAL_MATRIX){
828     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
829   }
830   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
831   PetscFunctionReturn(0);
832 }
833 
834 #undef __FUNCT__
835 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
836 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
837 {
838   PetscErrorCode ierr;
839   Mat            At;
840   PetscInt       *ati,*atj;
841 
842   PetscFunctionBegin;
843   /* create symbolic At */
844   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
845   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
846 
847   /* get symbolic C=At*B */
848   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
849 
850   /* clean up */
851   ierr = MatDestroy(&At);CHKERRQ(ierr);
852   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
853   PetscFunctionReturn(0);
854 }
855 
856 #undef __FUNCT__
857 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
858 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
859 {
860   PetscErrorCode ierr;
861   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
862   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
863   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
864   PetscLogDouble flops=0.0;
865   MatScalar      *aa=a->a,*ba,*ca,*caj;
866 
867   PetscFunctionBegin;
868   if (!c->a){
869     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
870     c->a      = ca;
871     c->free_a = PETSC_TRUE;
872   } else {
873     ca = c->a;
874   }
875   /* clear old values in C */
876   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
877 
878   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
879   for (i=0;i<am;i++) {
880     bj   = b->j + bi[i];
881     ba   = b->a + bi[i];
882     bnzi = bi[i+1] - bi[i];
883     anzi = ai[i+1] - ai[i];
884     for (j=0; j<anzi; j++) {
885       nextb = 0;
886       crow  = *aj++;
887       cjj   = cj + ci[crow];
888       caj   = ca + ci[crow];
889       /* perform sparse axpy operation.  Note cjj includes bj. */
890       for (k=0; nextb<bnzi; k++) {
891         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
892           caj[k] += (*aa)*(*(ba+nextb));
893           nextb++;
894         }
895       }
896       flops += 2*bnzi;
897       aa++;
898     }
899   }
900 
901   /* Assemble the final matrix and clean up */
902   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
903   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
904   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
905   PetscFunctionReturn(0);
906 }
907 
908 EXTERN_C_BEGIN
909 #undef __FUNCT__
910 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
911 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
912 {
913   PetscErrorCode ierr;
914 
915   PetscFunctionBegin;
916   if (scall == MAT_INITIAL_MATRIX){
917     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
918   }
919   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
920   PetscFunctionReturn(0);
921 }
922 EXTERN_C_END
923 
924 #undef __FUNCT__
925 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
926 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
927 {
928   PetscErrorCode ierr;
929 
930   PetscFunctionBegin;
931   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
932   (*C)->ops->matmult = MatMatMult_SeqAIJ_SeqDense;
933   PetscFunctionReturn(0);
934 }
935 
936 #undef __FUNCT__
937 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
938 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
939 {
940   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
941   PetscErrorCode ierr;
942   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
943   MatScalar      *aa;
944   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
945   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
946 
947   PetscFunctionBegin;
948   if (!cm || !cn) PetscFunctionReturn(0);
949   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);
950   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);
951   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);
952   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
953   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
954   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
955   for (col=0; col<cn-4; col += 4){  /* over columns of C */
956     colam = col*am;
957     for (i=0; i<am; i++) {        /* over rows of C in those columns */
958       r1 = r2 = r3 = r4 = 0.0;
959       n   = a->i[i+1] - a->i[i];
960       aj  = a->j + a->i[i];
961       aa  = a->a + a->i[i];
962       for (j=0; j<n; j++) {
963         r1 += (*aa)*b1[*aj];
964         r2 += (*aa)*b2[*aj];
965         r3 += (*aa)*b3[*aj];
966         r4 += (*aa++)*b4[*aj++];
967       }
968       c[colam + i]       = r1;
969       c[colam + am + i]  = r2;
970       c[colam + am2 + i] = r3;
971       c[colam + am3 + i] = r4;
972     }
973     b1 += bm4;
974     b2 += bm4;
975     b3 += bm4;
976     b4 += bm4;
977   }
978   for (;col<cn; col++){     /* over extra columns of C */
979     for (i=0; i<am; i++) {  /* over rows of C in those columns */
980       r1 = 0.0;
981       n   = a->i[i+1] - a->i[i];
982       aj  = a->j + a->i[i];
983       aa  = a->a + a->i[i];
984 
985       for (j=0; j<n; j++) {
986         r1 += (*aa++)*b1[*aj++];
987       }
988       c[col*am + i]     = r1;
989     }
990     b1 += bm;
991   }
992   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
993   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
994   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
995   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
996   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
997   PetscFunctionReturn(0);
998 }
999 
1000 /*
1001    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1002 */
1003 #undef __FUNCT__
1004 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1005 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1006 {
1007   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1008   PetscErrorCode ierr;
1009   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1010   MatScalar      *aa;
1011   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1012   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1013 
1014   PetscFunctionBegin;
1015   if (!cm || !cn) PetscFunctionReturn(0);
1016   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
1017   ierr = MatGetArray(C,&c);CHKERRQ(ierr);
1018   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1019 
1020   if (a->compressedrow.use){ /* use compressed row format */
1021     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1022       colam = col*am;
1023       arm   = a->compressedrow.nrows;
1024       ii    = a->compressedrow.i;
1025       ridx  = a->compressedrow.rindex;
1026       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1027 	r1 = r2 = r3 = r4 = 0.0;
1028 	n   = ii[i+1] - ii[i];
1029 	aj  = a->j + ii[i];
1030 	aa  = a->a + ii[i];
1031 	for (j=0; j<n; j++) {
1032 	  r1 += (*aa)*b1[*aj];
1033 	  r2 += (*aa)*b2[*aj];
1034 	  r3 += (*aa)*b3[*aj];
1035 	  r4 += (*aa++)*b4[*aj++];
1036 	}
1037 	c[colam       + ridx[i]] += r1;
1038 	c[colam + am  + ridx[i]] += r2;
1039 	c[colam + am2 + ridx[i]] += r3;
1040 	c[colam + am3 + ridx[i]] += r4;
1041       }
1042       b1 += bm4;
1043       b2 += bm4;
1044       b3 += bm4;
1045       b4 += bm4;
1046     }
1047     for (;col<cn; col++){     /* over extra columns of C */
1048       colam = col*am;
1049       arm   = a->compressedrow.nrows;
1050       ii    = a->compressedrow.i;
1051       ridx  = a->compressedrow.rindex;
1052       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1053 	r1 = 0.0;
1054 	n   = ii[i+1] - ii[i];
1055 	aj  = a->j + ii[i];
1056 	aa  = a->a + ii[i];
1057 
1058 	for (j=0; j<n; j++) {
1059 	  r1 += (*aa++)*b1[*aj++];
1060 	}
1061 	c[col*am + ridx[i]] += r1;
1062       }
1063       b1 += bm;
1064     }
1065   } else {
1066     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1067       colam = col*am;
1068       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1069 	r1 = r2 = r3 = r4 = 0.0;
1070 	n   = a->i[i+1] - a->i[i];
1071 	aj  = a->j + a->i[i];
1072 	aa  = a->a + a->i[i];
1073 	for (j=0; j<n; j++) {
1074 	  r1 += (*aa)*b1[*aj];
1075 	  r2 += (*aa)*b2[*aj];
1076 	  r3 += (*aa)*b3[*aj];
1077 	  r4 += (*aa++)*b4[*aj++];
1078 	}
1079 	c[colam + i]       += r1;
1080 	c[colam + am + i]  += r2;
1081 	c[colam + am2 + i] += r3;
1082 	c[colam + am3 + i] += r4;
1083       }
1084       b1 += bm4;
1085       b2 += bm4;
1086       b3 += bm4;
1087       b4 += bm4;
1088     }
1089     for (;col<cn; col++){     /* over extra columns of C */
1090       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1091 	r1 = 0.0;
1092 	n   = a->i[i+1] - a->i[i];
1093 	aj  = a->j + a->i[i];
1094 	aa  = a->a + a->i[i];
1095 
1096 	for (j=0; j<n; j++) {
1097 	  r1 += (*aa++)*b1[*aj++];
1098 	}
1099 	c[col*am + i]     += r1;
1100       }
1101       b1 += bm;
1102     }
1103   }
1104   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1105   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
1106   ierr = MatRestoreArray(C,&c);CHKERRQ(ierr);
1107   PetscFunctionReturn(0);
1108 }
1109 
1110 #undef __FUNCT__
1111 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1112 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1113 {
1114   PetscErrorCode ierr;
1115   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
1116   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1117   PetscInt       *bi=b->i,*bj=b->j;
1118   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1119   MatScalar      *btval,*btval_den,*ba=b->a;
1120   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1121 
1122   PetscFunctionBegin;
1123   btval_den=btdense->v;
1124   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1125   for (k=0; k<ncolors; k++) {
1126     ncolumns = coloring->ncolumns[k];
1127     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1128       col   = *(columns + colorforcol[k] + l);
1129       btcol = bj + bi[col];
1130       btval = ba + bi[col];
1131       anz   = bi[col+1] - bi[col];
1132       for (j=0; j<anz; j++){
1133         brow            = btcol[j];
1134         btval_den[brow] = btval[j];
1135       }
1136     }
1137     btval_den += m;
1138   }
1139   PetscFunctionReturn(0);
1140 }
1141 
1142 #undef __FUNCT__
1143 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1144 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1145 {
1146   PetscErrorCode ierr;
1147   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1148   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1149   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1150   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1151 
1152   PetscFunctionBegin;
1153   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1154   ierr = MatGetArray(Cden,&ca_den);CHKERRQ(ierr);
1155   cp_den = ca_den;
1156   for (k=0; k<ncolors; k++) {
1157     nrows = matcoloring->nrows[k];
1158     row   = rows  + colorforrow[k];
1159     idx   = spidx + colorforrow[k];
1160     for (l=0; l<nrows; l++){
1161       ca[idx[l]] = cp_den[row[l]];
1162     }
1163     cp_den += m;
1164   }
1165   ierr = MatRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1166   PetscFunctionReturn(0);
1167 }
1168 
1169 /*
1170  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1171  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1172  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1173  */
1174 #undef __FUNCT__
1175 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1176 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1177 {
1178   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1179   PetscErrorCode ierr;
1180   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1181   PetscInt       nz = a->i[m],row,*jj,mr,col;
1182   PetscInt       *cspidx;
1183 
1184   PetscFunctionBegin;
1185   *nn = n;
1186   if (!ia) PetscFunctionReturn(0);
1187   if (symmetric) {
1188     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1189     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,ia,ja);CHKERRQ(ierr);
1190   } else {
1191     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1192     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1193     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1194     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1195     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1196     jj = a->j;
1197     for (i=0; i<nz; i++) {
1198       collengths[jj[i]]++;
1199     }
1200     cia[0] = oshift;
1201     for (i=0; i<n; i++) {
1202       cia[i+1] = cia[i] + collengths[i];
1203     }
1204     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1205     jj   = a->j;
1206     for (row=0; row<m; row++) {
1207       mr = a->i[row+1] - a->i[row];
1208       for (i=0; i<mr; i++) {
1209         col = *jj++;
1210         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1211         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
1212       }
1213     }
1214     ierr = PetscFree(collengths);CHKERRQ(ierr);
1215     *ia = cia; *ja = cja;
1216     *spidx = cspidx;
1217   }
1218   PetscFunctionReturn(0);
1219 }
1220 
1221 #undef __FUNCT__
1222 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1223 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,PetscInt *ia[],PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1224 {
1225   PetscErrorCode ierr;
1226 
1227   PetscFunctionBegin;
1228   if (!ia) PetscFunctionReturn(0);
1229 
1230   ierr = PetscFree(*ia);CHKERRQ(ierr);
1231   ierr = PetscFree(*ja);CHKERRQ(ierr);
1232   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1233   PetscFunctionReturn(0);
1234 }
1235 
1236 #undef __FUNCT__
1237 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1238 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1239 {
1240   PetscErrorCode ierr;
1241   PetscInt       i,n,nrows,N,j,k,m,*row_idx,*ci,*cj,ncols,col,cm;
1242   const PetscInt *is;
1243   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1244   IS             *isa;
1245   PetscBool      done;
1246   PetscBool      flg1,flg2;
1247   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1248   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1249   PetscInt       *colorforcol,*columns,*columns_i;
1250 
1251   PetscFunctionBegin;
1252   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1253 
1254   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1255   ierr = PetscTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1256   ierr = PetscTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1257   if (flg1 || flg2) {
1258     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1259   }
1260 
1261   N         = mat->cmap->N/bs;
1262   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1263   c->N      = mat->cmap->N/bs;
1264   c->m      = mat->rmap->N/bs;
1265   c->rstart = 0;
1266 
1267   c->ncolors = nis;
1268   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1269   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1270   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1271   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1272   colorforrow[0]    = 0;
1273   rows_i            = rows;
1274   columnsforspidx_i = columnsforspidx;
1275 
1276   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1277   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1278   colorforcol[0] = 0;
1279   columns_i      = columns;
1280 
1281   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr); /* column-wise storage of mat */
1282   if (!done) SETERRQ1(((PetscObject)mat)->comm,PETSC_ERR_SUP,"MatGetColumnIJ() not supported for matrix type %s",((PetscObject)mat)->type_name);
1283 
1284   cm = c->m;
1285   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1286   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1287   for (i=0; i<nis; i++) {
1288     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1289     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1290     c->ncolumns[i] = n;
1291     if (n) {
1292       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1293     }
1294     colorforcol[i+1] = colorforcol[i] + n;
1295     columns_i       += n;
1296 
1297     /* fast, crude version requires O(N*N) work */
1298     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1299 
1300     /* loop over columns*/
1301     for (j=0; j<n; j++) {
1302       col     = is[j];
1303       row_idx = cj + ci[col];
1304       m       = ci[col+1] - ci[col];
1305       /* loop over columns marking them in rowhit */
1306       for (k=0; k<m; k++) {
1307         idxhit[*row_idx]   = spidx[ci[col] + k];
1308         rowhit[*row_idx++] = col + 1;
1309       }
1310     }
1311     /* count the number of hits */
1312     nrows = 0;
1313     for (j=0; j<cm; j++) {
1314       if (rowhit[j]) nrows++;
1315     }
1316     c->nrows[i]      = nrows;
1317     colorforrow[i+1] = colorforrow[i] + nrows;
1318 
1319     nrows       = 0;
1320     for (j=0; j<cm; j++) {
1321       if (rowhit[j]) {
1322         rows_i[nrows]            = j;
1323         columnsforspidx_i[nrows] = idxhit[j];
1324         nrows++;
1325       }
1326     }
1327     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1328     rows_i += nrows; columnsforspidx_i += nrows;
1329   }
1330   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,&done);CHKERRQ(ierr);
1331   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1332   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1333 #if defined(PETSC_USE_DEBUG)
1334   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1335 #endif
1336 
1337   c->colorforrow     = colorforrow;
1338   c->rows            = rows;
1339   c->columnsforspidx = columnsforspidx;
1340   c->colorforcol     = colorforcol;
1341   c->columns         = columns;
1342   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1343   PetscFunctionReturn(0);
1344 }
1345