xref: /petsc/src/mat/impls/aij/seq/matrart.c (revision 0e9bae810fdaeb60e2713eaa8ddb89f42e079fd1)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = P * A * P^T
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h>
8 #include <../src/mat/utils/freespace.h>
9 #include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/
10 
11 /*
12      MatApplyPAPt_Symbolic_SeqAIJ_SeqAIJ - Forms the symbolic product of two SeqAIJ matrices
13            C = P * A * P^T;
14 
15      Note: C is assumed to be uncreated.
16            If this is not the case, Destroy C before calling this routine.
17 */
18 #undef __FUNCT__
19 #define __FUNCT__ "MatApplyPAPt_Symbolic_SeqAIJ_SeqAIJ"
20 PetscErrorCode MatApplyPAPt_Symbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat *C)
21 {
22   /* Note: This code is virtually identical to that of MatApplyPtAP_SeqAIJ_Symbolic */
23   /*        and MatMatMult_SeqAIJ_SeqAIJ_Symbolic.  Perhaps they could be merged nicely. */
24   PetscErrorCode     ierr;
25   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
26   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
27   PetscInt           *ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pti,*ptj,*ptjj;
28   PetscInt           *ci,*cj,*paj,*padenserow,*pasparserow,*denserow,*sparserow;
29   PetscInt           an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
30   PetscInt           i,j,k,pnzi,arow,anzj,panzi,ptrow,ptnzj,cnzi;
31   MatScalar          *ca;
32 
33   PetscFunctionBegin;
34   /* some error checking which could be moved into interface layer */
35   if (pn!=am) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",pn,am);
36   if (am!=an) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %D != %D",am, an);
37 
38   /* Set up timers */
39   ierr = PetscLogEventBegin(MAT_Applypapt_symbolic,A,P,0,0);CHKERRQ(ierr);
40 
41   /* Create ij structure of P^T */
42   ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
43 
44   /* Allocate ci array, arrays for fill computation and */
45   /* free space for accumulating nonzero column info */
46   ierr = PetscMalloc(((pm+1)*1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
47   ci[0] = 0;
48 
49   ierr = PetscMalloc4(an,PetscInt,&padenserow,an,PetscInt,&pasparserow,pm,PetscInt,&denserow,pm,PetscInt,&sparserow);CHKERRQ(ierr);
50   ierr = PetscMemzero(padenserow,an*sizeof(PetscInt));CHKERRQ(ierr);
51   ierr = PetscMemzero(pasparserow,an*sizeof(PetscInt));CHKERRQ(ierr);
52   ierr = PetscMemzero(denserow,pm*sizeof(PetscInt));CHKERRQ(ierr);
53   ierr = PetscMemzero(sparserow,pm*sizeof(PetscInt));CHKERRQ(ierr);
54 
55   /* Set initial free space to be nnz(A) scaled by aspect ratio of Pt. */
56   /* This should be reasonable if sparsity of PAPt is similar to that of A. */
57   ierr          = PetscFreeSpaceGet((ai[am]/pn)*pm,&free_space);
58   current_space = free_space;
59 
60   /* Determine fill for each row of C: */
61   for (i=0;i<pm;i++) {
62     pnzi  = pi[i+1] - pi[i];
63     panzi = 0;
64     /* Get symbolic sparse row of PA: */
65     for (j=0;j<pnzi;j++) {
66       arow = *pj++;
67       anzj = ai[arow+1] - ai[arow];
68       ajj  = aj + ai[arow];
69       for (k=0;k<anzj;k++) {
70         if (!padenserow[ajj[k]]) {
71           padenserow[ajj[k]]   = -1;
72           pasparserow[panzi++] = ajj[k];
73         }
74       }
75     }
76     /* Using symbolic row of PA, determine symbolic row of C: */
77     paj    = pasparserow;
78     cnzi   = 0;
79     for (j=0;j<panzi;j++) {
80       ptrow = *paj++;
81       ptnzj = pti[ptrow+1] - pti[ptrow];
82       ptjj  = ptj + pti[ptrow];
83       for (k=0;k<ptnzj;k++) {
84         if (!denserow[ptjj[k]]) {
85           denserow[ptjj[k]] = -1;
86           sparserow[cnzi++] = ptjj[k];
87         }
88       }
89     }
90 
91     /* sort sparse representation */
92     ierr = PetscSortInt(cnzi,sparserow);CHKERRQ(ierr);
93 
94     /* If free space is not available, make more free space */
95     /* Double the amount of total space in the list */
96     if (current_space->local_remaining<cnzi) {
97       ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,&current_space);CHKERRQ(ierr);
98     }
99 
100     /* Copy data into free space, and zero out dense row */
101     ierr = PetscMemcpy(current_space->array,sparserow,cnzi*sizeof(PetscInt));CHKERRQ(ierr);
102     current_space->array           += cnzi;
103     current_space->local_used      += cnzi;
104     current_space->local_remaining -= cnzi;
105 
106     for (j=0;j<panzi;j++) {
107       padenserow[pasparserow[j]] = 0;
108     }
109     for (j=0;j<cnzi;j++) {
110       denserow[sparserow[j]] = 0;
111     }
112     ci[i+1] = ci[i] + cnzi;
113   }
114   /* column indices are in the list of free space */
115   /* Allocate space for cj, initialize cj, and */
116   /* destroy list of free space and other temporary array(s) */
117   ierr = PetscMalloc((ci[pm]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
118   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
119   ierr = PetscFree4(padenserow,pasparserow,denserow,sparserow);CHKERRQ(ierr);
120 
121   /* Allocate space for ca */
122   ierr = PetscMalloc((ci[pm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
123   ierr = PetscMemzero(ca,(ci[pm]+1)*sizeof(MatScalar));CHKERRQ(ierr);
124 
125   /* put together the new matrix */
126   ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,pm,pm,ci,cj,ca,C);CHKERRQ(ierr);
127   (*C)->rmap->bs = P->cmap->bs;
128   (*C)->cmap->bs = P->cmap->bs;
129 
130   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
131   /* Since these are PETSc arrays, change flags to free them as necessary. */
132   c = (Mat_SeqAIJ *)((*C)->data);
133   c->free_a  = PETSC_TRUE;
134   c->free_ij = PETSC_TRUE;
135   c->nonew   = 0;
136 
137   /* Clean up. */
138   ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
139 
140   ierr = PetscLogEventEnd(MAT_Applypapt_symbolic,A,P,0,0);CHKERRQ(ierr);
141   PetscFunctionReturn(0);
142 }
143 
144 /*
145      MatApplyPAPt_Numeric_SeqAIJ - Forms the numeric product of two SeqAIJ matrices
146            C = P * A * P^T;
147      Note: C must have been created by calling MatApplyPAPt_Symbolic_SeqAIJ.
148 */
149 #undef __FUNCT__
150 #define __FUNCT__ "MatApplyPAPt_Numeric_SeqAIJ_SeqAIJ"
151 PetscErrorCode MatApplyPAPt_Numeric_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat C)
152 {
153   PetscErrorCode ierr;
154   PetscInt       flops=0;
155   Mat_SeqAIJ     *a  = (Mat_SeqAIJ *) A->data;
156   Mat_SeqAIJ     *p  = (Mat_SeqAIJ *) P->data;
157   Mat_SeqAIJ     *c  = (Mat_SeqAIJ *) C->data;
158   PetscInt       *ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj=p->j,*paj,*pajdense,*ptj;
159   PetscInt       *ci=c->i,*cj=c->j;
160   PetscInt       an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N,cn=C->cmap->N,cm=C->rmap->N;
161   PetscInt       i,j,k,k1,k2,pnzi,anzj,panzj,arow,ptcol,ptnzj,cnzi;
162   MatScalar      *aa=a->a,*pa=p->a,*pta=p->a,*ptaj,*paa,*aaj,*ca=c->a,sum;
163 
164   PetscFunctionBegin;
165   /* This error checking should be unnecessary if the symbolic was performed */
166   if (pm!=cm) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",pm,cm);
167   if (pn!=am) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",pn,am);
168   if (am!=an) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %D != %D",am, an);
169   if (pm!=cn) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",pm, cn);
170 
171   /* Set up timers */
172   ierr = PetscLogEventBegin(MAT_Applypapt_numeric,A,P,C,0);CHKERRQ(ierr);
173   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
174 
175   ierr = PetscMalloc3(an,MatScalar,&paa,an,PetscInt,&paj,an,PetscInt,&pajdense);CHKERRQ(ierr);
176   ierr = PetscMemzero(paa,an*(sizeof(MatScalar)+2*sizeof(PetscInt)));CHKERRQ(ierr);
177 
178   for (i=0;i<pm;i++) {
179     /* Form sparse row of P*A */
180     pnzi  = pi[i+1] - pi[i];
181     panzj = 0;
182     for (j=0;j<pnzi;j++) {
183       arow = *pj++;
184       anzj = ai[arow+1] - ai[arow];
185       ajj  = aj + ai[arow];
186       aaj  = aa + ai[arow];
187       for (k=0;k<anzj;k++) {
188         if (!pajdense[ajj[k]]) {
189           pajdense[ajj[k]] = -1;
190           paj[panzj++]     = ajj[k];
191         }
192         paa[ajj[k]] += (*pa)*aaj[k];
193       }
194       flops += 2*anzj;
195       pa++;
196     }
197 
198     /* Sort the j index array for quick sparse axpy. */
199     ierr = PetscSortInt(panzj,paj);CHKERRQ(ierr);
200 
201     /* Compute P*A*P^T using sparse inner products. */
202     /* Take advantage of pre-computed (i,j) of C for locations of non-zeros. */
203     cnzi = ci[i+1] - ci[i];
204     for (j=0;j<cnzi;j++) {
205       /* Form sparse inner product of current row of P*A with (*cj++) col of P^T. */
206       ptcol = *cj++;
207       ptnzj = pi[ptcol+1] - pi[ptcol];
208       ptj   = pjj + pi[ptcol];
209       ptaj  = pta + pi[ptcol];
210       sum   = 0.;
211       k1    = 0;
212       k2    = 0;
213       while ((k1<panzj) && (k2<ptnzj)) {
214         if (paj[k1]==ptj[k2]) {
215           sum += paa[paj[k1++]]*ptaj[k2++];
216         } else if (paj[k1] < ptj[k2]) {
217           k1++;
218         } else /* if (paj[k1] > ptj[k2]) */ {
219           k2++;
220         }
221       }
222       *ca++ = sum;
223     }
224 
225     /* Zero the current row info for P*A */
226     for (j=0;j<panzj;j++) {
227       paa[paj[j]]      = 0.;
228       pajdense[paj[j]] = 0;
229     }
230   }
231 
232   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
233   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
234   ierr = PetscFree3(paa,paj,pajdense);CHKERRQ(ierr);
235   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
236   ierr = PetscLogEventEnd(MAT_Applypapt_numeric,A,P,C,0);CHKERRQ(ierr);
237   PetscFunctionReturn(0);
238 }
239 
240 #undef __FUNCT__
241 #define __FUNCT__ "MatApplyPAPt_SeqAIJ_SeqAIJ"
242 PetscErrorCode MatApplyPAPt_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat *C)
243 {
244   PetscErrorCode ierr;
245 
246   PetscFunctionBegin;
247   ierr = PetscLogEventBegin(MAT_Applypapt,A,P,0,0);CHKERRQ(ierr);
248   ierr = MatApplyPAPt_Symbolic_SeqAIJ_SeqAIJ(A,P,C);CHKERRQ(ierr);
249   ierr = MatApplyPAPt_Numeric_SeqAIJ_SeqAIJ(A,P,*C);CHKERRQ(ierr);
250   ierr = PetscLogEventEnd(MAT_Applypapt,A,P,0,0);CHKERRQ(ierr);
251   PetscFunctionReturn(0);
252 }
253 
254 /*--------------------------------------------------*/
255 /*
256   Defines projective product routines where A is a SeqAIJ matrix
257           C = R * A * R^T
258 */
259 
260 #undef __FUNCT__
261 #define __FUNCT__ "PetscContainerDestroy_Mat_RARt"
262 PetscErrorCode PetscContainerDestroy_Mat_RARt(void *ptr)
263 {
264   PetscErrorCode ierr;
265   Mat_RARt       *rart=(Mat_RARt*)ptr;
266 
267   PetscFunctionBegin;
268   ierr = MatTransposeColoringDestroy(&rart->matcoloring);CHKERRQ(ierr);
269   ierr = MatDestroy(&rart->Rt);CHKERRQ(ierr);
270   ierr = MatDestroy(&rart->RARt);CHKERRQ(ierr);
271   ierr = PetscFree(rart->work);CHKERRQ(ierr);
272   ierr = PetscFree(rart);CHKERRQ(ierr);
273   PetscFunctionReturn(0);
274 }
275 
276 #undef __FUNCT__
277 #define __FUNCT__ "MatDestroy_SeqAIJ_RARt"
278 PetscErrorCode MatDestroy_SeqAIJ_RARt(Mat A)
279 {
280   PetscErrorCode ierr;
281   PetscContainer container;
282   Mat_RARt       *rart=PETSC_NULL;
283 
284   PetscFunctionBegin;
285   ierr = PetscObjectQuery((PetscObject)A,"Mat_RARt",(PetscObject *)&container);CHKERRQ(ierr);
286   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
287   ierr = PetscContainerGetPointer(container,(void **)&rart);CHKERRQ(ierr);
288   A->ops->destroy   = rart->destroy;
289   if (A->ops->destroy) {
290     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
291   }
292   ierr = PetscObjectCompose((PetscObject)A,"Mat_RARt",0);CHKERRQ(ierr);
293   PetscFunctionReturn(0);
294 }
295 
296 #undef __FUNCT__
297 #define __FUNCT__ "MatRARtSymbolic_SeqAIJ_SeqAIJ"
298 PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat R,PetscReal fill,Mat *C)
299 {
300   PetscErrorCode      ierr;
301   Mat                 P;
302   PetscInt            *rti,*rtj;
303   Mat_RARt            *rart;
304   PetscContainer      container;
305   MatTransposeColoring matcoloring;
306   ISColoring           iscoloring;
307   Mat                  Rt_dense,RARt_dense;
308   PetscLogDouble       GColor=0.0,MCCreate=0.0,MDenCreate=0.0,t0,tf,etime=0.0;
309   Mat_SeqAIJ           *c;
310 
311   PetscFunctionBegin;
312   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
313   /* create symbolic P=Rt */
314   ierr = MatGetSymbolicTranspose_SeqAIJ(R,&rti,&rtj);CHKERRQ(ierr);
315   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,R->cmap->n,R->rmap->n,rti,rtj,PETSC_NULL,&P);CHKERRQ(ierr);
316 
317   /* get symbolic C=Pt*A*P */
318   ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ(A,P,fill,C);CHKERRQ(ierr);
319   (*C)->rmap->bs = R->rmap->bs;
320   (*C)->cmap->bs = R->rmap->bs;
321 
322   /* create a supporting struct */
323   ierr = PetscNew(Mat_RARt,&rart);CHKERRQ(ierr);
324 
325   /* attach the supporting struct to C */
326   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
327   ierr = PetscContainerSetPointer(container,rart);CHKERRQ(ierr);
328   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_RARt);CHKERRQ(ierr);
329   ierr = PetscObjectCompose((PetscObject)(*C),"Mat_RARt",(PetscObject)container);CHKERRQ(ierr);
330   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
331   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
332   etime += tf - t0;
333 
334   /* Create MatTransposeColoring from symbolic C=R*A*R^T */
335   c=(Mat_SeqAIJ*)(*C)->data;
336   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
337   ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
338   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
339   GColor += tf - t0;
340 
341   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
342   ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
343   rart->matcoloring = matcoloring;
344   ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
345   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
346   MCCreate += tf - t0;
347 
348   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
349   /* Create Rt_dense */
350   ierr = MatCreate(PETSC_COMM_SELF,&Rt_dense);CHKERRQ(ierr);
351   ierr = MatSetSizes(Rt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
352   ierr = MatSetType(Rt_dense,MATSEQDENSE);CHKERRQ(ierr);
353   ierr = MatSeqDenseSetPreallocation(Rt_dense,PETSC_NULL);CHKERRQ(ierr);
354   Rt_dense->assembled = PETSC_TRUE;
355   rart->Rt            = Rt_dense;
356 
357   /* Create RARt_dense = R*A*Rt_dense */
358   ierr = MatCreate(PETSC_COMM_SELF,&RARt_dense);CHKERRQ(ierr);
359   ierr = MatSetSizes(RARt_dense,(*C)->rmap->n,matcoloring->ncolors,(*C)->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
360   ierr = MatSetType(RARt_dense,MATSEQDENSE);CHKERRQ(ierr);
361   ierr = MatSeqDenseSetPreallocation(RARt_dense,PETSC_NULL);CHKERRQ(ierr);
362   rart->RARt = RARt_dense;
363 
364   /* Allocate work array to store columns of A*R^T used in MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense() */
365   ierr = PetscMalloc(A->rmap->n*4*sizeof(PetscScalar),&rart->work);CHKERRQ(ierr);
366 
367   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
368   MDenCreate += tf - t0;
369 
370   rart->destroy = (*C)->ops->destroy;
371   (*C)->ops->destroy = MatDestroy_SeqAIJ_RARt;
372 
373   /* clean up */
374   ierr = MatRestoreSymbolicTranspose_SeqAIJ(R,&rti,&rtj);CHKERRQ(ierr);
375   ierr = MatDestroy(&P);CHKERRQ(ierr);
376 
377 #if defined(PETSC_USE_INFO)
378   {
379   PetscReal density= (PetscReal)(c->nz)/(RARt_dense->rmap->n*RARt_dense->cmap->n);
380   ierr = PetscInfo6(*C,"RARt_den %D %D; Rt_den %D %D, (RARt->nz %D)/(m*ncolors)=%g\n",RARt_dense->rmap->n,RARt_dense->cmap->n,Rt_dense->rmap->n,Rt_dense->cmap->n,c->nz,density);
381   ierr = PetscInfo5(*C,"Sym = GetColor %g + MColorCreate %g + MDenCreate %g + other %g = %g\n",GColor,MCCreate,MDenCreate,etime,GColor+MCCreate+MDenCreate+etime);
382   }
383 #endif
384   PetscFunctionReturn(0);
385 }
386 
387 /*
388  RAB = R * A * B, R and A in seqaij format, B in dense format;
389 */
390 #undef __FUNCT__
391 #define __FUNCT__ "MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense"
392 PetscErrorCode MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(Mat R,Mat A,Mat B,Mat RAB,PetscScalar *work)
393 {
394   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*r=(Mat_SeqAIJ*)R->data;
395   PetscErrorCode ierr;
396   PetscScalar    *b,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
397   MatScalar      *aa,*ra;
398   PetscInt       cn=B->cmap->n,bm=B->rmap->n,col,i,j,n,*ai=a->i,*aj,am=A->rmap->n;
399   PetscInt       am2=2*am,am3=3*am,bm4=4*bm;
400   PetscScalar    *d,*c,*c2,*c3,*c4;
401   PetscInt       *rj,rm=R->rmap->n,dm=RAB->rmap->n,dn=RAB->cmap->n;
402   PetscInt       rm2=2*rm,rm3=3*rm,colrm;
403 
404   PetscFunctionBegin;
405   if (!dm || !dn) PetscFunctionReturn(0);
406   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);
407   if (am != R->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in R %D not equal rows in A %D\n",R->cmap->n,am);
408   if (R->rmap->n != RAB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in RAB %D not equal rows in R %D\n",RAB->rmap->n,R->rmap->n);
409   if (B->cmap->n != RAB->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in RAB %D not equal columns in B %D\n",RAB->cmap->n,B->cmap->n);
410 
411   ierr = MatDenseGetArray(B,&b);CHKERRQ(ierr);
412   ierr = MatDenseGetArray(RAB,&d);CHKERRQ(ierr);
413   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
414   c = work; c2 = c + am; c3 = c2 + am; c4 = c3 + am;
415   for (col=0; col<cn-4; col += 4){  /* over columns of C */
416     for (i=0; i<am; i++) {        /* over rows of A in those columns */
417       r1 = r2 = r3 = r4 = 0.0;
418       n   = ai[i+1] - ai[i];
419       aj  = a->j + ai[i];
420       aa  = a->a + ai[i];
421       for (j=0; j<n; j++) {
422         r1 += (*aa)*b1[*aj];
423         r2 += (*aa)*b2[*aj];
424         r3 += (*aa)*b3[*aj];
425         r4 += (*aa++)*b4[*aj++];
426       }
427       c[i]       = r1;
428       c[am  + i] = r2;
429       c[am2 + i] = r3;
430       c[am3 + i] = r4;
431     }
432     b1 += bm4;
433     b2 += bm4;
434     b3 += bm4;
435     b4 += bm4;
436 
437     /* RAB[:,col] = R*C[:,col] */
438     colrm = col*rm;
439     for (i=0; i<rm; i++) {        /* over rows of R in those columns */
440       r1 = r2 = r3 = r4 = 0.0;
441       n   = r->i[i+1] - r->i[i];
442       rj  = r->j + r->i[i];
443       ra  = r->a + r->i[i];
444       for (j=0; j<n; j++) {
445         r1 += (*ra)*c[*rj];
446         r2 += (*ra)*c2[*rj];
447         r3 += (*ra)*c3[*rj];
448         r4 += (*ra++)*c4[*rj++];
449       }
450       d[colrm + i]       = r1;
451       d[colrm + rm + i]  = r2;
452       d[colrm + rm2 + i] = r3;
453       d[colrm + rm3 + i] = r4;
454     }
455   }
456   for (;col<cn; col++){     /* over extra columns of C */
457     for (i=0; i<am; i++) {  /* over rows of A in those columns */
458       r1 = 0.0;
459       n   = a->i[i+1] - a->i[i];
460       aj  = a->j + a->i[i];
461       aa  = a->a + a->i[i];
462       for (j=0; j<n; j++) {
463         r1 += (*aa++)*b1[*aj++];
464       }
465       c[i]     = r1;
466     }
467     b1 += bm;
468 
469     for (i=0; i<rm; i++) {  /* over rows of R in those columns */
470       r1 = 0.0;
471       n   = r->i[i+1] - r->i[i];
472       rj  = r->j + r->i[i];
473       ra  = r->a + r->i[i];
474       for (j=0; j<n; j++) {
475         r1 += (*ra++)*c[*rj++];
476       }
477       d[col*rm + i]     = r1;
478     }
479   }
480   ierr = PetscLogFlops(cn*2.0*(a->nz + r->nz));CHKERRQ(ierr);
481 
482   ierr = MatDenseRestoreArray(B,&b);CHKERRQ(ierr);
483   ierr = MatDenseRestoreArray(RAB,&d);CHKERRQ(ierr);
484   ierr = MatAssemblyBegin(RAB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
485   ierr = MatAssemblyEnd(RAB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
486   PetscFunctionReturn(0);
487 }
488 
489 #undef __FUNCT__
490 #define __FUNCT__ "MatRARtNumeric_SeqAIJ_SeqAIJ"
491 PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ(Mat A,Mat R,Mat C)
492 {
493   PetscErrorCode        ierr;
494   Mat_RARt              *rart;
495   PetscContainer        container;
496   MatTransposeColoring  matcoloring;
497   Mat                   Rt,RARt;
498   PetscLogDouble        Mult_sp_den=0.0,app1=0.0,app2=0.0,t0,tf;
499 
500   PetscFunctionBegin;
501   ierr = PetscObjectQuery((PetscObject)C,"Mat_RARt",(PetscObject *)&container);CHKERRQ(ierr);
502   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
503   ierr  = PetscContainerGetPointer(container,(void **)&rart);CHKERRQ(ierr);
504 
505   /* Get dense Rt by Apply MatTransposeColoring to R */
506   matcoloring = rart->matcoloring;
507   Rt          = rart->Rt;
508   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
509   ierr = MatTransColoringApplySpToDen(matcoloring,R,Rt);CHKERRQ(ierr);
510   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
511   app1 += tf - t0;
512 
513   /* Get dense RARt = R*A*Rt */
514   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
515   RARt = rart->RARt;
516   ierr = MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(R,A,Rt,RARt,rart->work);CHKERRQ(ierr);
517   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
518   Mult_sp_den += tf - t0;
519 
520   /* Recover C from C_dense */
521   ierr = PetscGetTime(&t0);CHKERRQ(ierr);
522   ierr = MatTransColoringApplyDenToSp(matcoloring,RARt,C);CHKERRQ(ierr);
523   ierr = PetscGetTime(&tf);CHKERRQ(ierr);
524   app2 += tf - t0;
525 
526 #if defined(PETSC_USE_INFO)
527   ierr = PetscInfo4(C,"Num = ColorApp %g + %g + Mult_sp_den %g  = %g\n",app1,app2,Mult_sp_den,app1+app2+Mult_sp_den);
528 #endif
529   PetscFunctionReturn(0);
530 }
531 
532 EXTERN_C_BEGIN
533 #undef __FUNCT__
534 #define __FUNCT__ "MatRARt_SeqAIJ_SeqAIJ"
535 PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
536 {
537   PetscErrorCode ierr;
538 
539   PetscFunctionBegin;
540   if (scall == MAT_INITIAL_MATRIX){
541     ierr = MatRARtSymbolic_SeqAIJ_SeqAIJ(A,R,fill,C);CHKERRQ(ierr);
542   }
543   ierr = MatRARtNumeric_SeqAIJ_SeqAIJ(A,R,*C);CHKERRQ(ierr);
544   PetscFunctionReturn(0);
545 }
546 EXTERN_C_END
547