xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 3b1b96249de37060d5a8cf86c9be203d0200b5d5)
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 
906     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
907     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
908 
909     multtrans->matcoloring = matcoloring;
910 
911     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
912 
913     /* Create Bt_dense and C_dense = A*Bt_dense */
914     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
915     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
916     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
917     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
918 
919     Bt_dense->assembled = PETSC_TRUE;
920     multtrans->Bt_den   = Bt_dense;
921 
922     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
923     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
924     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
925     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
926 
927     Bt_dense->assembled = PETSC_TRUE;
928     multtrans->ABt_den  = C_dense;
929 
930 #if defined(PETSC_USE_INFO)
931     {
932       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
933       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);
934     }
935 #endif
936   }
937   /* clean up */
938   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
939   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
940   PetscFunctionReturn(0);
941 }
942 
943 /* #define USE_ARRAY - for sparse dot product. Slower than !USE_ARRAY */
944 #undef __FUNCT__
945 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
946 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
947 {
948   PetscErrorCode      ierr;
949   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
950   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
951   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
952   PetscLogDouble      flops=0.0;
953   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
954   Mat_MatMatTransMult *multtrans;
955   PetscContainer      container;
956 #if defined(USE_ARRAY)
957   MatScalar *spdot;
958 #endif
959 
960   PetscFunctionBegin;
961   /* clear old values in C */
962   if (!c->a) {
963     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
964     c->a      = ca;
965     c->free_a = PETSC_TRUE;
966   } else {
967     ca =  c->a;
968   }
969   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
970 
971   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatTransMult",(PetscObject*)&container);CHKERRQ(ierr);
972   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
973   ierr = PetscContainerGetPointer(container,(void**)&multtrans);CHKERRQ(ierr);
974   if (multtrans->usecoloring) {
975     MatTransposeColoring matcoloring = multtrans->matcoloring;
976     Mat                  Bt_dense;
977     PetscInt             m,n;
978     Mat                  C_dense = multtrans->ABt_den;
979     PetscLogDouble       t0,t1,t2,t3,Bt_den,C_den,C_sp;
980 
981     /* Get Bt_dense by Apply MatTransposeColoring to B */
982     ierr = PetscTime(&t0);CHKERRQ(ierr);
983     Bt_dense = multtrans->Bt_den;
984     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
985     ierr = PetscTime(&t1);CHKERRQ(ierr);
986     Bt_den = t1 - t0;
987 
988     /* C_dense = A*Bt_dense */
989     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
990     ierr = PetscTime(&t2);CHKERRQ(ierr);
991     C_den = t2 - t1;
992 
993     /* Recover C from C_dense */
994     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
995     ierr = PetscTime(&t3);CHKERRQ(ierr);
996     C_sp = t3 - t2;
997 #if defined(PETSC_USE_INFO)
998     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);
999     ierr     = MatGetLocalSize(Bt_dense,&m,&n);CHKERRQ(ierr);
1000     ierr = PetscInfo4(C,"Bt_den: %d x %d, B: %d x %d\n",m,n,m,C->cmap->n);CHKERRQ(ierr);
1001 #endif
1002     PetscFunctionReturn(0);
1003   }
1004 
1005 #if defined(USE_ARRAY)
1006   /* allocate an array for implementing sparse inner-product */
1007   ierr = PetscMalloc((A->cmap->n+1)*sizeof(MatScalar),&spdot);CHKERRQ(ierr);
1008   ierr = PetscMemzero(spdot,(A->cmap->n+1)*sizeof(MatScalar));CHKERRQ(ierr);
1009 #endif
1010 
1011   for (i=0; i<cm; i++) {
1012     anzi = ai[i+1] - ai[i];
1013     acol = aj + ai[i];
1014     aval = aa + ai[i];
1015     cnzi = ci[i+1] - ci[i];
1016     ccol = cj + ci[i];
1017     cval = ca + ci[i];
1018     for (j=0; j<cnzi; j++) {
1019       brow = ccol[j];
1020       bnzj = bi[brow+1] - bi[brow];
1021       bcol = bj + bi[brow];
1022       bval = ba + bi[brow];
1023 
1024       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1025 #if defined(USE_ARRAY)
1026       /* put ba to spdot array */
1027       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = bval[nextb];
1028       /* c(i,j)=A[i,:]*B[j,:]^T */
1029       for (nexta=0; nexta<anzi; nexta++) {
1030         cval[j] += spdot[acol[nexta]]*aval[nexta];
1031       }
1032       /* zero spdot array */
1033       for (nextb=0; nextb<bnzj; nextb++) spdot[bcol[nextb]] = 0.0;
1034 #else
1035       nexta = 0; nextb = 0;
1036       while (nexta<anzi && nextb<bnzj) {
1037         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1038         if (nexta == anzi) break;
1039         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1040         if (nextb == bnzj) break;
1041         if (acol[nexta] == bcol[nextb]) {
1042           cval[j] += aval[nexta]*bval[nextb];
1043           nexta++; nextb++;
1044           flops += 2;
1045         }
1046       }
1047 #endif
1048     }
1049   }
1050   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1051   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1052   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1053 #if defined(USE_ARRAY)
1054   ierr = PetscFree(spdot);
1055 #endif
1056   PetscFunctionReturn(0);
1057 }
1058 
1059 #undef __FUNCT__
1060 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
1061 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1062 {
1063   PetscErrorCode ierr;
1064 
1065   PetscFunctionBegin;
1066   if (scall == MAT_INITIAL_MATRIX) {
1067     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1068   }
1069   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1070   PetscFunctionReturn(0);
1071 }
1072 
1073 #undef __FUNCT__
1074 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1075 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1076 {
1077   PetscErrorCode ierr;
1078   Mat            At;
1079   PetscInt       *ati,*atj;
1080 
1081   PetscFunctionBegin;
1082   /* create symbolic At */
1083   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1084   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1085 
1086   At->rmap->bs = A->cmap->bs;
1087   At->cmap->bs = B->cmap->bs;
1088 
1089   /* get symbolic C=At*B */
1090   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1091 
1092   /* clean up */
1093   ierr = MatDestroy(&At);CHKERRQ(ierr);
1094   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1095   PetscFunctionReturn(0);
1096 }
1097 
1098 #undef __FUNCT__
1099 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1100 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1101 {
1102   PetscErrorCode ierr;
1103   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1104   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1105   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1106   PetscLogDouble flops=0.0;
1107   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1108 
1109   PetscFunctionBegin;
1110   if (!c->a) {
1111     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1112 
1113     c->a      = ca;
1114     c->free_a = PETSC_TRUE;
1115   } else {
1116     ca = c->a;
1117   }
1118   /* clear old values in C */
1119   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1120 
1121   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1122   for (i=0; i<am; i++) {
1123     bj   = b->j + bi[i];
1124     ba   = b->a + bi[i];
1125     bnzi = bi[i+1] - bi[i];
1126     anzi = ai[i+1] - ai[i];
1127     for (j=0; j<anzi; j++) {
1128       nextb = 0;
1129       crow  = *aj++;
1130       cjj   = cj + ci[crow];
1131       caj   = ca + ci[crow];
1132       /* perform sparse axpy operation.  Note cjj includes bj. */
1133       for (k=0; nextb<bnzi; k++) {
1134         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1135           caj[k] += (*aa)*(*(ba+nextb));
1136           nextb++;
1137         }
1138       }
1139       flops += 2*bnzi;
1140       aa++;
1141     }
1142   }
1143 
1144   /* Assemble the final matrix and clean up */
1145   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1146   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1147   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1148   PetscFunctionReturn(0);
1149 }
1150 
1151 #undef __FUNCT__
1152 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1153 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1154 {
1155   PetscErrorCode ierr;
1156 
1157   PetscFunctionBegin;
1158   if (scall == MAT_INITIAL_MATRIX) {
1159     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1160     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1161     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1162   }
1163   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1164   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1165   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1166   PetscFunctionReturn(0);
1167 }
1168 
1169 #undef __FUNCT__
1170 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1171 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1172 {
1173   PetscErrorCode ierr;
1174 
1175   PetscFunctionBegin;
1176   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1177 
1178   (*C)->ops->matmultnumeric = MatMatMultNumeric_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[colam + 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       colam = col*am;
1337       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1338         r1 = 0.0;
1339         n  = a->i[i+1] - a->i[i];
1340         aj = a->j + a->i[i];
1341         aa = a->a + a->i[i];
1342 
1343         for (j=0; j<n; j++) {
1344           r1 += (*aa++)*b1[*aj++];
1345         }
1346         c[colam + i] += r1;
1347       }
1348       b1 += bm;
1349     }
1350   }
1351   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1352   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1353   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1354   PetscFunctionReturn(0);
1355 }
1356 
1357 #undef __FUNCT__
1358 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1359 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1360 {
1361   PetscErrorCode ierr;
1362   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1363   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1364   PetscInt       *bi      = b->i,*bj=b->j;
1365   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1366   MatScalar      *btval,*btval_den,*ba=b->a;
1367   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1368 
1369   PetscFunctionBegin;
1370   btval_den=btdense->v;
1371   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1372   for (k=0; k<ncolors; k++) {
1373     ncolumns = coloring->ncolumns[k];
1374     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1375       col   = *(columns + colorforcol[k] + l);
1376       btcol = bj + bi[col];
1377       btval = ba + bi[col];
1378       anz   = bi[col+1] - bi[col];
1379       for (j=0; j<anz; j++) {
1380         brow            = btcol[j];
1381         btval_den[brow] = btval[j];
1382       }
1383     }
1384     btval_den += m;
1385   }
1386   PetscFunctionReturn(0);
1387 }
1388 
1389 #undef __FUNCT__
1390 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1391 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1392 {
1393   PetscErrorCode ierr;
1394   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1395   PetscInt       k,l,*row,*idx,m,ncolors=matcoloring->ncolors,nrows;
1396   PetscScalar    *ca_den,*cp_den,*ca=csp->a;
1397   PetscInt       *rows=matcoloring->rows,*spidx=matcoloring->columnsforspidx,*colorforrow=matcoloring->colorforrow;
1398 
1399   PetscFunctionBegin;
1400   ierr   = MatGetLocalSize(Csp,&m,NULL);CHKERRQ(ierr);
1401   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1402   cp_den = ca_den;
1403   for (k=0; k<ncolors; k++) {
1404     nrows = matcoloring->nrows[k];
1405     row   = rows  + colorforrow[k];
1406     idx   = spidx + colorforrow[k];
1407     for (l=0; l<nrows; l++) {
1408       ca[idx[l]] = cp_den[row[l]];
1409     }
1410     cp_den += m;
1411   }
1412   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1413   PetscFunctionReturn(0);
1414 }
1415 
1416 /*
1417  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1418  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1419  spidx[], index of a->j, to be used for setting 'columnsforspidx' in MatTransposeColoringCreate_SeqAIJ().
1420  */
1421 #undef __FUNCT__
1422 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1423 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1424 {
1425   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1426   PetscErrorCode ierr;
1427   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1428   PetscInt       nz = a->i[m],row,*jj,mr,col;
1429   PetscInt       *cspidx;
1430 
1431   PetscFunctionBegin;
1432   *nn = n;
1433   if (!ia) PetscFunctionReturn(0);
1434   if (symmetric) {
1435     SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1436     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1437   } else {
1438     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1439     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1440     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1441     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1442     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1443     jj   = a->j;
1444     for (i=0; i<nz; i++) {
1445       collengths[jj[i]]++;
1446     }
1447     cia[0] = oshift;
1448     for (i=0; i<n; i++) {
1449       cia[i+1] = cia[i] + collengths[i];
1450     }
1451     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1452     jj   = a->j;
1453     for (row=0; row<m; row++) {
1454       mr = a->i[row+1] - a->i[row];
1455       for (i=0; i<mr; i++) {
1456         col = *jj++;
1457 
1458         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1459         cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
1460       }
1461     }
1462     ierr   = PetscFree(collengths);CHKERRQ(ierr);
1463     *ia    = cia; *ja = cja;
1464     *spidx = cspidx;
1465   }
1466   PetscFunctionReturn(0);
1467 }
1468 
1469 #undef __FUNCT__
1470 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1471 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1472 {
1473   PetscErrorCode ierr;
1474 
1475   PetscFunctionBegin;
1476   if (!ia) PetscFunctionReturn(0);
1477 
1478   ierr = PetscFree(*ia);CHKERRQ(ierr);
1479   ierr = PetscFree(*ja);CHKERRQ(ierr);
1480   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1481   PetscFunctionReturn(0);
1482 }
1483 
1484 #undef __FUNCT__
1485 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1486 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1487 {
1488   PetscErrorCode ierr;
1489   PetscInt       i,n,nrows,N,j,k,m,ncols,col,cm;
1490   const PetscInt *is,*ci,*cj,*row_idx;
1491   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1492   IS             *isa;
1493   PetscBool      flg1,flg2;
1494   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1495   PetscInt       *colorforrow,*rows,*rows_i,*columnsforspidx,*columnsforspidx_i,*idxhit,*spidx;
1496   PetscInt       *colorforcol,*columns,*columns_i;
1497 
1498   PetscFunctionBegin;
1499   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1500 
1501   /* this is ugly way to get blocksize but cannot call MatGetBlockSize() because AIJ can have bs > 1 */
1502   ierr = PetscObjectTypeCompare((PetscObject)mat,MATSEQBAIJ,&flg1);CHKERRQ(ierr);
1503   ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIBAIJ,&flg2);CHKERRQ(ierr);
1504   if (flg1 || flg2) {
1505     ierr = MatGetBlockSize(mat,&bs);CHKERRQ(ierr);
1506   }
1507 
1508   N         = mat->cmap->N/bs;
1509   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1510   c->N      = mat->cmap->N/bs;
1511   c->m      = mat->rmap->N/bs;
1512   c->rstart = 0;
1513 
1514   c->ncolors = nis;
1515   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
1516   ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
1517   ierr       = PetscMalloc2(csp->nz+1,PetscInt,&rows,csp->nz+1,PetscInt,&columnsforspidx);CHKERRQ(ierr);
1518   ierr       = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforrow);CHKERRQ(ierr);
1519 
1520   colorforrow[0]    = 0;
1521   rows_i            = rows;
1522   columnsforspidx_i = columnsforspidx;
1523 
1524   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1525   ierr = PetscMalloc((N+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1526 
1527   colorforcol[0] = 0;
1528   columns_i      = columns;
1529 
1530   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr); /* column-wise storage of mat */
1531 
1532   cm   = c->m;
1533   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1534   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1535   for (i=0; i<nis; i++) {
1536     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1537     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1538 
1539     c->ncolumns[i] = n;
1540     if (n) {
1541       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1542     }
1543     colorforcol[i+1] = colorforcol[i] + n;
1544     columns_i       += n;
1545 
1546     /* fast, crude version requires O(N*N) work */
1547     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1548 
1549     /* loop over columns*/
1550     for (j=0; j<n; j++) {
1551       col     = is[j];
1552       row_idx = cj + ci[col];
1553       m       = ci[col+1] - ci[col];
1554       /* loop over columns marking them in rowhit */
1555       for (k=0; k<m; k++) {
1556         idxhit[*row_idx]   = spidx[ci[col] + k];
1557         rowhit[*row_idx++] = col + 1;
1558       }
1559     }
1560     /* count the number of hits */
1561     nrows = 0;
1562     for (j=0; j<cm; j++) {
1563       if (rowhit[j]) nrows++;
1564     }
1565     c->nrows[i]      = nrows;
1566     colorforrow[i+1] = colorforrow[i] + nrows;
1567 
1568     nrows = 0;
1569     for (j=0; j<cm; j++) {
1570       if (rowhit[j]) {
1571         rows_i[nrows]            = j;
1572         columnsforspidx_i[nrows] = idxhit[j];
1573         nrows++;
1574       }
1575     }
1576     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1577     rows_i += nrows; columnsforspidx_i += nrows;
1578   }
1579   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1580   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1581   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1582 #if defined(PETSC_USE_DEBUG)
1583   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1584 #endif
1585 
1586   c->colorforrow     = colorforrow;
1587   c->rows            = rows;
1588   c->columnsforspidx = columnsforspidx;
1589   c->colorforcol     = colorforcol;
1590   c->columns         = columns;
1591 
1592   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1593   PetscFunctionReturn(0);
1594 }
1595