xref: /petsc/src/ksp/pc/impls/gamg/agg.c (revision 9ae82921df069a58776bfe4da82b38e8ff7dd41c)
1 /*
2  GAMG geometric-algebric multiogrid PC - Mark Adams 2011
3  */
4 
5 #include <../src/ksp/pc/impls/gamg/gamg.h>        /*I "petscpc.h" I*/
6 #include <petsc-private/kspimpl.h>
7 
8 #include <assert.h>
9 #include <petscblaslapack.h>
10 
11 typedef struct {
12   PetscInt nsmooths;
13   PetscBool sym_graph;
14   PetscBool square_graph;
15 }PC_GAMG_AGG;
16 
17 #undef __FUNCT__
18 #define __FUNCT__ "PCGAMGSetNSmooths"
19 /*@
20    PCGAMGSetNSmooths - Set number of smoothing steps (1 is typical)
21 
22    Not Collective on PC
23 
24    Input Parameters:
25 .  pc - the preconditioner context
26 
27    Options Database Key:
28 .  -pc_gamg_agg_nsmooths
29 
30    Level: intermediate
31 
32    Concepts: Aggregation AMG preconditioner
33 
34 .seealso: ()
35 @*/
36 PetscErrorCode PCGAMGSetNSmooths(PC pc, PetscInt n)
37 {
38   PetscErrorCode ierr;
39 
40   PetscFunctionBegin;
41   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
42   ierr = PetscTryMethod(pc,"PCGAMGSetNSmooths_C",(PC,PetscInt),(pc,n));CHKERRQ(ierr);
43   PetscFunctionReturn(0);
44 }
45 
46 EXTERN_C_BEGIN
47 #undef __FUNCT__
48 #define __FUNCT__ "PCGAMGSetNSmooths_GAMG"
49 PetscErrorCode PCGAMGSetNSmooths_GAMG(PC pc, PetscInt n)
50 {
51   PC_MG           *mg = (PC_MG*)pc->data;
52   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
53   PC_GAMG_AGG     *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
54 
55   PetscFunctionBegin;
56   pc_gamg_agg->nsmooths = n;
57   PetscFunctionReturn(0);
58 }
59 EXTERN_C_END
60 
61 #undef __FUNCT__
62 #define __FUNCT__ "PCGAMGSetSymGraph"
63 /*@
64    PCGAMGSetSymGraph -
65 
66    Not Collective on PC
67 
68    Input Parameters:
69 .  pc - the preconditioner context
70 
71    Options Database Key:
72 .  -pc_gamg_sym_graph
73 
74    Level: intermediate
75 
76    Concepts: Aggregation AMG preconditioner
77 
78 .seealso: ()
79 @*/
80 PetscErrorCode PCGAMGSetSymGraph(PC pc, PetscBool n)
81 {
82   PetscErrorCode ierr;
83 
84   PetscFunctionBegin;
85   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
86   ierr = PetscTryMethod(pc,"PCGAMGSetSymGraph_C",(PC,PetscBool),(pc,n));CHKERRQ(ierr);
87   PetscFunctionReturn(0);
88 }
89 
90 EXTERN_C_BEGIN
91 #undef __FUNCT__
92 #define __FUNCT__ "PCGAMGSetSymGraph_GAMG"
93 PetscErrorCode PCGAMGSetSymGraph_GAMG(PC pc, PetscBool n)
94 {
95   PC_MG           *mg = (PC_MG*)pc->data;
96   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
97   PC_GAMG_AGG      *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
98 
99   PetscFunctionBegin;
100   pc_gamg_agg->sym_graph = n;
101   PetscFunctionReturn(0);
102 }
103 EXTERN_C_END
104 
105 #undef __FUNCT__
106 #define __FUNCT__ "PCGAMGSetSquareGraph"
107 /*@
108    PCGAMGSetSquareGraph -
109 
110    Not Collective on PC
111 
112    Input Parameters:
113 .  pc - the preconditioner context
114 
115    Options Database Key:
116 .  -pc_gamg_square_graph
117 
118    Level: intermediate
119 
120    Concepts: Aggregation AMG preconditioner
121 
122 .seealso: ()
123 @*/
124 PetscErrorCode PCGAMGSetSquareGraph(PC pc, PetscBool n)
125 {
126   PetscErrorCode ierr;
127 
128   PetscFunctionBegin;
129   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
130   ierr = PetscTryMethod(pc,"PCGAMGSetSquareGraph_C",(PC,PetscBool),(pc,n));CHKERRQ(ierr);
131   PetscFunctionReturn(0);
132 }
133 
134 EXTERN_C_BEGIN
135 #undef __FUNCT__
136 #define __FUNCT__ "PCGAMGSetSquareGraph_GAMG"
137 PetscErrorCode PCGAMGSetSquareGraph_GAMG(PC pc, PetscBool n)
138 {
139   PC_MG           *mg = (PC_MG*)pc->data;
140   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
141   PC_GAMG_AGG      *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
142 
143   PetscFunctionBegin;
144   pc_gamg_agg->square_graph = n;
145   PetscFunctionReturn(0);
146 }
147 EXTERN_C_END
148 
149 /* -------------------------------------------------------------------------- */
150 /*
151    PCSetFromOptions_GAMG_AGG
152 
153   Input Parameter:
154    . pc -
155 */
156 #undef __FUNCT__
157 #define __FUNCT__ "PCSetFromOptions_GAMG_AGG"
158 PetscErrorCode PCSetFromOptions_GAMG_AGG( PC pc )
159 {
160   PetscErrorCode  ierr;
161   PC_MG           *mg = (PC_MG*)pc->data;
162   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
163   PC_GAMG_AGG      *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
164   PetscBool        flag;
165 
166   PetscFunctionBegin;
167   /* call base class */
168   ierr = PCSetFromOptions_GAMG( pc ); CHKERRQ(ierr);
169 
170   ierr = PetscOptionsHead("GAMG-AGG options"); CHKERRQ(ierr);
171   {
172     /* -pc_gamg_agg_nsmooths */
173     pc_gamg_agg->nsmooths = 0;
174     ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths",
175                            "smoothing steps for smoothed aggregation, usually 1 (0)",
176                            "PCGAMGSetNSmooths",
177                            pc_gamg_agg->nsmooths,
178                            &pc_gamg_agg->nsmooths,
179                            &flag);
180     CHKERRQ(ierr);
181 
182     /* -pc_gamg_sym_graph */
183     pc_gamg_agg->sym_graph = PETSC_FALSE;
184     ierr = PetscOptionsBool("-pc_gamg_sym_graph",
185                             "Set for asymmetric matrices",
186                             "PCGAMGSetSymGraph",
187                             pc_gamg_agg->sym_graph,
188                             &pc_gamg_agg->sym_graph,
189                             &flag);
190     CHKERRQ(ierr);
191 
192     /* -pc_gamg_square_graph */
193     pc_gamg_agg->square_graph = PETSC_TRUE;
194     ierr = PetscOptionsBool("-pc_gamg_square_graph",
195                             "For faster coarsening and lower coarse grid complexity",
196                             "PCGAMGSetSquareGraph",
197                             pc_gamg_agg->square_graph,
198                             &pc_gamg_agg->square_graph,
199                             &flag);
200     CHKERRQ(ierr);
201   }
202   ierr = PetscOptionsTail();CHKERRQ(ierr);
203 
204   PetscFunctionReturn(0);
205 }
206 
207 /* -------------------------------------------------------------------------- */
208 /*
209    PCDestroy_AGG
210 
211   Input Parameter:
212    . pc -
213 */
214 #undef __FUNCT__
215 #define __FUNCT__ "PCDestroy_AGG"
216 PetscErrorCode PCDestroy_AGG( PC pc )
217 {
218   PetscErrorCode  ierr;
219   PC_MG           *mg = (PC_MG*)pc->data;
220   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
221   PC_GAMG_AGG      *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
222 
223   PetscFunctionBegin;
224   if( pc_gamg_agg ) {
225     ierr = PetscFree(pc_gamg_agg);CHKERRQ(ierr);
226     pc_gamg_agg = 0;
227   }
228 
229   /* call base class */
230   ierr = PCDestroy_GAMG( pc );CHKERRQ(ierr);
231 
232   PetscFunctionReturn(0);
233 }
234 
235 /* -------------------------------------------------------------------------- */
236 /*
237    PCSetCoordinates_AGG
238      - collective
239 
240    Input Parameter:
241    . pc - the preconditioner context
242    . ndm - dimesion of data (used for dof/vertex for Stokes)
243    . a_nloc - number of vertices local
244    . coords - [a_nloc][ndm] - interleaved coordinate data: {x_0, y_0, z_0, x_1, y_1, ...}
245 */
246 EXTERN_C_BEGIN
247 #undef __FUNCT__
248 #define __FUNCT__ "PCSetCoordinates_AGG"
249 PetscErrorCode PCSetCoordinates_AGG( PC pc, PetscInt ndm, PetscInt a_nloc, PetscReal *coords )
250 {
251   PC_MG          *mg = (PC_MG*)pc->data;
252   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
253   PetscErrorCode  ierr;
254   PetscInt        arrsz,kk,ii,jj,nloc,ndatarows,bs;
255   Mat             mat = pc->pmat;
256   /* MPI_Comm     wcomm = ((PetscObject)pc)->comm; */
257 
258   PetscFunctionBegin;
259   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
260   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
261   nloc = a_nloc;
262 
263   /* SA: null space vectors */
264   ierr = MatGetBlockSize( mat, &bs ); CHKERRQ( ierr ); /* this does not work for Stokes */
265   if( coords && bs==1 ) pc_gamg->data_cell_cols = 1; /* scalar w/ coords and SA (not needed) */
266   else if( coords ) {
267     if(ndm > bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"degrees of motion %d > block size %d",ndm,bs);
268     pc_gamg->data_cell_cols = (ndm==2 ? (bs+1) : (bs+3)); /* elasticity */
269   }
270   else pc_gamg->data_cell_cols = bs; /* no data, force SA with constant null space vectors */
271   pc_gamg->data_cell_rows = ndatarows = bs;
272   assert(pc_gamg->data_cell_cols>0);
273   arrsz = nloc*pc_gamg->data_cell_rows*pc_gamg->data_cell_cols;
274 
275   /* create data - syntactic sugar that should be refactored at some point */
276   if (pc_gamg->data==0 || (pc_gamg->data_sz != arrsz)) {
277     ierr = PetscFree( pc_gamg->data );  CHKERRQ(ierr);
278     ierr = PetscMalloc((arrsz+1)*sizeof(PetscReal), &pc_gamg->data ); CHKERRQ(ierr);
279     /* pc_gamg->data != null if nloc==0: flag for called */
280   }
281   /* copy data in - column oriented */
282   for(kk=0;kk<nloc;kk++){
283     const PetscInt M = nloc*pc_gamg->data_cell_rows;
284     PetscReal *data = &pc_gamg->data[kk*ndatarows];
285     if( pc_gamg->data_cell_cols==1 ) *data = 1.0;
286     else {
287       for(ii=0;ii<ndatarows;ii++)
288         for(jj=0;jj<ndatarows;jj++)
289           if(ii==jj)data[ii*M + jj] = 1.0; /* translational modes */
290           else data[ii*M + jj] = 0.0;
291       if( coords ) {
292         if( ndm == 2 ){ /* rotational modes */
293           data += 2*M;
294           data[0] = -coords[2*kk+1];
295           data[1] =  coords[2*kk];
296         }
297         else {
298           data += 3*M;
299           data[0] = 0.0;             data[M+0] =  coords[3*kk+2]; data[2*M+0] = -coords[3*kk+1];
300           data[1] = -coords[3*kk+2]; data[M+1] = 0.0;             data[2*M+1] =  coords[3*kk];
301           data[2] =  coords[3*kk+1]; data[M+2] = -coords[3*kk];   data[2*M+2] = 0.0;
302         }
303       }
304     }
305   }
306 
307   pc_gamg->data_sz = arrsz;
308 
309   PetscFunctionReturn(0);
310 }
311 EXTERN_C_END
312 
313 typedef PetscInt NState;
314 static const NState NOT_DONE=-2;
315 static const NState DELETED=-1;
316 static const NState REMOVED=-3;
317 #define IS_SELECTED(s) (s!=DELETED && s!=NOT_DONE && s!=REMOVED)
318 
319 /* -------------------------------------------------------------------------- */
320 /*
321    smoothAggs - greedy grab of with G1 (unsquared graph) -- AIJ specific
322      - AGG-MG specific: clears singletons out of 'selected_2'
323 
324    Input Parameter:
325    . Gmat_2 - glabal matrix of graph (data not defined)
326    . Gmat_1 - base graph to grab with
327    Input/Output Parameter:
328    . aggs_2 - linked list of aggs with gids )
329 */
330 #undef __FUNCT__
331 #define __FUNCT__ "smoothAggs"
332 static PetscErrorCode smoothAggs( const Mat Gmat_2, /* base (squared) graph */
333                                   const Mat Gmat_1, /* base graph */
334                                   /* const IS selected_2, [nselected local] selected vertices */
335                                   PetscCoarsenData *aggs_2 /* [nselected local] global ID of aggregate */
336                                   )
337 {
338   PetscErrorCode ierr;
339   PetscBool      isMPI;
340   Mat_SeqAIJ    *matA_1, *matB_1=0, *matA_2, *matB_2=0;
341   MPI_Comm       wcomm = ((PetscObject)Gmat_2)->comm;
342   PetscMPIInt    mype,npe;
343   PetscInt       lid,*ii,*idx,ix,Iend,my0,kk,n,j;
344   Mat_MPIAIJ    *mpimat_2 = 0, *mpimat_1=0;
345   const PetscInt nloc = Gmat_2->rmap->n;
346   PetscScalar   *cpcol_1_state,*cpcol_2_state,*cpcol_2_par_orig,*lid_parent_gid;
347   PetscInt      *lid_cprowID_1;
348   NState        *lid_state;
349   Vec            ghost_par_orig2;
350 
351   PetscFunctionBegin;
352   ierr = MPI_Comm_rank( wcomm, &mype );   CHKERRQ(ierr);
353   ierr = MPI_Comm_size( wcomm, &npe );   CHKERRQ(ierr);
354   ierr = MatGetOwnershipRange(Gmat_1,&my0,&Iend);  CHKERRQ(ierr);
355 
356   if( PETSC_FALSE ) {
357     PetscViewer viewer; char fname[32]; static int llev=0;
358     sprintf(fname,"Gmat2_%d.m",llev++);
359     PetscViewerASCIIOpen(wcomm,fname,&viewer);
360     ierr = PetscViewerSetFormat( viewer, PETSC_VIEWER_ASCII_MATLAB);  CHKERRQ(ierr);
361     ierr = MatView(Gmat_2, viewer ); CHKERRQ(ierr);
362     ierr = PetscViewerDestroy( &viewer );
363   }
364 
365   /* get submatrices */
366   ierr = PetscObjectTypeCompare( (PetscObject)Gmat_1, MATMPIAIJ, &isMPI ); CHKERRQ(ierr);
367   if(isMPI) {
368     /* grab matrix objects */
369     mpimat_2 = (Mat_MPIAIJ*)Gmat_2->data;
370     mpimat_1 = (Mat_MPIAIJ*)Gmat_1->data;
371     matA_1 = (Mat_SeqAIJ*)mpimat_1->A->data;
372     matB_1 = (Mat_SeqAIJ*)mpimat_1->B->data;
373     matA_2 = (Mat_SeqAIJ*)mpimat_2->A->data;
374     matB_2 = (Mat_SeqAIJ*)mpimat_2->B->data;
375 
376     /* force compressed row storage for B matrix in AuxMat */
377     matB_1->compressedrow.check = PETSC_TRUE;
378     ierr = MatCheckCompressedRow(mpimat_1->B,&matB_1->compressedrow,matB_1->i,Gmat_1->rmap->n,-1.0);
379     CHKERRQ(ierr);
380 
381     ierr = PetscMalloc( nloc*sizeof(PetscInt), &lid_cprowID_1 ); CHKERRQ(ierr);
382     for( lid = 0 ; lid < nloc ; lid++ ) lid_cprowID_1[lid] = -1;
383     for (ix=0; ix<matB_1->compressedrow.nrows; ix++) {
384       PetscInt lid = matB_1->compressedrow.rindex[ix];
385       lid_cprowID_1[lid] = ix;
386     }
387   }
388   else {
389     matA_1 = (Mat_SeqAIJ*)Gmat_1->data;
390     matA_2 = (Mat_SeqAIJ*)Gmat_2->data;
391     lid_cprowID_1 = PETSC_NULL;
392   }
393   assert( matA_1 && !matA_1->compressedrow.use );
394   assert( matB_1==0 || matB_1->compressedrow.use );
395   assert( matA_2 && !matA_2->compressedrow.use );
396   assert( matB_2==0 || matB_2->compressedrow.use );
397 
398   /* get state of locals and selected gid for deleted */
399   ierr = PetscMalloc( nloc*sizeof(NState), &lid_state ); CHKERRQ(ierr);
400   ierr = PetscMalloc( nloc*sizeof(PetscScalar), &lid_parent_gid ); CHKERRQ(ierr);
401   for( lid = 0 ; lid < nloc ; lid++ ) {
402     lid_parent_gid[lid] = -1.0;
403     lid_state[lid] = DELETED;
404   }
405 
406   /* set lid_state */
407   for( lid = 0 ; lid < nloc ; lid++ ) {
408     PetscCDPos pos;
409     ierr = PetscCDGetHeadPos(aggs_2,lid,&pos); CHKERRQ(ierr);
410     if( pos ) {
411       PetscInt gid1;
412       ierr = PetscLLNGetID( pos, &gid1 ); CHKERRQ(ierr); assert(gid1==lid+my0);
413       lid_state[lid] = gid1;
414     }
415   }
416 
417   /* map local to selected local, DELETED means a ghost owns it */
418   for(lid=kk=0;lid<nloc;lid++){
419     NState state = lid_state[lid];
420     if( IS_SELECTED(state) ){
421       PetscCDPos pos;
422       ierr = PetscCDGetHeadPos(aggs_2,lid,&pos); CHKERRQ(ierr);
423       while(pos){
424         PetscInt gid1;
425         ierr = PetscLLNGetID( pos, &gid1 ); CHKERRQ(ierr);
426         ierr = PetscCDGetNextPos(aggs_2,lid,&pos); CHKERRQ(ierr);
427 
428         if( gid1 >= my0 && gid1 < Iend ){
429           lid_parent_gid[gid1-my0] = (PetscScalar)(lid + my0);
430         }
431       }
432     }
433   }
434   /* get 'cpcol_1/2_state' & cpcol_2_par_orig - uses mpimat_1/2->lvec for temp space */
435   if (isMPI) {
436     Vec          tempVec;
437     /* get 'cpcol_1_state' */
438     ierr = MatGetVecs( Gmat_1, &tempVec, 0 );         CHKERRQ(ierr);
439     for(kk=0,j=my0;kk<nloc;kk++,j++){
440       PetscScalar v = (PetscScalar)lid_state[kk];
441       ierr = VecSetValues( tempVec, 1, &j, &v, INSERT_VALUES );  CHKERRQ(ierr);
442     }
443     ierr = VecAssemblyBegin( tempVec ); CHKERRQ(ierr);
444     ierr = VecAssemblyEnd( tempVec ); CHKERRQ(ierr);
445     ierr = VecScatterBegin(mpimat_1->Mvctx,tempVec, mpimat_1->lvec,INSERT_VALUES,SCATTER_FORWARD);
446     CHKERRQ(ierr);
447     ierr =   VecScatterEnd(mpimat_1->Mvctx,tempVec, mpimat_1->lvec,INSERT_VALUES,SCATTER_FORWARD);
448     CHKERRQ(ierr);
449     ierr = VecGetArray( mpimat_1->lvec, &cpcol_1_state ); CHKERRQ(ierr);
450     /* get 'cpcol_2_state' */
451     ierr = VecScatterBegin(mpimat_2->Mvctx,tempVec, mpimat_2->lvec,INSERT_VALUES,SCATTER_FORWARD);
452     CHKERRQ(ierr);
453     ierr =   VecScatterEnd(mpimat_2->Mvctx,tempVec, mpimat_2->lvec,INSERT_VALUES,SCATTER_FORWARD);
454     CHKERRQ(ierr);
455     ierr = VecGetArray( mpimat_2->lvec, &cpcol_2_state ); CHKERRQ(ierr);
456     /* get 'cpcol_2_par_orig' */
457     for(kk=0,j=my0;kk<nloc;kk++,j++){
458       PetscScalar v = (PetscScalar)lid_parent_gid[kk];
459       ierr = VecSetValues( tempVec, 1, &j, &v, INSERT_VALUES );  CHKERRQ(ierr);
460     }
461     ierr = VecAssemblyBegin( tempVec ); CHKERRQ(ierr);
462     ierr = VecAssemblyEnd( tempVec ); CHKERRQ(ierr);
463     ierr = VecDuplicate( mpimat_2->lvec, &ghost_par_orig2 ); CHKERRQ(ierr);
464     ierr = VecScatterBegin(mpimat_2->Mvctx,tempVec, ghost_par_orig2,INSERT_VALUES,SCATTER_FORWARD);
465     CHKERRQ(ierr);
466     ierr =   VecScatterEnd(mpimat_2->Mvctx,tempVec, ghost_par_orig2,INSERT_VALUES,SCATTER_FORWARD);
467     CHKERRQ(ierr);
468     ierr = VecGetArray( ghost_par_orig2, &cpcol_2_par_orig ); CHKERRQ(ierr);
469 
470     ierr = VecDestroy( &tempVec ); CHKERRQ(ierr);
471   } /* ismpi */
472 
473   /* doit */
474   for(lid=0;lid<nloc;lid++){
475     NState state = lid_state[lid];
476     if( IS_SELECTED(state) ) {
477       /* steal locals */
478       ii = matA_1->i; n = ii[lid+1] - ii[lid];
479       idx = matA_1->j + ii[lid];
480       for (j=0; j<n; j++) {
481         PetscInt lidj = idx[j], sgid;
482         NState statej = lid_state[lidj];
483         if (statej==DELETED && (sgid=(PetscInt)PetscRealPart(lid_parent_gid[lidj])) != lid+my0) { /* steal local */
484           lid_parent_gid[lidj] = (PetscScalar)(lid+my0); /* send this if sgid is not local */
485           if( sgid >= my0 && sgid < Iend ){       /* I'm stealing this local from a local sgid */
486             PetscInt hav=0,slid=sgid-my0,gidj=lidj+my0;
487             PetscCDPos pos,last=PETSC_NULL;
488             /* looking for local from local so id_llist_2 works */
489             ierr = PetscCDGetHeadPos(aggs_2,slid,&pos); CHKERRQ(ierr);
490             while(pos){
491               PetscInt gid;
492               ierr = PetscLLNGetID( pos, &gid ); CHKERRQ(ierr);
493               if( gid == gidj ) {
494                 assert(last);
495                 ierr = PetscCDRemoveNextNode( aggs_2, slid, last ); CHKERRQ(ierr);
496                 ierr = PetscCDAppendNode( aggs_2, lid, pos );       CHKERRQ(ierr);
497                 hav = 1;
498                 break;
499               }
500               else last = pos;
501 
502               ierr = PetscCDGetNextPos(aggs_2,slid,&pos); CHKERRQ(ierr);
503             }
504             if(hav!=1){
505               if(hav==0)SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"failed to find adj in 'selected' lists - structurally unsymmetric matrix");
506               SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"found node %d times???",hav);
507             }
508           }
509           else{            /* I'm stealing this local, owned by a ghost */
510             assert(sgid==-1);
511             ierr = PetscCDAppendID( aggs_2, lid, lidj+my0 );      CHKERRQ(ierr);
512           }
513         }
514       } /* local neighbors */
515     }
516     else if( state == DELETED && lid_cprowID_1 ) {
517       PetscInt sgidold = (PetscInt)PetscRealPart(lid_parent_gid[lid]);
518       /* see if I have a selected ghost neighbor that will steal me */
519       if( (ix=lid_cprowID_1[lid]) != -1 ){
520         ii = matB_1->compressedrow.i; n = ii[ix+1] - ii[ix];
521         idx = matB_1->j + ii[ix];
522         for( j=0 ; j<n ; j++ ) {
523           PetscInt cpid = idx[j];
524           NState statej = (NState)PetscRealPart(cpcol_1_state[cpid]);
525           if( IS_SELECTED(statej) && sgidold != (PetscInt)statej ) { /* ghost will steal this, remove from my list */
526             lid_parent_gid[lid] = (PetscScalar)statej; /* send who selected */
527             if( sgidold>=my0 && sgidold<Iend ) { /* this was mine */
528               PetscInt hav=0,oldslidj=sgidold-my0;
529               PetscCDPos pos,last=PETSC_NULL;
530               /* remove from 'oldslidj' list */
531               ierr = PetscCDGetHeadPos(aggs_2,oldslidj,&pos); CHKERRQ(ierr);
532               while( pos ) {
533                 PetscInt gid;
534                 ierr = PetscLLNGetID( pos, &gid ); CHKERRQ(ierr);
535                 if( lid+my0 == gid ) {
536                   /* id_llist_2[lastid] = id_llist_2[flid];   /\* remove lid from oldslidj list *\/ */
537                   assert(last);
538                   ierr = PetscCDRemoveNextNode( aggs_2, oldslidj, last ); CHKERRQ(ierr);
539                   /* ghost (PetscScalar)statej will add this later */
540                   hav = 1;
541                   break;
542                 }
543                 else last = pos;
544 
545                 ierr = PetscCDGetNextPos(aggs_2,oldslidj,&pos); CHKERRQ(ierr);
546               }
547               if(hav!=1){
548                 if(hav==0)SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"failed to find adj in 'selected' lists - structurally unsymmetric matrix");
549                 SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"found node %d times???",hav);
550               }
551             }
552             else {
553               /* ghosts remove this later */
554             }
555           }
556         }
557       }
558     } /* selected/deleted */
559   } /* node loop */
560 
561   if( isMPI ) {
562     PetscScalar *cpcol_2_parent,*cpcol_2_gid;
563     Vec          tempVec,ghostgids2,ghostparents2;
564     PetscInt     cpid,nghost_2;
565     GAMGHashTable gid_cpid;
566 
567     ierr = VecGetSize( mpimat_2->lvec, &nghost_2 );   CHKERRQ(ierr);
568     ierr = MatGetVecs( Gmat_2, &tempVec, 0 );         CHKERRQ(ierr);
569 
570     /* get 'cpcol_2_parent' */
571     for(kk=0,j=my0;kk<nloc;kk++,j++){
572       ierr = VecSetValues( tempVec, 1, &j, &lid_parent_gid[kk], INSERT_VALUES );  CHKERRQ(ierr);
573     }
574     ierr = VecAssemblyBegin( tempVec ); CHKERRQ(ierr);
575     ierr = VecAssemblyEnd( tempVec ); CHKERRQ(ierr);
576     ierr = VecDuplicate( mpimat_2->lvec, &ghostparents2 ); CHKERRQ(ierr);
577     ierr = VecScatterBegin(mpimat_2->Mvctx,tempVec, ghostparents2,INSERT_VALUES,SCATTER_FORWARD);
578     CHKERRQ(ierr);
579     ierr =   VecScatterEnd(mpimat_2->Mvctx,tempVec, ghostparents2,INSERT_VALUES,SCATTER_FORWARD);
580     CHKERRQ(ierr);
581     ierr = VecGetArray( ghostparents2, &cpcol_2_parent ); CHKERRQ(ierr);
582 
583     /* get 'cpcol_2_gid' */
584     for(kk=0,j=my0;kk<nloc;kk++,j++){
585       PetscScalar v = (PetscScalar)j;
586       ierr = VecSetValues( tempVec, 1, &j, &v, INSERT_VALUES );  CHKERRQ(ierr);
587     }
588     ierr = VecAssemblyBegin( tempVec ); CHKERRQ(ierr);
589     ierr = VecAssemblyEnd( tempVec ); CHKERRQ(ierr);
590     ierr = VecDuplicate( mpimat_2->lvec, &ghostgids2 ); CHKERRQ(ierr);
591     ierr = VecScatterBegin(mpimat_2->Mvctx,tempVec, ghostgids2,INSERT_VALUES,SCATTER_FORWARD);
592     CHKERRQ(ierr);
593     ierr =   VecScatterEnd(mpimat_2->Mvctx,tempVec, ghostgids2,INSERT_VALUES,SCATTER_FORWARD);
594     CHKERRQ(ierr);
595     ierr = VecGetArray( ghostgids2, &cpcol_2_gid ); CHKERRQ(ierr);
596 
597     ierr = VecDestroy( &tempVec ); CHKERRQ(ierr);
598 
599     /* look for deleted ghosts and add to table */
600     ierr = GAMGTableCreate( 2*nghost_2, &gid_cpid ); CHKERRQ(ierr);
601     for( cpid = 0 ; cpid < nghost_2 ; cpid++ ) {
602       NState state = (NState)PetscRealPart(cpcol_2_state[cpid]);
603       if( state==DELETED ) {
604         PetscInt sgid_new = (PetscInt)PetscRealPart(cpcol_2_parent[cpid]);
605         PetscInt sgid_old = (PetscInt)PetscRealPart(cpcol_2_par_orig[cpid]);
606         if( sgid_old == -1 && sgid_new != -1 ) {
607           PetscInt gid = (PetscInt)PetscRealPart(cpcol_2_gid[cpid]);
608           ierr = GAMGTableAdd( &gid_cpid, gid, cpid ); CHKERRQ(ierr);
609         }
610       }
611     }
612 
613     /* look for deleted ghosts and see if they moved - remove it */
614     for(lid=0;lid<nloc;lid++){
615       NState state = lid_state[lid];
616       if( IS_SELECTED(state) ){
617         PetscCDPos pos,last=PETSC_NULL;
618         /* look for deleted ghosts and see if they moved */
619         ierr = PetscCDGetHeadPos(aggs_2,lid,&pos); CHKERRQ(ierr);
620         while(pos){
621           PetscInt gid;
622           ierr = PetscLLNGetID( pos, &gid ); CHKERRQ(ierr);
623 
624           if( gid < my0 || gid >= Iend ) {
625             ierr = GAMGTableFind( &gid_cpid, gid, &cpid ); CHKERRQ(ierr);
626             if( cpid != -1 ) {
627               /* a moved ghost - */
628               /* id_llist_2[lastid] = id_llist_2[flid];    /\* remove 'flid' from list *\/ */
629               ierr = PetscCDRemoveNextNode( aggs_2, lid, last ); CHKERRQ(ierr);
630             }
631             else last = pos;
632           }
633           else last = pos;
634 
635           ierr = PetscCDGetNextPos(aggs_2,lid,&pos); CHKERRQ(ierr);
636         } /* loop over list of deleted */
637       } /* selected */
638     }
639     ierr = GAMGTableDestroy( &gid_cpid ); CHKERRQ(ierr);
640 
641     /* look at ghosts, see if they changed - and it */
642     for( cpid = 0 ; cpid < nghost_2 ; cpid++ ){
643       PetscInt sgid_new = (PetscInt)PetscRealPart(cpcol_2_parent[cpid]);
644       if( sgid_new >= my0 && sgid_new < Iend ) { /* this is mine */
645         PetscInt gid = (PetscInt)PetscRealPart(cpcol_2_gid[cpid]);
646         PetscInt slid_new=sgid_new-my0,hav=0;
647         PetscCDPos pos;
648         /* search for this gid to see if I have it */
649         ierr = PetscCDGetHeadPos(aggs_2,slid_new,&pos); CHKERRQ(ierr);
650         while(pos){
651           PetscInt gidj;
652           ierr = PetscLLNGetID( pos, &gidj ); CHKERRQ(ierr);
653           ierr = PetscCDGetNextPos(aggs_2,slid_new,&pos); CHKERRQ(ierr);
654 
655           if( gidj == gid ) { hav = 1; break; }
656         }
657         if( hav != 1 ){
658           /* insert 'flidj' into head of llist */
659           ierr = PetscCDAppendID( aggs_2, slid_new, gid );      CHKERRQ(ierr);
660         }
661       }
662     }
663 
664     ierr = VecRestoreArray( mpimat_1->lvec, &cpcol_1_state ); CHKERRQ(ierr);
665     ierr = VecRestoreArray( mpimat_2->lvec, &cpcol_2_state ); CHKERRQ(ierr);
666     ierr = VecRestoreArray( ghostparents2, &cpcol_2_parent ); CHKERRQ(ierr);
667     ierr = VecRestoreArray( ghostgids2, &cpcol_2_gid ); CHKERRQ(ierr);
668     ierr = PetscFree( lid_cprowID_1 );  CHKERRQ(ierr);
669     ierr = VecDestroy( &ghostgids2 ); CHKERRQ(ierr);
670     ierr = VecDestroy( &ghostparents2 ); CHKERRQ(ierr);
671     ierr = VecDestroy( &ghost_par_orig2 ); CHKERRQ(ierr);
672   }
673 
674   ierr = PetscFree( lid_parent_gid );  CHKERRQ(ierr);
675   ierr = PetscFree( lid_state );  CHKERRQ(ierr);
676 
677   PetscFunctionReturn(0);
678 }
679 
680 /* -------------------------------------------------------------------------- */
681 /*
682    PCSetData_AGG - called if data is not set with PCSetCoordinates.
683       Looks in Mat for near null space.
684       Does not work for Stokes
685 
686   Input Parameter:
687    . pc -
688    . a_A - matrix to get (near) null space out of.
689 */
690 #undef __FUNCT__
691 #define __FUNCT__ "PCSetData_AGG"
692 PetscErrorCode PCSetData_AGG( PC pc, Mat a_A )
693 {
694   PetscErrorCode  ierr;
695   PC_MG          *mg = (PC_MG*)pc->data;
696   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
697   MatNullSpace mnull;
698 
699   PetscFunctionBegin;
700   ierr = MatGetNearNullSpace( a_A, &mnull ); CHKERRQ(ierr);
701   if( !mnull ) {
702     PetscInt bs,NN,MM;
703     ierr = MatGetBlockSize( a_A, &bs ); CHKERRQ( ierr );
704     ierr = MatGetLocalSize( a_A, &MM, &NN ); CHKERRQ( ierr );  assert(MM%bs==0);
705 PetscPrintf(((PetscObject)a_A)->comm,"[%d]%s bs=%d MM=%d\n",0,__FUNCT__,bs,MM);
706     ierr = PCSetCoordinates_AGG( pc, bs, MM/bs, PETSC_NULL ); CHKERRQ(ierr);
707   }
708   else {
709     PetscReal *nullvec;
710     PetscBool has_const;
711     PetscInt i,j,mlocal,nvec,bs;
712     const Vec *vecs; const PetscScalar *v;
713     ierr = MatGetLocalSize(a_A,&mlocal,PETSC_NULL);CHKERRQ(ierr);
714     ierr = MatNullSpaceGetVecs( mnull, &has_const, &nvec, &vecs ); CHKERRQ(ierr);
715     ierr = PetscMalloc((nvec+!!has_const)*mlocal*sizeof *nullvec,&nullvec);CHKERRQ(ierr);
716     if (has_const) for (i=0; i<mlocal; i++) nullvec[i] = 1.0;
717     for (i=0; i<nvec; i++) {
718       ierr = VecGetArrayRead(vecs[i],&v);CHKERRQ(ierr);
719       for (j=0; j<mlocal; j++) nullvec[(i+!!has_const)*mlocal + j] = PetscRealPart(v[j]);
720       ierr = VecRestoreArrayRead(vecs[i],&v);CHKERRQ(ierr);
721     }
722     pc_gamg->data = nullvec;
723     pc_gamg->data_cell_cols = (nvec+!!has_const);
724     ierr = MatGetBlockSize( a_A, &bs ); CHKERRQ( ierr ); /* this does not work for Stokes */
725     pc_gamg->data_cell_rows = bs;
726   }
727   PetscFunctionReturn(0);
728 }
729 
730 /* -------------------------------------------------------------------------- */
731 /*
732  formProl0
733 
734    Input Parameter:
735    . agg_llists - list of arrays with aggregates
736    . bs - block size
737    . nSAvec - column bs of new P
738    . my0crs - global index of start of locals
739    . data_stride - bs*(nloc nodes + ghost nodes)
740    . data_in[data_stride*nSAvec] - local data on fine grid
741    . flid_fgid[data_stride/bs] - make local to global IDs, includes ghosts in 'locals_llist'
742   Output Parameter:
743    . a_data_out - in with fine grid data (w/ghosts), out with coarse grid data
744    . a_Prol - prolongation operator
745 */
746 #undef __FUNCT__
747 #define __FUNCT__ "formProl0"
748 static PetscErrorCode formProl0(const PetscCoarsenData *agg_llists,/* list from selected vertices of aggregate unselected vertices */
749                                 const PetscInt bs,          /* (row) block size */
750                                 const PetscInt nSAvec,      /* column bs */
751                                 const PetscInt my0crs,      /* global index of start of locals */
752                                 const PetscInt data_stride, /* (nloc+nghost)*bs */
753                                 PetscReal      data_in[],   /* [data_stride][nSAvec] */
754                                 const PetscInt flid_fgid[], /* [data_stride/bs] */
755                                 PetscReal **a_data_out,
756                                 Mat a_Prol /* prolongation operator (output)*/
757                                 )
758 {
759   PetscErrorCode ierr;
760   PetscInt  Istart,my0,Iend,nloc,clid,flid,aggID,kk,jj,ii,mm,ndone,nSelected,minsz,nghosts,out_data_stride;
761   MPI_Comm       wcomm = ((PetscObject)a_Prol)->comm;
762   PetscMPIInt    mype, npe;
763   PetscReal      *out_data;
764   PetscCDPos         pos;
765   GAMGHashTable  fgid_flid;
766 
767 /* #define OUT_AGGS */
768 #ifdef OUT_AGGS
769   static PetscInt llev = 0; char fname[32]; FILE *file = PETSC_NULL; PetscInt pM;
770 #endif
771 
772   PetscFunctionBegin;
773   ierr = MPI_Comm_rank(wcomm,&mype);CHKERRQ(ierr);
774   ierr = MPI_Comm_size(wcomm,&npe);CHKERRQ(ierr);
775   ierr = MatGetOwnershipRange( a_Prol, &Istart, &Iend );    CHKERRQ(ierr);
776   nloc = (Iend-Istart)/bs; my0 = Istart/bs; assert((Iend-Istart)%bs==0);
777   Iend /= bs;
778   nghosts = data_stride/bs - nloc;
779 
780   ierr = GAMGTableCreate( 2*nghosts, &fgid_flid ); CHKERRQ(ierr);
781   for(kk=0;kk<nghosts;kk++) {
782     ierr = GAMGTableAdd( &fgid_flid, flid_fgid[nloc+kk], nloc+kk ); CHKERRQ(ierr);
783   }
784 
785 #ifdef OUT_AGGS
786   sprintf(fname,"aggs_%d_%d.m",llev++,mype);
787   if(llev==1) {
788     file = fopen(fname,"w");
789   }
790   MatGetSize( a_Prol, &pM, &jj );
791 #endif
792 
793   /* count selected -- same as number of cols of P */
794   for(nSelected=mm=0;mm<nloc;mm++) {
795     PetscBool ise;
796     ierr = PetscCDEmptyAt( agg_llists, mm, &ise ); CHKERRQ(ierr);
797     if( !ise ) nSelected++;
798   }
799   ierr = MatGetOwnershipRangeColumn( a_Prol, &ii, &jj ); CHKERRQ(ierr);
800   assert((ii/nSAvec)==my0crs); assert(nSelected==(jj-ii)/nSAvec);
801 
802   /* aloc space for coarse point data (output) */
803   out_data_stride = nSelected*nSAvec;
804   ierr = PetscMalloc( out_data_stride*nSAvec*sizeof(PetscReal), &out_data ); CHKERRQ(ierr);
805   for(ii=0;ii<out_data_stride*nSAvec;ii++) {
806     out_data[ii]=1.e300;
807   }
808   *a_data_out = out_data; /* output - stride nSelected*nSAvec */
809 
810   /* find points and set prolongation */
811   minsz = 100;
812   ndone = 0;
813   for( mm = clid = 0 ; mm < nloc ; mm++ ){
814     ierr = PetscCDSizeAt( agg_llists, mm, &jj ); CHKERRQ(ierr);
815     if( jj > 0 ) {
816       const PetscInt lid = mm, cgid = my0crs + clid;
817       PetscInt cids[100]; /* max bs */
818       PetscBLASInt asz=jj,M=asz*bs,N=nSAvec,INFO;
819       PetscBLASInt   Mdata=M+((N-M>0)?N-M:0),LDA=Mdata,LWORK=N*bs;
820       PetscScalar    *qqc,*qqr,*TAU,*WORK;
821       PetscInt       *fids;
822       PetscReal      *data;
823       /* count agg */
824       if( asz<minsz ) minsz = asz;
825 
826       /* get block */
827       ierr = PetscMalloc( (Mdata*N)*sizeof(PetscScalar), &qqc ); CHKERRQ(ierr);
828       ierr = PetscMalloc( (M*N)*sizeof(PetscScalar), &qqr ); CHKERRQ(ierr);
829       ierr = PetscMalloc( N*sizeof(PetscScalar), &TAU ); CHKERRQ(ierr);
830       ierr = PetscMalloc( LWORK*sizeof(PetscScalar), &WORK ); CHKERRQ(ierr);
831       ierr = PetscMalloc( M*sizeof(PetscInt), &fids ); CHKERRQ(ierr);
832 
833       aggID = 0;
834       ierr = PetscCDGetHeadPos(agg_llists,lid,&pos); CHKERRQ(ierr);
835       while(pos){
836         PetscInt gid1;
837         ierr = PetscLLNGetID( pos, &gid1 ); CHKERRQ(ierr);
838         ierr = PetscCDGetNextPos(agg_llists,lid,&pos); CHKERRQ(ierr);
839 
840         if( gid1 >= my0 && gid1 < Iend ) flid = gid1 - my0;
841         else {
842           ierr = GAMGTableFind( &fgid_flid, gid1, &flid ); CHKERRQ(ierr);
843           assert(flid>=0);
844         }
845         /* copy in B_i matrix - column oriented */
846         data = &data_in[flid*bs];
847         for( kk = ii = 0; ii < bs ; ii++ ) {
848           for( jj = 0; jj < N ; jj++ ) {
849             PetscReal d = data[jj*data_stride + ii];
850             qqc[jj*Mdata + aggID*bs + ii] = d;
851           }
852         }
853 #ifdef OUT_AGGS
854         if(llev==1) {
855           char str[] = "plot(%e,%e,'r*'), hold on,\n", col[] = "rgbkmc", sim[] = "*os+h>d<vx^";
856           PetscInt MM,pi,pj;
857           str[12] = col[(clid+17*mype)%6]; str[13] = sim[(clid+17*mype)%11];
858           MM = (PetscInt)(PetscSqrtReal((PetscReal)pM));
859           pj = gid1/MM; pi = gid1%MM;
860           fprintf(file,str,(double)pi,(double)pj);
861           /* fprintf(file,str,data[2*data_stride+1],-data[2*data_stride]); */
862         }
863 #endif
864         /* set fine IDs */
865         for(kk=0;kk<bs;kk++) fids[aggID*bs + kk] = flid_fgid[flid]*bs + kk;
866 
867         aggID++;
868       }
869 
870       /* pad with zeros */
871       for( ii = asz*bs; ii < Mdata ; ii++ ) {
872 	for( jj = 0; jj < N ; jj++, kk++ ) {
873 	  qqc[jj*Mdata + ii] = .0;
874 	}
875       }
876 
877       ndone += aggID;
878       /* QR */
879       LAPACKgeqrf_( &Mdata, &N, qqc, &LDA, TAU, WORK, &LWORK, &INFO );
880       if( INFO != 0 ) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"xGEQRS error");
881       /* get R - column oriented - output B_{i+1} */
882       {
883         PetscReal *data = &out_data[clid*nSAvec];
884         for( jj = 0; jj < nSAvec ; jj++ ) {
885           for( ii = 0; ii < nSAvec ; ii++ ) {
886             assert(data[jj*out_data_stride + ii] == 1.e300);
887             if( ii <= jj ) data[jj*out_data_stride + ii] = PetscRealPart(qqc[jj*Mdata + ii]);
888 	    else data[jj*out_data_stride + ii] = 0.;
889           }
890         }
891       }
892 
893       /* get Q - row oriented */
894       LAPACKungqr_( &Mdata, &N, &N, qqc, &LDA, TAU, WORK, &LWORK, &INFO );
895       if( INFO != 0 ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"xORGQR error arg %d",-INFO);
896 
897       for( ii = 0 ; ii < M ; ii++ ){
898         for( jj = 0 ; jj < N ; jj++ ) {
899           qqr[N*ii + jj] = qqc[jj*Mdata + ii];
900         }
901       }
902 
903       /* add diagonal block of P0 */
904       for(kk=0;kk<N;kk++) {
905         cids[kk] = N*cgid + kk; /* global col IDs in P0 */
906       }
907       ierr = MatSetValues(a_Prol,M,fids,N,cids,qqr,INSERT_VALUES); CHKERRQ(ierr);
908 
909       ierr = PetscFree( qqc );  CHKERRQ(ierr);
910       ierr = PetscFree( qqr );  CHKERRQ(ierr);
911       ierr = PetscFree( TAU );  CHKERRQ(ierr);
912       ierr = PetscFree( WORK );  CHKERRQ(ierr);
913       ierr = PetscFree( fids );  CHKERRQ(ierr);
914       clid++;
915     } /* coarse agg */
916   } /* for all fine nodes */
917   ierr = MatAssemblyBegin(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
918   ierr = MatAssemblyEnd(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
919 
920 /* ierr = MPI_Allreduce( &ndone, &ii, 1, MPIU_INT, MPIU_SUM, wcomm ); */
921 /* MatGetSize( a_Prol, &kk, &jj ); */
922 /* ierr = MPI_Allreduce( &minsz, &jj, 1, MPIU_INT, MPIU_MIN, wcomm ); */
923 /* PetscPrintf(wcomm," **** [%d]%s %d total done, %d nodes (%d local done), min agg. size = %d\n",mype,__FUNCT__,ii,kk/bs,ndone,jj); */
924 
925 #ifdef OUT_AGGS
926   if(llev==1) fclose(file);
927 #endif
928   ierr = GAMGTableDestroy( &fgid_flid ); CHKERRQ(ierr);
929 
930   PetscFunctionReturn(0);
931 }
932 
933 /* -------------------------------------------------------------------------- */
934 /*
935    PCGAMGgraph_AGG
936 
937   Input Parameter:
938    . pc - this
939    . Amat - matrix on this fine level
940   Output Parameter:
941    . a_Gmat -
942 */
943 #undef __FUNCT__
944 #define __FUNCT__ "PCGAMGgraph_AGG"
945 PetscErrorCode PCGAMGgraph_AGG( PC pc,
946                                 const Mat Amat,
947                                 Mat *a_Gmat
948                                 )
949 {
950   PetscErrorCode ierr;
951   PC_MG          *mg = (PC_MG*)pc->data;
952   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
953   const PetscInt verbose = pc_gamg->verbose;
954   const PetscReal vfilter = pc_gamg->threshold;
955   PC_GAMG_AGG    *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
956   PetscMPIInt    mype,npe;
957   Mat            Gmat;
958   MPI_Comm       wcomm = ((PetscObject)Amat)->comm;
959   PetscBool  set,flg,symm;
960 
961   PetscFunctionBegin;
962 #if defined PETSC_USE_LOG
963   ierr = PetscLogEventBegin(PC_GAMGGgraph_AGG,0,0,0,0);CHKERRQ(ierr);
964 #endif
965   ierr = MPI_Comm_rank( wcomm, &mype);  CHKERRQ(ierr);
966   ierr = MPI_Comm_size( wcomm, &npe);   CHKERRQ(ierr);
967 
968   ierr = MatIsSymmetricKnown(Amat, &set, &flg);        CHKERRQ(ierr);
969   symm = (PetscBool)(pc_gamg_agg->sym_graph || !(set && flg));
970 
971   ierr  = PCGAMGCreateGraph( Amat, &Gmat ); CHKERRQ( ierr );
972   ierr  = PCGAMGFilterGraph( &Gmat, vfilter, symm, verbose ); CHKERRQ( ierr );
973 
974   *a_Gmat = Gmat;
975 
976 #if defined PETSC_USE_LOG
977   ierr = PetscLogEventEnd(PC_GAMGGgraph_AGG,0,0,0,0);CHKERRQ(ierr);
978 #endif
979   PetscFunctionReturn(0);
980 }
981 
982 /* -------------------------------------------------------------------------- */
983 /*
984    PCGAMGCoarsen_AGG
985 
986   Input Parameter:
987    . a_pc - this
988   Input/Output Parameter:
989    . a_Gmat1 - graph on this fine level - coarsening can change this (squares it)
990   Output Parameter:
991    . agg_lists - list of aggregates
992 */
993 #undef __FUNCT__
994 #define __FUNCT__ "PCGAMGCoarsen_AGG"
995 PetscErrorCode PCGAMGCoarsen_AGG( PC a_pc,
996                                   Mat *a_Gmat1,
997                                   PetscCoarsenData **agg_lists
998                                   )
999 {
1000   PetscErrorCode ierr;
1001   PC_MG          *mg = (PC_MG*)a_pc->data;
1002   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
1003   PC_GAMG_AGG    *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
1004   Mat             mat,Gmat2, Gmat1 = *a_Gmat1; /* squared graph */
1005   IS              perm;
1006   PetscInt        Ii,nloc,bs,n,m;
1007   PetscInt *permute;
1008   PetscBool *bIndexSet;
1009   MatCoarsen crs;
1010   MPI_Comm        wcomm = ((PetscObject)Gmat1)->comm;
1011   PetscMPIInt     mype,npe;
1012 
1013   PetscFunctionBegin;
1014 #if defined PETSC_USE_LOG
1015   ierr = PetscLogEventBegin(PC_GAMGCoarsen_AGG,0,0,0,0);CHKERRQ(ierr);
1016 #endif
1017   ierr = MPI_Comm_rank( wcomm, &mype);  CHKERRQ(ierr);
1018   ierr = MPI_Comm_size( wcomm, &npe);   CHKERRQ(ierr);
1019   ierr = MatGetLocalSize( Gmat1, &n, &m ); CHKERRQ(ierr);
1020   ierr = MatGetBlockSize( Gmat1, &bs ); CHKERRQ(ierr); assert(bs==1);
1021   nloc = n/bs;
1022 
1023   if( pc_gamg_agg->square_graph ) {
1024     ierr = MatTransposeMatMult( Gmat1, Gmat1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Gmat2 );
1025     CHKERRQ(ierr);
1026   }
1027   else Gmat2 = Gmat1;
1028 
1029   /* get MIS aggs */
1030   /* randomize */
1031   ierr = PetscMalloc( nloc*sizeof(PetscInt), &permute ); CHKERRQ(ierr);
1032   ierr = PetscMalloc( nloc*sizeof(PetscBool), &bIndexSet ); CHKERRQ(ierr);
1033   for ( Ii = 0; Ii < nloc ; Ii++ ){
1034     bIndexSet[Ii] = PETSC_FALSE;
1035     permute[Ii] = Ii;
1036   }
1037   srand(1); /* make deterministic */
1038   for ( Ii = 0; Ii < nloc ; Ii++ ) {
1039     PetscInt iSwapIndex = rand()%nloc;
1040     if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
1041       PetscInt iTemp = permute[iSwapIndex];
1042       permute[iSwapIndex] = permute[Ii];
1043       permute[Ii] = iTemp;
1044       bIndexSet[iSwapIndex] = PETSC_TRUE;
1045     }
1046   }
1047   ierr = PetscFree( bIndexSet );  CHKERRQ(ierr);
1048 
1049   ierr = ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_USE_POINTER, &perm);
1050   CHKERRQ(ierr);
1051 #if defined PETSC_GAMG_USE_LOG
1052   ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET4],0,0,0,0);CHKERRQ(ierr);
1053 #endif
1054   ierr = MatCoarsenCreate( wcomm, &crs ); CHKERRQ(ierr);
1055   /* ierr = MatCoarsenSetType( crs, MATCOARSENMIS ); CHKERRQ(ierr); */
1056   ierr = MatCoarsenSetFromOptions( crs ); CHKERRQ(ierr);
1057   ierr = MatCoarsenSetGreedyOrdering( crs, perm ); CHKERRQ(ierr);
1058   ierr = MatCoarsenSetAdjacency( crs, Gmat2 ); CHKERRQ(ierr);
1059   ierr = MatCoarsenSetVerbose( crs, pc_gamg->verbose ); CHKERRQ(ierr);
1060   ierr = MatCoarsenSetStrictAggs( crs, PETSC_TRUE ); CHKERRQ(ierr);
1061   ierr = MatCoarsenApply( crs ); CHKERRQ(ierr);
1062   ierr = MatCoarsenGetData( crs, agg_lists ); CHKERRQ(ierr); /* output */
1063   ierr = MatCoarsenDestroy( &crs ); CHKERRQ(ierr);
1064 
1065   ierr = ISDestroy( &perm );                    CHKERRQ(ierr);
1066   ierr = PetscFree( permute );  CHKERRQ(ierr);
1067 #if defined PETSC_GAMG_USE_LOG
1068   ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET4],0,0,0,0);CHKERRQ(ierr);
1069 #endif
1070   /* smooth aggs */
1071   if( Gmat2 != Gmat1 ) {
1072     const PetscCoarsenData *llist = *agg_lists;
1073     ierr = smoothAggs( Gmat2, Gmat1, *agg_lists ); CHKERRQ(ierr);
1074     ierr = MatDestroy( &Gmat1 );  CHKERRQ(ierr);
1075     *a_Gmat1 = Gmat2; /* output */
1076     ierr = PetscCDGetMat( llist, &mat );  CHKERRQ(ierr);
1077     if(mat) SETERRQ(wcomm,PETSC_ERR_ARG_WRONG, "Auxilary matrix with squared graph????");
1078   }
1079   else {
1080     const PetscCoarsenData *llist = *agg_lists;
1081     /* see if we have a matrix that takes pecedence (returned from MatCoarsenAppply) */
1082     ierr = PetscCDGetMat( llist, &mat );   CHKERRQ(ierr);
1083     if( mat ) {
1084       ierr = MatDestroy( &Gmat1 );  CHKERRQ(ierr);
1085       *a_Gmat1 = mat; /* output */
1086     }
1087   }
1088 #if defined PETSC_USE_LOG
1089   ierr = PetscLogEventEnd(PC_GAMGCoarsen_AGG,0,0,0,0);CHKERRQ(ierr);
1090 #endif
1091   PetscFunctionReturn(0);
1092 }
1093 
1094 /* -------------------------------------------------------------------------- */
1095 /*
1096  PCGAMGProlongator_AGG
1097 
1098  Input Parameter:
1099  . pc - this
1100  . Amat - matrix on this fine level
1101  . Graph - used to get ghost data for nodes in
1102  . agg_lists - list of aggregates
1103  Output Parameter:
1104  . a_P_out - prolongation operator to the next level
1105  */
1106 #undef __FUNCT__
1107 #define __FUNCT__ "PCGAMGProlongator_AGG"
1108 PetscErrorCode PCGAMGProlongator_AGG( PC pc,
1109                                       const Mat Amat,
1110                                       const Mat Gmat,
1111                                       PetscCoarsenData *agg_lists,
1112                                       Mat *a_P_out
1113                                       )
1114 {
1115   PC_MG          *mg = (PC_MG*)pc->data;
1116   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
1117   const PetscInt verbose = pc_gamg->verbose;
1118   const PetscInt data_cols = pc_gamg->data_cell_cols;
1119   PetscErrorCode ierr;
1120   PetscInt       Istart,Iend,nloc,ii,jj,kk,my0,nLocalSelected,bs;
1121   Mat            Prol;
1122   PetscMPIInt    mype, npe;
1123   MPI_Comm       wcomm = ((PetscObject)Amat)->comm;
1124   const PetscInt col_bs = data_cols;
1125   PetscReal      *data_w_ghost;
1126   PetscInt       myCrs0, nbnodes=0, *flid_fgid;
1127 
1128   PetscFunctionBegin;
1129 #if defined PETSC_USE_LOG
1130   ierr = PetscLogEventBegin(PC_GAMGProlongator_AGG,0,0,0,0);CHKERRQ(ierr);
1131 #endif
1132   ierr = MPI_Comm_rank( wcomm, &mype);  CHKERRQ(ierr);
1133   ierr = MPI_Comm_size( wcomm, &npe);   CHKERRQ(ierr);
1134   ierr = MatGetOwnershipRange( Amat, &Istart, &Iend ); CHKERRQ(ierr);
1135   ierr  = MatGetBlockSize( Amat, &bs ); CHKERRQ( ierr );
1136   nloc = (Iend-Istart)/bs; my0 = Istart/bs; assert((Iend-Istart)%bs==0);
1137 
1138   /* get 'nLocalSelected' */
1139   for( ii=0, nLocalSelected = 0 ; ii < nloc ; ii++ ){
1140     PetscBool ise;
1141     /* filter out singletons 0 or 1? */
1142     ierr = PetscCDEmptyAt( agg_lists, ii, &ise ); CHKERRQ(ierr);
1143     if( !ise ) nLocalSelected++;
1144   }
1145 
1146   /* create prolongator, create P matrix */
1147   ierr = MatCreate( wcomm, &Prol ); CHKERRQ(ierr);
1148   ierr = MatSetSizes(Prol,nloc*bs,nLocalSelected*col_bs,PETSC_DETERMINE,PETSC_DETERMINE);
1149   CHKERRQ(ierr);
1150   ierr = MatSetBlockSizes( Prol, bs, col_bs ); CHKERRQ(ierr);
1151   ierr = MatSetType( Prol, MATAIJ );   CHKERRQ(ierr);
1152   ierr = MatSeqAIJSetPreallocation( Prol, data_cols, PETSC_NULL);  CHKERRQ(ierr);
1153   ierr = MatMPIAIJSetPreallocation(Prol,data_cols, PETSC_NULL,data_cols, PETSC_NULL);CHKERRQ(ierr);
1154   /* nloc*bs, nLocalSelected*col_bs, */
1155   /* PETSC_DETERMINE, PETSC_DETERMINE, */
1156   /* data_cols, PETSC_NULL, data_cols, PETSC_NULL, */
1157   /* &Prol ); */
1158 
1159   /* can get all points "removed" */
1160   ierr =  MatGetSize( Prol, &kk, &ii ); CHKERRQ(ierr);
1161   if( ii==0 ) {
1162     if( verbose ) {
1163       PetscPrintf(wcomm,"[%d]%s no selected points on coarse grid\n",mype,__FUNCT__);
1164     }
1165     ierr = MatDestroy( &Prol );  CHKERRQ(ierr);
1166     *a_P_out = PETSC_NULL;  /* out */
1167     PetscFunctionReturn(0);
1168   }
1169   if( verbose ) {
1170     PetscPrintf(wcomm,"\t\t[%d]%s New grid %d nodes\n",mype,__FUNCT__,ii/col_bs);
1171   }
1172   ierr = MatGetOwnershipRangeColumn( Prol, &myCrs0, &kk ); CHKERRQ(ierr);
1173 
1174   assert((kk-myCrs0)%col_bs==0);
1175   myCrs0 = myCrs0/col_bs;
1176   assert((kk/col_bs-myCrs0)==nLocalSelected);
1177 
1178   /* create global vector of data in 'data_w_ghost' */
1179 #if defined PETSC_GAMG_USE_LOG
1180   ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET7],0,0,0,0);CHKERRQ(ierr);
1181 #endif
1182   if (npe > 1) { /*  */
1183     PetscReal *tmp_gdata,*tmp_ldata,*tp2;
1184     ierr = PetscMalloc( nloc*sizeof(PetscReal), &tmp_ldata ); CHKERRQ(ierr);
1185     for( jj = 0 ; jj < data_cols ; jj++ ){
1186       for( kk = 0 ; kk < bs ; kk++) {
1187         PetscInt ii,stride;
1188         const PetscReal *tp = pc_gamg->data + jj*bs*nloc + kk;
1189         for( ii = 0 ; ii < nloc ; ii++, tp += bs ){
1190           tmp_ldata[ii] = *tp;
1191         }
1192         ierr = PCGAMGGetDataWithGhosts( Gmat, 1, tmp_ldata, &stride, &tmp_gdata );
1193         CHKERRQ(ierr);
1194 
1195         if(jj==0 && kk==0) { /* now I know how many todal nodes - allocate */
1196           ierr = PetscMalloc( stride*bs*data_cols*sizeof(PetscReal), &data_w_ghost ); CHKERRQ(ierr);
1197           nbnodes = bs*stride;
1198         }
1199         tp2 = data_w_ghost + jj*bs*stride + kk;
1200         for( ii = 0 ; ii < stride ; ii++, tp2 += bs ){
1201           *tp2 = tmp_gdata[ii];
1202         }
1203         ierr = PetscFree( tmp_gdata ); CHKERRQ(ierr);
1204       }
1205     }
1206     ierr = PetscFree( tmp_ldata ); CHKERRQ(ierr);
1207   }
1208   else {
1209     nbnodes = bs*nloc;
1210     data_w_ghost = (PetscReal*)pc_gamg->data;
1211   }
1212 
1213   /* get P0 */
1214   if( npe > 1 ){
1215     PetscReal *fid_glid_loc,*fiddata;
1216     PetscInt stride;
1217 
1218     ierr = PetscMalloc( nloc*sizeof(PetscReal), &fid_glid_loc ); CHKERRQ(ierr);
1219     for(kk=0;kk<nloc;kk++) fid_glid_loc[kk] = (PetscReal)(my0+kk);
1220     ierr = PCGAMGGetDataWithGhosts( Gmat, 1, fid_glid_loc, &stride, &fiddata );
1221     CHKERRQ(ierr);
1222     ierr = PetscMalloc( stride*sizeof(PetscInt), &flid_fgid ); CHKERRQ(ierr);
1223     for(kk=0;kk<stride;kk++) flid_fgid[kk] = (PetscInt)fiddata[kk];
1224     ierr = PetscFree( fiddata ); CHKERRQ(ierr);
1225 
1226     assert(stride==nbnodes/bs);
1227     ierr = PetscFree( fid_glid_loc ); CHKERRQ(ierr);
1228   }
1229   else {
1230     ierr = PetscMalloc( nloc*sizeof(PetscInt), &flid_fgid ); CHKERRQ(ierr);
1231     for(kk=0;kk<nloc;kk++) flid_fgid[kk] = my0 + kk;
1232   }
1233 #if defined PETSC_GAMG_USE_LOG
1234   ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET7],0,0,0,0);CHKERRQ(ierr);
1235   ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET8],0,0,0,0);CHKERRQ(ierr);
1236 #endif
1237   {
1238     PetscReal *data_out = PETSC_NULL;
1239     ierr = formProl0( agg_lists, bs, data_cols, myCrs0, nbnodes,
1240                       data_w_ghost, flid_fgid, &data_out, Prol );
1241     CHKERRQ(ierr);
1242     ierr = PetscFree( pc_gamg->data ); CHKERRQ( ierr );
1243     pc_gamg->data = data_out;
1244     pc_gamg->data_cell_rows = data_cols;
1245     pc_gamg->data_sz = data_cols*data_cols*nLocalSelected;
1246   }
1247 #if defined PETSC_GAMG_USE_LOG
1248   ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET8],0,0,0,0);CHKERRQ(ierr);
1249 #endif
1250   if (npe > 1) ierr = PetscFree( data_w_ghost );      CHKERRQ(ierr);
1251   ierr = PetscFree( flid_fgid ); CHKERRQ(ierr);
1252 
1253   *a_P_out = Prol;  /* out */
1254 #if defined PETSC_USE_LOG
1255   ierr = PetscLogEventEnd(PC_GAMGProlongator_AGG,0,0,0,0);CHKERRQ(ierr);
1256 #endif
1257   PetscFunctionReturn(0);
1258 }
1259 
1260 /* -------------------------------------------------------------------------- */
1261 /*
1262    PCGAMGOptprol_AGG
1263 
1264   Input Parameter:
1265    . pc - this
1266    . Amat - matrix on this fine level
1267  In/Output Parameter:
1268    . a_P_out - prolongation operator to the next level
1269 */
1270 #undef __FUNCT__
1271 #define __FUNCT__ "PCGAMGOptprol_AGG"
1272 PetscErrorCode PCGAMGOptprol_AGG( PC pc,
1273                                   const Mat Amat,
1274                                   Mat *a_P
1275                                   )
1276 {
1277   PetscErrorCode ierr;
1278   PC_MG          *mg = (PC_MG*)pc->data;
1279   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
1280   const PetscInt verbose = pc_gamg->verbose;
1281   PC_GAMG_AGG    *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;
1282   PetscInt       jj;
1283   PetscMPIInt    mype,npe;
1284   Mat            Prol = *a_P;
1285   MPI_Comm       wcomm = ((PetscObject)Amat)->comm;
1286 
1287   PetscFunctionBegin;
1288 #if defined PETSC_USE_LOG
1289   ierr = PetscLogEventBegin(PC_GAMGOptprol_AGG,0,0,0,0);CHKERRQ(ierr);
1290 #endif
1291   ierr = MPI_Comm_rank( wcomm, &mype);  CHKERRQ(ierr);
1292   ierr = MPI_Comm_size( wcomm, &npe);   CHKERRQ(ierr);
1293 
1294   /* smooth P0 */
1295   for( jj = 0 ; jj < pc_gamg_agg->nsmooths ; jj++ ){
1296     Mat tMat;
1297     Vec diag;
1298     PetscReal alpha, emax, emin;
1299 #if defined PETSC_GAMG_USE_LOG
1300     ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET9],0,0,0,0);CHKERRQ(ierr);
1301 #endif
1302     if( jj == 0 ) {
1303       KSP eksp;
1304       Vec bb, xx;
1305       PC pc;
1306       ierr = MatGetVecs( Amat, &bb, 0 );         CHKERRQ(ierr);
1307       ierr = MatGetVecs( Amat, &xx, 0 );         CHKERRQ(ierr);
1308       {
1309         PetscRandom    rctx;
1310         ierr = PetscRandomCreate(wcomm,&rctx);CHKERRQ(ierr);
1311         ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
1312         ierr = VecSetRandom(bb,rctx);CHKERRQ(ierr);
1313         ierr = PetscRandomDestroy( &rctx ); CHKERRQ(ierr);
1314       }
1315       ierr = KSPCreate(wcomm,&eksp);                            CHKERRQ(ierr);
1316       ierr = KSPAppendOptionsPrefix( eksp, "gamg_est_");         CHKERRQ(ierr);
1317       ierr = KSPSetFromOptions( eksp );    CHKERRQ(ierr);
1318       ierr = KSPSetInitialGuessNonzero( eksp, PETSC_FALSE );    CHKERRQ(ierr);
1319       ierr = KSPSetOperators( eksp, Amat, Amat, SAME_NONZERO_PATTERN );
1320       CHKERRQ( ierr );
1321       ierr = KSPGetPC( eksp, &pc );                              CHKERRQ( ierr );
1322       ierr = PCSetType( pc, PCJACOBI ); CHKERRQ(ierr);  /* smoother */
1323       ierr = KSPSetTolerances(eksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,10);
1324       CHKERRQ(ierr);
1325       ierr = KSPSetNormType( eksp, KSP_NORM_NONE );                 CHKERRQ(ierr);
1326       ierr = KSPSetComputeSingularValues( eksp,PETSC_TRUE );        CHKERRQ(ierr);
1327 
1328       /* solve - keep stuff out of logging */
1329       ierr = PetscLogEventDeactivate(KSP_Solve);CHKERRQ(ierr);
1330       ierr = PetscLogEventDeactivate(PC_Apply);CHKERRQ(ierr);
1331       ierr = KSPSolve( eksp, bb, xx );                              CHKERRQ(ierr);
1332       ierr = PetscLogEventActivate(KSP_Solve);CHKERRQ(ierr);
1333       ierr = PetscLogEventActivate(PC_Apply);CHKERRQ(ierr);
1334 
1335       ierr = KSPComputeExtremeSingularValues( eksp, &emax, &emin ); CHKERRQ(ierr);
1336       if( verbose ) {
1337         PetscPrintf(wcomm,"\t\t\t%s smooth P0: max eigen=%e min=%e PC=%s\n",
1338                     __FUNCT__,emax,emin,PCJACOBI);
1339       }
1340       ierr = VecDestroy( &xx );       CHKERRQ(ierr);
1341       ierr = VecDestroy( &bb );       CHKERRQ(ierr);
1342       ierr = KSPDestroy( &eksp );     CHKERRQ(ierr);
1343 
1344       if( pc_gamg->emax_id == -1 ) {
1345         ierr = PetscObjectComposedDataRegister( &pc_gamg->emax_id );
1346         assert(pc_gamg->emax_id != -1 );
1347       }
1348       ierr = PetscObjectComposedDataSetScalar( (PetscObject)Amat, pc_gamg->emax_id, emax ); CHKERRQ(ierr);
1349     }
1350 
1351     /* smooth P1 := (I - omega/lam D^{-1}A)P0 */
1352     ierr = MatMatMult( Amat, Prol, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &tMat );   CHKERRQ(ierr);
1353     ierr = MatGetVecs( Amat, &diag, 0 );    CHKERRQ(ierr);
1354     ierr = MatGetDiagonal( Amat, diag );    CHKERRQ(ierr); /* effectively PCJACOBI */
1355     ierr = VecReciprocal( diag );         CHKERRQ(ierr);
1356     ierr = MatDiagonalScale( tMat, diag, 0 ); CHKERRQ(ierr);
1357     ierr = VecDestroy( &diag );           CHKERRQ(ierr);
1358     alpha = -1.5/emax;
1359     ierr = MatAYPX( tMat, alpha, Prol, SUBSET_NONZERO_PATTERN );           CHKERRQ(ierr);
1360     ierr = MatDestroy( &Prol );  CHKERRQ(ierr);
1361     Prol = tMat;
1362 #if defined PETSC_GAMG_USE_LOG
1363     ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET9],0,0,0,0);CHKERRQ(ierr);
1364 #endif
1365   }
1366 #if defined PETSC_USE_LOG
1367   ierr = PetscLogEventEnd(PC_GAMGOptprol_AGG,0,0,0,0);CHKERRQ(ierr);
1368 #endif
1369   *a_P = Prol;
1370 
1371   PetscFunctionReturn(0);
1372 }
1373 
1374 /* -------------------------------------------------------------------------- */
1375 /*
1376    PCGAMGKKTProl_AGG
1377 
1378   Input Parameter:
1379    . pc - this
1380    . Prol11 - matrix on this fine level
1381    . A21 - matrix on this fine level
1382  In/Output Parameter:
1383    . a_P22 - prolongation operator to the next level
1384 */
1385 #undef __FUNCT__
1386 #define __FUNCT__ "PCGAMGKKTProl_AGG"
1387 PetscErrorCode PCGAMGKKTProl_AGG( PC pc,
1388                                   const Mat Prol11,
1389                                   const Mat A21,
1390                                   Mat *a_P22
1391                                   )
1392 {
1393   PetscErrorCode ierr;
1394   PC_MG          *mg = (PC_MG*)pc->data;
1395   PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
1396   const PetscInt verbose = pc_gamg->verbose;
1397   /* PC_GAMG_AGG    *pc_gamg_agg = (PC_GAMG_AGG*)pc_gamg->subctx;  */
1398   PetscMPIInt    mype,npe;
1399   Mat            Prol22,Tmat,Gmat;
1400   MPI_Comm       wcomm = ((PetscObject)pc)->comm;
1401   PetscCoarsenData *agg_lists;
1402 
1403   PetscFunctionBegin;
1404 #if defined PETSC_USE_LOG
1405   ierr = PetscLogEventBegin(PC_GAMGKKTProl_AGG,0,0,0,0); CHKERRQ(ierr);
1406 #endif
1407   ierr = MPI_Comm_rank( wcomm, &mype);  CHKERRQ(ierr);
1408   ierr = MPI_Comm_size( wcomm, &npe);   CHKERRQ(ierr);
1409 
1410   /* form C graph */
1411   ierr = MatMatMult( A21, Prol11, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Tmat);   CHKERRQ(ierr);
1412   ierr = MatMatTransposeMult(Tmat, Tmat, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Gmat ); CHKERRQ(ierr);
1413   ierr = MatDestroy(&Tmat);      CHKERRQ(ierr);
1414   ierr  = PCGAMGFilterGraph(&Gmat, 0.0, PETSC_FALSE, verbose); CHKERRQ(ierr);
1415 
1416   /* coarsen constraints */
1417   {
1418     MatCoarsen crs;
1419     ierr = MatCoarsenCreate( wcomm, &crs ); CHKERRQ(ierr);
1420     ierr = MatCoarsenSetType( crs, MATCOARSENMIS ); CHKERRQ(ierr);
1421     ierr = MatCoarsenSetAdjacency( crs, Gmat ); CHKERRQ(ierr);
1422     ierr = MatCoarsenSetVerbose( crs, verbose ); CHKERRQ(ierr);
1423     ierr = MatCoarsenSetStrictAggs( crs, PETSC_TRUE ); CHKERRQ(ierr);
1424     ierr = MatCoarsenApply( crs ); CHKERRQ(ierr);
1425     ierr = MatCoarsenGetData( crs, &agg_lists ); CHKERRQ(ierr);
1426     ierr = MatCoarsenDestroy( &crs ); CHKERRQ(ierr);
1427   }
1428 
1429   /* form simple prolongation 'Prol22' */
1430   {
1431     PetscInt ii,mm,clid,my0,nloc,nLocalSelected;
1432     PetscScalar val = 1.0;
1433     /* get 'nLocalSelected' */
1434     ierr = MatGetLocalSize( Gmat, &nloc, &ii ); CHKERRQ(ierr);
1435     for( ii=0, nLocalSelected = 0 ; ii < nloc ; ii++ ){
1436       PetscBool ise;
1437       /* filter out singletons 0 or 1? */
1438       ierr = PetscCDEmptyAt( agg_lists, ii, &ise ); CHKERRQ(ierr);
1439       if( !ise ) nLocalSelected++;
1440     }
1441 
1442     ierr = MatCreate(wcomm,&Prol22);CHKERRQ(ierr);
1443     ierr = MatSetSizes( Prol22,nloc, nLocalSelected,
1444                         PETSC_DETERMINE, PETSC_DETERMINE);
1445     CHKERRQ(ierr);
1446     ierr = MatSetType( Prol22, MATAIJ );       CHKERRQ(ierr);
1447     ierr = MatSeqAIJSetPreallocation(Prol22,1,PETSC_NULL); CHKERRQ(ierr);
1448     ierr = MatMPIAIJSetPreallocation(Prol22,1,PETSC_NULL,1,PETSC_NULL);
1449     CHKERRQ(ierr);
1450     /* ierr = MatCreateAIJ( wcomm, */
1451     /*                      nloc, nLocalSelected, */
1452     /*                      PETSC_DETERMINE, PETSC_DETERMINE, */
1453     /*                      1, PETSC_NULL, 1, PETSC_NULL, */
1454     /*                      &Prol22 ); */
1455 
1456     ierr = MatGetOwnershipRange( Prol22, &my0, &ii );    CHKERRQ(ierr);
1457     nloc = ii - my0;
1458 
1459     /* make aggregates */
1460     for( mm = clid = 0 ; mm < nloc ; mm++ ){
1461       ierr = PetscCDSizeAt( agg_lists, mm, &ii ); CHKERRQ(ierr);
1462       if( ii > 0 ) {
1463         PetscInt asz=ii,cgid=my0+clid,rids[1000];
1464         PetscCDPos pos;
1465         if(asz>1000)SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Very large aggregate: %d",asz);
1466         ii = 0;
1467         ierr = PetscCDGetHeadPos(agg_lists,mm,&pos); CHKERRQ(ierr);
1468         while(pos){
1469           PetscInt gid1;
1470           ierr = PetscLLNGetID( pos, &gid1 ); CHKERRQ(ierr);
1471           ierr = PetscCDGetNextPos(agg_lists,mm,&pos); CHKERRQ(ierr);
1472 
1473           rids[ii++] = gid1;
1474         }
1475         assert(ii==asz);
1476         /* add diagonal block of P0 */
1477         ierr = MatSetValues(Prol22,asz,rids,1,&cgid,&val,INSERT_VALUES); CHKERRQ(ierr);
1478 
1479         clid++;
1480       } /* coarse agg */
1481     } /* for all fine nodes */
1482     ierr = MatAssemblyBegin(Prol22,MAT_FINAL_ASSEMBLY);  CHKERRQ(ierr);
1483     ierr = MatAssemblyEnd(Prol22,MAT_FINAL_ASSEMBLY);    CHKERRQ(ierr);
1484   }
1485 
1486   /* clean up */
1487   ierr = MatDestroy( &Gmat );      CHKERRQ(ierr);
1488   ierr = PetscCDDestroy( agg_lists );  CHKERRQ(ierr);
1489 #if defined PETSC_USE_LOG
1490   ierr = PetscLogEventEnd(PC_GAMGKKTProl_AGG,0,0,0,0);CHKERRQ(ierr);
1491 #endif
1492   *a_P22 = Prol22;
1493 
1494   PetscFunctionReturn(0);
1495 }
1496 
1497 /* -------------------------------------------------------------------------- */
1498 /*
1499    PCCreateGAMG_AGG
1500 
1501   Input Parameter:
1502    . pc -
1503 */
1504 #undef __FUNCT__
1505 #define __FUNCT__ "PCCreateGAMG_AGG"
1506 PetscErrorCode  PCCreateGAMG_AGG( PC pc )
1507 {
1508   PetscErrorCode  ierr;
1509   PC_MG           *mg = (PC_MG*)pc->data;
1510   PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
1511   PC_GAMG_AGG      *pc_gamg_agg;
1512 
1513   PetscFunctionBegin;
1514   /* create sub context for SA */
1515   ierr = PetscNewLog( pc, PC_GAMG_AGG, &pc_gamg_agg ); CHKERRQ(ierr);
1516   assert(!pc_gamg->subctx);
1517   pc_gamg->subctx = pc_gamg_agg;
1518 
1519   pc->ops->setfromoptions = PCSetFromOptions_GAMG_AGG;
1520   pc->ops->destroy        = PCDestroy_AGG;
1521   /* reset does not do anything; setup not virtual */
1522 
1523   /* set internal function pointers */
1524   pc_gamg->graph = PCGAMGgraph_AGG;
1525   pc_gamg->coarsen = PCGAMGCoarsen_AGG;
1526   pc_gamg->prolongator = PCGAMGProlongator_AGG;
1527   pc_gamg->optprol = PCGAMGOptprol_AGG;
1528   pc_gamg->formkktprol = PCGAMGKKTProl_AGG;
1529 
1530   pc_gamg->createdefaultdata = PCSetData_AGG;
1531 
1532   ierr = PetscObjectComposeFunctionDynamic( (PetscObject)pc,
1533                                             "PCSetCoordinates_C",
1534                                             "PCSetCoordinates_AGG",
1535                                             PCSetCoordinates_AGG);
1536   PetscFunctionReturn(0);
1537 }
1538