xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 1086fb861de8e1d1df73e6d89a2d99b932efb7e6)
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 <../src/mat/utils/petscheap.h>
10 #include <petscbt.h>
11 #include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/
12 /*
13 #define DEBUG_MATMATMULT
14  */
15 
16 #undef __FUNCT__
17 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
18 PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
19 {
20   PetscErrorCode ierr;
21   PetscBool      scalable=PETSC_FALSE,scalable_fast=PETSC_FALSE,heap = PETSC_FALSE,btheap = PETSC_FALSE;
22 
23   PetscFunctionBegin;
24   if (scall == MAT_INITIAL_MATRIX){
25     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
26     ierr = PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,PETSC_NULL);CHKERRQ(ierr);
28     ierr = PetscOptionsBool("-matmatmult_heap","Use heap implementation of symbolic factorization C=A*B","",heap,&heap,PETSC_NULL);CHKERRQ(ierr);
29     ierr = PetscOptionsBool("-matmatmult_btheap","Use btheap implementation of symbolic factorization C=A*B","",btheap,&btheap,PETSC_NULL);CHKERRQ(ierr);
30     ierr = PetscOptionsEnd();CHKERRQ(ierr);
31     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
32     if (scalable_fast){
33       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
34     } else if (scalable){
35       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
36     } else if (heap) {
37       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
38     } else if (btheap) {
39       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
40     } else {
41       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
42     }
43     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
44   }
45   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
46   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
47   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
48   PetscFunctionReturn(0);
49 }
50 
51 #undef __FUNCT__
52 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
53 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
54 {
55   PetscErrorCode     ierr;
56   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
57   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
58   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
59   PetscReal          afill;
60   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
61   PetscBT            lnkbt;
62   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
63 
64   PetscFunctionBegin;
65   /* Get ci and cj */
66   /*---------------*/
67   /* Allocate ci array, arrays for fill computation and */
68   /* free space for accumulating nonzero column info */
69   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
70   ci[0] = 0;
71 
72   /* create and initialize a linked list */
73   nlnk_max = a->rmax*b->rmax;
74   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
75   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
76 
77   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
78   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
79   current_space = free_space;
80 
81   /* Determine ci and cj */
82   for (i=0; i<am; i++) {
83     anzi = ai[i+1] - ai[i];
84     aj   = a->j + ai[i];
85     for (j=0; j<anzi; j++){
86       brow = aj[j];
87       bnzj = bi[brow+1] - bi[brow];
88       bj   = b->j + bi[brow];
89       /* add non-zero cols of B into the sorted linked list lnk */
90       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
91     }
92     cnzi = lnk[0];
93 
94     /* If free space is not available, make more free space */
95     /* Double the amount of total space in the list */
96     if (current_space->local_remaining<cnzi) {
97       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
98       ndouble++;
99     }
100 
101     /* Copy data into free space, then initialize lnk */
102     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
103     current_space->array           += cnzi;
104     current_space->local_used      += cnzi;
105     current_space->local_remaining -= cnzi;
106     ci[i+1] = ci[i] + cnzi;
107   }
108 
109   /* Column indices are in the list of free space */
110   /* Allocate space for cj, initialize cj, and */
111   /* destroy list of free space and other temporary array(s) */
112   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
113   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
114   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
115 
116   /* put together the new symbolic matrix */
117   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
118   (*C)->rmap->bs = A->rmap->bs;
119   (*C)->cmap->bs = B->cmap->bs;
120 
121   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
122   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
123   c = (Mat_SeqAIJ *)((*C)->data);
124   c->free_a  = PETSC_FALSE;
125   c->free_ij = PETSC_TRUE;
126   c->nonew   = 0;
127   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
128 
129   /* set MatInfo */
130   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
131   if (afill < 1.0) afill = 1.0;
132   c->maxnz                     = ci[am];
133   c->nz                        = ci[am];
134   (*C)->info.mallocs           = ndouble;
135   (*C)->info.fill_ratio_given  = fill;
136   (*C)->info.fill_ratio_needed = afill;
137 
138 #if defined(PETSC_USE_INFO)
139   if (ci[am]) {
140     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
141     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
142   } else {
143     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
144   }
145 #endif
146   PetscFunctionReturn(0);
147 }
148 
149 #undef __FUNCT__
150 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
151 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
152 {
153   PetscErrorCode ierr;
154   PetscLogDouble flops=0.0;
155   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
156   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
157   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
158   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
159   PetscInt       am=A->rmap->n,cm=C->rmap->n;
160   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
161   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
162   PetscScalar    *ab_dense;
163 
164   PetscFunctionBegin;
165   /* printf("MatMatMultNumeric_SeqAIJ_SeqAIJ...ca %p\n",c->a); */
166   if (!c->a){ /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
167     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
168     c->a      = ca;
169     c->free_a = PETSC_TRUE;
170 
171     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
172     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
173     c->matmult_abdense = ab_dense;
174   } else {
175     ca       = c->a;
176     ab_dense = c->matmult_abdense;
177   }
178 
179   /* clean old values in C */
180   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
181   /* Traverse A row-wise. */
182   /* Build the ith row in C by summing over nonzero columns in A, */
183   /* the rows of B corresponding to nonzeros of A. */
184   for (i=0; i<am; i++) {
185     anzi = ai[i+1] - ai[i];
186     for (j=0; j<anzi; j++) {
187       brow = aj[j];
188       bnzi = bi[brow+1] - bi[brow];
189       bjj  = bj + bi[brow];
190       baj  = ba + bi[brow];
191       /* perform dense axpy */
192       valtmp = aa[j];
193       for (k=0; k<bnzi; k++) {
194         ab_dense[bjj[k]] += valtmp*baj[k];
195       }
196       flops += 2*bnzi;
197     }
198     aj += anzi; aa += anzi;
199 
200     cnzi = ci[i+1] - ci[i];
201     for (k=0; k<cnzi; k++) {
202       ca[k]          += ab_dense[cj[k]];
203       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
204     }
205     flops += cnzi;
206     cj += cnzi; ca += cnzi;
207   }
208   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
209   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
210   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
211   PetscFunctionReturn(0);
212 }
213 
214 #undef __FUNCT__
215 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
216 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
217 {
218   PetscErrorCode ierr;
219   PetscLogDouble flops=0.0;
220   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
221   Mat_SeqAIJ     *b = (Mat_SeqAIJ *)B->data;
222   Mat_SeqAIJ     *c = (Mat_SeqAIJ *)C->data;
223   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
224   PetscInt       am=A->rmap->N,cm=C->rmap->N;
225   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
226   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
227   PetscInt       nextb;
228 
229   PetscFunctionBegin;
230 #if defined(DEBUG_MATMATMULT)
231   ierr = PetscPrintf(PETSC_COMM_SELF,"MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable...\n");CHKERRQ(ierr);
232 #endif
233   /* clean old values in C */
234   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
235   /* Traverse A row-wise. */
236   /* Build the ith row in C by summing over nonzero columns in A, */
237   /* the rows of B corresponding to nonzeros of A. */
238   for (i=0;i<am;i++) {
239     anzi = ai[i+1] - ai[i];
240     cnzi = ci[i+1] - ci[i];
241     for (j=0;j<anzi;j++) {
242       brow = aj[j];
243       bnzi = bi[brow+1] - bi[brow];
244       bjj  = bj + bi[brow];
245       baj  = ba + bi[brow];
246       /* perform sparse axpy */
247       valtmp = aa[j];
248       nextb  = 0;
249       for (k=0; nextb<bnzi; k++) {
250         if (cj[k] == bjj[nextb]){ /* ccol == bcol */
251           ca[k] += valtmp*baj[nextb++];
252         }
253       }
254       flops += 2*bnzi;
255     }
256     aj += anzi; aa += anzi;
257     cj += cnzi; ca += cnzi;
258   }
259 
260   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
261   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
262   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
263   PetscFunctionReturn(0);
264 }
265 
266 #undef __FUNCT__
267 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
268 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
269 {
270   PetscErrorCode     ierr;
271   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
272   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
273   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
274   MatScalar          *ca;
275   PetscReal          afill;
276   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
277   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
278 
279   PetscFunctionBegin;
280   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
281   /*-----------------------------------------------------------------------------------------*/
282   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
283   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
284   ci[0] = 0;
285 
286   /* create and initialize a linked list */
287   nlnk_max = a->rmax*b->rmax;
288   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
289   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
290 
291   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
292   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
293   current_space = free_space;
294 
295   /* Determine ci and cj */
296   for (i=0; i<am; i++) {
297     anzi = ai[i+1] - ai[i];
298     aj   = a->j + ai[i];
299     for (j=0; j<anzi; j++){
300       brow = aj[j];
301       bnzj = bi[brow+1] - bi[brow];
302       bj   = b->j + bi[brow];
303       /* add non-zero cols of B into the sorted linked list lnk */
304       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
305     }
306     cnzi = lnk[1];
307 
308     /* If free space is not available, make more free space */
309     /* Double the amount of total space in the list */
310     if (current_space->local_remaining<cnzi) {
311       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
312       ndouble++;
313     }
314 
315     /* Copy data into free space, then initialize lnk */
316     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
317     current_space->array           += cnzi;
318     current_space->local_used      += cnzi;
319     current_space->local_remaining -= cnzi;
320     ci[i+1] = ci[i] + cnzi;
321   }
322 
323   /* Column indices are in the list of free space */
324   /* Allocate space for cj, initialize cj, and */
325   /* destroy list of free space and other temporary array(s) */
326   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
327   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
328   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
329 
330   /* Allocate space for ca */
331   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
332   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
333 
334   /* put together the new symbolic matrix */
335   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
336   (*C)->rmap->bs = A->rmap->bs;
337   (*C)->cmap->bs = B->cmap->bs;
338 
339   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
340   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
341   c = (Mat_SeqAIJ *)((*C)->data);
342   c->free_a   = PETSC_TRUE;
343   c->free_ij  = PETSC_TRUE;
344   c->nonew    = 0;
345   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
346 
347   /* set MatInfo */
348   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
349   if (afill < 1.0) afill = 1.0;
350   c->maxnz                     = ci[am];
351   c->nz                        = ci[am];
352   (*C)->info.mallocs           = ndouble;
353   (*C)->info.fill_ratio_given  = fill;
354   (*C)->info.fill_ratio_needed = afill;
355 
356 #if defined(PETSC_USE_INFO)
357   if (ci[am]) {
358     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
359     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
360   } else {
361     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
362   }
363 #endif
364   PetscFunctionReturn(0);
365 }
366 
367 
368 #undef __FUNCT__
369 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
370 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
371 {
372   PetscErrorCode     ierr;
373   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
374   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
375   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
376   MatScalar          *ca;
377   PetscReal          afill;
378   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
379   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
380 
381   PetscFunctionBegin;
382   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
383   /*---------------------------------------------------------------------------------------------*/
384   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
385   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
386   ci[0] = 0;
387 
388   /* create and initialize a linked list */
389   nlnk_max = a->rmax*b->rmax;
390   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
391   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
392 
393   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
394   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
395   current_space = free_space;
396 
397   /* Determine ci and cj */
398   for (i=0; i<am; i++) {
399     anzi = ai[i+1] - ai[i];
400     aj   = a->j + ai[i];
401     for (j=0; j<anzi; j++){
402       brow = aj[j];
403       bnzj = bi[brow+1] - bi[brow];
404       bj   = b->j + bi[brow];
405       /* add non-zero cols of B into the sorted linked list lnk */
406       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
407     }
408     cnzi = lnk[0];
409 
410     /* If free space is not available, make more free space */
411     /* Double the amount of total space in the list */
412     if (current_space->local_remaining<cnzi) {
413       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
414       ndouble++;
415     }
416 
417     /* Copy data into free space, then initialize lnk */
418     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
419     current_space->array           += cnzi;
420     current_space->local_used      += cnzi;
421     current_space->local_remaining -= cnzi;
422     ci[i+1] = ci[i] + cnzi;
423   }
424 
425   /* Column indices are in the list of free space */
426   /* Allocate space for cj, initialize cj, and */
427   /* destroy list of free space and other temporary array(s) */
428   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
429   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
430   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
431 
432   /* Allocate space for ca */
433   /*-----------------------*/
434   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
435   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
436 
437   /* put together the new symbolic matrix */
438   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,ca,C);CHKERRQ(ierr);
439   (*C)->rmap->bs = A->rmap->bs;
440   (*C)->cmap->bs = B->cmap->bs;
441 
442   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
443   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
444   c = (Mat_SeqAIJ *)((*C)->data);
445   c->free_a   = PETSC_TRUE;
446   c->free_ij  = PETSC_TRUE;
447   c->nonew    = 0;
448   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
449 
450   /* set MatInfo */
451   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
452   if (afill < 1.0) afill = 1.0;
453   c->maxnz                     = ci[am];
454   c->nz                        = ci[am];
455   (*C)->info.mallocs           = ndouble;
456   (*C)->info.fill_ratio_given  = fill;
457   (*C)->info.fill_ratio_needed = afill;
458 
459 #if defined(PETSC_USE_INFO)
460   if (ci[am]) {
461     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
462     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
463   } else {
464     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
465   }
466 #endif
467   PetscFunctionReturn(0);
468 }
469 
470 #undef __FUNCT__
471 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
472 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
473 {
474   PetscErrorCode     ierr;
475   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
476   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
477   PetscInt           *ci,*cj,*bb;
478   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
479   PetscReal          afill;
480   PetscInt           i,j,col,ndouble = 0;
481   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
482   PetscHeap          h;
483 
484   PetscFunctionBegin;
485   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
486   /*---------------------------------------------------------------------------------------------*/
487   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
488   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
489   ci[0] = 0;
490 
491   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
492   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
493   current_space = free_space;
494 
495   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
496   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
497 
498   /* Determine ci and cj */
499   for (i=0; i<am; i++) {
500     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
501     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
502     ci[i+1] = ci[i];
503     /* Populate the min heap */
504     for (j=0; j<anzi; j++) {
505       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
506       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
507         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
508       }
509     }
510     /* Pick off the min element, adding it to free space */
511     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
512     while (j >= 0) {
513       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
514         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
515         ndouble++;
516       }
517       *(current_space->array++) = col;
518       current_space->local_used++;
519       current_space->local_remaining--;
520       ci[i+1]++;
521 
522       /* stash if anything else remains in this row of B */
523       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
524       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
525         PetscInt j2,col2;
526         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
527         if (col2 != col) break;
528         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
529         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
530       }
531       /* Put any stashed elements back into the min heap */
532       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
533       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
534     }
535   }
536   ierr = PetscFree(bb);CHKERRQ(ierr);
537   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
538 
539   /* Column indices are in the list of free space */
540   /* Allocate space for cj, initialize cj, and */
541   /* destroy list of free space and other temporary array(s) */
542   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
543   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
544 
545   /* put together the new symbolic matrix */
546   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
547   (*C)->rmap->bs = A->rmap->bs;
548   (*C)->cmap->bs = B->cmap->bs;
549 
550   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
551   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
552   c = (Mat_SeqAIJ *)((*C)->data);
553   c->free_a   = PETSC_TRUE;
554   c->free_ij  = PETSC_TRUE;
555   c->nonew    = 0;
556   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
557 
558   /* set MatInfo */
559   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
560   if (afill < 1.0) afill = 1.0;
561   c->maxnz                     = ci[am];
562   c->nz                        = ci[am];
563   (*C)->info.mallocs           = ndouble;
564   (*C)->info.fill_ratio_given  = fill;
565   (*C)->info.fill_ratio_needed = afill;
566 
567 #if defined(PETSC_USE_INFO)
568   if (ci[am]) {
569     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
570     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
571   } else {
572     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
573   }
574 #endif
575   PetscFunctionReturn(0);
576 }
577 
578 #undef __FUNCT__
579 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
580 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
581 {
582   PetscErrorCode     ierr;
583   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
584   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
585   PetscInt           *ci,*cj,*bb;
586   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
587   PetscReal          afill;
588   PetscInt           i,j,col,ndouble = 0;
589   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
590   PetscHeap          h;
591   PetscBT            bt;
592 
593   PetscFunctionBegin;
594   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
595   /*---------------------------------------------------------------------------------------------*/
596   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
597   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
598   ci[0] = 0;
599 
600   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
601   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
602   current_space = free_space;
603 
604   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
605   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
606   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
607 
608   /* Determine ci and cj */
609   for (i=0; i<am; i++) {
610     const PetscInt anzi  = ai[i+1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
611     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
612     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
613     ci[i+1] = ci[i];
614     /* Populate the min heap */
615     for (j=0; j<anzi; j++) {
616       PetscInt brow = acol[j];
617       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
618         PetscInt bcol = bj[bb[j]];
619         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
620           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
621           bb[j]++;
622           break;
623         }
624       }
625     }
626     /* Pick off the min element, adding it to free space */
627     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
628     while (j >= 0) {
629       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
630         fptr = PETSC_NULL;                      /* need PetscBTMemzero */
631         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
632         ndouble++;
633       }
634       *(current_space->array++) = col;
635       current_space->local_used++;
636       current_space->local_remaining--;
637       ci[i+1]++;
638 
639       /* stash if anything else remains in this row of B */
640       for ( ; bb[j] < bi[acol[j]+1]; bb[j]++) {
641         PetscInt bcol = bj[bb[j]];
642         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
643           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
644           bb[j]++;
645           break;
646         }
647       }
648       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
649     }
650     if (fptr) {                 /* Clear the bits for this row */
651       for ( ; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
652     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
653       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
654     }
655   }
656   ierr = PetscFree(bb);CHKERRQ(ierr);
657   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
658   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
659 
660   /* Column indices are in the list of free space */
661   /* Allocate space for cj, initialize cj, and */
662   /* destroy list of free space and other temporary array(s) */
663   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
664   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
665 
666   /* put together the new symbolic matrix */
667   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bn,ci,cj,PETSC_NULL,C);CHKERRQ(ierr);
668   (*C)->rmap->bs = A->rmap->bs;
669   (*C)->cmap->bs = B->cmap->bs;
670 
671   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
672   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
673   c = (Mat_SeqAIJ *)((*C)->data);
674   c->free_a   = PETSC_TRUE;
675   c->free_ij  = PETSC_TRUE;
676   c->nonew    = 0;
677   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
678 
679   /* set MatInfo */
680   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
681   if (afill < 1.0) afill = 1.0;
682   c->maxnz                     = ci[am];
683   c->nz                        = ci[am];
684   (*C)->info.mallocs           = ndouble;
685   (*C)->info.fill_ratio_given  = fill;
686   (*C)->info.fill_ratio_needed = afill;
687 
688 #if defined(PETSC_USE_INFO)
689   if (ci[am]) {
690     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
691     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
692   } else {
693     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
694   }
695 #endif
696   PetscFunctionReturn(0);
697 }
698 
699 /* This routine is not used. Should be removed! */
700 #undef __FUNCT__
701 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
702 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
703 {
704   PetscErrorCode ierr;
705 
706   PetscFunctionBegin;
707   if (scall == MAT_INITIAL_MATRIX){
708     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
709   }
710   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
711   PetscFunctionReturn(0);
712 }
713 
714 #undef __FUNCT__
715 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
716 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
717 {
718   PetscErrorCode      ierr;
719   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
720 
721   PetscFunctionBegin;
722   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
723   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
724   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
725   ierr = PetscFree(multtrans);CHKERRQ(ierr);
726   PetscFunctionReturn(0);
727 }
728 
729 #undef __FUNCT__
730 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
731 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
732 {
733   PetscErrorCode      ierr;
734   PetscContainer      container;
735   Mat_MatMatTransMult *multtrans=PETSC_NULL;
736 
737   PetscFunctionBegin;
738   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
739   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
740   ierr = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
741   A->ops->destroy   = multtrans->destroy;
742   if (A->ops->destroy) {
743     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
744   }
745   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
746   PetscFunctionReturn(0);
747 }
748 
749 #undef __FUNCT__
750 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
751 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
752 {
753   PetscErrorCode      ierr;
754   Mat                 Bt;
755   PetscInt            *bti,*btj;
756   Mat_MatMatTransMult *multtrans;
757   PetscContainer      container;
758   PetscLogDouble      t0,tf,etime2=0.0;
759 
760   PetscFunctionBegin;
761   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
762    /* create symbolic Bt */
763   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
764   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,PETSC_NULL,&Bt);CHKERRQ(ierr);
765   Bt->rmap->bs = A->cmap->bs;
766   Bt->cmap->bs = B->cmap->bs;
767 
768   /* get symbolic C=A*Bt */
769   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
770 
771   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
772   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
773 
774   /* attach the supporting struct to C */
775   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
776   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
777   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
778   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
779   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
780 
781   multtrans->usecoloring = PETSC_FALSE;
782   multtrans->destroy = (*C)->ops->destroy;
783   (*C)->ops->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
784 
785   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
786   etime2 += tf - t0;
787 
788   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmattransmult_color",&multtrans->usecoloring,PETSC_NULL);CHKERRQ(ierr);
789   if (multtrans->usecoloring){
790     /* Create MatTransposeColoring from symbolic C=A*B^T */
791     MatTransposeColoring matcoloring;
792     ISColoring           iscoloring;
793     Mat                  Bt_dense,C_dense;
794     PetscLogDouble       etime0=0.0,etime01=0.0,etime1=0.0;
795 
796     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
797     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
798     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
799     etime0 += tf - t0;
800 
801     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
802     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
803     multtrans->matcoloring = matcoloring;
804     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
805     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
806     etime01 += tf - t0;
807 
808     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
809     /* Create Bt_dense and C_dense = A*Bt_dense */
810     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
811     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
812     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
813     ierr = MatSeqDenseSetPreallocation(Bt_dense,PETSC_NULL);CHKERRQ(ierr);
814     Bt_dense->assembled = PETSC_TRUE;
815     multtrans->Bt_den = Bt_dense;
816 
817     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
818     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
819     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
820     ierr = MatSeqDenseSetPreallocation(C_dense,PETSC_NULL);CHKERRQ(ierr);
821     Bt_dense->assembled = PETSC_TRUE;
822     multtrans->ABt_den = C_dense;
823     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
824     etime1 += tf - t0;
825 
826 #if defined(PETSC_USE_INFO)
827     {
828     Mat_SeqAIJ *c=(Mat_SeqAIJ*)(*C)->data;
829     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));
830     ierr = PetscInfo5(*C,"Sym = GetColor %g + ColorCreate %g + MatDenseCreate %g + non-colorSym %g = %g\n",etime0,etime01,etime1,etime2,etime0+etime01+etime1+etime2);
831     }
832 #endif
833   }
834   /* clean up */
835   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
836   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
837 
838 
839 
840 #if defined(INEFFICIENT_ALGORITHM)
841   /* The algorithm below computes am*bm sparse inner-product - inefficient! It will be deleted later. */
842   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
843   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
844   PetscInt           *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*ci,*cj,*acol,*bcol;
845   PetscInt           am=A->rmap->N,bm=B->rmap->N;
846   PetscInt           i,j,anzi,bnzj,cnzi,nlnk,*lnk,nspacedouble=0,ka,kb,index[1];
847   MatScalar          *ca;
848   PetscBT            lnkbt;
849   PetscReal          afill;
850 
851   /* Allocate row pointer array ci  */
852   ierr = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
853   ci[0] = 0;
854 
855   /* Create and initialize a linked list for C columns */
856   nlnk = bm+1;
857   ierr = PetscLLCreate(bm,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
858 
859   /* Initial FreeSpace with size fill*(nnz(A)+nnz(B)) */
860   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
861   current_space = free_space;
862 
863   /* Determine symbolic info for each row of the product A*B^T: */
864   for (i=0; i<am; i++) {
865     anzi = ai[i+1] - ai[i];
866     cnzi = 0;
867     acol = aj + ai[i];
868     for (j=0; j<bm; j++){
869       bnzj = bi[j+1] - bi[j];
870       bcol= bj + bi[j];
871       /* sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
872       ka = 0; kb = 0;
873       while (ka < anzi && kb < bnzj){
874         while (acol[ka] < bcol[kb] && ka < anzi) ka++;
875         if (ka == anzi) break;
876         while (acol[ka] > bcol[kb] && kb < bnzj) kb++;
877         if (kb == bnzj) break;
878         if (acol[ka] == bcol[kb]){ /* add nonzero c(i,j) to lnk */
879           index[0] = j;
880           ierr = PetscLLAdd(1,index,bm,nlnk,lnk,lnkbt);CHKERRQ(ierr);
881           cnzi++;
882           break;
883         }
884       }
885     }
886 
887     /* If free space is not available, make more free space */
888     /* Double the amount of total space in the list */
889     if (current_space->local_remaining<cnzi) {
890       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
891       nspacedouble++;
892     }
893 
894     /* Copy data into free space, then initialize lnk */
895     ierr = PetscLLClean(bm,bm,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
896     current_space->array           += cnzi;
897     current_space->local_used      += cnzi;
898     current_space->local_remaining -= cnzi;
899 
900     ci[i+1] = ci[i] + cnzi;
901   }
902 
903 
904   /* Column indices are in the list of free space.
905      Allocate array cj, copy column indices to cj, and destroy list of free space */
906   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
907   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
908   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
909 
910   /* Allocate space for ca */
911   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
912   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
913 
914   /* put together the new symbolic matrix */
915   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,am,bm,ci,cj,ca,C);CHKERRQ(ierr);
916   (*C)->rmap->bs = A->cmap->bs;
917   (*C)->cmap->bs = B->cmap->bs;
918 
919   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
920   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
921   c = (Mat_SeqAIJ *)((*C)->data);
922   c->free_a   = PETSC_TRUE;
923   c->free_ij  = PETSC_TRUE;
924   c->nonew    = 0;
925 
926   /* set MatInfo */
927   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
928   if (afill < 1.0) afill = 1.0;
929   c->maxnz                     = ci[am];
930   c->nz                        = ci[am];
931   (*C)->info.mallocs           = nspacedouble;
932   (*C)->info.fill_ratio_given  = fill;
933   (*C)->info.fill_ratio_needed = afill;
934 
935 #if defined(PETSC_USE_INFO)
936   if (ci[am]) {
937     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
938     ierr = PetscInfo1((*C),"Use MatMatTransposeMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
939   } else {
940     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
941   }
942 #endif
943 #endif
944   PetscFunctionReturn(0);
945 }
946 
947 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
948 #undef __FUNCT__
949 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
950 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
951 {
952   PetscErrorCode ierr;
953   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
954   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
955   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
956   PetscLogDouble flops=0.0;
957   MatScalar      *aa=a->a,*aval,*ba=b->a,*bval,*ca,*cval;
958   Mat_MatMatTransMult *multtrans;
959   PetscContainer      container;
960 #if defined(USE_ARRAY)
961   MatScalar      *spdot;
962 #endif
963 
964   PetscFunctionBegin;
965   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject *)&container);CHKERRQ(ierr);
966   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
967   ierr  = PetscContainerGetPointer(container,(void **)&multtrans);CHKERRQ(ierr);
968   if (multtrans->usecoloring){
969     MatTransposeColoring  matcoloring = multtrans->matcoloring;
970     Mat                   Bt_dense;
971     PetscInt              m,n;
972     PetscLogDouble t0,tf,etime0=0.0,etime1=0.0,etime2=0.0;
973     Mat C_dense = multtrans->ABt_den;
974 
975     Bt_dense = multtrans->Bt_den;
976     ierr = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
977 
978     /* Get Bt_dense by Apply MatTransposeColoring to B */
979     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
980     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
981     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
982     etime0 += tf - t0;
983 
984     /* C_dense = A*Bt_dense */
985     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
986     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
987     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
988     etime2 += tf - t0;
989 
990     /* Recover C from C_dense */
991     ierr = PetscGetTime(&t0);CHKERRQ(ierr);
992     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
993     ierr = PetscGetTime(&tf);CHKERRQ(ierr);
994     etime1 += tf - t0;
995 #if defined(PETSC_USE_INFO)
996     ierr = PetscInfo4(C,"Num = ColoringApply: %g %g + Mult_sp_dense %g = %g\n",etime0,etime1,etime2,etime0+etime1+etime2);
997 #endif
998     PetscFunctionReturn(0);
999   }
1000 
1001 #if defined(USE_ARRAY)
1002   /* allocate an array for implementing sparse inner-product */
1003   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
1004   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
1005 #endif
1006 
1007   /* clear old values in C */
1008   if (!c->a){
1009     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1010     c->a      = ca;
1011     c->free_a = PETSC_TRUE;
1012   } else {
1013     ca =  c->a;
1014   }
1015   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1016 
1017   for (i=0; i<cm; i++) {
1018     anzi = ai[i+1] - ai[i];
1019     acol = aj + ai[i];
1020     aval = aa + ai[i];
1021     cnzi = ci[i+1] - ci[i];
1022     ccol = cj + ci[i];
1023     cval = ca + ci[i];
1024     for (j=0; j<cnzi; j++){
1025       brow = ccol[j];
1026       bnzj = bi[brow+1] - bi[brow];
1027       bcol = bj + bi[brow];
1028       bval = ba + bi[brow];
1029 
1030       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1031 #if defined(USE_ARRAY)
1032       /* put ba to spdot array */
1033       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
1034       /* c(i,j)=A[i,:]*B[j,:]^T */
1035       for (nexta=0; nexta<anzi; nexta++){
1036         cval[j] += spdot[acol[nexta]]*aval[nexta];
1037       }
1038       /* zero spdot array */
1039       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1040 #else
1041       nexta = 0; nextb = 0;
1042       while (nexta<anzi && nextb<bnzj){
1043         while (acol[nexta] < bcol[nextb] && nexta < anzi) nexta++;
1044         if (nexta == anzi) break;
1045         while (acol[nexta] > bcol[nextb] && nextb < bnzj) nextb++;
1046         if (nextb == bnzj) break;
1047         if (acol[nexta] == bcol[nextb]){
1048           cval[j] += aval[nexta]*bval[nextb];
1049           nexta++; nextb++;
1050           flops += 2;
1051         }
1052       }
1053 #endif
1054     }
1055   }
1056   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1057   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1058   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1059 #if defined(USE_ARRAY)
1060   ierr = PetscFree(spdot);
1061 #endif
1062   PetscFunctionReturn(0);
1063 }
1064 
1065 #undef __FUNCT__
1066 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1067 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C) {
1068   PetscErrorCode ierr;
1069 
1070   PetscFunctionBegin;
1071   if (scall == MAT_INITIAL_MATRIX){
1072     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1073   }
1074   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1075   PetscFunctionReturn(0);
1076 }
1077 
1078 #undef __FUNCT__
1079 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1080 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1081 {
1082   PetscErrorCode ierr;
1083   Mat            At;
1084   PetscInt       *ati,*atj;
1085 
1086   PetscFunctionBegin;
1087   /* create symbolic At */
1088   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1089   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,PETSC_NULL,&At);CHKERRQ(ierr);
1090   At->rmap->bs = A->cmap->bs;
1091   At->cmap->bs = B->cmap->bs;
1092 
1093   /* get symbolic C=At*B */
1094   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1095 
1096   /* clean up */
1097   ierr = MatDestroy(&At);CHKERRQ(ierr);
1098   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1099   PetscFunctionReturn(0);
1100 }
1101 
1102 #undef __FUNCT__
1103 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1104 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1105 {
1106   PetscErrorCode ierr;
1107   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1108   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1109   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1110   PetscLogDouble flops=0.0;
1111   MatScalar      *aa=a->a,*ba,*ca,*caj;
1112 
1113   PetscFunctionBegin;
1114   if (!c->a){
1115     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1116     c->a      = ca;
1117     c->free_a = PETSC_TRUE;
1118   } else {
1119     ca = c->a;
1120   }
1121   /* clear old values in C */
1122   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1123 
1124   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1125   for (i=0;i<am;i++) {
1126     bj   = b->j + bi[i];
1127     ba   = b->a + bi[i];
1128     bnzi = bi[i+1] - bi[i];
1129     anzi = ai[i+1] - ai[i];
1130     for (j=0; j<anzi; j++) {
1131       nextb = 0;
1132       crow  = *aj++;
1133       cjj   = cj + ci[crow];
1134       caj   = ca + ci[crow];
1135       /* perform sparse axpy operation.  Note cjj includes bj. */
1136       for (k=0; nextb<bnzi; k++) {
1137         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1138           caj[k] += (*aa)*(*(ba+nextb));
1139           nextb++;
1140         }
1141       }
1142       flops += 2*bnzi;
1143       aa++;
1144     }
1145   }
1146 
1147   /* Assemble the final matrix and clean up */
1148   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1149   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1150   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1151   PetscFunctionReturn(0);
1152 }
1153 
1154 EXTERN_C_BEGIN
1155 #undef __FUNCT__
1156 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1157 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1158 {
1159   PetscErrorCode ierr;
1160 
1161   PetscFunctionBegin;
1162   if (scall == MAT_INITIAL_MATRIX){
1163     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1164   }
1165   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1166   PetscFunctionReturn(0);
1167 }
1168 EXTERN_C_END
1169 
1170 #undef __FUNCT__
1171 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1172 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1173 {
1174   PetscErrorCode ierr;
1175 
1176   PetscFunctionBegin;
1177   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1178   (*C)->ops->matmult = MatMatMult_SeqAIJ_SeqDense;
1179   PetscFunctionReturn(0);
1180 }
1181 
1182 #undef __FUNCT__
1183 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1184 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1185 {
1186   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1187   PetscErrorCode ierr;
1188   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1189   MatScalar      *aa;
1190   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1191   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1192 
1193   PetscFunctionBegin;
1194   if (!cm || !cn) PetscFunctionReturn(0);
1195   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);
1196   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);
1197   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);
1198   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1199   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1200   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1201   for (col=0; col<cn-4; col += 4){  /* over columns of C */
1202     colam = col*am;
1203     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1204       r1 = r2 = r3 = r4 = 0.0;
1205       n   = a->i[i+1] - a->i[i];
1206       aj  = a->j + a->i[i];
1207       aa  = a->a + a->i[i];
1208       for (j=0; j<n; j++) {
1209         r1 += (*aa)*b1[*aj];
1210         r2 += (*aa)*b2[*aj];
1211         r3 += (*aa)*b3[*aj];
1212         r4 += (*aa++)*b4[*aj++];
1213       }
1214       c[colam + i]       = r1;
1215       c[colam + am + i]  = r2;
1216       c[colam + am2 + i] = r3;
1217       c[colam + am3 + i] = r4;
1218     }
1219     b1 += bm4;
1220     b2 += bm4;
1221     b3 += bm4;
1222     b4 += bm4;
1223   }
1224   for (;col<cn; col++){     /* over extra columns of C */
1225     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1226       r1 = 0.0;
1227       n   = a->i[i+1] - a->i[i];
1228       aj  = a->j + a->i[i];
1229       aa  = a->a + a->i[i];
1230 
1231       for (j=0; j<n; j++) {
1232         r1 += (*aa++)*b1[*aj++];
1233       }
1234       c[col*am + i]     = r1;
1235     }
1236     b1 += bm;
1237   }
1238   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1239   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1240   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1241   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1242   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1243   PetscFunctionReturn(0);
1244 }
1245 
1246 /*
1247    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1248 */
1249 #undef __FUNCT__
1250 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1251 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1252 {
1253   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1254   PetscErrorCode ierr;
1255   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1256   MatScalar      *aa;
1257   PetscInt       cm=C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1258   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1259 
1260   PetscFunctionBegin;
1261   if (!cm || !cn) PetscFunctionReturn(0);
1262   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1263   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1264   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1265 
1266   if (a->compressedrow.use){ /* use compressed row format */
1267     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1268       colam = col*am;
1269       arm   = a->compressedrow.nrows;
1270       ii    = a->compressedrow.i;
1271       ridx  = a->compressedrow.rindex;
1272       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1273 	r1 = r2 = r3 = r4 = 0.0;
1274 	n   = ii[i+1] - ii[i];
1275 	aj  = a->j + ii[i];
1276 	aa  = a->a + ii[i];
1277 	for (j=0; j<n; j++) {
1278 	  r1 += (*aa)*b1[*aj];
1279 	  r2 += (*aa)*b2[*aj];
1280 	  r3 += (*aa)*b3[*aj];
1281 	  r4 += (*aa++)*b4[*aj++];
1282 	}
1283 	c[colam       + ridx[i]] += r1;
1284 	c[colam + am  + ridx[i]] += r2;
1285 	c[colam + am2 + ridx[i]] += r3;
1286 	c[colam + am3 + ridx[i]] += r4;
1287       }
1288       b1 += bm4;
1289       b2 += bm4;
1290       b3 += bm4;
1291       b4 += bm4;
1292     }
1293     for (;col<cn; col++){     /* over extra columns of C */
1294       colam = col*am;
1295       arm   = a->compressedrow.nrows;
1296       ii    = a->compressedrow.i;
1297       ridx  = a->compressedrow.rindex;
1298       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1299 	r1 = 0.0;
1300 	n   = ii[i+1] - ii[i];
1301 	aj  = a->j + ii[i];
1302 	aa  = a->a + ii[i];
1303 
1304 	for (j=0; j<n; j++) {
1305 	  r1 += (*aa++)*b1[*aj++];
1306 	}
1307 	c[col*am + ridx[i]] += r1;
1308       }
1309       b1 += bm;
1310     }
1311   } else {
1312     for (col=0; col<cn-4; col += 4){  /* over columns of C */
1313       colam = col*am;
1314       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1315 	r1 = r2 = r3 = r4 = 0.0;
1316 	n   = a->i[i+1] - a->i[i];
1317 	aj  = a->j + a->i[i];
1318 	aa  = a->a + a->i[i];
1319 	for (j=0; j<n; j++) {
1320 	  r1 += (*aa)*b1[*aj];
1321 	  r2 += (*aa)*b2[*aj];
1322 	  r3 += (*aa)*b3[*aj];
1323 	  r4 += (*aa++)*b4[*aj++];
1324 	}
1325 	c[colam + i]       += r1;
1326 	c[colam + am + i]  += r2;
1327 	c[colam + am2 + i] += r3;
1328 	c[colam + am3 + i] += r4;
1329       }
1330       b1 += bm4;
1331       b2 += bm4;
1332       b3 += bm4;
1333       b4 += bm4;
1334     }
1335     for (;col<cn; col++){     /* over extra columns of C */
1336       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1337 	r1 = 0.0;
1338 	n   = a->i[i+1] - a->i[i];
1339 	aj  = a->j + a->i[i];
1340 	aa  = a->a + a->i[i];
1341 
1342 	for (j=0; j<n; j++) {
1343 	  r1 += (*aa++)*b1[*aj++];
1344 	}
1345 	c[col*am + i]     += r1;
1346       }
1347       b1 += bm;
1348     }
1349   }
1350   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1351   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1352   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1353   PetscFunctionReturn(0);
1354 }
1355 
1356 #undef __FUNCT__
1357 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1358 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1359 {
1360   PetscErrorCode ierr;
1361   Mat_SeqAIJ     *b = (Mat_SeqAIJ*)B->data;
1362   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1363   PetscInt       *bi=b->i,*bj=b->j;
1364   PetscInt       m=Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1365   MatScalar      *btval,*btval_den,*ba=b->a;
1366   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1367 
1368   PetscFunctionBegin;
1369   btval_den=btdense->v;
1370   ierr = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1371   for (k=0; k<ncolors; k++) {
1372     ncolumns = coloring->ncolumns[k];
1373     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1374       col   = *(columns + colorforcol[k] + l);
1375       btcol = bj + bi[col];
1376       btval = ba + bi[col];
1377       anz   = bi[col+1] - bi[col];
1378       for (j=0; j<anz; j++){
1379         brow            = btcol[j];
1380         btval_den[brow] = btval[j];
1381       }
1382     }
1383     btval_den += m;
1384   }
1385   PetscFunctionReturn(0);
1386 }
1387 
1388 #undef __FUNCT__
1389 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1390 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1391 {
1392   PetscErrorCode ierr;
1393   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1394   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1395   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1396   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1397 
1398   PetscFunctionBegin;
1399   ierr = MatGetLocalSize(Csp,&m,PETSC_NULL);CHKERRQ(ierr);
1400   ierr = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1401   cp_den = ca_den;
1402   for (k=0; k<ncolors; k++) {
1403     nrows = matcoloring->nrows[k];
1404     row   = rows  + colorforrow[k];
1405     idx   = spidx + colorforrow[k];
1406     for (l=0; l<nrows; l++){
1407       ca[idx[l]] = cp_den[row[l]];
1408     }
1409     cp_den += m;
1410   }
1411   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1412   PetscFunctionReturn(0);
1413 }
1414 
1415 /*
1416  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1417  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1418  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1419  */
1420 #undef __FUNCT__
1421 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1422 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1423 {
1424   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1425   PetscErrorCode ierr;
1426   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1427   PetscInt       nz = a->i[m],row,*jj,mr,col;
1428   PetscInt       *cspidx;
1429 
1430   PetscFunctionBegin;
1431   *nn = n;
1432   if (!ia) PetscFunctionReturn(0);
1433   if (symmetric) {
1434     SETERRQ(((PetscObject)A)->comm,PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1435     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1436   } else {
1437     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1438     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1439     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1440     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1441     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1442     jj = a->j;
1443     for (i=0; i<nz; i++) {
1444       collengths[jj[i]]++;
1445     }
1446     cia[0] = oshift;
1447     for (i=0; i<n; i++) {
1448       cia[i+1] = cia[i] + collengths[i];
1449     }
1450     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1451     jj   = a->j;
1452     for (row=0; row<m; row++) {
1453       mr = a->i[row+1] - a->i[row];
1454       for (i=0; i<mr; i++) {
1455         col = *jj++;
1456         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1457         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
1458       }
1459     }
1460     ierr = PetscFree(collengths);CHKERRQ(ierr);
1461     *ia = cia; *ja = cja;
1462     *spidx = cspidx;
1463   }
1464   PetscFunctionReturn(0);
1465 }
1466 
1467 #undef __FUNCT__
1468 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1469 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool  symmetric,PetscBool  inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1470 {
1471   PetscErrorCode ierr;
1472 
1473   PetscFunctionBegin;
1474   if (!ia) PetscFunctionReturn(0);
1475 
1476   ierr = PetscFree(*ia);CHKERRQ(ierr);
1477   ierr = PetscFree(*ja);CHKERRQ(ierr);
1478   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1479   PetscFunctionReturn(0);
1480 }
1481 
1482 #undef __FUNCT__
1483 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1484 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1485 {
1486   PetscErrorCode ierr;
1487   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
1488   const PetscInt *is,*ci,*cj,*row_idx;
1489   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1490   IS             *isa;
1491   PetscBool      flg1,flg2;
1492   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1493   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1494   PetscInt       *colorforcol,*columns,*columns_i;
1495 
1496   PetscFunctionBegin;
1497   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1498 
1499   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1500   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1501   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1502   if (flg1 || flg2) {
1503     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1504   }
1505 
1506   N         = mat->cmap->N/bs;
1507   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1508   c->N      = mat->cmap->N/bs;
1509   c->m      = mat->rmap->N/bs;
1510   c->rstart = 0;
1511 
1512   c->ncolors = nis;
1513   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1514   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1515   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1516   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1517   colorforrow[0]    = 0;
1518   rows_i            = rows;
1519   columnsforspidx_i = columnsforspidx;
1520 
1521   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1522   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1523   colorforcol[0] = 0;
1524   columns_i      = columns;
1525 
1526   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1527 
1528   cm = c->m;
1529   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1530   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1531   for (i=0; i<nis; i++) {
1532     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1533     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1534     c->ncolumns[i] = n;
1535     if (n) {
1536       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1537     }
1538     colorforcol[i+1] = colorforcol[i] + n;
1539     columns_i       += n;
1540 
1541     /* fast, crude version requires O(N*N) work */
1542     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1543 
1544     /* loop over columns*/
1545     for (j=0; j<n; j++) {
1546       col     = is[j];
1547       row_idx = cj + ci[col];
1548       m       = ci[col+1] - ci[col];
1549       /* loop over columns marking them in rowhit */
1550       for (k=0; k<m; k++) {
1551         idxhit[*row_idx]   = spidx[ci[col] + k];
1552         rowhit[*row_idx++] = col + 1;
1553       }
1554     }
1555     /* count the number of hits */
1556     nrows = 0;
1557     for (j=0; j<cm; j++) {
1558       if (rowhit[j]) nrows++;
1559     }
1560     c->nrows[i]      = nrows;
1561     colorforrow[i+1] = colorforrow[i] + nrows;
1562 
1563     nrows       = 0;
1564     for (j=0; j<cm; j++) {
1565       if (rowhit[j]) {
1566         rows_i[nrows]            = j;
1567         columnsforspidx_i[nrows] = idxhit[j];
1568         nrows++;
1569       }
1570     }
1571     ierr = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1572     rows_i += nrows; columnsforspidx_i += nrows;
1573   }
1574   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,PETSC_NULL);CHKERRQ(ierr);
1575   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1576   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1577 #if defined(PETSC_USE_DEBUG)
1578   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1579 #endif
1580 
1581   c->colorforrow     = colorforrow;
1582   c->rows            = rows;
1583   c->columnsforspidx = columnsforspidx;
1584   c->colorforcol     = colorforcol;
1585   c->columns         = columns;
1586   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1587   PetscFunctionReturn(0);
1588 }
1589