xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 4d478ae76771a501e2c3958c67bfeb93cdb5fe87)
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>
12 #include <petsctime.h>
13 
14 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);
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,llcondensed = 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,NULL);CHKERRQ(ierr);
27     ierr = PetscOptionsBool("-matmatmult_scalable_fast","Use a scalable but slower C=A*B","",scalable_fast,&scalable_fast,NULL);CHKERRQ(ierr);
28     ierr = PetscOptionsBool("-matmatmult_heap","Use heap implementation of symbolic factorization C=A*B","",heap,&heap,NULL);CHKERRQ(ierr);
29     ierr = PetscOptionsBool("-matmatmult_btheap","Use btheap implementation of symbolic factorization C=A*B","",btheap,&btheap,NULL);CHKERRQ(ierr);
30     ierr = PetscOptionsBool("-matmatmult_llcondensed","Use LLCondensed to for symbolic C=A*B","",llcondensed,&llcondensed,NULL);CHKERRQ(ierr);
31     ierr = PetscOptionsEnd();CHKERRQ(ierr);
32     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
33     if (scalable_fast) {
34       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
35     } else if (scalable) {
36       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
37     } else if (heap) {
38       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
39     } else if (btheap) {
40       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
41     } else if (llcondensed) {
42       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
43     } else {
44       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
45     }
46     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
47   }
48 
49   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
50   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
51   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
52   PetscFunctionReturn(0);
53 }
54 
55 #undef __FUNCT__
56 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed"
57 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
58 {
59   PetscErrorCode     ierr;
60   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
61   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
62   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
63   PetscReal          afill;
64   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
65   PetscBT            lnkbt;
66   PetscFreeSpaceList free_space=NULL,current_space=NULL;
67 
68   PetscFunctionBegin;
69   /* Get ci and cj */
70   /*---------------*/
71   /* Allocate ci array, arrays for fill computation and */
72   /* free space for accumulating nonzero column info */
73   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
74   ci[0] = 0;
75 
76   /* create and initialize a linked list */
77   nlnk_max = a->rmax*b->rmax;
78   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn;
79   ierr = PetscLLCondensedCreate(nlnk_max,bn,&lnk,&lnkbt);CHKERRQ(ierr);
80 
81   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
82   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
83 
84   current_space = free_space;
85 
86   /* Determine ci and cj */
87   for (i=0; i<am; i++) {
88     anzi = ai[i+1] - ai[i];
89     aj   = a->j + ai[i];
90     for (j=0; j<anzi; j++) {
91       brow = aj[j];
92       bnzj = bi[brow+1] - bi[brow];
93       bj   = b->j + bi[brow];
94       /* add non-zero cols of B into the sorted linked list lnk */
95       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
96     }
97     cnzi = lnk[0];
98 
99     /* If free space is not available, make more free space */
100     /* Double the amount of total space in the list */
101     if (current_space->local_remaining<cnzi) {
102       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
103       ndouble++;
104     }
105 
106     /* Copy data into free space, then initialize lnk */
107     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
108 
109     current_space->array           += cnzi;
110     current_space->local_used      += cnzi;
111     current_space->local_remaining -= cnzi;
112 
113     ci[i+1] = ci[i] + cnzi;
114   }
115 
116   /* Column indices are in the list of free space */
117   /* Allocate space for cj, initialize cj, and */
118   /* destroy list of free space and other temporary array(s) */
119   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
120   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
121   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
122 
123   /* put together the new symbolic matrix */
124   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
125 
126   (*C)->rmap->bs = A->rmap->bs;
127   (*C)->cmap->bs = B->cmap->bs;
128 
129   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
130   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
131   c                         = (Mat_SeqAIJ*)((*C)->data);
132   c->free_a                 = PETSC_FALSE;
133   c->free_ij                = PETSC_TRUE;
134   c->nonew                  = 0;
135   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
136 
137   /* set MatInfo */
138   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
139   if (afill < 1.0) afill = 1.0;
140   c->maxnz                     = ci[am];
141   c->nz                        = ci[am];
142   (*C)->info.mallocs           = ndouble;
143   (*C)->info.fill_ratio_given  = fill;
144   (*C)->info.fill_ratio_needed = afill;
145 
146 #if defined(PETSC_USE_INFO)
147   if (ci[am]) {
148     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
149     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
150   } else {
151     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
152   }
153 #endif
154   PetscFunctionReturn(0);
155 }
156 
157 #undef __FUNCT__
158 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ"
159 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
160 {
161   PetscErrorCode ierr;
162   PetscLogDouble flops=0.0;
163   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
164   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
165   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
166   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
167   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
168   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
169   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
170   PetscScalar    *ab_dense;
171 
172   PetscFunctionBegin;
173   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
174     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
175     c->a      = ca;
176     c->free_a = PETSC_TRUE;
177 
178     ierr = PetscMalloc(B->cmap->N*sizeof(PetscScalar),&ab_dense);CHKERRQ(ierr);
179     ierr = PetscMemzero(ab_dense,B->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
180 
181     c->matmult_abdense = ab_dense;
182   } else {
183     ca       = c->a;
184     ab_dense = c->matmult_abdense;
185   }
186 
187   /* clean old values in C */
188   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
189   /* Traverse A row-wise. */
190   /* Build the ith row in C by summing over nonzero columns in A, */
191   /* the rows of B corresponding to nonzeros of A. */
192   for (i=0; i<am; i++) {
193     anzi = ai[i+1] - ai[i];
194     for (j=0; j<anzi; j++) {
195       brow = aj[j];
196       bnzi = bi[brow+1] - bi[brow];
197       bjj  = bj + bi[brow];
198       baj  = ba + bi[brow];
199       /* perform dense axpy */
200       valtmp = aa[j];
201       for (k=0; k<bnzi; k++) {
202         ab_dense[bjj[k]] += valtmp*baj[k];
203       }
204       flops += 2*bnzi;
205     }
206     aj += anzi; aa += anzi;
207 
208     cnzi = ci[i+1] - ci[i];
209     for (k=0; k<cnzi; k++) {
210       ca[k]          += ab_dense[cj[k]];
211       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
212     }
213     flops += cnzi;
214     cj    += cnzi; ca += cnzi;
215   }
216   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
217   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
218   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
219   PetscFunctionReturn(0);
220 }
221 
222 #undef __FUNCT__
223 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable"
224 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
225 {
226   PetscErrorCode ierr;
227   PetscLogDouble flops=0.0;
228   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
229   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
230   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
231   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
232   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
233   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
234   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
235   PetscInt       nextb;
236 
237   PetscFunctionBegin;
238   /* clean old values in C */
239   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
240   /* Traverse A row-wise. */
241   /* Build the ith row in C by summing over nonzero columns in A, */
242   /* the rows of B corresponding to nonzeros of A. */
243   for (i=0; i<am; i++) {
244     anzi = ai[i+1] - ai[i];
245     cnzi = ci[i+1] - ci[i];
246     for (j=0; j<anzi; j++) {
247       brow = aj[j];
248       bnzi = bi[brow+1] - bi[brow];
249       bjj  = bj + bi[brow];
250       baj  = ba + bi[brow];
251       /* perform sparse axpy */
252       valtmp = aa[j];
253       nextb  = 0;
254       for (k=0; nextb<bnzi; k++) {
255         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
256           ca[k] += valtmp*baj[nextb++];
257         }
258       }
259       flops += 2*bnzi;
260     }
261     aj += anzi; aa += anzi;
262     cj += cnzi; ca += cnzi;
263   }
264 
265   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
266   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
267   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
268   PetscFunctionReturn(0);
269 }
270 
271 #undef __FUNCT__
272 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast"
273 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
274 {
275   PetscErrorCode     ierr;
276   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
277   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
278   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
279   MatScalar          *ca;
280   PetscReal          afill;
281   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
282   PetscFreeSpaceList free_space=NULL,current_space=NULL;
283 
284   PetscFunctionBegin;
285   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
286   /*-----------------------------------------------------------------------------------------*/
287   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
288   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
289   ci[0] = 0;
290 
291   /* create and initialize a linked list */
292   nlnk_max = a->rmax*b->rmax;
293   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
294   ierr = PetscLLCondensedCreate_fast(nlnk_max,&lnk);CHKERRQ(ierr);
295 
296   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
297   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
298   current_space = free_space;
299 
300   /* Determine ci and cj */
301   for (i=0; i<am; i++) {
302     anzi = ai[i+1] - ai[i];
303     aj   = a->j + ai[i];
304     for (j=0; j<anzi; j++) {
305       brow = aj[j];
306       bnzj = bi[brow+1] - bi[brow];
307       bj   = b->j + bi[brow];
308       /* add non-zero cols of B into the sorted linked list lnk */
309       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
310     }
311     cnzi = lnk[1];
312 
313     /* If free space is not available, make more free space */
314     /* Double the amount of total space in the list */
315     if (current_space->local_remaining<cnzi) {
316       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
317       ndouble++;
318     }
319 
320     /* Copy data into free space, then initialize lnk */
321     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
322 
323     current_space->array           += cnzi;
324     current_space->local_used      += cnzi;
325     current_space->local_remaining -= cnzi;
326 
327     ci[i+1] = ci[i] + cnzi;
328   }
329 
330   /* Column indices are in the list of free space */
331   /* Allocate space for cj, initialize cj, and */
332   /* destroy list of free space and other temporary array(s) */
333   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
334   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
335   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
336 
337   /* Allocate space for ca */
338   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
339   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
340 
341   /* put together the new symbolic matrix */
342   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
343 
344   (*C)->rmap->bs = A->rmap->bs;
345   (*C)->cmap->bs = B->cmap->bs;
346 
347   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
348   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
349   c          = (Mat_SeqAIJ*)((*C)->data);
350   c->free_a  = PETSC_TRUE;
351   c->free_ij = PETSC_TRUE;
352   c->nonew   = 0;
353 
354   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
355 
356   /* set MatInfo */
357   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
358   if (afill < 1.0) afill = 1.0;
359   c->maxnz                     = ci[am];
360   c->nz                        = ci[am];
361   (*C)->info.mallocs           = ndouble;
362   (*C)->info.fill_ratio_given  = fill;
363   (*C)->info.fill_ratio_needed = afill;
364 
365 #if defined(PETSC_USE_INFO)
366   if (ci[am]) {
367     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
368     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
369   } else {
370     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
371   }
372 #endif
373   PetscFunctionReturn(0);
374 }
375 
376 
377 #undef __FUNCT__
378 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable"
379 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
380 {
381   PetscErrorCode     ierr;
382   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
383   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
384   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
385   MatScalar          *ca;
386   PetscReal          afill;
387   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,nlnk_max,*lnk,ndouble=0;
388   PetscFreeSpaceList free_space=NULL,current_space=NULL;
389 
390   PetscFunctionBegin;
391   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
392   /*---------------------------------------------------------------------------------------------*/
393   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
394   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
395   ci[0] = 0;
396 
397   /* create and initialize a linked list */
398   nlnk_max = a->rmax*b->rmax;
399   if (!nlnk_max || nlnk_max > bn) nlnk_max = bn; /* in case rmax is not defined for A or B */
400   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
401 
402   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
403   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
404   current_space = free_space;
405 
406   /* Determine ci and cj */
407   for (i=0; i<am; i++) {
408     anzi = ai[i+1] - ai[i];
409     aj   = a->j + ai[i];
410     for (j=0; j<anzi; j++) {
411       brow = aj[j];
412       bnzj = bi[brow+1] - bi[brow];
413       bj   = b->j + bi[brow];
414       /* add non-zero cols of B into the sorted linked list lnk */
415       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
416     }
417     cnzi = lnk[0];
418 
419     /* If free space is not available, make more free space */
420     /* Double the amount of total space in the list */
421     if (current_space->local_remaining<cnzi) {
422       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
423       ndouble++;
424     }
425 
426     /* Copy data into free space, then initialize lnk */
427     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
428 
429     current_space->array           += cnzi;
430     current_space->local_used      += cnzi;
431     current_space->local_remaining -= cnzi;
432 
433     ci[i+1] = ci[i] + cnzi;
434   }
435 
436   /* Column indices are in the list of free space */
437   /* Allocate space for cj, initialize cj, and */
438   /* destroy list of free space and other temporary array(s) */
439   ierr = PetscMalloc((ci[am]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
440   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
441   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
442 
443   /* Allocate space for ca */
444   /*-----------------------*/
445   ierr = PetscMalloc((ci[am]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
446   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
447 
448   /* put together the new symbolic matrix */
449   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
450 
451   (*C)->rmap->bs = A->rmap->bs;
452   (*C)->cmap->bs = B->cmap->bs;
453 
454   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
455   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
456   c          = (Mat_SeqAIJ*)((*C)->data);
457   c->free_a  = PETSC_TRUE;
458   c->free_ij = PETSC_TRUE;
459   c->nonew   = 0;
460 
461   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
462 
463   /* set MatInfo */
464   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
465   if (afill < 1.0) afill = 1.0;
466   c->maxnz                     = ci[am];
467   c->nz                        = ci[am];
468   (*C)->info.mallocs           = ndouble;
469   (*C)->info.fill_ratio_given  = fill;
470   (*C)->info.fill_ratio_needed = afill;
471 
472 #if defined(PETSC_USE_INFO)
473   if (ci[am]) {
474     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
475     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
476   } else {
477     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
478   }
479 #endif
480   PetscFunctionReturn(0);
481 }
482 
483 #undef __FUNCT__
484 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap"
485 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
486 {
487   PetscErrorCode     ierr;
488   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
489   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
490   PetscInt           *ci,*cj,*bb;
491   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
492   PetscReal          afill;
493   PetscInt           i,j,col,ndouble = 0;
494   PetscFreeSpaceList free_space=NULL,current_space=NULL;
495   PetscHeap          h;
496 
497   PetscFunctionBegin;
498   /* Get ci and cj - by merging sorted rows using a heap */
499   /*---------------------------------------------------------------------------------------------*/
500   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
501   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
502   ci[0] = 0;
503 
504   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
505   ierr          = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
506   current_space = free_space;
507 
508   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
509   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
510 
511   /* Determine ci and cj */
512   for (i=0; i<am; i++) {
513     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 */
514     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
515     ci[i+1] = ci[i];
516     /* Populate the min heap */
517     for (j=0; j<anzi; j++) {
518       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
519       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
520         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
521       }
522     }
523     /* Pick off the min element, adding it to free space */
524     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
525     while (j >= 0) {
526       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
527         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
528         ndouble++;
529       }
530       *(current_space->array++) = col;
531       current_space->local_used++;
532       current_space->local_remaining--;
533       ci[i+1]++;
534 
535       /* stash if anything else remains in this row of B */
536       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
537       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
538         PetscInt j2,col2;
539         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
540         if (col2 != col) break;
541         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
542         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
543       }
544       /* Put any stashed elements back into the min heap */
545       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
546       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
547     }
548   }
549   ierr = PetscFree(bb);CHKERRQ(ierr);
550   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
551 
552   /* Column indices are in the list of free space */
553   /* Allocate space for cj, initialize cj, and */
554   /* destroy list of free space and other temporary array(s) */
555   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
556   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
557 
558   /* put together the new symbolic matrix */
559   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
560 
561   (*C)->rmap->bs = A->rmap->bs;
562   (*C)->cmap->bs = B->cmap->bs;
563 
564   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
565   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
566   c          = (Mat_SeqAIJ*)((*C)->data);
567   c->free_a  = PETSC_TRUE;
568   c->free_ij = PETSC_TRUE;
569   c->nonew   = 0;
570 
571   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
572 
573   /* set MatInfo */
574   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
575   if (afill < 1.0) afill = 1.0;
576   c->maxnz                     = ci[am];
577   c->nz                        = ci[am];
578   (*C)->info.mallocs           = ndouble;
579   (*C)->info.fill_ratio_given  = fill;
580   (*C)->info.fill_ratio_needed = afill;
581 
582 #if defined(PETSC_USE_INFO)
583   if (ci[am]) {
584     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
585     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
586   } else {
587     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
588   }
589 #endif
590   PetscFunctionReturn(0);
591 }
592 
593 #undef __FUNCT__
594 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap"
595 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
596 {
597   PetscErrorCode     ierr;
598   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
599   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
600   PetscInt           *ci,*cj,*bb;
601   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
602   PetscReal          afill;
603   PetscInt           i,j,col,ndouble = 0;
604   PetscFreeSpaceList free_space=NULL,current_space=NULL;
605   PetscHeap          h;
606   PetscBT            bt;
607 
608   PetscFunctionBegin;
609   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
610   /*---------------------------------------------------------------------------------------------*/
611   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
612   ierr  = PetscMalloc(((am+1)+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
613   ci[0] = 0;
614 
615   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
616   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+bi[bm])),&free_space);CHKERRQ(ierr);
617 
618   current_space = free_space;
619 
620   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
621   ierr = PetscMalloc(a->rmax*sizeof(PetscInt),&bb);CHKERRQ(ierr);
622   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
623 
624   /* Determine ci and cj */
625   for (i=0; i<am; i++) {
626     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 */
627     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
628     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
629     ci[i+1] = ci[i];
630     /* Populate the min heap */
631     for (j=0; j<anzi; j++) {
632       PetscInt brow = acol[j];
633       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
634         PetscInt bcol = bj[bb[j]];
635         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
636           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
637           bb[j]++;
638           break;
639         }
640       }
641     }
642     /* Pick off the min element, adding it to free space */
643     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
644     while (j >= 0) {
645       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
646         fptr = NULL;                      /* need PetscBTMemzero */
647         ierr = PetscFreeSpaceGet(PetscMin(2*current_space->total_array_size,16 << 20),&current_space);CHKERRQ(ierr);
648         ndouble++;
649       }
650       *(current_space->array++) = col;
651       current_space->local_used++;
652       current_space->local_remaining--;
653       ci[i+1]++;
654 
655       /* stash if anything else remains in this row of B */
656       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
657         PetscInt bcol = bj[bb[j]];
658         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
659           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
660           bb[j]++;
661           break;
662         }
663       }
664       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
665     }
666     if (fptr) {                 /* Clear the bits for this row */
667       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
668     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
669       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
670     }
671   }
672   ierr = PetscFree(bb);CHKERRQ(ierr);
673   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
674   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
675 
676   /* Column indices are in the list of free space */
677   /* Allocate space for cj, initialize cj, and */
678   /* destroy list of free space and other temporary array(s) */
679   ierr = PetscMalloc(ci[am]*sizeof(PetscInt),&cj);CHKERRQ(ierr);
680   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
681 
682   /* put together the new symbolic matrix */
683   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
684 
685   (*C)->rmap->bs = A->rmap->bs;
686   (*C)->cmap->bs = B->cmap->bs;
687 
688   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
689   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
690   c          = (Mat_SeqAIJ*)((*C)->data);
691   c->free_a  = PETSC_TRUE;
692   c->free_ij = PETSC_TRUE;
693   c->nonew   = 0;
694 
695   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
696 
697   /* set MatInfo */
698   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
699   if (afill < 1.0) afill = 1.0;
700   c->maxnz                     = ci[am];
701   c->nz                        = ci[am];
702   (*C)->info.mallocs           = ndouble;
703   (*C)->info.fill_ratio_given  = fill;
704   (*C)->info.fill_ratio_needed = afill;
705 
706 #if defined(PETSC_USE_INFO)
707   if (ci[am]) {
708     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
709     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
710   } else {
711     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
712   }
713 #endif
714   PetscFunctionReturn(0);
715 }
716 
717 #undef __FUNCT__
718 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqAIJ"
719 /* concatenate unique entries and then sort */
720 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
721 {
722   PetscErrorCode     ierr;
723   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
724   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
725   PetscInt           *ci,*cj;
726   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
727   PetscReal          afill;
728   PetscInt           i,j,ndouble = 0;
729   PetscSegBuffer     seg,segrow;
730   char               *seen;
731 
732   PetscFunctionBegin;
733   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
734   ci[0] = 0;
735 
736   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
737   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
738   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
739   ierr = PetscMalloc(bn*sizeof(char),&seen);CHKERRQ(ierr);
740   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
741 
742   /* Determine ci and cj */
743   for (i=0; i<am; i++) {
744     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 */
745     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
746     PetscInt packlen = 0,*PETSC_RESTRICT crow;
747     /* Pack segrow */
748     for (j=0; j<anzi; j++) {
749       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
750       for (k=bjstart; k<bjend; k++) {
751         PetscInt bcol = bj[k];
752         if (!seen[bcol]) { /* new entry */
753           PetscInt *PETSC_RESTRICT slot;
754           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
755           *slot = bcol;
756           seen[bcol] = 1;
757           packlen++;
758         }
759       }
760     }
761     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
762     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
763     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
764     ci[i+1] = ci[i] + packlen;
765     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
766   }
767   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
768   ierr = PetscFree(seen);CHKERRQ(ierr);
769 
770   /* Column indices are in the segmented buffer */
771   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
772   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
773 
774   /* put together the new symbolic matrix */
775   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
776 
777   (*C)->rmap->bs = A->rmap->bs;
778   (*C)->cmap->bs = B->cmap->bs;
779 
780   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
781   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
782   c          = (Mat_SeqAIJ*)((*C)->data);
783   c->free_a  = PETSC_TRUE;
784   c->free_ij = PETSC_TRUE;
785   c->nonew   = 0;
786 
787   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
788 
789   /* set MatInfo */
790   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
791   if (afill < 1.0) afill = 1.0;
792   c->maxnz                     = ci[am];
793   c->nz                        = ci[am];
794   (*C)->info.mallocs           = ndouble;
795   (*C)->info.fill_ratio_given  = fill;
796   (*C)->info.fill_ratio_needed = afill;
797 
798 #if defined(PETSC_USE_INFO)
799   if (ci[am]) {
800     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",ndouble,fill,afill);CHKERRQ(ierr);
801     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
802   } else {
803     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
804   }
805 #endif
806   PetscFunctionReturn(0);
807 }
808 
809 /* This routine is not used. Should be removed! */
810 #undef __FUNCT__
811 #define __FUNCT__ "MatMatTransposeMult_SeqAIJ_SeqAIJ"
812 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
813 {
814   PetscErrorCode ierr;
815 
816   PetscFunctionBegin;
817   if (scall == MAT_INITIAL_MATRIX) {
818     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
819     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
820     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
821   }
822   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
823   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
824   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
825   PetscFunctionReturn(0);
826 }
827 
828 #undef __FUNCT__
829 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatTransMult"
830 PetscErrorCode PetscContainerDestroy_Mat_MatMatTransMult(void *ptr)
831 {
832   PetscErrorCode      ierr;
833   Mat_MatMatTransMult *multtrans=(Mat_MatMatTransMult*)ptr;
834 
835   PetscFunctionBegin;
836   ierr = MatTransposeColoringDestroy(&multtrans->matcoloring);CHKERRQ(ierr);
837   ierr = MatDestroy(&multtrans->Bt_den);CHKERRQ(ierr);
838   ierr = MatDestroy(&multtrans->ABt_den);CHKERRQ(ierr);
839   ierr = PetscFree(multtrans);CHKERRQ(ierr);
840   PetscFunctionReturn(0);
841 }
842 
843 #undef __FUNCT__
844 #define __FUNCT__ "MatDestroy_SeqAIJ_MatMatMultTrans"
845 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
846 {
847   PetscErrorCode      ierr;
848   PetscContainer      container;
849   Mat_MatMatTransMult *multtrans=NULL;
850 
851   PetscFunctionBegin;
852   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatTransMult",(PetscObject*)&container);CHKERRQ(ierr);
853   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
854   ierr = PetscContainerGetPointer(container,(void**)&multtrans);CHKERRQ(ierr);
855 
856   A->ops->destroy = multtrans->destroy;
857   if (A->ops->destroy) {
858     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
859   }
860   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatTransMult",0);CHKERRQ(ierr);
861   PetscFunctionReturn(0);
862 }
863 
864 #undef __FUNCT__
865 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
866 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
867 {
868   PetscErrorCode      ierr;
869   Mat                 Bt;
870   PetscInt            *bti,*btj;
871   Mat_MatMatTransMult *multtrans;
872   PetscContainer      container;
873 
874   PetscFunctionBegin;
875   /* create symbolic Bt */
876   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
877   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
878 
879   Bt->rmap->bs = A->cmap->bs;
880   Bt->cmap->bs = B->cmap->bs;
881 
882   /* get symbolic C=A*Bt */
883   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
884 
885   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
886   ierr = PetscNew(Mat_MatMatTransMult,&multtrans);CHKERRQ(ierr);
887 
888   /* attach the supporting struct to C */
889   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
890   ierr = PetscContainerSetPointer(container,multtrans);CHKERRQ(ierr);
891   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatTransMult);CHKERRQ(ierr);
892   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_MatMatTransMult",(PetscObject)container);CHKERRQ(ierr);
893   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
894 
895   multtrans->usecoloring = PETSC_FALSE;
896   multtrans->destroy     = (*C)->ops->destroy;
897   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
898 
899   ierr = PetscOptionsGetBool(NULL,"-matmattransmult_color",&multtrans->usecoloring,NULL);CHKERRQ(ierr);
900   if (multtrans->usecoloring) {
901     /* Create MatTransposeColoring from symbolic C=A*B^T */
902     MatTransposeColoring matcoloring;
903     ISColoring           iscoloring;
904     Mat                  Bt_dense,C_dense;
905     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
906     /* inode causes memory problem, don't know why */
907     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
908 
909     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
910     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
911 
912     multtrans->matcoloring = matcoloring;
913 
914     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
915 
916     /* Create Bt_dense and C_dense = A*Bt_dense */
917     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
918     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
919     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
920     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
921 
922     Bt_dense->assembled = PETSC_TRUE;
923     multtrans->Bt_den   = Bt_dense;
924 
925     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
926     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
927     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
928     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
929 
930     Bt_dense->assembled = PETSC_TRUE;
931     multtrans->ABt_den  = C_dense;
932 
933 #if defined(PETSC_USE_INFO)
934     {
935       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
936       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));CHKERRQ(ierr);
937     }
938 #endif
939   }
940   /* clean up */
941   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
942   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
943   PetscFunctionReturn(0);
944 }
945 
946 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
947 #undef __FUNCT__
948 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
949 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
950 {
951   PetscErrorCode      ierr;
952   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
953   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
954   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
955   PetscLogDouble      flops=0.0;
956   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
957   Mat_MatMatTransMult *multtrans;
958   PetscContainer      container;
959 #if defined(USE_ARRAY)
960   MatScalar *spdot;
961 #endif
962 
963   PetscFunctionBegin;
964   /* clear old values in C */
965   if (!c->a) {
966     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
967     c->a      = ca;
968     c->free_a = PETSC_TRUE;
969   } else {
970     ca =  c->a;
971   }
972   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
973 
974   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject*)&container);CHKERRQ(ierr);
975   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
976   ierr = PetscContainerGetPointer(container,(void**)&multtrans);CHKERRQ(ierr);
977   if (multtrans->usecoloring) {
978     MatTransposeColoring matcoloring = multtrans->matcoloring;
979     Mat                  Bt_dense;
980     PetscInt             m,n;
981     Mat                  C_dense = multtrans->ABt_den;
982     PetscLogDouble       t0,t1,t2,t3,Bt_den,C_den,C_sp;
983 
984     /* Get Bt_dense by Apply MatTransposeColoring to B */
985     ierr = PetscTime(&t0);CHKERRQ(ierr);
986     Bt_dense = multtrans->Bt_den;
987     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
988     ierr = PetscTime(&t1);CHKERRQ(ierr);
989     Bt_den = t1 - t0;
990 
991     /* C_dense = A*Bt_dense */
992     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
993     ierr = PetscTime(&t2);CHKERRQ(ierr);
994     C_den = t2 - t1;
995 
996     /* Recover C from C_dense */
997     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
998     ierr = PetscTime(&t3);CHKERRQ(ierr);
999     C_sp = t3 - t2;
1000 #if defined(PETSC_USE_INFO)
1001     ierr = PetscInfo4(C,"Coloring A*B^T = Bt_den %g + C_den %g + C_sp %g = %g;\n",Bt_den,C_den,C_sp,Bt_den+C_den+C_sp);CHKERRQ(ierr);
1002     ierr     = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
1003     ierr = PetscInfo4(C,"Bt_den: %d x %d, B: %d x %d\n",m,n,m,C->cmap->n);CHKERRQ(ierr);
1004 #endif
1005     PetscFunctionReturn(0);
1006   }
1007 
1008 #if defined(USE_ARRAY)
1009   /* allocate an array for implementing sparse inner-product */
1010   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
1011   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
1012 #endif
1013 
1014   for (i=0; i<cm; i++) {
1015     anzi = ai[i+1] - ai[i];
1016     acol = aj + ai[i];
1017     aval = aa + ai[i];
1018     cnzi = ci[i+1] - ci[i];
1019     ccol = cj + ci[i];
1020     cval = ca + ci[i];
1021     for (j=0; j<cnzi; j++) {
1022       brow = ccol[j];
1023       bnzj = bi[brow+1] - bi[brow];
1024       bcol = bj + bi[brow];
1025       bval = ba + bi[brow];
1026 
1027       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1028 #if defined(USE_ARRAY)
1029       /* put ba to spdot array */
1030       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
1031       /* c(i,j)=A[i,:]*B[j,:]^T */
1032       for (nexta=0; nexta<anzi; nexta++) {
1033         cval[j] += spdot[acol[nexta]]*aval[nexta];
1034       }
1035       /* zero spdot array */
1036       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1037 #else
1038       nexta = 0; nextb = 0;
1039       while (nexta<anzi && nextb<bnzj) {
1040         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1041         if (nexta == anzi) break;
1042         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1043         if (nextb == bnzj) break;
1044         if (acol[nexta] == bcol[nextb]) {
1045           cval[j] += aval[nexta]*bval[nextb];
1046           nexta++; nextb++;
1047           flops += 2;
1048         }
1049       }
1050 #endif
1051     }
1052   }
1053   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1054   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1055   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1056 #if defined(USE_ARRAY)
1057   ierr = PetscFree(spdot);
1058 #endif
1059   PetscFunctionReturn(0);
1060 }
1061 
1062 #undef __FUNCT__
1063 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1064 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1065 {
1066   PetscErrorCode ierr;
1067 
1068   PetscFunctionBegin;
1069   if (scall == MAT_INITIAL_MATRIX) {
1070     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1071   }
1072   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1073   PetscFunctionReturn(0);
1074 }
1075 
1076 #undef __FUNCT__
1077 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1078 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1079 {
1080   PetscErrorCode ierr;
1081   Mat            At;
1082   PetscInt       *ati,*atj;
1083 
1084   PetscFunctionBegin;
1085   /* create symbolic At */
1086   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1087   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1088 
1089   At->rmap->bs = A->cmap->bs;
1090   At->cmap->bs = B->cmap->bs;
1091 
1092   /* get symbolic C=At*B */
1093   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1094 
1095   /* clean up */
1096   ierr = MatDestroy(&At);CHKERRQ(ierr);
1097   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1098   PetscFunctionReturn(0);
1099 }
1100 
1101 #undef __FUNCT__
1102 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1103 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1104 {
1105   PetscErrorCode ierr;
1106   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1107   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1108   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1109   PetscLogDouble flops=0.0;
1110   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1111 
1112   PetscFunctionBegin;
1113   if (!c->a) {
1114     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1115 
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 #undef __FUNCT__
1155 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1156 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1157 {
1158   PetscErrorCode ierr;
1159 
1160   PetscFunctionBegin;
1161   if (scall == MAT_INITIAL_MATRIX) {
1162     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1163     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1164     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1165   }
1166   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1167   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1168   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1169   PetscFunctionReturn(0);
1170 }
1171 
1172 #undef __FUNCT__
1173 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1174 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1175 {
1176   PetscErrorCode ierr;
1177 
1178   PetscFunctionBegin;
1179   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1180 
1181   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1182   PetscFunctionReturn(0);
1183 }
1184 
1185 #undef __FUNCT__
1186 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1187 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1188 {
1189   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1190   PetscErrorCode ierr;
1191   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1192   MatScalar      *aa;
1193   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1194   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1195 
1196   PetscFunctionBegin;
1197   if (!cm || !cn) PetscFunctionReturn(0);
1198   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);
1199   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);
1200   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);
1201   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1202   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1203   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1204   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1205     colam = col*am;
1206     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1207       r1 = r2 = r3 = r4 = 0.0;
1208       n  = a->i[i+1] - a->i[i];
1209       aj = a->j + a->i[i];
1210       aa = a->a + a->i[i];
1211       for (j=0; j<n; j++) {
1212         r1 += (*aa)*b1[*aj];
1213         r2 += (*aa)*b2[*aj];
1214         r3 += (*aa)*b3[*aj];
1215         r4 += (*aa++)*b4[*aj++];
1216       }
1217       c[colam + i]       = r1;
1218       c[colam + am + i]  = r2;
1219       c[colam + am2 + i] = r3;
1220       c[colam + am3 + i] = r4;
1221     }
1222     b1 += bm4;
1223     b2 += bm4;
1224     b3 += bm4;
1225     b4 += bm4;
1226   }
1227   for (; col<cn; col++) {     /* over extra columns of C */
1228     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1229       r1 = 0.0;
1230       n  = a->i[i+1] - a->i[i];
1231       aj = a->j + a->i[i];
1232       aa = a->a + a->i[i];
1233 
1234       for (j=0; j<n; j++) {
1235         r1 += (*aa++)*b1[*aj++];
1236       }
1237       c[col*am + i] = r1;
1238     }
1239     b1 += bm;
1240   }
1241   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1242   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1243   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1244   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1245   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1246   PetscFunctionReturn(0);
1247 }
1248 
1249 /*
1250    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1251 */
1252 #undef __FUNCT__
1253 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1254 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1255 {
1256   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1257   PetscErrorCode ierr;
1258   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1259   MatScalar      *aa;
1260   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1261   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1262 
1263   PetscFunctionBegin;
1264   if (!cm || !cn) PetscFunctionReturn(0);
1265   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1266   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1267   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1268 
1269   if (a->compressedrow.use) { /* use compressed row format */
1270     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1271       colam = col*am;
1272       arm   = a->compressedrow.nrows;
1273       ii    = a->compressedrow.i;
1274       ridx  = a->compressedrow.rindex;
1275       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1276         r1 = r2 = r3 = r4 = 0.0;
1277         n  = ii[i+1] - ii[i];
1278         aj = a->j + ii[i];
1279         aa = a->a + ii[i];
1280         for (j=0; j<n; j++) {
1281           r1 += (*aa)*b1[*aj];
1282           r2 += (*aa)*b2[*aj];
1283           r3 += (*aa)*b3[*aj];
1284           r4 += (*aa++)*b4[*aj++];
1285         }
1286         c[colam       + ridx[i]] += r1;
1287         c[colam + am  + ridx[i]] += r2;
1288         c[colam + am2 + ridx[i]] += r3;
1289         c[colam + am3 + ridx[i]] += r4;
1290       }
1291       b1 += bm4;
1292       b2 += bm4;
1293       b3 += bm4;
1294       b4 += bm4;
1295     }
1296     for (; col<cn; col++) {     /* over extra columns of C */
1297       colam = col*am;
1298       arm   = a->compressedrow.nrows;
1299       ii    = a->compressedrow.i;
1300       ridx  = a->compressedrow.rindex;
1301       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1302         r1 = 0.0;
1303         n  = ii[i+1] - ii[i];
1304         aj = a->j + ii[i];
1305         aa = a->a + ii[i];
1306 
1307         for (j=0; j<n; j++) {
1308           r1 += (*aa++)*b1[*aj++];
1309         }
1310         c[colam + ridx[i]] += r1;
1311       }
1312       b1 += bm;
1313     }
1314   } else {
1315     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1316       colam = col*am;
1317       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1318         r1 = r2 = r3 = r4 = 0.0;
1319         n  = a->i[i+1] - a->i[i];
1320         aj = a->j + a->i[i];
1321         aa = a->a + a->i[i];
1322         for (j=0; j<n; j++) {
1323           r1 += (*aa)*b1[*aj];
1324           r2 += (*aa)*b2[*aj];
1325           r3 += (*aa)*b3[*aj];
1326           r4 += (*aa++)*b4[*aj++];
1327         }
1328         c[colam + i]       += r1;
1329         c[colam + am + i]  += r2;
1330         c[colam + am2 + i] += r3;
1331         c[colam + am3 + i] += r4;
1332       }
1333       b1 += bm4;
1334       b2 += bm4;
1335       b3 += bm4;
1336       b4 += bm4;
1337     }
1338     for (; col<cn; col++) {     /* over extra columns of C */
1339       colam = col*am;
1340       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1341         r1 = 0.0;
1342         n  = a->i[i+1] - a->i[i];
1343         aj = a->j + a->i[i];
1344         aa = a->a + a->i[i];
1345 
1346         for (j=0; j<n; j++) {
1347           r1 += (*aa++)*b1[*aj++];
1348         }
1349         c[colam + i] += r1;
1350       }
1351       b1 += bm;
1352     }
1353   }
1354   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1355   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1356   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1357   PetscFunctionReturn(0);
1358 }
1359 
1360 #undef __FUNCT__
1361 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1362 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1363 {
1364   PetscErrorCode ierr;
1365   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1366   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1367   PetscInt       *bi      = b->i,*bj=b->j;
1368   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1369   MatScalar      *btval,*btval_den,*ba=b->a;
1370   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1371 
1372   PetscFunctionBegin;
1373   btval_den=btdense->v;
1374   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1375   for (k=0; k<ncolors; k++) {
1376     ncolumns = coloring->ncolumns[k];
1377     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1378       col   = *(columns + colorforcol[k] + l);
1379       btcol = bj + bi[col];
1380       btval = ba + bi[col];
1381       anz   = bi[col+1] - bi[col];
1382       for (j=0; j<anz; j++) {
1383         brow            = btcol[j];
1384         btval_den[brow] = btval[j];
1385       }
1386     }
1387     btval_den += m;
1388   }
1389   PetscFunctionReturn(0);
1390 }
1391 
1392 #undef __FUNCT__
1393 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1394 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1395 {
1396   PetscErrorCode ierr;
1397   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1398   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1399   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1400   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1401 
1402   PetscFunctionBegin;
1403   ierr   = MatGetLocalSize(Csp,&m,NULL);CHKERRQ(ierr);
1404   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1405   cp_den = ca_den;
1406   for (k=0; k<ncolors; k++) {
1407     nrows = matcoloring->nrows[k];
1408     row   = rows  + colorforrow[k];
1409     idx   = spidx + colorforrow[k];
1410     for (l=0; l<nrows; l++) {
1411       ca[idx[l]] = cp_den[row[l]];
1412     }
1413     cp_den += m;
1414   }
1415   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1416   PetscFunctionReturn(0);
1417 }
1418 
1419 /*
1420  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1421  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1422  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1423  */
1424 #undef __FUNCT__
1425 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1426 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1427 {
1428   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1429   PetscErrorCode ierr;
1430   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1431   PetscInt       nz = a->i[m],row,*jj,mr,col;
1432   PetscInt       *cspidx;
1433 
1434   PetscFunctionBegin;
1435   *nn = n;
1436   if (!ia) PetscFunctionReturn(0);
1437   if (symmetric) {
1438     SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1439     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1440   } else {
1441     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1442     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1443     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1444     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1445     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1446     jj   = a->j;
1447     for (i=0; i<nz; i++) {
1448       collengths[jj[i]]++;
1449     }
1450     cia[0] = oshift;
1451     for (i=0; i<n; i++) {
1452       cia[i+1] = cia[i] + collengths[i];
1453     }
1454     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1455     jj   = a->j;
1456     for (row=0; row<m; row++) {
1457       mr = a->i[row+1] - a->i[row];
1458       for (i=0; i<mr; i++) {
1459         col = *jj++;
1460 
1461         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1462         cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
1463       }
1464     }
1465     ierr   = PetscFree(collengths);CHKERRQ(ierr);
1466     *ia    = cia; *ja = cja;
1467     *spidx = cspidx;
1468   }
1469   PetscFunctionReturn(0);
1470 }
1471 
1472 #undef __FUNCT__
1473 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1474 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1475 {
1476   PetscErrorCode ierr;
1477 
1478   PetscFunctionBegin;
1479   if (!ia) PetscFunctionReturn(0);
1480 
1481   ierr = PetscFree(*ia);CHKERRQ(ierr);
1482   ierr = PetscFree(*ja);CHKERRQ(ierr);
1483   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1484   PetscFunctionReturn(0);
1485 }
1486 
1487 #undef __FUNCT__
1488 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1489 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1490 {
1491   PetscErrorCode ierr;
1492   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
1493   const PetscInt *is,*ci,*cj,*row_idx;
1494   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1495   IS             *isa;
1496   PetscBool      flg1,flg2;
1497   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1498   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1499   PetscInt       *colorforcol,*columns,*columns_i;
1500 
1501   PetscFunctionBegin;
1502   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1503 
1504   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1505   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1506   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1507   if (flg1 || flg2) {
1508     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1509   }
1510 
1511   N         = mat->cmap->N/bs;
1512   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1513   c->N      = mat->cmap->N/bs;
1514   c->m      = mat->rmap->N/bs;
1515   c->rstart = 0;
1516 
1517   c->ncolors = nis;
1518   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1519   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1520   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1521   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1522 
1523   colorforrow[0]    = 0;
1524   rows_i            = rows;
1525   columnsforspidx_i = columnsforspidx;
1526 
1527   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1528   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1529 
1530   colorforcol[0] = 0;
1531   columns_i      = columns;
1532 
1533   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1534 
1535   cm   = c->m;
1536   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1537   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1538   for (i=0; i<nis; i++) {
1539     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1540     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1541 
1542     c->ncolumns[i] = n;
1543     if (n) {
1544       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1545     }
1546     colorforcol[i+1] = colorforcol[i] + n;
1547     columns_i       += n;
1548 
1549     /* fast, crude version requires O(N*N) work */
1550     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1551 
1552     /* loop over columns*/
1553     for (j=0; j<n; j++) {
1554       col     = is[j];
1555       row_idx = cj + ci[col];
1556       m       = ci[col+1] - ci[col];
1557       /* loop over columns marking them in rowhit */
1558       for (k=0; k<m; k++) {
1559         idxhit[*row_idx]   = spidx[ci[col] + k];
1560         rowhit[*row_idx++] = col + 1;
1561       }
1562     }
1563     /* count the number of hits */
1564     nrows = 0;
1565     for (j=0; j<cm; j++) {
1566       if (rowhit[j]) nrows++;
1567     }
1568     c->nrows[i]      = nrows;
1569     colorforrow[i+1] = colorforrow[i] + nrows;
1570 
1571     nrows = 0;
1572     for (j=0; j<cm; j++) {
1573       if (rowhit[j]) {
1574         rows_i[nrows]            = j;
1575         columnsforspidx_i[nrows] = idxhit[j];
1576         nrows++;
1577       }
1578     }
1579     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1580     rows_i += nrows; columnsforspidx_i += nrows;
1581   }
1582   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1583   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1584   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1585 #if defined(PETSC_USE_DEBUG)
1586   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1587 #endif
1588 
1589   c->colorforrow     = colorforrow;
1590   c->rows            = rows;
1591   c->columnsforspidx = columnsforspidx;
1592   c->colorforcol     = colorforcol;
1593   c->columns         = columns;
1594 
1595   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1596   PetscFunctionReturn(0);
1597 }
1598