/[escript]/trunk/paso/src/AMG.c
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revision 3351 by gross, Tue Nov 16 02:39:40 2010 UTC revision 3827 by lgao, Tue Feb 14 11:42:08 2012 UTC
# Line 14  Line 14 
14    
15  /**************************************************************/  /**************************************************************/
16    
17  /* Paso: AMG preconditioner                                  */  /* Paso: AMG preconditioner  (local version)                  */
18    
19  /**************************************************************/  /**************************************************************/
20    
21  /* Author: artak@uq.edu.au, l.gross@uq.edu.au                                */  /* Author: artak@uq.edu.au, l.gross@uq.edu.au                 */
22    
23  /**************************************************************/  /**************************************************************/
24    
25  #define SHOW_TIMING FALSE  #define SHOW_TIMING FALSE
26    #define MY_DEBUG 0
27    #define MY_DEBUG1 1
28    
29  #include "Paso.h"  #include "Paso.h"
30  #include "Preconditioner.h"  #include "Preconditioner.h"
# Line 30  Line 32 
32  #include "PasoUtil.h"  #include "PasoUtil.h"
33  #include "UMFPACK.h"  #include "UMFPACK.h"
34  #include "MKL.h"  #include "MKL.h"
35    #include<stdio.h>
36    
37    
38  /**************************************************************/  /**************************************************************/
39    
40  /* free all memory used by AMG                                */  /* free all memory used by AMG                                */
41    
42  void Paso_Preconditioner_LocalAMG_free(Paso_Preconditioner_LocalAMG * in) {  void Paso_Preconditioner_AMG_free(Paso_Preconditioner_AMG * in) {
43       if (in!=NULL) {       if (in!=NULL) {
44      Paso_Preconditioner_LocalSmoother_free(in->Smoother);      Paso_Preconditioner_Smoother_free(in->Smoother);
45      Paso_SparseMatrix_free(in->P);      Paso_SystemMatrix_free(in->P);
46      Paso_SparseMatrix_free(in->R);      Paso_SystemMatrix_free(in->R);
47      Paso_SparseMatrix_free(in->A_C);      Paso_SystemMatrix_free(in->A_C);
48      Paso_Preconditioner_LocalAMG_free(in->AMG_C);      Paso_Preconditioner_AMG_free(in->AMG_C);
49      MEMFREE(in->r);      MEMFREE(in->r);
50      MEMFREE(in->x_C);      MEMFREE(in->x_C);
51      MEMFREE(in->b_C);      MEMFREE(in->b_C);
52    
       
53      MEMFREE(in);      MEMFREE(in);
54       }       }
55  }  }
56    
57    index_t Paso_Preconditioner_AMG_getMaxLevel(const Paso_Preconditioner_AMG * in) {
58       if (in->AMG_C == NULL) {
59          return in->level;
60       } else {
61          return Paso_Preconditioner_AMG_getMaxLevel(in->AMG_C);
62       }
63    }
64    double Paso_Preconditioner_AMG_getCoarseLevelSparsity(const Paso_Preconditioner_AMG * in) {
65          if (in->AMG_C == NULL) {
66         if (in->A_C == NULL) {
67            return 1.;
68         } else {
69            return Paso_SystemMatrix_getSparsity(in->A_C);
70         }
71          } else {
72            return Paso_Preconditioner_AMG_getCoarseLevelSparsity(in->AMG_C);
73          }
74    }
75    dim_t Paso_Preconditioner_AMG_getNumCoarseUnknwons(const Paso_Preconditioner_AMG * in) {
76       if (in->AMG_C == NULL) {
77          if (in->A_C == NULL) {
78         return 0;
79          } else {
80         return Paso_SystemMatrix_getTotalNumRows(in->A_C);
81          }
82       } else {
83         return Paso_Preconditioner_AMG_getNumCoarseUnknwons(in->AMG_C);
84       }
85    }
86  /*****************************************************************  /*****************************************************************
87    
88     constructs AMG     constructs AMG
89        
90  ******************************************************************/  ******************************************************************/
91  Paso_Preconditioner_LocalAMG* Paso_Preconditioner_LocalAMG_alloc(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {  Paso_Preconditioner_AMG* Paso_Preconditioner_AMG_alloc(Paso_SystemMatrix *A_p,dim_t level,Paso_Options* options) {
92    
93    Paso_Preconditioner_LocalAMG* out=NULL;    Paso_Preconditioner_AMG* out=NULL;
94      Paso_SystemMatrix *A_C;
95    bool_t verbose=options->verbose;    bool_t verbose=options->verbose;
96    
97      const dim_t my_n=A_p->mainBlock->numRows;
98      const dim_t overlap_n=A_p->row_coupleBlock->numRows;
99        
100    Paso_SparseMatrix *Atemp=NULL, *A_C=NULL;    const dim_t n = my_n + overlap_n;
101    const dim_t n=A_p->numRows;  
102    const dim_t n_block=A_p->row_block_size;    const dim_t n_block=A_p->row_block_size;
103    index_t* split_marker=NULL, *counter=NULL, *mask_C=NULL, *rows_in_F=NULL, *S=NULL, *degree=NULL;  //  const dim_t n_block=A_p->block_size;
104    dim_t n_F=0, n_C=0, i;    index_t* F_marker=NULL, *counter=NULL, *mask_C=NULL, *rows_in_F;
105      dim_t i, n_F, n_C, F_flag, *F_set=NULL;
106    double time0=0;    double time0=0;
107    const double theta = options->coarsening_threshold;    const double theta = options->coarsening_threshold;
108    const double tau = options->diagonal_dominance_threshold;    const double tau = options->diagonal_dominance_threshold;
109        const double sparsity=Paso_SystemMatrix_getSparsity(A_p);
110        const dim_t total_n=Paso_SystemMatrix_getGlobalTotalNumRows(A_p);
111      const dim_t global_n=Paso_SystemMatrix_getGlobalNumRows(A_p);
112    
113    
114    /*    /*
115        is the input matrix A suitable for coarsening        is the input matrix A suitable for coarsening?
116                
117    */    */
118    if ( (A_p->pattern->len >= options->min_coarse_sparsity * n * n ) || (n <= options->min_coarse_matrix_size) || (level > options->level_max) ) {    if ( (sparsity >= options->min_coarse_sparsity) ||
119       if (verbose) printf("Paso_Solver: AMG level %d (limit = %d) stopped. sparsity = %e (limit = %e), unknowns = %d (limit = %d)\n",  //       (total_n <= options->min_coarse_matrix_size) ||
120      level,  options->level_max, A_p->pattern->len/(1.*n * n), options->min_coarse_sparsity, n, options->min_coarse_matrix_size  );           (global_n <= options->min_coarse_matrix_size) ||
121       return NULL;         (level > options->level_max) ) {
122    }  
123            if (verbose) {
124              /*
125                  print stopping condition:
126                          - 'SPAR' = min_coarse_matrix_sparsity exceeded
127                          - 'SIZE' = min_coarse_matrix_size exceeded
128                          - 'LEVEL' = level_max exceeded
129              */
130              printf("Paso_Preconditioner: AMG: termination of coarsening by ");
131    
132              if (sparsity >= options->min_coarse_sparsity)
133                  printf("SPAR");
134    
135              if (total_n <= options->min_coarse_matrix_size)
136                  printf("SIZE");
137    
138              if (level > options->level_max)
139                  printf("LEVEL");
140    
141              printf("\n");
142    
143            printf("Paso_Preconditioner: AMG level %d (limit = %d) stopped. sparsity = %e (limit = %e), unknowns = %d (limit = %d)\n",
144               level,  options->level_max, sparsity, options->min_coarse_sparsity, total_n, options->min_coarse_matrix_size);  
145    
146           }
147    
148           return NULL;
149      }  else {
150       /* Start Coarsening : */       /* Start Coarsening : */
151        
152         /* this is the table for strong connections combining mainBlock, col_coupleBlock and row_coupleBlock */
153         const dim_t len_S=A_p->mainBlock->pattern->len + A_p->col_coupleBlock->pattern->len + A_p->row_coupleBlock->pattern->len  + A_p->row_coupleBlock->numRows * A_p->col_coupleBlock->numCols;
154    
155       split_marker=TMPMEMALLOC(n,index_t);       dim_t* degree_S=TMPMEMALLOC(n, dim_t);
156         index_t *offset_S=TMPMEMALLOC(n, index_t);
157         index_t *S=TMPMEMALLOC(len_S, index_t);
158         dim_t* degree_ST=TMPMEMALLOC(n, dim_t);
159         index_t *offset_ST=TMPMEMALLOC(n, index_t);
160         index_t *ST=TMPMEMALLOC(len_S, index_t);
161        
162        
163         F_marker=TMPMEMALLOC(n,index_t);
164       counter=TMPMEMALLOC(n,index_t);       counter=TMPMEMALLOC(n,index_t);
165       degree=TMPMEMALLOC(n, dim_t);  
166       S=TMPMEMALLOC(A_p->pattern->len, index_t);       if ( !( Esys_checkPtr(F_marker) || Esys_checkPtr(counter) || Esys_checkPtr(degree_S) || Esys_checkPtr(offset_S) || Esys_checkPtr(S)
167       if ( !( Esys_checkPtr(split_marker) || Esys_checkPtr(counter) || Esys_checkPtr(degree) || Esys_checkPtr(S) ) ) {      || Esys_checkPtr(degree_ST) || Esys_checkPtr(offset_ST) || Esys_checkPtr(ST) ) ) {
168       /*      /*
169               make sure that corresponding values in the row_coupleBlock and col_coupleBlock are identical
170        */
171            Paso_SystemMatrix_copyColCoupleBlock(A_p);
172            Paso_SystemMatrix_copyRemoteCoupleBlock(A_p, FALSE);
173    
174        /*
175            set splitting of unknows:            set splitting of unknows:
176                  
177           */           */
178       time0=Esys_timer();       time0=Esys_timer();
179       if (n_block>1) {       if (n_block>1) {
180             Paso_Preconditioner_AMG_setStrongConnections_Block(A_p, degree, S, theta,tau);             Paso_Preconditioner_AMG_setStrongConnections_Block(A_p, degree_S, offset_S, S, theta,tau);
181       } else {       } else {
182             Paso_Preconditioner_AMG_setStrongConnections(A_p, degree, S, theta,tau);             Paso_Preconditioner_AMG_setStrongConnections(A_p, degree_S, offset_S, S, theta,tau);
183       }       }
184       Paso_Preconditioner_AMG_RungeStuebenSearch(n, A_p->pattern->ptr, degree, S, split_marker);       Paso_Preconditioner_AMG_transposeStrongConnections(n, degree_S, offset_S, S, n, degree_ST, offset_ST, ST);
185    //   Paso_SystemMatrix_extendedRowsForST(A_p, degree_ST, offset_ST, ST);
186    
187         Paso_Preconditioner_AMG_CIJPCoarsening(n,my_n,F_marker,
188                                degree_S, offset_S, S, degree_ST, offset_ST, ST,
189                            A_p->col_coupler->connector,A_p->col_distribution);
190          
191    
192             /* in BoomerAMG if interpolation is used FF connectivity is required */
193    /*MPI:
194             if (options->interpolation_method == PASO_CLASSIC_INTERPOLATION_WITH_FF_COUPLING)
195                                 Paso_Preconditioner_AMG_enforceFFConnectivity(n, A_p->pattern->ptr, degree_S, S, F_marker);  
196    */
197    
198       options->coarsening_selection_time=Esys_timer()-time0 + MAX(0, options->coarsening_selection_time);       options->coarsening_selection_time=Esys_timer()-time0 + MAX(0, options->coarsening_selection_time);
       
199       if (Esys_noError() ) {       if (Esys_noError() ) {
200          #pragma omp parallel for private(i) schedule(static)          #pragma omp parallel for private(i) schedule(static)
201          for (i = 0; i < n; ++i) split_marker[i]= (split_marker[i] == PASO_AMG_IN_F);          for (i = 0; i < n; ++i) F_marker[i]=(F_marker[i] ==  PASO_AMG_IN_F);
202            
203          /*          /*
204             count number of unkowns to be eliminated:             count number of unkowns to be eliminated:
205          */          */
206          n_F=Paso_Util_cumsum_maskedTrue(n,counter, split_marker);          n_F=Paso_Util_cumsum_maskedTrue(n,counter, F_marker);
207          n_C=n-n_F;          n_C=n-n_F;
208          if (verbose) printf("Paso_Solver: AMG level %d: %d unknowns are flagged for elimination. %d left.\n",level,n_F,n-n_F);          if (verbose) printf("Paso_Preconditioner: AMG (non-local) level %d: %d unknowns are flagged for elimination. %d left.\n",level,n_F,n-n_F);
209        
210          if ( n_F == 0 ) {  /*  is a nasty case. a direct solver should be used, return NULL */              /* collect n_F values on all processes, a direct solver should
211                    be used if any n_F value is 0 */
212                F_set = TMPMEMALLOC(A_p->mpi_info->size, dim_t);
213                MPI_Allgather(&n_F, 1, MPI_INT, F_set, 1, MPI_INT, A_p->mpi_info->comm);
214                F_flag = 1;
215                for (i=0; i<A_p->mpi_info->size; i++) {
216                    if (F_set[i] == 0) {
217                      F_flag = 0;
218                      break;
219                    }
220                }
221                TMPMEMFREE(F_set);
222            
223    //          if ( n_F == 0 ) {  /*  is a nasty case. a direct solver should be used, return NULL */
224                if (F_flag == 0) {
225             out = NULL;             out = NULL;
226          } else {          } else {
227             out=MEMALLOC(1,Paso_Preconditioner_LocalAMG);             out=MEMALLOC(1,Paso_Preconditioner_AMG);
228             if (! Esys_checkPtr(out)) {             if (! Esys_checkPtr(out)) {
229            out->level = level;            out->level = level;
230            out->n = n;            out->n = n;
# Line 123  Paso_Preconditioner_LocalAMG* Paso_Preco Line 233  Paso_Preconditioner_LocalAMG* Paso_Preco
233            out->A_C = NULL;            out->A_C = NULL;
234            out->P = NULL;              out->P = NULL;  
235            out->R = NULL;                      out->R = NULL;          
236            out->post_sweeps = options->post_sweeps;  //        out->post_sweeps = options->post_sweeps;
237            out->pre_sweeps  = options->pre_sweeps;  //        out->pre_sweeps  = options->pre_sweeps;
238              out->post_sweeps = 2;
239              out->pre_sweeps = 2;
240            out->r = NULL;            out->r = NULL;
241            out->x_C = NULL;            out->x_C = NULL;
242            out->b_C = NULL;            out->b_C = NULL;
# Line 137  Paso_Preconditioner_LocalAMG* Paso_Preco Line 249  Paso_Preconditioner_LocalAMG* Paso_Preco
249             Esys_checkPtr(rows_in_F);             Esys_checkPtr(rows_in_F);
250             if ( Esys_noError() ) {             if ( Esys_noError() ) {
251    
252            out->Smoother = Paso_Preconditioner_LocalSmoother_alloc(A_p, (options->smoother == PASO_JACOBI), verbose);            out->Smoother = Paso_Preconditioner_Smoother_alloc(A_p, (options->smoother == PASO_JACOBI), 0, verbose);
253                
254            if ( n_F < n ) { /* if nothing is been removed we have a diagonal dominant matrix and we just run a few steps of the smoother */            if (n_C != 0) {
255                   /* if nothing has been removed we have a diagonal dominant matrix and we just run a few steps of the smoother */
256        
257              /* allocate helpers :*/              /* allocate helpers :*/
258              out->x_C=MEMALLOC(n_block*n_C,double);              out->x_C=MEMALLOC(n_block*n_C,double);
# Line 156  Paso_Preconditioner_LocalAMG* Paso_Preco Line 269  Paso_Preconditioner_LocalAMG* Paso_Preco
269                 {                 {
270                    #pragma omp for schedule(static)                    #pragma omp for schedule(static)
271                    for (i = 0; i < n; ++i) {                    for (i = 0; i < n; ++i) {
272                   if  (split_marker[i]) rows_in_F[counter[i]]=i;                   if  (F_marker[i]) rows_in_F[counter[i]]=i;
                   }  
                }  
                /*  create mask of C nodes with value >-1 gives new id */  
                i=Paso_Util_cumsum_maskedFalse(n,counter, split_marker);  
   
                #pragma omp parallel for private(i) schedule(static)  
                for (i = 0; i < n; ++i) {  
                   if  (split_marker[i]) {  
                  mask_C[i]=-1;  
                   } else {  
                  mask_C[i]=counter[i];;  
273                    }                    }
274                 }                 }
275                   /*  create mask of C nodes with value >-1, gives new id */
276                   i=Paso_Util_cumsum_maskedFalse(n, mask_C, F_marker);
277                 /*                 /*
278                    get Restriction :                      get Prolongation :    
279                 */                                   */                  
280    
281                 time0=Esys_timer();                 time0=Esys_timer();
282                 out->P=Paso_Preconditioner_AMG_getDirectProlongation(A_p,degree,S,n_C,mask_C);  
283                 if (SHOW_TIMING) printf("timing: level %d: getProlongation: %e\n",level, Esys_timer()-time0);                 out->P=Paso_Preconditioner_AMG_getProlongation(A_p,offset_S, degree_S,S,n_C,mask_C, options->interpolation_method);
284    
285              }              }
286    
287              /*                    /*      
288                 construct Prolongation operator as transposed of restriction operator:                 construct Restriction operator as transposed of Prolongation operator:
289              */              */
290    
291              if ( Esys_noError()) {              if ( Esys_noError()) {
292                 time0=Esys_timer();                 time0=Esys_timer();
293                 out->R=Paso_SparseMatrix_getTranspose(out->P);  
294                 if (SHOW_TIMING) printf("timing: level %d: Paso_SparseMatrix_getTranspose: %e\n",level,Esys_timer()-time0);                 out->R=Paso_Preconditioner_AMG_getRestriction(out->P);
295    
296                   if (SHOW_TIMING) printf("timing: level %d: Paso_SystemMatrix_getTranspose: %e\n",level,Esys_timer()-time0);
297              }                    }      
298              /*              /*
299              construct coarse level matrix:                          construct coarse level matrix:
300              */                          */
301              if ( Esys_noError()) {                          if ( Esys_noError()) {
302                 time0=Esys_timer();                             time0=Esys_timer();
303                 Atemp=Paso_SparseMatrix_MatrixMatrix(A_p,out->P);  
304                 A_C=Paso_SparseMatrix_MatrixMatrix(out->R,Atemp);                             A_C = Paso_Preconditioner_AMG_buildInterpolationOperator(A_p, out->P, out->R);
305                 Paso_SparseMatrix_free(Atemp);  
306                 if (SHOW_TIMING) printf("timing: level %d : construct coarse matrix: %e\n",level,Esys_timer()-time0);                                         if (SHOW_TIMING) printf("timing: level %d : construct coarse matrix: %e\n",level,Esys_timer()-time0);
307              }                          }
308    
               
309              /*              /*
310                 constructe courser level:                 constructe courser level:
311                                
312              */              */
313              if ( Esys_noError()) {              if ( Esys_noError()) {
314                 out->AMG_C=Paso_Preconditioner_LocalAMG_alloc(A_C,level+1,options);                 out->AMG_C=Paso_Preconditioner_AMG_alloc(A_C,level+1,options);
315              }              }
316    
317              if ( Esys_noError()) {              if ( Esys_noError()) {
318                 if ( out->AMG_C == NULL ) {                if ( out->AMG_C == NULL ) {
319                      /* merge the system matrix into 1 rank when
320                     it's not suitable coarsening due to the
321                     total number of unknowns are too small */
322                      out->A_C=A_C;
323                    out->reordering = options->reordering;                    out->reordering = options->reordering;
324                    out->refinements = options->coarse_matrix_refinements;                                out->refinements = options->coarse_matrix_refinements;
325                    /* no coarse level matrix has been constructed. use direct solver */                    out->verbose = verbose;
326                    #ifdef MKL                    out->options_smoother = options->smoother;
327                      out->A_C=Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, A_C);                } else {
                     Paso_SparseMatrix_free(A_C);  
                     out->A_C->solver_package = PASO_MKL;  
                     if (verbose) printf("Paso_Solver: AMG: use MKL direct solver on the coarsest level (number of unknowns = %d).\n",n_C);  
                   #else  
                     #ifdef UMFPACK  
                        out->A_C=Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_CSC, A_C);  
                        Paso_SparseMatrix_free(A_C);  
                        out->A_C->solver_package = PASO_UMFPACK;  
                        if (verbose) printf("Paso_Solver: AMG: use UMFPACK direct solver on the coarsest level (number of unknowns = %d).\n",n_C);  
                     #else  
                        out->A_C=A_C;  
                        out->A_C->solver_p=Paso_Preconditioner_LocalSmoother_alloc(out->A_C, (options->smoother == PASO_JACOBI), verbose);  
                        out->A_C->solver_package = PASO_SMOOTHER;  
                        if (verbose) printf("Paso_Solver: AMG: use smoother on the coarsest level (number of unknowns = %d).\n",n_C);  
                     #endif  
                   #endif  
                } else {  
328                    /* finally we set some helpers for the solver step */                    /* finally we set some helpers for the solver step */
329                    out->A_C=A_C;                    out->A_C=A_C;
330                 }                }
331              }                      }        
332            }            }
333             }             }
# Line 238  Paso_Preconditioner_LocalAMG* Paso_Preco Line 335  Paso_Preconditioner_LocalAMG* Paso_Preco
335             TMPMEMFREE(rows_in_F);             TMPMEMFREE(rows_in_F);
336          }          }
337       }       }
338    
339    }    }
340    TMPMEMFREE(counter);    TMPMEMFREE(counter);
341    TMPMEMFREE(split_marker);    TMPMEMFREE(F_marker);
342    TMPMEMFREE(degree);    TMPMEMFREE(degree_S);
343      TMPMEMFREE(offset_S);
344    TMPMEMFREE(S);    TMPMEMFREE(S);
345      TMPMEMFREE(degree_ST);
346      TMPMEMFREE(offset_ST);
347      TMPMEMFREE(ST);
348      
349      }
350    
351    if (Esys_noError()) {    if (Esys_noError()) {
352       return out;       return out;
353    } else  {    } else  {
354       Paso_Preconditioner_LocalAMG_free(out);       Paso_Preconditioner_AMG_free(out);
355       return NULL;       return NULL;
356    }    }
357  }  }
358    
359    
360  void Paso_Preconditioner_LocalAMG_solve(Paso_SparseMatrix* A, Paso_Preconditioner_LocalAMG * amg, double * x, double * b) {  void Paso_Preconditioner_AMG_solve(Paso_SystemMatrix* A, Paso_Preconditioner_AMG * amg, double * x, double * b) {
361       const dim_t n = amg->n * amg->n_block;       const dim_t n = A->mainBlock->numRows * A->mainBlock->row_block_size;
362       double time0=0;       double time0=0;
363       const dim_t post_sweeps=amg->post_sweeps;       const dim_t post_sweeps=amg->post_sweeps;
364       const dim_t pre_sweeps=amg->pre_sweeps;       const dim_t pre_sweeps=amg->pre_sweeps;
365         int rank = A->mpi_info->rank;
366    
367       /* presmoothing */       /* presmoothing */
368       time0=Esys_timer();       time0=Esys_timer();
369       Paso_Preconditioner_LocalSmoother_solve(A, amg->Smoother, x, b, pre_sweeps, FALSE);       Paso_Preconditioner_Smoother_solve(A, amg->Smoother, x, b, pre_sweeps, FALSE);
370    
371       time0=Esys_timer()-time0;       time0=Esys_timer()-time0;
372       if (SHOW_TIMING) printf("timing: level %d: Presmooting: %e\n",amg->level, time0);       if (SHOW_TIMING) printf("timing: level %d: Presmoothing: %e\n",amg->level, time0);
373       /* end of presmoothing */       /* end of presmoothing */
374            
375       if (amg->n_F < amg->n) { /* is there work on the coarse level? */       if (amg->n_F < amg->n) { /* is there work on the coarse level? */
376           time0=Esys_timer();           time0=Esys_timer();
377    
378       Paso_Copy(n, amg->r, b);                            /*  r <- b */       Paso_Copy(n, amg->r, b);                            /*  r <- b */
379       Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,A,x,1.,amg->r); /*r=r-Ax*/       Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(-1.,A,x,1.,amg->r); /*r=r-Ax*/
380       Paso_SparseMatrix_MatrixVector_CSR_OFFSET0_DIAG(1.,amg->R,amg->r,0.,amg->b_C);  /* b_c = R*r  */       Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(1.,amg->R,amg->r,0.,amg->b_C);  /* b_c = R*r  */
381    
382           time0=Esys_timer()-time0;           time0=Esys_timer()-time0;
383       /* coarse level solve */       /* coarse level solve */
384       if ( amg->AMG_C == NULL) {       if ( amg->AMG_C == NULL) {
385          time0=Esys_timer();          time0=Esys_timer();
386          /*  A_C is the coarsest level */          /*  A_C is the coarsest level */
387          switch (amg->A_C->solver_package) {          Paso_Preconditioner_AMG_mergeSolve(amg);
388             case (PASO_MKL):  
           Paso_MKL(amg->A_C, amg->x_C,amg->b_C, amg->reordering, amg->refinements, SHOW_TIMING);  
           break;  
            case (PASO_UMFPACK):  
           Paso_UMFPACK(amg->A_C, amg->x_C,amg->b_C, amg->refinements, SHOW_TIMING);  
           break;  
            case (PASO_SMOOTHER):  
           Paso_Preconditioner_LocalSmoother_solve(amg->A_C, amg->Smoother,amg->x_C,amg->b_C,pre_sweeps, FALSE);  
           break;  
         }  
389          if (SHOW_TIMING) printf("timing: level %d: DIRECT SOLVER: %e\n",amg->level,Esys_timer()-time0);          if (SHOW_TIMING) printf("timing: level %d: DIRECT SOLVER: %e\n",amg->level,Esys_timer()-time0);
390       } else {       } else {
391          Paso_Preconditioner_LocalAMG_solve(amg->A_C, amg->AMG_C,amg->x_C,amg->b_C); /* x_C=AMG(b_C)     */          Paso_Preconditioner_AMG_solve(amg->A_C, amg->AMG_C,amg->x_C,amg->b_C); /* x_C=AMG(b_C)     */
392       }         }
393    
394       time0=time0+Esys_timer();       time0=time0+Esys_timer();
395       Paso_SparseMatrix_MatrixVector_CSR_OFFSET0_DIAG(1.,amg->P,amg->x_C,1.,x); /* x = x + P*x_c */           Paso_SystemMatrix_MatrixVector_CSR_OFFSET0(1.,amg->P,amg->x_C,1.,x); /* x = x + P*x_c */    
396        
397           /*postsmoothing*/           /*postsmoothing*/
398                
399          /*solve Ax=b with initial guess x */          /*solve Ax=b with initial guess x */
400          time0=Esys_timer();          time0=Esys_timer();
401          Paso_Preconditioner_LocalSmoother_solve(A, amg->Smoother, x, b, post_sweeps, TRUE);          Paso_Preconditioner_Smoother_solve(A, amg->Smoother, x, b, post_sweeps, TRUE);
402          time0=Esys_timer()-time0;          time0=Esys_timer()-time0;
403          if (SHOW_TIMING) printf("timing: level %d: Postsmoothing: %e\n",amg->level,time0);          if (SHOW_TIMING) printf("timing: level %d: Postsmoothing: %e\n",amg->level,time0);
404          /*end of postsmoothing*/          /*end of postsmoothing*/
       
405       }       }
406    
407       return;       return;
408  }  }
409    
# Line 315  void Paso_Preconditioner_LocalAMG_solve( Line 415  void Paso_Preconditioner_LocalAMG_solve(
415  in the sense that |A_{ij}| >= theta * max_k |A_{ik}|  in the sense that |A_{ij}| >= theta * max_k |A_{ik}|
416  */  */
417    
418  void Paso_Preconditioner_AMG_setStrongConnections(Paso_SparseMatrix* A,  void Paso_Preconditioner_AMG_setStrongConnections(Paso_SystemMatrix* A,
419                        dim_t *degree, index_t *S,                            dim_t *degree_S, index_t *offset_S, index_t *S,
420                        const double theta, const double tau)                        const double theta, const double tau)
421  {  {
    const dim_t n=A->numRows;  
    index_t iptr, i,j;  
    dim_t kdeg;  
    double max_offdiagonal, threshold, sum_row, main_row, fnorm;  
422    
423       const dim_t my_n=A->mainBlock->numRows;
424       const dim_t overlap_n=A->row_coupleBlock->numRows;
425      
426       index_t iptr, i;
427       double *threshold_p=NULL;
428       index_t rank=A->mpi_info->rank;
429    
430        #pragma omp parallel for private(i,iptr,max_offdiagonal, threshold,j, kdeg, sum_row, main_row, fnorm) schedule(static)     threshold_p = TMPMEMALLOC(2*my_n, double);
431        for (i=0;i<n;++i) {    
432                 #pragma omp parallel for private(i,iptr) schedule(static)
433       max_offdiagonal = 0.;     for (i=0;i<my_n;++i) {        
434       sum_row=0;      
435       main_row=0;       register double max_offdiagonal = 0.;
436         register double sum_row=0;
437         register double main_row=0;
438         register dim_t kdeg=0;
439             register const index_t koffset=A->mainBlock->pattern->ptr[i]+A->col_coupleBlock->pattern->ptr[i];
440    
441            
442         /* collect information for row i: */
443       #pragma ivdep       #pragma ivdep
444       for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {       for (iptr=A->mainBlock->pattern->ptr[i];iptr<A->mainBlock->pattern->ptr[i+1]; ++iptr) {
445          j=A->pattern->index[iptr];          register index_t j=A->mainBlock->pattern->index[iptr];
446          fnorm=ABS(A->val[iptr]);          register double fnorm=ABS(A->mainBlock->val[iptr]);
           
447          if( j != i) {          if( j != i) {
448             max_offdiagonal = MAX(max_offdiagonal,fnorm);             max_offdiagonal = MAX(max_offdiagonal,fnorm);
449             sum_row+=fnorm;             sum_row+=fnorm;
450          } else {          } else {
451             main_row=fnorm;             main_row=fnorm;
452          }          }
453    
454       }       }
455       threshold = theta*max_offdiagonal;  
456       kdeg=0;       #pragma ivdep
457       if (tau*main_row < sum_row) { /* no diagonal domainance */       for (iptr=A->col_coupleBlock->pattern->ptr[i];iptr<A->col_coupleBlock->pattern->ptr[i+1]; ++iptr) {
458          #pragma ivdep          register double fnorm=ABS(A->col_coupleBlock->val[iptr]);
459          for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {  
460             j=A->pattern->index[iptr];          max_offdiagonal = MAX(max_offdiagonal,fnorm);
461             if(ABS(A->val[iptr])>threshold && i!=j) {          sum_row+=fnorm;
           S[A->pattern->ptr[i]+kdeg] = j;  
           kdeg++;  
            }  
         }  
462       }       }
463       degree[i]=kdeg;  
464             /* inspect row i: */
465             {
466            const double threshold = theta*max_offdiagonal;
467                threshold_p[2*i+1]=threshold;
468            if (tau*main_row < sum_row) { /* no diagonal dominance */
469                   threshold_p[2*i]=1;
470               #pragma ivdep
471               for (iptr=A->mainBlock->pattern->ptr[i];iptr<A->mainBlock->pattern->ptr[i+1]; ++iptr) {
472                  register index_t j=A->mainBlock->pattern->index[iptr];
473                  if(ABS(A->mainBlock->val[iptr])>threshold && i!=j) {
474                 S[koffset+kdeg] = j;
475                 kdeg++;
476                  }
477               }
478    //         #pragma ivdep
479               for (iptr=A->col_coupleBlock->pattern->ptr[i];iptr<A->col_coupleBlock->pattern->ptr[i+1]; ++iptr) {
480                  register index_t j=A->col_coupleBlock->pattern->index[iptr];
481                  if(ABS(A->col_coupleBlock->val[iptr])>threshold) {
482                 S[koffset+kdeg] = j + my_n;
483                 kdeg++;
484                  }
485               }
486                } else {
487                   threshold_p[2*i]=-1;
488                }
489             }
490             offset_S[i]=koffset;
491         degree_S[i]=kdeg;
492        }        }
493    
494          /* now we need to distribute the threshold and the diagonal dominance indicator */
495          if (A->mpi_info->size > 1) {
496    
497              const index_t koffset_0=A->mainBlock->pattern->ptr[my_n]+A->col_coupleBlock->pattern->ptr[my_n]
498                     -A->mainBlock->pattern->ptr[0]-A->col_coupleBlock->pattern->ptr[0];
499          
500              double *remote_threshold=NULL;
501              
502          Paso_Coupler* threshold_coupler=Paso_Coupler_alloc(A->row_coupler->connector  ,2);
503              Paso_Coupler_startCollect(threshold_coupler,threshold_p);
504              Paso_Coupler_finishCollect(threshold_coupler);
505              remote_threshold=threshold_coupler->recv_buffer;
506    
507              #pragma omp parallel for private(i,iptr) schedule(static)
508              for (i=0; i<overlap_n; i++) {
509              const double threshold = remote_threshold[2*i+1];
510              register dim_t kdeg=0;
511                  register const index_t koffset=koffset_0+A->row_coupleBlock->pattern->ptr[i]+A->remote_coupleBlock->pattern->ptr[i];
512                  if (remote_threshold[2*i]>0) {
513            #pragma ivdep
514            for (iptr=A->row_coupleBlock->pattern->ptr[i];iptr<A->row_coupleBlock->pattern->ptr[i+1]; ++iptr) {
515                  register index_t j=A->row_coupleBlock->pattern->index[iptr];
516                  if(ABS(A->row_coupleBlock->val[iptr])>threshold) {
517                 S[koffset+kdeg] = j ;
518                 kdeg++;
519                  }
520            }
521    
522            #pragma ivdep
523            for (iptr=A->remote_coupleBlock->pattern->ptr[i];iptr<A->remote_coupleBlock->pattern->ptr[i+1]; iptr++) {
524              register index_t j=A->remote_coupleBlock->pattern->index[iptr];
525              if(ABS(A->remote_coupleBlock->val[iptr])>threshold && i!=j) {
526                  S[koffset+kdeg] = j + my_n;
527                  kdeg++;
528              }
529            }
530                  }
531                  offset_S[i+my_n]=koffset;
532              degree_S[i+my_n]=kdeg;
533              }
534    
535              Paso_Coupler_free(threshold_coupler);
536         }
537         TMPMEMFREE(threshold_p);
538  }  }
539    
540  /* theta = threshold for strong connections */  /* theta = threshold for strong connections */
# Line 366  void Paso_Preconditioner_AMG_setStrongCo Line 543  void Paso_Preconditioner_AMG_setStrongCo
543    
544  in the sense that |A_{ij}|_F >= theta * max_k |A_{ik}|_F  in the sense that |A_{ij}|_F >= theta * max_k |A_{ik}|_F
545  */  */
546  void Paso_Preconditioner_AMG_setStrongConnections_Block(Paso_SparseMatrix* A,  void Paso_Preconditioner_AMG_setStrongConnections_Block(Paso_SystemMatrix* A,
547                              dim_t *degree, index_t *S,                              dim_t *degree_S, index_t *offset_S, index_t *S,
548                              const double theta, const double tau)                              const double theta, const double tau)
549    
550  {  {
551     const dim_t n_block=A->row_block_size;     const dim_t block_size=A->block_size;
552     const dim_t n=A->numRows;     const dim_t my_n=A->mainBlock->numRows;
553     index_t iptr, i,j, bi;     const dim_t overlap_n=A->row_coupleBlock->numRows;
    dim_t kdeg, max_deg;  
    register double max_offdiagonal, threshold, fnorm, sum_row, main_row;  
    double *rtmp;  
554        
555       index_t iptr, i, bi;
556       double *threshold_p=NULL;
557        
558        #pragma omp parallel private(i,iptr,max_offdiagonal, kdeg, threshold,j, max_deg, fnorm, sum_row, main_row, rtmp)    
559        {     threshold_p = TMPMEMALLOC(2*my_n, double);
560       max_deg=0;  
561       #pragma omp for schedule(static)     #pragma omp parallel private(i,iptr,bi)
562       for (i=0;i<n;++i) max_deg=MAX(max_deg, A->pattern->ptr[i+1]-A->pattern->ptr[i]);     {
563      
564          dim_t max_deg=0;
565          double *rtmp=NULL;
566    
567          #pragma omp for schedule(static)
568          for (i=0;i<my_n;++i) max_deg=MAX(max_deg, A->mainBlock->pattern->ptr[i+1]-A->mainBlock->pattern->ptr[i]
569                         +A->col_coupleBlock->pattern->ptr[i+1]-A->col_coupleBlock->pattern->ptr[i]);
570                
571       rtmp=TMPMEMALLOC(max_deg, double);        rtmp=TMPMEMALLOC(max_deg, double);
572                
573       #pragma omp for schedule(static)        #pragma omp for schedule(static)
574       for (i=0;i<n;++i) {        for (i=0;i<my_n;++i) {        
575         register double max_offdiagonal = 0.;
576         register double sum_row=0;
577         register double main_row=0;
578         register index_t rtmp_offset=-A->mainBlock->pattern->ptr[i];
579         register dim_t kdeg=0;
580         register const index_t koffset=A->mainBlock->pattern->ptr[i]+A->col_coupleBlock->pattern->ptr[i];
581            
582          max_offdiagonal = 0.;       /* collect information for row i: */
583          sum_row=0;       for (iptr=A->mainBlock->pattern->ptr[i];iptr<A->mainBlock->pattern->ptr[i+1]; ++iptr) {
584          main_row=0;          register index_t j=A->mainBlock->pattern->index[iptr];
585          for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {          register double fnorm=0;
586             j=A->pattern->index[iptr];          #pragma ivdep
587             fnorm=0;          for(bi=0;bi<block_size;++bi) {
588             #pragma ivdep              register double  rtmp2= A->mainBlock->val[iptr*block_size+bi];
589             for(bi=0;bi<n_block*n_block;++bi) fnorm+=A->val[iptr*n_block*n_block+bi]*A->val[iptr*n_block*n_block+bi];             fnorm+=rtmp2*rtmp2;
            fnorm=sqrt(fnorm);  
            rtmp[iptr-A->pattern->ptr[i]]=fnorm;  
            if( j != i) {  
           max_offdiagonal = MAX(max_offdiagonal,fnorm);  
           sum_row+=fnorm;  
            } else {  
           main_row=fnorm;  
            }  
590          }          }
591          threshold = theta*max_offdiagonal;          fnorm=sqrt(fnorm);
592            rtmp[iptr+rtmp_offset]=fnorm;
593            
594            if( j != i) {
595               max_offdiagonal = MAX(max_offdiagonal,fnorm);
596               sum_row+=fnorm;
597            } else {
598               main_row=fnorm;
599            }
600        
601         }
602                
603          kdeg=0;           rtmp_offset+=A->mainBlock->pattern->ptr[i+1]-A->col_coupleBlock->pattern->ptr[i];
604          if (tau*main_row < sum_row) { /* no diagonal domainance */       for (iptr=A->col_coupleBlock->pattern->ptr[i];iptr<A->col_coupleBlock->pattern->ptr[i+1]; ++iptr) {
605            register double fnorm=0;
606            #pragma ivdep
607            for(bi=0;bi<block_size;++bi) {
608               register double rtmp2 = A->col_coupleBlock->val[iptr*block_size+bi];
609               fnorm+=rtmp2*rtmp2;
610            }
611            fnorm=sqrt(fnorm);
612            
613            rtmp[iptr+rtmp_offset]=fnorm;
614            max_offdiagonal = MAX(max_offdiagonal,fnorm);
615            sum_row+=fnorm;
616         }
617        
618          
619         /* inspect row i: */
620         {
621            const double threshold = theta*max_offdiagonal;
622            rtmp_offset=-A->mainBlock->pattern->ptr[i];
623            
624            threshold_p[2*i+1]=threshold;
625            if (tau*main_row < sum_row) { /* no diagonal dominance */
626               threshold_p[2*i]=1;
627               #pragma ivdep
628               for (iptr=A->mainBlock->pattern->ptr[i];iptr<A->mainBlock->pattern->ptr[i+1]; ++iptr) {
629              register index_t j=A->mainBlock->pattern->index[iptr];
630              if(rtmp[iptr+rtmp_offset] > threshold && i!=j) {
631                 S[koffset+kdeg] = j;
632                 kdeg++;
633              }
634               }
635               rtmp_offset+=A->mainBlock->pattern->ptr[i+1]-A->col_coupleBlock->pattern->ptr[i];
636             #pragma ivdep             #pragma ivdep
637             for (iptr=A->pattern->ptr[i];iptr<A->pattern->ptr[i+1]; ++iptr) {             for (iptr=A->col_coupleBlock->pattern->ptr[i];iptr<A->col_coupleBlock->pattern->ptr[i+1]; ++iptr) {
638            j=A->pattern->index[iptr];            register index_t j=A->col_coupleBlock->pattern->index[iptr];
639            if(rtmp[iptr-A->pattern->ptr[i]] > threshold && i!=j) {            if( rtmp[iptr+rtmp_offset] >threshold) {
640               S[A->pattern->ptr[i]+kdeg] = j;               S[koffset+kdeg] = j + my_n;
641               kdeg++;               kdeg++;
642            }            }
643             }             }
644            } else {
645               threshold_p[2*i]=-1;
646            }
647         }
648         offset_S[i]=koffset;
649         degree_S[i]=kdeg;
650          }
651          TMPMEMFREE(rtmp);
652       }
653       /* now we need to distribute the threshold and the diagonal dominance indicator */
654       if (A->mpi_info->size > 1) {
655          
656          const index_t koffset_0=A->mainBlock->pattern->ptr[my_n]+A->col_coupleBlock->pattern->ptr[my_n]
657                                 -A->mainBlock->pattern->ptr[0]-A->col_coupleBlock->pattern->ptr[0];
658          
659          double *remote_threshold=NULL;
660          
661          Paso_Coupler* threshold_coupler=Paso_Coupler_alloc(A->row_coupler->connector  ,2);
662          Paso_Coupler_startCollect(threshold_coupler,threshold_p);
663          Paso_Coupler_finishCollect(threshold_coupler);
664          remote_threshold=threshold_coupler->recv_buffer;
665          
666          #pragma omp parallel for private(i,iptr) schedule(static)
667          for (i=0; i<overlap_n; i++) {
668        
669         const double threshold2 = remote_threshold[2*i+1]*remote_threshold[2*i+1];
670         register dim_t kdeg=0;
671         register const index_t koffset=koffset_0+A->row_coupleBlock->pattern->ptr[i]+A->remote_coupleBlock->pattern->ptr[i];
672         if (remote_threshold[2*i]>0) {
673            #pragma ivdep
674            for (iptr=A->row_coupleBlock->pattern->ptr[i];iptr<A->row_coupleBlock->pattern->ptr[i+1]; ++iptr) {
675               register index_t j=A->row_coupleBlock->pattern->index[iptr];
676               register double fnorm2=0;
677               #pragma ivdepremote_threshold[2*i]
678               for(bi=0;bi<block_size;++bi) {
679              register double rtmp2 = A->row_coupleBlock->val[iptr*block_size+bi];
680              fnorm2+=rtmp2*rtmp2;
681               }
682              
683               if(fnorm2 > threshold2 ) {
684              S[koffset+kdeg] = j ;
685              kdeg++;
686               }
687          }          }
         degree[i]=kdeg;  
      }        
      TMPMEMFREE(rtmp);  
       } /* end of parallel region */  
   
 }    
688    
689  /* the runge stueben coarsening algorithm: */          #pragma ivdep
690  void Paso_Preconditioner_AMG_RungeStuebenSearch(const dim_t n, const index_t* offset,              for (iptr=A->remote_coupleBlock->pattern->ptr[i];iptr<A->remote_coupleBlock->pattern->ptr[i+1]; ++iptr) {
691                           const dim_t* degree, const index_t* S,                 register index_t j=A->remote_coupleBlock->pattern->index[iptr];
692                           index_t*split_marker)                 register double fnorm2=0;
693                   #pragma ivdepremote_threshold[2*i]
694                   for(bi=0;bi<block_size;++bi) {
695                      register double rtmp2 = A->remote_coupleBlock->val[iptr*block_size+bi];
696                      fnorm2+=rtmp2*rtmp2;
697                   }
698                   if(fnorm2 > threshold2 && i != j) {
699                      S[koffset+kdeg] = j + my_n;
700                      kdeg++;
701                   }
702                }
703            
704         }
705         offset_S[i+my_n]=koffset;
706         degree_S[i+my_n]=kdeg;
707          }
708          Paso_Coupler_free(threshold_coupler);
709       }
710       TMPMEMFREE(threshold_p);
711    }
712    
713    void Paso_Preconditioner_AMG_transposeStrongConnections(const dim_t n, const dim_t* degree_S, const index_t* offset_S, const index_t* S,
714                                const dim_t nT, dim_t* degree_ST, index_t* offset_ST,index_t* ST)
715  {  {
716     const bool_t usePanel=FALSE;     index_t i, j;
717         dim_t p;
718     index_t *lambda=NULL, *ST=NULL, *notInPanel=NULL, *panel=NULL, lambda_max, lambda_k;     dim_t len=0;
719     dim_t i,k, p, q, *degreeT=NULL, len_panel, len_panel_new;     #pragma omp parallel for private(i) schedule(static)
720     register index_t j, itmp;     for (i=0; i<nT ;++i) {
721            degree_ST[i]=0;
    if (n<=0) return; /* make sure that the return of Paso_Util_arg_max is not pointing to nirvana */  
     
    lambda=TMPMEMALLOC(n, index_t); Esys_checkPtr(lambda);  
    degreeT=TMPMEMALLOC(n, dim_t); Esys_checkPtr(degreeT);  
    ST=TMPMEMALLOC(offset[n], index_t);  Esys_checkPtr(ST);  
    if (usePanel) {  
       notInPanel=TMPMEMALLOC(n, bool_t); Esys_checkPtr(notInPanel);  
       panel=TMPMEMALLOC(n, index_t); Esys_checkPtr(panel);  
722     }     }
723       for (i=0; i<n ;++i) {
724          for (p=0; p<degree_S[i]; ++p) degree_ST[ S[offset_S[i]+p] ]++;
725       }
726       for (i=0; i<nT ;++i) {
727          offset_ST[i]=len;
728          len+=degree_ST[i];
729          degree_ST[i]=0;
730       }
731       for (i=0; i<n ;++i) {
732          for (p=0; p<degree_S[i]; ++p) {
733           j=S[offset_S[i]+p];
734           ST[offset_ST[j]+degree_ST[j]]=i;
735           degree_ST[j]++;
736          }
737       }
738    }
739    
740    int compareindex(const void *a, const void *b)
741    {
742      return (*(int *)a - *(int *)b);
743    }
744    
745    void Paso_Preconditioner_AMG_CIJPCoarsening(const dim_t n, const dim_t my_n, index_t*split_marker,
746                            const dim_t* degree_S, const index_t* offset_S, const index_t* S,
747                            const dim_t* degree_ST, const index_t* offset_ST, const index_t* ST,
748                            Paso_Connector* col_connector, Paso_Distribution* col_dist)
749    {
750       dim_t i, numUndefined,   iter=0;
751      index_t iptr, jptr, kptr;
752      double *random=NULL, *w=NULL, *Status=NULL;
753      index_t * ST_flag=NULL;
754      index_t rank=col_connector->mpi_info->rank;
755    
756      Paso_Coupler* w_coupler=Paso_Coupler_alloc(col_connector  ,1);
757        
758        w=TMPMEMALLOC(n, double);
759        Status=TMPMEMALLOC(n, double);
760     if (Esys_noError() ) {    random = Paso_Distribution_createRandomVector(col_dist,1);
761        /* initialize  split_marker and split_marker :*/    ST_flag=TMPMEMALLOC(offset_ST[n-1]+ degree_ST[n-1], index_t);
762        /* those unknows which are not influenced go into F, the rest is available for F or C */  
763        #pragma omp parallel for private(i) schedule(static)    #pragma omp parallel for private(i)
764        for (i=0;i<n;++i) {    for (i=0; i< my_n; ++i) {
765       degreeT[i]=0;        w[i]=degree_ST[i]+random[i];
766       if (degree[i]>0) {        if (degree_ST[i] < 1) {
767          lambda[i]=0;         Status[i]=-100; /* F point  */
768          split_marker[i]=PASO_AMG_UNDECIDED;        } else {
769       } else {         Status[i]=1; /* status undefined */
         split_marker[i]=PASO_AMG_IN_F;  
         lambda[i]=-1;  
      }  
770        }        }
771        /* create transpose :*/    }
772        for (i=0;i<n;++i) {  
773          for (p=0; p<degree[i]; ++p) {    #pragma omp parallel for private(i, iptr)
774             j=S[offset[i]+p];    for (i=0; i< n; ++i) {
775             ST[offset[j]+degreeT[j]]=i;        for( iptr =0 ; iptr < degree_ST[i]; ++iptr)  {
776             degreeT[j]++;       ST_flag[offset_ST[i]+iptr]=1;
         }  
777        }        }
778        /* lambda[i] = |undecided k in ST[i]| + 2 * |F-unknown in ST[i]| */    }  
779        #pragma omp parallel for private(i, j, itmp) schedule(static)  
780        for (i=0;i<n;++i) {    
781       if (split_marker[i]==PASO_AMG_UNDECIDED) {    numUndefined = Paso_Distribution_numPositives(Status, col_dist, 1 );
782          itmp=lambda[i];    printf(" coarsening loop start: num of undefined rows = %d \n",numUndefined);
783          for (p=0; p<degreeT[i]; ++p) {    iter=0;
784             j=ST[offset[i]+p];    while (numUndefined > 0) {
785             if (split_marker[j]==PASO_AMG_UNDECIDED) {       Paso_Coupler_fillOverlap(n, w, w_coupler);
786            itmp++;  
787             } else {  /* at this point there are no C points */        /* calculate the maximum value of neighbours following active strong connections:
788            itmp+=2;          w2[i]=MAX(w[k]) with k in ST[i] or S[i] and (i,k) connection is still active  */      
789          #pragma omp parallel for private(i, iptr)
790          for (i=0; i<my_n; ++i) {
791         if (Status[i]>0) { /* status is still undefined */
792    
793            register bool_t inD=TRUE;
794            const double wi=w[i];
795    
796            for( iptr =0 ; iptr < degree_S[i]; ++iptr) {
797               const index_t k=S[offset_S[i]+iptr];
798               const index_t* start_p = &ST[offset_ST[k]];
799               const index_t* where_p=(index_t*)bsearch(&i, start_p, degree_ST[k], sizeof(index_t), Paso_comparIndex);
800    
801               if (ST_flag[offset_ST[k] + (index_t)(where_p-start_p)]>0) {
802              if (wi <= w[k] ) {
803                 inD=FALSE;
804                 break;
805              }
806             }             }
807            
808            }
809            
810            if (inD) {
811              for( iptr =0 ; iptr < degree_ST[i]; ++iptr) {
812                 const index_t k=ST[offset_ST[i]+iptr];
813                 if ( ST_flag[offset_ST[i]+iptr] > 0 ) {
814                           if (wi <= w[k] ) {
815                   inD=FALSE;
816                   break;
817                }
818                 }
819              }
820            }    
821            if (inD) {
822               Status[i]=0.; /* is in D */
823          }          }
         lambda[i]=itmp;  
824       }       }
825        
826        }        }
       if (usePanel) {  
      #pragma omp parallel for private(i) schedule(static)  
      for (i=0;i<n;++i) notInPanel[i]=TRUE;  
       }  
       /* start search :*/  
       i=Paso_Util_arg_max(n,lambda);  
       while (lambda[i]>-1) { /* is there any undecided unknown? */  
   
      if (usePanel) {  
         len_panel=0;  
         do {  
            /* the unknown i is moved to C */  
            split_marker[i]=PASO_AMG_IN_C;  
            lambda[i]=-1;  /* lambda from unavailable unknowns is set to -1 */  
             
            /* all undecided unknown strongly coupled to i are moved to F */  
            for (p=0; p<degreeT[i]; ++p) {  
           j=ST[offset[i]+p];  
             
           if (split_marker[j]==PASO_AMG_UNDECIDED) {  
               
              split_marker[j]=PASO_AMG_IN_F;  
              lambda[j]=-1;  
               
              for (q=0; q<degreeT[j]; ++q) {  
             k=ST[offset[j]+q];  
             if (split_marker[k]==PASO_AMG_UNDECIDED) {  
                lambda[k]++;  
                if (notInPanel[k]) {  
                   notInPanel[k]=FALSE;  
                   panel[len_panel]=k;  
                   len_panel++;  
                }  
827    
828              }    /* the unknown i is moved to C */        Paso_Coupler_fillOverlap(n, Status, w_coupler);
829              split_marker[i]=PASO_AMG_IN_C;  
830              lambda[i]=-1;  /* lambda from unavailable unknowns is set to -1 */  
831               }       /*   remove connection to D points :
832                    
833               for each i in D:
834              for each j in S_i:
835                 w[j]--
836                 ST_tag[j,i]=-1
837              for each j in ST[i]:
838                 ST_tag[i,j]=-1
839                 for each k in ST[j]:
840                if k in ST[i]:
841                   w[j]--;
842                ST_tag[j,k]=-1
843                
844         */
845         /* w is updated  for local rows only */
846         {
847            #pragma omp parallel for private(i, jptr)
848            for (i=0; i< my_n; ++i) {
849    
850               for (jptr=0; jptr<degree_ST[i]; ++jptr) {
851              const index_t j=ST[offset_ST[i]+jptr];
852              if ( (Status[j] == 0.) && (ST_flag[offset_ST[i]+jptr]>0) ) {
853                 w[i]--;
854                 ST_flag[offset_ST[i]+jptr]=-1;
855            }            }
856             }             }
857             for (p=0; p<degree[i]; ++p) {            
858            j=S[offset[i]+p];          }
859            if (split_marker[j]==PASO_AMG_UNDECIDED) {          #pragma omp parallel for private(i, jptr)
860               lambda[j]--;          for (i=my_n; i< n; ++i) {
861               if (notInPanel[j]) {             for (jptr=0; jptr<degree_ST[i]; ++jptr) {
862              notInPanel[j]=FALSE;            const index_t j = ST[offset_ST[i]+jptr];
863              panel[len_panel]=j;            if ( Status[j] == 0. ) ST_flag[offset_ST[i]+jptr]=-1;
             len_panel++;  
              }  
           }  
864             }             }
865            }
866    
867            
868            for (i=0; i< n; ++i) {
869               if ( Status[i] == 0. ) {
870    
871                         const index_t* start_p = &ST[offset_ST[i]];
872    
873             /* consolidate panel */               for (jptr=0; jptr<degree_ST[i]; ++jptr) {
874             /* remove lambda[q]=-1 */              const index_t j=ST[offset_ST[i]+jptr];
875             lambda_max=-1;              ST_flag[offset_ST[i]+jptr]=-1;
876             i=-1;              for (kptr=0; kptr<degree_ST[j]; ++kptr) {
877             len_panel_new=0;                 const index_t k=ST[offset_ST[j]+kptr];
878             for (q=0; q<len_panel; q++) {                 if (NULL != bsearch(&k, start_p, degree_ST[i], sizeof(index_t), Paso_comparIndex) ) { /* k in ST[i] ? */
879               k=panel[q];                    if (ST_flag[offset_ST[j]+kptr] >0) {
880               lambda_k=lambda[k];                   if (j< my_n ) {
881               if (split_marker[k]==PASO_AMG_UNDECIDED) {                      w[j]--;
882              panel[len_panel_new]=k;                   }
883              len_panel_new++;                   ST_flag[offset_ST[j]+kptr]=-1;
884                      }
885              if (lambda_max == lambda_k) {                 }
                if (k<i) i=k;  
             } else if (lambda_max < lambda_k) {  
                lambda_max =lambda_k;  
                i=k;  
886              }              }
887               }               }
            }  
            len_panel=len_panel_new;  
         } while (len_panel>0);      
      } else {  
         /* the unknown i is moved to C */  
         split_marker[i]=PASO_AMG_IN_C;  
         lambda[i]=-1;  /* lambda from unavailable unknowns is set to -1 */  
           
         /* all undecided unknown strongly coupled to i are moved to F */  
         for (p=0; p<degreeT[i]; ++p) {  
            j=ST[offset[i]+p];  
            if (split_marker[j]==PASO_AMG_UNDECIDED) {  
           
           split_marker[j]=PASO_AMG_IN_F;  
           lambda[j]=-1;  
           
           for (q=0; q<degreeT[j]; ++q) {  
              k=ST[offset[j]+q];  
              if (split_marker[k]==PASO_AMG_UNDECIDED) lambda[k]++;  
888            }            }
   
            }  
889          }          }
890          for (p=0; p<degree[i]; ++p) {       }
891             j=S[offset[i]+p];  
892             if(split_marker[j]==PASO_AMG_UNDECIDED) lambda[j]--;       /* adjust status */
893         #pragma omp parallel for private(i)
894         for (i=0; i< my_n; ++i) {
895            if ( Status[i] == 0. ) {
896               Status[i] = -10;   /* this is now a C point */
897            } else if (Status[i] == 1. && w[i]<1.) {
898               Status[i] = -100;   /* this is now a F point */  
899          }          }
           
900       }       }
901       i=Paso_Util_arg_max(n,lambda);      
902         i = numUndefined;
903         numUndefined = Paso_Distribution_numPositives(Status, col_dist, 1 );
904         if (numUndefined == i) {
905           Esys_setError(SYSTEM_ERROR, "Can NOT reduce numUndefined.");
906           return;
907         }
908    
909         iter++;
910         printf(" coarsening loop %d: num of undefined rows = %d \n",iter, numUndefined);
911    
912      } /* end of while loop */
913    
914      /* map to output :*/
915      Paso_Coupler_fillOverlap(n, Status, w_coupler);
916      #pragma omp parallel for private(i)
917      for (i=0; i< n; ++i) {
918         if (Status[i] > -50.) {
919            split_marker[i]=PASO_AMG_IN_C;
920         } else {
921            split_marker[i]=PASO_AMG_IN_F;
922         }
923      }
924      /* clean up : */
925      Paso_Coupler_free(w_coupler);
926      TMPMEMFREE(random);
927      TMPMEMFREE(w);
928      TMPMEMFREE(Status);
929      TMPMEMFREE(ST_flag);
930      
931      return;
932    }
933    
934    /* Merge the system matrix which is distributed on ranks into a complete
935       matrix on rank 0, then solve this matrix on rank 0 only */
936    Paso_SparseMatrix* Paso_Preconditioner_AMG_mergeSystemMatrix(Paso_SystemMatrix* A) {
937      index_t i, iptr, j, n, remote_n, total_n, len, offset, tag;
938      index_t row_block_size, col_block_size, block_size;
939      index_t size=A->mpi_info->size;
940      index_t rank=A->mpi_info->rank;
941      index_t *ptr=NULL, *idx=NULL, *ptr_global=NULL, *idx_global=NULL;
942      index_t *temp_n=NULL, *temp_len=NULL;
943      double  *val=NULL;
944      Paso_Pattern *pattern=NULL;
945      Paso_SparseMatrix *out=NULL;
946      #ifdef ESYS_MPI
947        MPI_Request* mpi_requests=NULL;
948        MPI_Status* mpi_stati=NULL;
949      #else
950        int *mpi_requests=NULL, *mpi_stati=NULL;
951      #endif
952    
953      if (size == 1) {
954        n = A->mainBlock->numRows;
955        ptr = TMPMEMALLOC(n, index_t);
956        #pragma omp parallel for private(i)
957        for (i=0; i<n; i++) ptr[i] = i;
958        out = Paso_SparseMatrix_getSubmatrix(A->mainBlock, n, n, ptr, ptr);
959        TMPMEMFREE(ptr);
960        return out;
961      }
962    
963      n = A->mainBlock->numRows;
964      block_size = A->block_size;
965    
966      /* Merge MainBlock and CoupleBlock to get a complete column entries
967         for each row allocated to current rank. Output (ptr, idx, val)
968         contains all info needed from current rank to merge a system
969         matrix  */
970      Paso_SystemMatrix_mergeMainAndCouple(A, &ptr, &idx, &val);
971    
972      #ifdef ESYS_MPI
973        mpi_requests=TMPMEMALLOC(size*2,MPI_Request);
974        mpi_stati=TMPMEMALLOC(size*2,MPI_Status);
975      #else
976        mpi_requests=TMPMEMALLOC(size*2,int);
977        mpi_stati=TMPMEMALLOC(size*2,int);
978      #endif
979    
980      /* Now, pass all info to rank 0 and merge them into one sparse
981         matrix */
982      if (rank == 0) {
983        /* First, copy local ptr values into ptr_global */
984        total_n=Paso_SystemMatrix_getGlobalNumRows(A);
985        ptr_global = MEMALLOC(total_n+1, index_t);
986        memcpy(ptr_global, ptr, (n+1) * sizeof(index_t));
987        iptr = n+1;
988        MEMFREE(ptr);
989        temp_n = TMPMEMALLOC(size, index_t);
990        temp_len = TMPMEMALLOC(size, index_t);
991        temp_n[0] = iptr;
992        
993        /* Second, receive ptr values from other ranks */
994        for (i=1; i<size; i++) {
995          remote_n = A->row_distribution->first_component[i+1] -
996             A->row_distribution->first_component[i];
997          MPI_Irecv(&(ptr_global[iptr]), remote_n, MPI_INT, i,
998                A->mpi_info->msg_tag_counter+i,
999                A->mpi_info->comm,
1000                &mpi_requests[i]);
1001          temp_n[i] = remote_n;
1002          iptr += remote_n;
1003        }
1004        MPI_Waitall(size-1, &(mpi_requests[1]), mpi_stati);
1005        A->mpi_info->msg_tag_counter += size;
1006    
1007        /* Then, prepare to receive idx and val from other ranks */
1008        len = 0;
1009        offset = -1;
1010        for (i=0; i<size; i++) {
1011          if (temp_n[i] > 0) {
1012        offset += temp_n[i];
1013        len += ptr_global[offset];
1014        temp_len[i] = ptr_global[offset];
1015          }else
1016        temp_len[i] = 0;
1017        }
1018    
1019        idx_global = MEMALLOC(len, index_t);
1020        iptr = temp_len[0];
1021        offset = n+1;
1022        for (i=1; i<size; i++) {
1023          len = temp_len[i];
1024          MPI_Irecv(&(idx_global[iptr]), len, MPI_INT, i,
1025                A->mpi_info->msg_tag_counter+i,
1026                A->mpi_info->comm,
1027                &mpi_requests[i]);
1028          remote_n = temp_n[i];
1029          for (j=0; j<remote_n; j++) {
1030        ptr_global[j+offset] = ptr_global[j+offset] + iptr;
1031        }        }
1032     }        offset += remote_n;
1033     TMPMEMFREE(lambda);        iptr += len;
1034     TMPMEMFREE(ST);      }
1035     TMPMEMFREE(degreeT);      memcpy(idx_global, idx, temp_len[0] * sizeof(index_t));
1036     TMPMEMFREE(panel);      MEMFREE(idx);
1037     TMPMEMFREE(notInPanel);      row_block_size = A->mainBlock->row_block_size;
1038        col_block_size = A->mainBlock->col_block_size;
1039        MPI_Waitall(size-1, &(mpi_requests[1]), mpi_stati);
1040        A->mpi_info->msg_tag_counter += size;
1041        TMPMEMFREE(temp_n);
1042    
1043        /* Then generate the sparse matrix */
1044        pattern = Paso_Pattern_alloc(A->mainBlock->pattern->type, total_n,
1045                total_n, ptr_global, idx_global);
1046        out = Paso_SparseMatrix_alloc(A->mainBlock->type, pattern,
1047                row_block_size, col_block_size, FALSE);
1048        Paso_Pattern_free(pattern);
1049    
1050        /* Finally, receive and copy the value */
1051        iptr = temp_len[0] * block_size;
1052        for (i=1; i<size; i++) {
1053          len = temp_len[i];
1054          MPI_Irecv(&(out->val[iptr]), len * block_size, MPI_DOUBLE, i,
1055                            A->mpi_info->msg_tag_counter+i,
1056                            A->mpi_info->comm,
1057                            &mpi_requests[i]);
1058          iptr += (len * block_size);
1059        }
1060        memcpy(out->val, val, temp_len[0] * sizeof(double) * block_size);
1061        MEMFREE(val);
1062        MPI_Waitall(size-1, &(mpi_requests[1]), mpi_stati);
1063        A->mpi_info->msg_tag_counter += size;
1064        TMPMEMFREE(temp_len);
1065      } else { /* it's not rank 0 */
1066    
1067        /* First, send out the local ptr */
1068        tag = A->mpi_info->msg_tag_counter+rank;
1069        MPI_Issend(&(ptr[1]), n, MPI_INT, 0, tag, A->mpi_info->comm,
1070                &mpi_requests[0]);
1071    
1072        /* Next, send out the local idx */
1073        len = ptr[n];
1074        tag += size;
1075        MPI_Issend(idx, len, MPI_INT, 0, tag, A->mpi_info->comm,
1076                &mpi_requests[1]);
1077    
1078        /* At last, send out the local val */
1079        len *= block_size;
1080        tag += size;
1081        MPI_Issend(val, len, MPI_DOUBLE, 0, tag, A->mpi_info->comm,
1082                &mpi_requests[2]);
1083    
1084        MPI_Waitall(3, mpi_requests, mpi_stati);
1085        A->mpi_info->msg_tag_counter = tag + size - rank;
1086        MEMFREE(ptr);
1087        MEMFREE(idx);
1088        MEMFREE(val);
1089    
1090        out = NULL;
1091      }
1092    
1093      TMPMEMFREE(mpi_requests);
1094      TMPMEMFREE(mpi_stati);
1095      return out;
1096    }
1097    
1098    
1099    void Paso_Preconditioner_AMG_mergeSolve(Paso_Preconditioner_AMG * amg) {
1100      Paso_SystemMatrix *A = amg->A_C;
1101      Paso_SparseMatrix *A_D, *A_temp;
1102      double* x=NULL;
1103      double* b=NULL;
1104      index_t rank = A->mpi_info->rank;
1105      index_t size = A->mpi_info->size;
1106      index_t i, n, p, count, n_block;
1107      index_t *counts, *offset, *dist;
1108    
1109      n_block = amg->n_block;
1110    
1111      A_D = Paso_Preconditioner_AMG_mergeSystemMatrix(A);
1112    
1113      /* First, gather x and b into rank 0 */
1114      dist = A->pattern->input_distribution->first_component;
1115      n = Paso_SystemMatrix_getGlobalNumRows(A);
1116      b = TMPMEMALLOC(n*n_block, double);
1117      x = TMPMEMALLOC(n*n_block, double);
1118      counts = TMPMEMALLOC(size, index_t);
1119      offset = TMPMEMALLOC(size, index_t);
1120    
1121      #pragma omp parallel for private(i,p)
1122      for (i=0; i<size; i++) {
1123        p = dist[i];
1124        counts[i] = (dist[i+1] - p)*n_block;
1125        offset[i] = p*n_block;
1126      }
1127      count = counts[rank];
1128      MPI_Gatherv(amg->b_C, count, MPI_DOUBLE, b, counts, offset, MPI_DOUBLE, 0, A->mpi_info->comm);
1129      MPI_Gatherv(amg->x_C, count, MPI_DOUBLE, x, counts, offset, MPI_DOUBLE, 0, A->mpi_info->comm);
1130    
1131      if (rank == 0) {
1132        /* solve locally */
1133        #ifdef MKL
1134          A_temp = Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, A_D);
1135          A_temp->solver_package = PASO_MKL;
1136          Paso_SparseMatrix_free(A_D);
1137          Paso_MKL(A_temp, x, b, amg->reordering, amg->refinements, SHOW_TIMING);
1138          Paso_SparseMatrix_free(A_temp);
1139        #else
1140          #ifdef UMFPACK
1141        A_temp = Paso_SparseMatrix_unroll(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_CSC, A_D);
1142        A_temp->solver_package = PASO_UMFPACK;
1143        Paso_SparseMatrix_free(A_D);
1144        Paso_UMFPACK(A_temp, x, b, amg->refinements, SHOW_TIMING);
1145        Paso_SparseMatrix_free(A_temp);
1146          #else
1147        A_D->solver_p = Paso_Preconditioner_LocalSmoother_alloc(A_D, (amg->options_smoother == PASO_JACOBI), amg->verbose);
1148        A_D->solver_package = PASO_SMOOTHER;
1149        Paso_Preconditioner_LocalSmoother_solve(A_D, A_D->solver_p, x, b, amg->pre_sweeps+amg->post_sweeps, FALSE);
1150        Paso_SparseMatrix_free(A_D);
1151          #endif
1152        #endif
1153      }
1154    
1155      /* now we need to distribute the solution to all ranks */
1156      MPI_Scatterv(x, counts, offset, MPI_DOUBLE, amg->x_C, count, MPI_DOUBLE, 0, A->mpi_info->comm);
1157    
1158      TMPMEMFREE(x);
1159      TMPMEMFREE(b);
1160      TMPMEMFREE(counts);
1161      TMPMEMFREE(offset);
1162  }  }

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