xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision f37c82fbca2ef2d9869799d3305350a5f272bd86)
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__ "MatDestroy_SeqAIJ_MatMatMultTrans"
830 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
831 {
832   PetscErrorCode      ierr;
833   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
834   Mat_MatMatTransMult *abt=a->abt;
835 
836   PetscFunctionBegin;
837   ierr = (abt->destroy)(A);CHKERRQ(ierr);
838   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
839   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
840   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
841   ierr = PetscFree(abt);CHKERRQ(ierr);
842   PetscFunctionReturn(0);
843 }
844 
845 #undef __FUNCT__
846 #define __FUNCT__ "MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ"
847 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
848 {
849   PetscErrorCode      ierr;
850   Mat                 Bt;
851   PetscInt            *bti,*btj;
852   Mat_MatMatTransMult *abt;
853   Mat_SeqAIJ          *c;
854 
855   PetscFunctionBegin;
856   /* create symbolic Bt */
857   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
858   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
859 
860   Bt->rmap->bs = A->cmap->bs;
861   Bt->cmap->bs = B->cmap->bs;
862 
863   /* get symbolic C=A*Bt */
864   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
865 
866   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
867   ierr   = PetscNew(Mat_MatMatTransMult,&abt);CHKERRQ(ierr);
868   c      = (Mat_SeqAIJ*)(*C)->data;
869   c->abt = abt;
870 
871   abt->usecoloring = PETSC_FALSE;
872   abt->destroy     = (*C)->ops->destroy;
873   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
874 
875   ierr = PetscOptionsGetBool(NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
876   if (abt->usecoloring) {
877     /* Create MatTransposeColoring from symbolic C=A*B^T */
878     MatTransposeColoring matcoloring;
879     ISColoring           iscoloring;
880     Mat                  Bt_dense,C_dense;
881     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
882     /* inode causes memory problem, don't know why */
883     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
884 
885     ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
886     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
887 
888     abt->matcoloring = matcoloring;
889 
890     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
891 
892     /* Create Bt_dense and C_dense = A*Bt_dense */
893     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
894     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
895     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
896     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
897 
898     Bt_dense->assembled = PETSC_TRUE;
899     abt->Bt_den   = Bt_dense;
900 
901     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
902     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
903     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
904     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
905 
906     Bt_dense->assembled = PETSC_TRUE;
907     abt->ABt_den  = C_dense;
908 
909 #if defined(PETSC_USE_INFO)
910     {
911       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
912       ierr = PetscInfo7(*C,"Use coloring of C=A*B^T; B^T: %D %D, Bt_dense: %D,%D; Cnz %D / (cm*ncolors %D) = %g\n",B->cmap->n,B->rmap->n,Bt_dense->rmap->n,Bt_dense->cmap->n,c->nz,A->rmap->n*matcoloring->ncolors,(PetscReal)(c->nz)/(A->rmap->n*matcoloring->ncolors));CHKERRQ(ierr);
913     }
914 #endif
915   }
916   /* clean up */
917   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
918   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
919   PetscFunctionReturn(0);
920 }
921 
922 #undef __FUNCT__
923 #define __FUNCT__ "MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ"
924 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
925 {
926   PetscErrorCode      ierr;
927   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
928   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
929   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
930   PetscLogDouble      flops=0.0;
931   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
932   Mat_MatMatTransMult *abt = c->abt;
933 
934   PetscFunctionBegin;
935   /* clear old values in C */
936   if (!c->a) {
937     ierr      = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
938     c->a      = ca;
939     c->free_a = PETSC_TRUE;
940   } else {
941     ca =  c->a;
942   }
943   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
944 
945   if (abt->usecoloring) {
946     MatTransposeColoring matcoloring = abt->matcoloring;
947     Mat                  Bt_dense,C_dense = abt->ABt_den;
948 
949     /* Get Bt_dense by Apply MatTransposeColoring to B */
950     Bt_dense = abt->Bt_den;
951     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
952 
953     /* C_dense = A*Bt_dense */
954     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
955 
956     /* Recover C from C_dense */
957     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
958     PetscFunctionReturn(0);
959   }
960 
961   for (i=0; i<cm; i++) {
962     anzi = ai[i+1] - ai[i];
963     acol = aj + ai[i];
964     aval = aa + ai[i];
965     cnzi = ci[i+1] - ci[i];
966     ccol = cj + ci[i];
967     cval = ca + ci[i];
968     for (j=0; j<cnzi; j++) {
969       brow = ccol[j];
970       bnzj = bi[brow+1] - bi[brow];
971       bcol = bj + bi[brow];
972       bval = ba + bi[brow];
973 
974       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
975       nexta = 0; nextb = 0;
976       while (nexta<anzi && nextb<bnzj) {
977         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
978         if (nexta == anzi) break;
979         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
980         if (nextb == bnzj) break;
981         if (acol[nexta] == bcol[nextb]) {
982           cval[j] += aval[nexta]*bval[nextb];
983           nexta++; nextb++;
984           flops += 2;
985         }
986       }
987     }
988   }
989   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
990   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
991   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
992   PetscFunctionReturn(0);
993 }
994 
995 #undef __FUNCT__
996 #define __FUNCT__ "MatTransposeMatMult_SeqAIJ_SeqAIJ"
997 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
998 {
999   PetscErrorCode ierr;
1000 
1001   PetscFunctionBegin;
1002   if (scall == MAT_INITIAL_MATRIX) {
1003     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1004     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1005     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1006   }
1007   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1008   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1009   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1010   PetscFunctionReturn(0);
1011 }
1012 
1013 #undef __FUNCT__
1014 #define __FUNCT__ "MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ"
1015 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1016 {
1017   PetscErrorCode ierr;
1018   Mat            At;
1019   PetscInt       *ati,*atj;
1020 
1021   PetscFunctionBegin;
1022   /* create symbolic At */
1023   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1024   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1025 
1026   At->rmap->bs = A->cmap->bs;
1027   At->cmap->bs = B->cmap->bs;
1028 
1029   /* get symbolic C=At*B */
1030   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1031 
1032   /* clean up */
1033   ierr = MatDestroy(&At);CHKERRQ(ierr);
1034   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1035   PetscFunctionReturn(0);
1036 }
1037 
1038 #undef __FUNCT__
1039 #define __FUNCT__ "MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ"
1040 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1041 {
1042   PetscErrorCode ierr;
1043   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1044   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1045   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1046   PetscLogDouble flops=0.0;
1047   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1048 
1049   PetscFunctionBegin;
1050   if (!c->a) {
1051     ierr = PetscMalloc((ci[cm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
1052 
1053     c->a      = ca;
1054     c->free_a = PETSC_TRUE;
1055   } else {
1056     ca = c->a;
1057   }
1058   /* clear old values in C */
1059   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1060 
1061   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1062   for (i=0; i<am; i++) {
1063     bj   = b->j + bi[i];
1064     ba   = b->a + bi[i];
1065     bnzi = bi[i+1] - bi[i];
1066     anzi = ai[i+1] - ai[i];
1067     for (j=0; j<anzi; j++) {
1068       nextb = 0;
1069       crow  = *aj++;
1070       cjj   = cj + ci[crow];
1071       caj   = ca + ci[crow];
1072       /* perform sparse axpy operation.  Note cjj includes bj. */
1073       for (k=0; nextb<bnzi; k++) {
1074         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1075           caj[k] += (*aa)*(*(ba+nextb));
1076           nextb++;
1077         }
1078       }
1079       flops += 2*bnzi;
1080       aa++;
1081     }
1082   }
1083 
1084   /* Assemble the final matrix and clean up */
1085   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1086   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1087   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1088   PetscFunctionReturn(0);
1089 }
1090 
1091 #undef __FUNCT__
1092 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqDense"
1093 PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1094 {
1095   PetscErrorCode ierr;
1096 
1097   PetscFunctionBegin;
1098   if (scall == MAT_INITIAL_MATRIX) {
1099     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1100     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1101     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1102   }
1103   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1104   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1105   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1106   PetscFunctionReturn(0);
1107 }
1108 
1109 #undef __FUNCT__
1110 #define __FUNCT__ "MatMatMultSymbolic_SeqAIJ_SeqDense"
1111 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1112 {
1113   PetscErrorCode ierr;
1114 
1115   PetscFunctionBegin;
1116   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1117 
1118   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1119   PetscFunctionReturn(0);
1120 }
1121 
1122 #undef __FUNCT__
1123 #define __FUNCT__ "MatMatMultNumeric_SeqAIJ_SeqDense"
1124 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1125 {
1126   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1127   PetscErrorCode ierr;
1128   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1129   MatScalar      *aa;
1130   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n;
1131   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam;
1132 
1133   PetscFunctionBegin;
1134   if (!cm || !cn) PetscFunctionReturn(0);
1135   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);
1136   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);
1137   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);
1138   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1139   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1140   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1141   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1142     colam = col*am;
1143     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1144       r1 = r2 = r3 = r4 = 0.0;
1145       n  = a->i[i+1] - a->i[i];
1146       aj = a->j + a->i[i];
1147       aa = a->a + a->i[i];
1148       for (j=0; j<n; j++) {
1149         r1 += (*aa)*b1[*aj];
1150         r2 += (*aa)*b2[*aj];
1151         r3 += (*aa)*b3[*aj];
1152         r4 += (*aa++)*b4[*aj++];
1153       }
1154       c[colam + i]       = r1;
1155       c[colam + am + i]  = r2;
1156       c[colam + am2 + i] = r3;
1157       c[colam + am3 + i] = r4;
1158     }
1159     b1 += bm4;
1160     b2 += bm4;
1161     b3 += bm4;
1162     b4 += bm4;
1163   }
1164   for (; col<cn; col++) {     /* over extra columns of C */
1165     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1166       r1 = 0.0;
1167       n  = a->i[i+1] - a->i[i];
1168       aj = a->j + a->i[i];
1169       aa = a->a + a->i[i];
1170 
1171       for (j=0; j<n; j++) {
1172         r1 += (*aa++)*b1[*aj++];
1173       }
1174       c[col*am + i] = r1;
1175     }
1176     b1 += bm;
1177   }
1178   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1179   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1180   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1181   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1182   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1183   PetscFunctionReturn(0);
1184 }
1185 
1186 /*
1187    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1188 */
1189 #undef __FUNCT__
1190 #define __FUNCT__ "MatMatMultNumericAdd_SeqAIJ_SeqDense"
1191 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1192 {
1193   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1194   PetscErrorCode ierr;
1195   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1196   MatScalar      *aa;
1197   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=B->rmap->n, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1198   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1199 
1200   PetscFunctionBegin;
1201   if (!cm || !cn) PetscFunctionReturn(0);
1202   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
1203   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1204   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1205 
1206   if (a->compressedrow.use) { /* use compressed row format */
1207     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1208       colam = col*am;
1209       arm   = a->compressedrow.nrows;
1210       ii    = a->compressedrow.i;
1211       ridx  = a->compressedrow.rindex;
1212       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1213         r1 = r2 = r3 = r4 = 0.0;
1214         n  = ii[i+1] - ii[i];
1215         aj = a->j + ii[i];
1216         aa = a->a + ii[i];
1217         for (j=0; j<n; j++) {
1218           r1 += (*aa)*b1[*aj];
1219           r2 += (*aa)*b2[*aj];
1220           r3 += (*aa)*b3[*aj];
1221           r4 += (*aa++)*b4[*aj++];
1222         }
1223         c[colam       + ridx[i]] += r1;
1224         c[colam + am  + ridx[i]] += r2;
1225         c[colam + am2 + ridx[i]] += r3;
1226         c[colam + am3 + ridx[i]] += r4;
1227       }
1228       b1 += bm4;
1229       b2 += bm4;
1230       b3 += bm4;
1231       b4 += bm4;
1232     }
1233     for (; col<cn; col++) {     /* over extra columns of C */
1234       colam = col*am;
1235       arm   = a->compressedrow.nrows;
1236       ii    = a->compressedrow.i;
1237       ridx  = a->compressedrow.rindex;
1238       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1239         r1 = 0.0;
1240         n  = ii[i+1] - ii[i];
1241         aj = a->j + ii[i];
1242         aa = a->a + ii[i];
1243 
1244         for (j=0; j<n; j++) {
1245           r1 += (*aa++)*b1[*aj++];
1246         }
1247         c[colam + ridx[i]] += r1;
1248       }
1249       b1 += bm;
1250     }
1251   } else {
1252     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1253       colam = col*am;
1254       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1255         r1 = r2 = r3 = r4 = 0.0;
1256         n  = a->i[i+1] - a->i[i];
1257         aj = a->j + a->i[i];
1258         aa = a->a + a->i[i];
1259         for (j=0; j<n; j++) {
1260           r1 += (*aa)*b1[*aj];
1261           r2 += (*aa)*b2[*aj];
1262           r3 += (*aa)*b3[*aj];
1263           r4 += (*aa++)*b4[*aj++];
1264         }
1265         c[colam + i]       += r1;
1266         c[colam + am + i]  += r2;
1267         c[colam + am2 + i] += r3;
1268         c[colam + am3 + i] += r4;
1269       }
1270       b1 += bm4;
1271       b2 += bm4;
1272       b3 += bm4;
1273       b4 += bm4;
1274     }
1275     for (; col<cn; col++) {     /* over extra columns of C */
1276       colam = col*am;
1277       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1278         r1 = 0.0;
1279         n  = a->i[i+1] - a->i[i];
1280         aj = a->j + a->i[i];
1281         aa = a->a + a->i[i];
1282 
1283         for (j=0; j<n; j++) {
1284           r1 += (*aa++)*b1[*aj++];
1285         }
1286         c[colam + i] += r1;
1287       }
1288       b1 += bm;
1289     }
1290   }
1291   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1292   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
1293   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1294   PetscFunctionReturn(0);
1295 }
1296 
1297 #undef __FUNCT__
1298 #define __FUNCT__ "MatTransColoringApplySpToDen_SeqAIJ"
1299 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1300 {
1301   PetscErrorCode ierr;
1302   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1303   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1304   PetscInt       *bi      = b->i,*bj=b->j;
1305   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1306   MatScalar      *btval,*btval_den,*ba=b->a;
1307   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1308 
1309   PetscFunctionBegin;
1310   btval_den=btdense->v;
1311   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1312   for (k=0; k<ncolors; k++) {
1313     ncolumns = coloring->ncolumns[k];
1314     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1315       col   = *(columns + colorforcol[k] + l);
1316       btcol = bj + bi[col];
1317       btval = ba + bi[col];
1318       anz   = bi[col+1] - bi[col];
1319       for (j=0; j<anz; j++) {
1320         brow            = btcol[j];
1321         btval_den[brow] = btval[j];
1322       }
1323     }
1324     btval_den += m;
1325   }
1326   PetscFunctionReturn(0);
1327 }
1328 
1329 #undef __FUNCT__
1330 #define __FUNCT__ "MatTransColoringApplyDenToSp_SeqAIJ"
1331 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1332 {
1333   PetscErrorCode ierr;
1334   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1335   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1336   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1337   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1338   PetscInt       nrows,*row,*idx;
1339   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1340 
1341   PetscFunctionBegin;
1342   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1343 
1344   if (brows > 0) {
1345     PetscInt *lstart,row_end,row_start;
1346     lstart = matcoloring->lstart;
1347     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1348 
1349     row_end = brows;
1350     if (row_end > m) row_end = m;
1351     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1352       ca_den_ptr = ca_den;
1353       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1354         nrows = matcoloring->nrows[k];
1355         row   = rows  + colorforrow[k];
1356         idx   = den2sp + colorforrow[k];
1357         for (l=lstart[k]; l<nrows; l++) {
1358           if (row[l] >= row_end) {
1359             lstart[k] = l;
1360             break;
1361           } else {
1362             ca[idx[l]] = ca_den_ptr[row[l]];
1363           }
1364         }
1365         ca_den_ptr += m;
1366       }
1367       row_end += brows;
1368       if (row_end > m) row_end = m;
1369     }
1370   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1371     ca_den_ptr = ca_den;
1372     for (k=0; k<ncolors; k++) {
1373       nrows = matcoloring->nrows[k];
1374       row   = rows  + colorforrow[k];
1375       idx   = den2sp + colorforrow[k];
1376       for (l=0; l<nrows; l++) {
1377         ca[idx[l]] = ca_den_ptr[row[l]];
1378       }
1379       ca_den_ptr += m;
1380     }
1381   }
1382 
1383   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1384 #if defined(PETSC_USE_INFO)
1385   if (matcoloring->brows > 0) {
1386     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1387   } else {
1388     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1389   }
1390 #endif
1391   PetscFunctionReturn(0);
1392 }
1393 
1394 /*
1395  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
1396  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
1397  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ().
1398  */
1399 #undef __FUNCT__
1400 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
1401 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1402 {
1403   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1404   PetscErrorCode ierr;
1405   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
1406   PetscInt       nz = a->i[m],row,*jj,mr,col;
1407   PetscInt       *cspidx;
1408 
1409   PetscFunctionBegin;
1410   *nn = n;
1411   if (!ia) PetscFunctionReturn(0);
1412   if (symmetric) {
1413     SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
1414     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
1415   } else {
1416     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
1417     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1418     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
1419     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
1420     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
1421     jj   = a->j;
1422     for (i=0; i<nz; i++) {
1423       collengths[jj[i]]++;
1424     }
1425     cia[0] = oshift;
1426     for (i=0; i<n; i++) {
1427       cia[i+1] = cia[i] + collengths[i];
1428     }
1429     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
1430     jj   = a->j;
1431     for (row=0; row<m; row++) {
1432       mr = a->i[row+1] - a->i[row];
1433       for (i=0; i<mr; i++) {
1434         col = *jj++;
1435 
1436         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
1437         cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
1438       }
1439     }
1440     ierr   = PetscFree(collengths);CHKERRQ(ierr);
1441     *ia    = cia; *ja = cja;
1442     *spidx = cspidx;
1443   }
1444   PetscFunctionReturn(0);
1445 }
1446 
1447 #undef __FUNCT__
1448 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
1449 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
1450 {
1451   PetscErrorCode ierr;
1452 
1453   PetscFunctionBegin;
1454   if (!ia) PetscFunctionReturn(0);
1455 
1456   ierr = PetscFree(*ia);CHKERRQ(ierr);
1457   ierr = PetscFree(*ja);CHKERRQ(ierr);
1458   ierr = PetscFree(*spidx);CHKERRQ(ierr);
1459   PetscFunctionReturn(0);
1460 }
1461 
1462 #undef __FUNCT__
1463 #define __FUNCT__ "MatTransposeColoringCreate_SeqAIJ"
1464 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1465 {
1466   PetscErrorCode ierr;
1467   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1468   const PetscInt *is,*ci,*cj,*row_idx;
1469   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1470   IS             *isa;
1471   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1472   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1473   PetscInt       *colorforcol,*columns,*columns_i,brows;
1474   PetscBool      flg;
1475 
1476   PetscFunctionBegin;
1477   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1478 
1479   /* bs >1 is not being tested yet! */
1480   Nbs       = mat->cmap->N/bs;
1481   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1482   c->N      = Nbs;
1483   c->m      = c->M;
1484   c->rstart = 0;
1485   c->brows  = 100;
1486 
1487   c->ncolors = nis;
1488   ierr = PetscMalloc3(nis,PetscInt,&c->ncolumns,nis,PetscInt,&c->nrows,nis+1,PetscInt,&colorforrow);CHKERRQ(ierr);
1489   ierr = PetscMalloc((csp->nz+1)*sizeof(PetscInt),&rows);CHKERRQ(ierr);
1490   ierr = PetscMalloc((csp->nz+1)*sizeof(PetscInt),&den2sp);CHKERRQ(ierr);
1491 
1492   brows = c->brows;
1493   ierr = PetscOptionsGetInt(NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1494   if (flg) c->brows = brows;
1495   if (brows > 0) {
1496     ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&c->lstart);CHKERRQ(ierr);
1497   }
1498 
1499   colorforrow[0] = 0;
1500   rows_i         = rows;
1501   den2sp_i       = den2sp;
1502 
1503   ierr = PetscMalloc((nis+1)*sizeof(PetscInt),&colorforcol);CHKERRQ(ierr);
1504   ierr = PetscMalloc((Nbs+1)*sizeof(PetscInt),&columns);CHKERRQ(ierr);
1505 
1506   colorforcol[0] = 0;
1507   columns_i      = columns;
1508 
1509   /* get column-wise storage of mat */
1510   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1511 
1512   cm   = c->m;
1513   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
1514   ierr = PetscMalloc((cm+1)*sizeof(PetscInt),&idxhit);CHKERRQ(ierr);
1515   for (i=0; i<nis; i++) { /* loop over color */
1516     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1517     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1518 
1519     c->ncolumns[i] = n;
1520     if (n) {
1521       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1522     }
1523     colorforcol[i+1] = colorforcol[i] + n;
1524     columns_i       += n;
1525 
1526     /* fast, crude version requires O(N*N) work */
1527     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1528 
1529     /* loop over columns*/
1530     for (j=0; j<n; j++) {
1531       col     = is[j];
1532       row_idx = cj + ci[col];
1533       m       = ci[col+1] - ci[col];
1534       /* loop over columns marking them in rowhit */
1535       for (k=0; k<m; k++) {
1536         idxhit[*row_idx]   = spidx[ci[col] + k];
1537         rowhit[*row_idx++] = col + 1;
1538       }
1539     }
1540     /* count the number of hits */
1541     nrows = 0;
1542     for (j=0; j<cm; j++) {
1543       if (rowhit[j]) nrows++;
1544     }
1545     c->nrows[i]      = nrows;
1546     colorforrow[i+1] = colorforrow[i] + nrows;
1547 
1548     nrows = 0;
1549     for (j=0; j<cm; j++) {
1550       if (rowhit[j]) {
1551         rows_i[nrows]   = j;
1552         den2sp_i[nrows] = idxhit[j];
1553         nrows++;
1554       }
1555     }
1556     den2sp_i += nrows;
1557 
1558     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1559     rows_i += nrows;
1560   }
1561   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1562   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1563   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1564   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1565 
1566   c->colorforrow = colorforrow;
1567   c->rows        = rows;
1568   c->den2sp      = den2sp;
1569   c->colorforcol = colorforcol;
1570   c->columns     = columns;
1571 
1572   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1573   PetscFunctionReturn(0);
1574 }
1575