Пример #1
0
int main(int argc, char *argv[])
{
  int num_PDE_eqns=1, N_levels=3, nsmooth=2;

  int leng, level, N_grid_pts, coarsest_level;
  int leng1,leng2;
  /* See Aztec User's Guide for more information on the */
  /* variables that follow.                             */

  int    proc_config[AZ_PROC_SIZE], options[AZ_OPTIONS_SIZE];
  double params[AZ_PARAMS_SIZE], status[AZ_STATUS_SIZE];

  /* data structure for matrix corresponding to the fine grid */

  double *val = NULL, *xxx, *rhs, solve_time, setup_time, start_time;
  AZ_MATRIX *Amat;
  AZ_PRECOND *Pmat = NULL;
  ML *ml;
  FILE *fp;
  int i, j, Nrigid, *garbage, nblocks=0, *blocks = NULL, *block_pde=NULL;
  struct AZ_SCALING *scaling;
  ML_Aggregate *ag;
  double *mode, *rigid=NULL, alpha; 
  char filename[80];
  int    one = 1;
  int    proc,nprocs;
  char pathfilename[100];

#ifdef ML_MPI
  MPI_Init(&argc,&argv);
  /* get number of processors and the name of this processor */
  AZ_set_proc_config(proc_config, MPI_COMM_WORLD);
  proc   = proc_config[AZ_node];
  nprocs = proc_config[AZ_N_procs];
#else
  AZ_set_proc_config(proc_config, AZ_NOT_MPI);
  proc   = 0;
  nprocs = 1;
#endif

   if (proc_config[AZ_node] == 0) {
      sprintf(pathfilename,"%s/inputfile",argv[1]);
      ML_Reader_ReadInput(pathfilename, &context);
   }
   else context = (struct reader_context *) ML_allocate(sizeof(struct reader_context));
   AZ_broadcast((char *) context,  sizeof(struct reader_context), proc_config,
                AZ_PACK);
   AZ_broadcast((char *) NULL        ,   0          , proc_config, AZ_SEND);

   N_levels = context->N_levels;
   printf("N_levels %d\n",N_levels);
   nsmooth   = context->nsmooth;
   num_PDE_eqns = context->N_dofPerNode;
   printf("num_PDE_eqns %d\n",num_PDE_eqns);

   ML_Set_PrintLevel(context->output_level);

  /* read in the number of matrix equations */
  leng = 0;
  if (proc_config[AZ_node] == 0) {
        sprintf(pathfilename,"%s/data_matrix.txt",argv[1]);
        fp=fopen(pathfilename,"r");
     if (fp==NULL) {
        printf("**ERR** couldn't open file data_matrix.txt\n");
        exit(1);
     }
        fscanf(fp,"%d",&leng);
     fclose(fp);
  }
  leng = AZ_gsum_int(leng, proc_config);

  N_grid_pts=leng/num_PDE_eqns;


  /* initialize the list of global indices. NOTE: the list of global */
  /* indices must be in ascending order so that subsequent calls to  */
  /* AZ_find_index() will function properly. */
#if 0
  if (proc_config[AZ_N_procs] == 1) i = AZ_linear;
  else i = AZ_file;
#endif
  i = AZ_linear;

  /* cannot use AZ_input_update for variable blocks (forgot why, but debugged through it)*/
  /* make a linear distribution of the matrix       */
  /* if the linear distribution does not align with the blocks, */
  /* this is corrected in ML_AZ_Reader_ReadVariableBlocks */
  leng1 = leng/nprocs;
  leng2 = leng-leng1*nprocs;
  if (proc >= leng2)
  {
     leng2 += (proc*leng1);
  }
  else
  {
     leng1++;
     leng2 = proc*leng1;
  }
  N_update = leng1;
  update = (int*)AZ_allocate((N_update+1)*sizeof(int));
  if (update==NULL)
  {
      (void) fprintf (stderr, "Not enough space to allocate 'update'\n");
      fflush(stderr); exit(EXIT_FAILURE);
  }
  for (i=0; i<N_update; i++) update[i] = i+leng2;
  
#if 0 /* debug */
  printf("proc %d N_update %d\n",proc_config[AZ_node],N_update);
  fflush(stdout);                   
#endif
  sprintf(pathfilename,"%s/data_vblocks.txt",argv[1]);
  ML_AZ_Reader_ReadVariableBlocks(pathfilename,&nblocks,&blocks,&block_pde,
                                  &N_update,&update,proc_config);
#if 0 /* debug */
  printf("proc %d N_update %d\n",proc_config[AZ_node],N_update);
  fflush(stdout);                   
#endif

  sprintf(pathfilename,"%s/data_matrix.txt",argv[1]);
  AZ_input_msr_matrix(pathfilename,update, &val, &bindx, N_update, proc_config);

  /* This code is to fix things up so that we are sure we have   */ 
  /* all blocks (including the ghost nodes) the same size.       */
  /* not sure, whether this is a good idea with variable blocks  */
  /* the examples inpufiles (see top of this file) don't need it */
  /* anyway                                                      */
  /*
  AZ_block_MSR(&bindx, &val, N_update, num_PDE_eqns, update);
  */
  AZ_transform_norowreordering(proc_config, &external, bindx, val,  update, &update_index,
	       &extern_index, &data_org, N_update, 0, 0, 0, &cpntr,
	       AZ_MSR_MATRIX);
	
  Amat = AZ_matrix_create( leng );

  AZ_set_MSR(Amat, bindx, val, data_org, 0, NULL, AZ_LOCAL);

  Amat->matrix_type  = data_org[AZ_matrix_type];
	
  data_org[AZ_N_rows]  = data_org[AZ_N_internal] + data_org[AZ_N_border];
			
  start_time = AZ_second();

  options[AZ_scaling] = AZ_none;

  ML_Create(&ml, N_levels);
			
			
  /* set up discretization matrix and matrix vector function */
  AZ_ML_Set_Amat(ml, 0, N_update, N_update, Amat, proc_config);

  ML_Set_ResidualOutputFrequency(ml, context->output);
  ML_Set_Tolerance(ml, context->tol);
  ML_Aggregate_Create( &ag );
  if (ML_strcmp(context->agg_coarsen_scheme,"Mis") == 0) {
     ML_Aggregate_Set_CoarsenScheme_MIS(ag);
  }
  else if (ML_strcmp(context->agg_coarsen_scheme,"Uncoupled") == 0) {
     ML_Aggregate_Set_CoarsenScheme_Uncoupled(ag);
  }
  else if (ML_strcmp(context->agg_coarsen_scheme,"Coupled") == 0) {
     ML_Aggregate_Set_CoarsenScheme_Coupled(ag);
  }
  else if (ML_strcmp(context->agg_coarsen_scheme,"Metis") == 0) {
     ML_Aggregate_Set_CoarsenScheme_METIS(ag);
     for (i=0; i<N_levels; i++)
        ML_Aggregate_Set_NodesPerAggr(ml,ag,i,9);
  }
  else if (ML_strcmp(context->agg_coarsen_scheme,"VBMetis") == 0) {
     /* when no blocks read, use standard metis assuming constant block sizes */
     if (!blocks) 
        ML_Aggregate_Set_CoarsenScheme_METIS(ag);
     else {
        ML_Aggregate_Set_CoarsenScheme_VBMETIS(ag);
        ML_Aggregate_Set_Vblocks_CoarsenScheme_VBMETIS(ag,0,N_levels,nblocks,
                                                       blocks,block_pde,N_update);
     }
     for (i=0; i<N_levels; i++)
        ML_Aggregate_Set_NodesPerAggr(ml,ag,i,9);
  }
  else {
     printf("**ERR** ML: Unknown aggregation scheme %s\n",context->agg_coarsen_scheme);
     exit(-1);
  }
  ML_Aggregate_Set_DampingFactor(ag, context->agg_damping);
  ML_Aggregate_Set_MaxCoarseSize( ag, context->maxcoarsesize);
  ML_Aggregate_Set_Threshold(ag, context->agg_thresh);

  if (ML_strcmp(context->agg_spectral_norm,"Calc") == 0) {
     ML_Set_SpectralNormScheme_Calc(ml);
  }
  else if (ML_strcmp(context->agg_spectral_norm,"Anorm") == 0) {
     ML_Set_SpectralNormScheme_Anorm(ml);
  }
  else {
     printf("**WRN** ML: Unknown spectral norm scheme %s\n",context->agg_spectral_norm);
  }

  /* read in the rigid body modes */

   Nrigid = 0;
   if (proc_config[AZ_node] == 0) {
      sprintf(filename,"data_nullsp%d.txt",Nrigid);
      sprintf(pathfilename,"%s/%s",argv[1],filename);
      while( (fp = fopen(pathfilename,"r")) != NULL) {
          fclose(fp);
          Nrigid++;
          sprintf(filename,"data_nullsp%d.txt",Nrigid);
          sprintf(pathfilename,"%s/%s",argv[1],filename);
      }
    }
    Nrigid = AZ_gsum_int(Nrigid,proc_config);

    if (Nrigid != 0) {
       rigid = (double *) ML_allocate( sizeof(double)*Nrigid*(N_update+1) );
       if (rigid == NULL) {
          printf("Error: Not enough space for rigid body modes\n");
       }
    }

   /* Set rhs */
   sprintf(pathfilename,"%s/data_rhs.txt",argv[1]);
   fp = fopen(pathfilename,"r");
   if (fp == NULL) {
      rhs=(double *)ML_allocate(leng*sizeof(double));
      if (proc_config[AZ_node] == 0) printf("taking linear vector for rhs\n");
      for (i = 0; i < N_update; i++) rhs[i] = (double) update[i];
   }
   else {
      fclose(fp);
      if (proc_config[AZ_node] == 0) printf("reading rhs from a file\n");
      AZ_input_msr_matrix(pathfilename, update, &rhs, &garbage, N_update, 
                          proc_config);
   }
   AZ_reorder_vec(rhs, data_org, update_index, NULL);

   for (i = 0; i < Nrigid; i++) {
      sprintf(filename,"data_nullsp%d.txt",i);
      sprintf(pathfilename,"%s/%s",argv[1],filename);
      AZ_input_msr_matrix(pathfilename, update, &mode, &garbage, N_update, 
                          proc_config);
      AZ_reorder_vec(mode, data_org, update_index, NULL);

#if 0 /* test the given rigid body mode, output-vector should be ~0 */
       Amat->matvec(mode, rigid, Amat, proc_config);
       for (j = 0; j < N_update; j++) printf("this is %d %e\n",j,rigid[j]);
#endif

    for (j = 0; j < i; j++) {
       alpha = -AZ_gdot(N_update, mode, &(rigid[j*N_update]), proc_config)/
                  AZ_gdot(N_update, &(rigid[j*N_update]), &(rigid[j*N_update]), 
                               proc_config);
       DAXPY_F77(&N_update, &alpha,  &(rigid[j*N_update]),  &one, mode, &one);
    }
   
    /* rhs orthogonalization */

    alpha = -AZ_gdot(N_update, mode, rhs, proc_config)/
                    AZ_gdot(N_update, mode, mode, proc_config);
    DAXPY_F77(&N_update, &alpha,  mode,  &one, rhs, &one);

    for (j = 0; j < N_update; j++) rigid[i*N_update+j] = mode[j];
    free(mode);
    free(garbage);
  }

  for (j = 0; j < Nrigid; j++) {
     alpha = -AZ_gdot(N_update, rhs, &(rigid[j*N_update]), proc_config)/
              AZ_gdot(N_update, &(rigid[j*N_update]), &(rigid[j*N_update]), 
                      proc_config);
     DAXPY_F77(&N_update, &alpha,  &(rigid[j*N_update]),  &one, rhs, &one);
  }

#if 0 /* for testing the default nullsp */
  ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, 6, NULL, N_update);
#else
  if (Nrigid != 0) {
     ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, Nrigid, rigid, N_update);
  }
#endif
  if (rigid) ML_free(rigid);

  ag->keep_agg_information = 1;
  coarsest_level = ML_Gen_MGHierarchy_UsingAggregation(ml, 0, 
                                            ML_INCREASING, ag);
  coarsest_level--;                                            

  if ( proc_config[AZ_node] == 0 )
	printf("Coarse level = %d \n", coarsest_level);
	
#if 0
  /* set up smoothers */
  if (!blocks)
     blocks = (int *) ML_allocate(sizeof(int)*N_update);
#endif

  for (level = 0; level < coarsest_level; level++) {

      num_PDE_eqns = ml->Amat[level].num_PDEs;
		
     /*  Sparse approximate inverse smoother that acutally does both */
     /*  pre and post smoothing.                                     */

     if (ML_strcmp(context->smoother,"Parasails") == 0) {
        ML_Gen_Smoother_ParaSails(ml , level, ML_PRESMOOTHER, nsmooth, 
                                parasails_sym, parasails_thresh, 
                                parasails_nlevels, parasails_filter,
                                (int) parasails_loadbal, parasails_factorized);
     }

     /* This is the symmetric Gauss-Seidel smoothing that we usually use. */
     /* In parallel, it is not a true Gauss-Seidel in that each processor */
     /* does a Gauss-Seidel on its local submatrix independent of the     */
     /* other processors.                                                 */

     else if (ML_strcmp(context->smoother,"GaussSeidel") == 0) {
       ML_Gen_Smoother_GaussSeidel(ml , level, ML_BOTH, nsmooth,1.);
     }
     else if (ML_strcmp(context->smoother,"SymGaussSeidel") == 0) {
       ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.);
     }
     else if (ML_strcmp(context->smoother,"Poly") == 0) {
       ML_Gen_Smoother_Cheby(ml, level, ML_BOTH, 30., nsmooth);
     }
     else if (ML_strcmp(context->smoother,"BlockGaussSeidel") == 0) {
       ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_BOTH, nsmooth,1.,
					 num_PDE_eqns);
     }
     else if (ML_strcmp(context->smoother,"VBSymGaussSeidel") == 0) {
         if (blocks)    ML_free(blocks);
         if (block_pde) ML_free(block_pde);
         blocks    = NULL;
         block_pde = NULL;
         nblocks   = 0;
         ML_Aggregate_Get_Vblocks_CoarsenScheme_VBMETIS(ag,level,N_levels,&nblocks,
                                                        &blocks,&block_pde);
         if (blocks==NULL) ML_Gen_Blocks_Aggregates(ag, level, &nblocks, &blocks);
         ML_Gen_Smoother_VBlockSymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.,
                                              nblocks, blocks);
     }

     /* This is a true Gauss Seidel in parallel. This seems to work for  */
     /* elasticity problems.  However, I don't believe that this is very */
     /* efficient in parallel.                                           */       
     /*
      nblocks = ml->Amat[level].invec_leng;
      for (i =0; i < nblocks; i++) blocks[i] = i;
      ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml , level, ML_PRESMOOTHER,
                                                  nsmooth, 1., nblocks, blocks);
      ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml, level, ML_POSTSMOOTHER,
                                                  nsmooth, 1., nblocks, blocks);
     */

     /* Jacobi Smoothing                                                 */

     else if (ML_strcmp(context->smoother,"Jacobi") == 0) {
        ML_Gen_Smoother_Jacobi(ml , level, ML_PRESMOOTHER, nsmooth,.4);
        ML_Gen_Smoother_Jacobi(ml , level, ML_POSTSMOOTHER, nsmooth,.4);
     }

     /*  This does a block Gauss-Seidel (not true GS in parallel)        */
     /*  where each processor has 'nblocks' blocks.                      */
     /* */

     else if (ML_strcmp(context->smoother,"Metis") == 0) {
         if (blocks)    ML_free(blocks);
         if (block_pde) ML_free(block_pde);
         nblocks = 250;
         ML_Gen_Blocks_Metis(ml, level, &nblocks, &blocks);
         ML_Gen_Smoother_VBlockSymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.,
                                        nblocks, blocks);
     }
     else {
         printf("unknown smoother %s\n",context->smoother);
         exit(1);
     }
   }
	
   /* set coarse level solver */
   nsmooth   = context->coarse_its;
   /*  Sparse approximate inverse smoother that acutally does both */
   /*  pre and post smoothing.                                     */

   if (ML_strcmp(context->coarse_solve,"Parasails") == 0) {
        ML_Gen_Smoother_ParaSails(ml , coarsest_level, ML_PRESMOOTHER, nsmooth, 
                                parasails_sym, parasails_thresh, 
                                parasails_nlevels, parasails_filter,
                                (int) parasails_loadbal, parasails_factorized);
   }

   else if (ML_strcmp(context->coarse_solve,"GaussSeidel") == 0) {
       ML_Gen_Smoother_GaussSeidel(ml , coarsest_level, ML_BOTH, nsmooth,1.);
   }
   else if (ML_strcmp(context->coarse_solve,"Poly") == 0) {
     ML_Gen_Smoother_Cheby(ml, coarsest_level, ML_BOTH, 30., nsmooth);
   }
   else if (ML_strcmp(context->coarse_solve,"SymGaussSeidel") == 0) {
       ML_Gen_Smoother_SymGaussSeidel(ml , coarsest_level, ML_BOTH, nsmooth,1.);
   }
   else if (ML_strcmp(context->coarse_solve,"BlockGaussSeidel") == 0) {
       ML_Gen_Smoother_BlockGaussSeidel(ml, coarsest_level, ML_BOTH, nsmooth,1.,
					num_PDE_eqns);
   }
   else if (ML_strcmp(context->coarse_solve,"Aggregate") == 0) {
         if (blocks)    ML_free(blocks);
         if (block_pde) ML_free(block_pde);
         ML_Gen_Blocks_Aggregates(ag, coarsest_level, &nblocks, &blocks);
         ML_Gen_Smoother_VBlockSymGaussSeidel(ml , coarsest_level, ML_BOTH, 
                                        nsmooth,1., nblocks, blocks);
   }
   else if (ML_strcmp(context->coarse_solve,"Jacobi") == 0) {
        ML_Gen_Smoother_Jacobi(ml , coarsest_level, ML_BOTH, nsmooth,.5);
   }
   else if (ML_strcmp(context->coarse_solve,"Metis") == 0) {
         if (blocks)    ML_free(blocks);
         if (block_pde) ML_free(block_pde);
         nblocks = 250;
         ML_Gen_Blocks_Metis(ml, coarsest_level, &nblocks, &blocks);
         ML_Gen_Smoother_VBlockSymGaussSeidel(ml , coarsest_level, ML_BOTH, 
                                              nsmooth,1., nblocks, blocks);
   }
   else if (ML_strcmp(context->coarse_solve,"SuperLU") == 0) {
      ML_Gen_CoarseSolverSuperLU( ml, coarsest_level);
   }
   else if (ML_strcmp(context->coarse_solve,"Amesos") == 0) {
      ML_Gen_Smoother_Amesos(ml,coarsest_level,ML_AMESOS_KLU,-1, 0.0);
   }
   else {
         printf("unknown coarse grid solver %s\n",context->coarse_solve);
         exit(1);
   }
		
   ML_Gen_Solver(ml, ML_MGV, 0, coarsest_level); 

   AZ_defaults(options, params);
	
   if (ML_strcmp(context->krylov,"Cg") == 0) {
      options[AZ_solver]   = AZ_cg;
   }
   else if (ML_strcmp(context->krylov,"Bicgstab") == 0) {
      options[AZ_solver]   = AZ_bicgstab;
   }
   else if (ML_strcmp(context->krylov,"Tfqmr") == 0) {
      options[AZ_solver]   = AZ_tfqmr;
   }
   else if (ML_strcmp(context->krylov,"Gmres") == 0) {
      options[AZ_solver]   = AZ_gmres;
   }
   else {
      printf("unknown krylov method %s\n",context->krylov);
   }
   if (blocks)            ML_free(blocks);
   if (block_pde)         ML_free(block_pde);
   options[AZ_scaling]  = AZ_none;
   options[AZ_precond]  = AZ_user_precond;
   options[AZ_conv]     = AZ_r0;
   options[AZ_output]   = 1;
   options[AZ_max_iter] = context->max_outer_its;
   options[AZ_poly_ord] = 5;
   options[AZ_kspace]   = 130;
   params[AZ_tol]       = context->tol;
   options[AZ_output]   = context->output;
   ML_free(context);
	
   AZ_set_ML_preconditioner(&Pmat, Amat, ml, options); 
   setup_time = AZ_second() - start_time;
	
   xxx = (double *) malloc( leng*sizeof(double));

   for (iii = 0; iii < leng; iii++) xxx[iii] = 0.0; 
	

   /* Set x */
   /*
   there is no initguess supplied with these examples for the moment....
   */
   fp = fopen("initguessfile","r");
   if (fp != NULL) {
      fclose(fp);
      if (proc_config[AZ_node]== 0) printf("reading initial guess from file\n");
      AZ_input_msr_matrix("data_initguess.txt", update, &xxx, &garbage, N_update, 
                          proc_config);

      options[AZ_conv] = AZ_expected_values;
   }
   else if (proc_config[AZ_node]== 0) printf("taking 0 initial guess \n");

   AZ_reorder_vec(xxx, data_org, update_index, NULL);

   /* if Dirichlet BC ... put the answer in */

   for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++) {
      if ( (val[i] > .99999999) && (val[i] < 1.0000001))
         xxx[i] = rhs[i];      
   }

   fp = fopen("AZ_no_multilevel.dat","r");
   scaling = AZ_scaling_create();
   start_time = AZ_second();
   if (fp != NULL) {
      fclose(fp);
      options[AZ_precond] = AZ_none;
      options[AZ_scaling] = AZ_sym_diag;
      options[AZ_ignore_scaling] = AZ_TRUE;

      options[AZ_keep_info] = 1;
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling); 

/*
      options[AZ_pre_calc] = AZ_reuse;
      options[AZ_conv] = AZ_expected_values;
      if (proc_config[AZ_node] == 0) 
              printf("\n-------- Second solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling); 
      if (proc_config[AZ_node] == 0) 
              printf("\n-------- Third solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling); 
*/
   }
   else {
      options[AZ_keep_info] = 1;
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling); 
      options[AZ_pre_calc] = AZ_reuse;
      options[AZ_conv] = AZ_expected_values;
/*
      if (proc_config[AZ_node] == 0) 
              printf("\n-------- Second solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling); 
      if (proc_config[AZ_node] == 0) 
              printf("\n-------- Third solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling); 
*/
   }
   solve_time = AZ_second() - start_time;

   if (proc_config[AZ_node] == 0) 
      printf("Solve time = %e, MG Setup time = %e\n", solve_time, setup_time);

   if (proc_config[AZ_node] == 0) 
     printf("Printing out a few entries of the solution ...\n");

   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 7) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 23) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 47) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 101) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 171) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}

   ML_Aggregate_Destroy(&ag);
   ML_Destroy(&ml);
   AZ_free((void *) Amat->data_org);
   AZ_free((void *) Amat->val);
   AZ_free((void *) Amat->bindx);
   AZ_free((void *) update);
   AZ_free((void *) external);
   AZ_free((void *) extern_index);
   AZ_free((void *) update_index);
   AZ_scaling_destroy(&scaling);
   if (Amat  != NULL) AZ_matrix_destroy(&Amat);
   if (Pmat  != NULL) AZ_precond_destroy(&Pmat);
   free(xxx);
   free(rhs);

#ifdef ML_MPI
  MPI_Finalize();
#endif
	
  return 0;
	
}
Пример #2
0
int main(int argc, char *argv[])
{
	int num_PDE_eqns=6, N_levels=4, nsmooth=2;

	int    leng, level, N_grid_pts, coarsest_level;

  /* See Aztec User's Guide for more information on the */
  /* variables that follow.                             */

  int    proc_config[AZ_PROC_SIZE], options[AZ_OPTIONS_SIZE];
  double params[AZ_PARAMS_SIZE], status[AZ_STATUS_SIZE];

  /* data structure for matrix corresponding to the fine grid */

  double *val = NULL, *xxx, *rhs, solve_time, setup_time, start_time;
  AZ_MATRIX *Amat;
  AZ_PRECOND *Pmat = NULL;
  ML *ml;
  FILE *fp;
  int i, j, Nrigid, *garbage = NULL;
#ifdef ML_partition
  int nblocks;
  int *block_list = NULL;
  int k;
#endif
  struct AZ_SCALING *scaling;
  ML_Aggregate *ag;
double *mode, *rigid;
char filename[80];
double alpha;
int allocated = 0;
int old_prec, old_sol;
double old_tol;
/*
double *Amode, beta, biggest;
int big_ind = -1, ii;
*/
ML_Operator *Amatrix;
int *rowi_col = NULL, rowi_N, count2, ccc;
double *rowi_val = NULL;
double max_diag, min_diag, max_sum, sum;
 int nBlocks, *blockIndices, Ndof;
#ifdef ML_partition
   FILE *fp2;
   int count;

   if (argc != 2) {
     printf("Usage: ml_read_elas num_processors\n");
     exit(1);
   }
   else sscanf(argv[1],"%d",&nblocks);
#endif

#ifdef HAVE_MPI
  MPI_Init(&argc,&argv);
  /* get number of processors and the name of this processor */

  AZ_set_proc_config(proc_config, MPI_COMM_WORLD);
#else
  AZ_set_proc_config(proc_config, AZ_NOT_MPI);
#endif

  /* read in the number of matrix equations */
  leng = 0;
  if (proc_config[AZ_node] == 0) {
#    ifdef binary
	fp=fopen(".data","rb");
#    else
	fp=fopen(".data","r");
#    endif
     if (fp==NULL) {
        printf("couldn't open file .data\n");
        exit(1);
     }
#    ifdef binary
        fread(&leng, sizeof(int), 1, fp);
#    else
        fscanf(fp,"%d",&leng);
#    endif
     fclose(fp);
  }
  leng = AZ_gsum_int(leng, proc_config);

  N_grid_pts=leng/num_PDE_eqns;

  /* initialize the list of global indices. NOTE: the list of global */
  /* indices must be in ascending order so that subsequent calls to  */
  /* AZ_find_index() will function properly. */

  if (proc_config[AZ_N_procs] == 1) i = AZ_linear;
  else i = AZ_file;
  AZ_read_update(&N_update, &update, proc_config, N_grid_pts, num_PDE_eqns,i);

  AZ_read_msr_matrix(update, &val, &bindx, N_update, proc_config);


  /* This code is to fix things up so that we are sure we have */
  /* all block (including the ghost nodes the same size.       */

  AZ_block_MSR(&bindx, &val, N_update, num_PDE_eqns, update);

  AZ_transform_norowreordering(proc_config, &external, bindx, val,  update, &update_index,
	       &extern_index, &data_org, N_update, 0, 0, 0, &cpntr,
	       AZ_MSR_MATRIX);

  Amat = AZ_matrix_create( leng );
  AZ_set_MSR(Amat, bindx, val, data_org, 0, NULL, AZ_LOCAL);

  Amat->matrix_type  = data_org[AZ_matrix_type];

  data_org[AZ_N_rows]  = data_org[AZ_N_internal] + data_org[AZ_N_border];

#ifdef SCALE_ME
  ML_MSR_sym_diagonal_scaling(Amat, proc_config, &scaling_vect);
#endif

  start_time = AZ_second();

  options[AZ_scaling] = AZ_none;
  ML_Create(&ml, N_levels);
  ML_Set_PrintLevel(10);


  /* set up discretization matrix and matrix vector function */

  AZ_ML_Set_Amat(ml, N_levels-1, N_update, N_update, Amat, proc_config);

#ifdef ML_partition

  /* this code is meant to partition the matrices so that things can be */
  /* run in parallel later.                                             */
  /* It is meant to be run on only one processor.                       */
#ifdef	MB_MODIF
  fp2 = fopen(".update","w");
#else
  fp2 = fopen("partition_file","w");
#endif

  ML_Operator_AmalgamateAndDropWeak(&(ml->Amat[N_levels-1]), num_PDE_eqns, 0.0);
  ML_Gen_Blocks_Metis(ml, N_levels-1, &nblocks, &block_list);

  for (i = 0; i < nblocks; i++) {
     count = 0;
     for (j = 0; j < ml->Amat[N_levels-1].outvec_leng; j++) {
        if (block_list[j] == i) count++;
     }
     fprintf(fp2,"   %d\n",count*num_PDE_eqns);
     for (j = 0; j < ml->Amat[N_levels-1].outvec_leng; j++) {
        if (block_list[j] == i) {
           for (k = 0; k < num_PDE_eqns; k++)  fprintf(fp2,"%d\n",j*num_PDE_eqns+k);
        }
     }
  }
  fclose(fp2);
  ML_Operator_UnAmalgamateAndDropWeak(&(ml->Amat[N_levels-1]),num_PDE_eqns,0.0);
#ifdef	MB_MODIF
  printf(" partition file dumped in .update\n");
#endif
  exit(1);
#endif

  ML_Aggregate_Create( &ag );
/*
  ML_Aggregate_Set_CoarsenScheme_MIS(ag);
*/
#ifdef MB_MODIF
  ML_Aggregate_Set_DampingFactor(ag,1.50);
#else
  ML_Aggregate_Set_DampingFactor(ag,1.5);
#endif
  ML_Aggregate_Set_CoarsenScheme_METIS(ag);
  ML_Aggregate_Set_NodesPerAggr( ml, ag, -1, 35);
  /*
  ML_Aggregate_Set_Phase3AggregateCreationAggressiveness(ag, 10.001);
  */


  ML_Aggregate_Set_Threshold(ag, 0.0);
  ML_Aggregate_Set_MaxCoarseSize( ag, 300);


  /* read in the rigid body modes */

   Nrigid = 0;

  /* to ensure compatibility with RBM dumping software */
   if (proc_config[AZ_node] == 0) {

      sprintf(filename,"rigid_body_mode%02d",Nrigid+1);
      while( (fp = fopen(filename,"r")) != NULL) {
	which_filename = 1;
          fclose(fp);
          Nrigid++;
          sprintf(filename,"rigid_body_mode%02d",Nrigid+1);
      }
      sprintf(filename,"rigid_body_mode%d",Nrigid+1);
      while( (fp = fopen(filename,"r")) != NULL) {
          fclose(fp);
          Nrigid++;
          sprintf(filename,"rigid_body_mode%d",Nrigid+1);
      }
    }

    Nrigid = AZ_gsum_int(Nrigid,proc_config);

    if (Nrigid != 0) {
       rigid = (double *) ML_allocate( sizeof(double)*Nrigid*(N_update+1) );
       if (rigid == NULL) {
          printf("Error: Not enough space for rigid body modes\n");
       }
    }

    rhs   = (double *) malloc(leng*sizeof(double));
    xxx   = (double *) malloc(leng*sizeof(double));

    for (iii = 0; iii < leng; iii++) xxx[iii] = 0.0;



    for (i = 0; i < Nrigid; i++) {
       if (which_filename == 1) sprintf(filename,"rigid_body_mode%02d",i+1);
       else sprintf(filename,"rigid_body_mode%d",i+1);
       AZ_input_msr_matrix(filename,update,&mode,&garbage,N_update,proc_config);
       AZ_reorder_vec(mode, data_org, update_index, NULL);
       /* here is something to stick a rigid body mode as the initial */
       /* The idea is to solve A x = 0 without smoothing with a two   */
       /* level method. If everything is done properly, we should     */
       /* converge in 2 iterations.                                   */
       /* Note: we must also zero out components of the rigid body    */
       /* mode that correspond to Dirichlet bcs.                      */

       if (i == -4) {
          for (iii = 0; iii < leng; iii++) xxx[iii] = mode[iii];

          ccc = 0;
          Amatrix = &(ml->Amat[N_levels-1]);
          for (iii = 0; iii < Amatrix->outvec_leng; iii++) {
             ML_get_matrix_row(Amatrix,1,&iii,&allocated,&rowi_col,&rowi_val,
                               &rowi_N, 0);
             count2 = 0;
             for (j = 0; j < rowi_N; j++) if (rowi_val[j] != 0.) count2++;
             if (count2 <= 1) { xxx[iii] = 0.; ccc++; }
          }
          free(rowi_col); free(rowi_val);
          allocated = 0; rowi_col = NULL; rowi_val = NULL;
       }

       /*
        *  Rescale matrix/rigid body modes and checking
        *
        AZ_sym_rescale_sl(mode, Amat->data_org, options, proc_config, scaling);
        Amat->matvec(mode, rigid, Amat, proc_config);
        for (j = 0; j < N_update; j++) printf("this is %d %e\n",j,rigid[j]);
        */

        /* Here is some code to check that the rigid body modes are  */
        /* really rigid body modes. The idea is to multiply by A and */
        /* then to zero out things that we "think" are boundaries.   */
        /* In this hardwired example, things near boundaries         */
        /* correspond to matrix rows that do not have 81 nonzeros.   */
        /*

        Amode = (double *) malloc(leng*sizeof(double));
        Amat->matvec(mode, Amode, Amat, proc_config);
        j = 0;
        biggest = 0.0;
        for (ii = 0; ii < N_update; ii++) {
           if ( Amat->bindx[ii+1] - Amat->bindx[ii] != 80) {
              Amode[ii] = 0.; j++;
           }
           else {
              if ( fabs(Amode[ii]) > biggest) {
                 biggest=fabs(Amode[ii]); big_ind = ii;
              }
           }
        }
        printf("%d entries zeroed out of %d elements\n",j,N_update);
        alpha = AZ_gdot(N_update, Amode, Amode, proc_config);
        beta  = AZ_gdot(N_update,  mode,  mode, proc_config);
        printf("||A r||^2 =%e, ||r||^2 = %e, ratio = %e\n",
               alpha,beta,alpha/beta);
        printf("the biggest is %e at row %d\n",biggest,big_ind);
        free(Amode);

        */

        /* orthogonalize mode with respect to previous modes. */

        for (j = 0; j < i; j++) {
           alpha = -AZ_gdot(N_update, mode, &(rigid[j*N_update]), proc_config)/
                    AZ_gdot(N_update, &(rigid[j*N_update]),
                               &(rigid[j*N_update]), proc_config);
	   /*           daxpy_(&N_update,&alpha,&(rigid[j*N_update]),  &one, mode, &one); */
        }
#ifndef	MB_MODIF
       printf(" after mb %e %e %e\n",mode[0],mode[1],mode[2]);
#endif

        for (j = 0; j < N_update; j++) rigid[i*N_update+j] = mode[j];
        free(mode);
        free(garbage); garbage = NULL;

    }

    if (Nrigid != 0) {
             ML_Aggregate_Set_BlockDiagScaling(ag);
       ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, Nrigid, rigid, N_update);
       free(rigid);
    }
#ifdef SCALE_ME
    ML_Aggregate_Scale_NullSpace(ag, scaling_vect, N_update);
#endif

    coarsest_level = ML_Gen_MGHierarchy_UsingAggregation(ml, N_levels-1,
				ML_DECREASING, ag);
   AZ_defaults(options, params);
   coarsest_level = N_levels - coarsest_level;
   if ( proc_config[AZ_node] == 0 )
	printf("Coarse level = %d \n", coarsest_level);

   /* set up smoothers */

   for (level = N_levels-1; level > coarsest_level; level--) {

/*
      ML_Gen_Smoother_BlockGaussSeidel(ml, level,ML_BOTH, 1, 1., num_PDE_eqns);
*/

    /*  Sparse approximate inverse smoother that acutally does both */
    /*  pre and post smoothing.                                     */
    /*
      ML_Gen_Smoother_ParaSails(ml , level, ML_PRESMOOTHER, nsmooth,
                                parasails_sym, parasails_thresh,
                                parasails_nlevels, parasails_filter,
                                parasails_loadbal, parasails_factorized);
     */

     /* This is the symmetric Gauss-Seidel smoothing that we usually use. */
     /* In parallel, it is not a true Gauss-Seidel in that each processor */
     /* does a Gauss-Seidel on its local submatrix independent of the     */
     /* other processors.                                                 */

     /* ML_Gen_Smoother_Cheby(ml, level, ML_BOTH, 30., nsmooth); */
     Ndof = ml->Amat[level].invec_leng;

     ML_Gen_Blocks_Aggregates(ag, level, &nBlocks, &blockIndices);

     ML_Gen_Smoother_BlockDiagScaledCheby(ml, level, ML_BOTH, 30.,nsmooth,
					  nBlocks, blockIndices);

     /*
      ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_BOTH, nsmooth,1.);
     */


      /* This is a true Gauss Seidel in parallel. This seems to work for  */
      /* elasticity problems.  However, I don't believe that this is very */
      /* efficient in parallel.                                           */
     /*
      nblocks = ml->Amat[level].invec_leng/num_PDE_eqns;
      blocks = (int *) ML_allocate(sizeof(int)*N_update);
      for (i =0; i < ml->Amat[level].invec_leng; i++)
         blocks[i] = i/num_PDE_eqns;

      ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml , level, ML_PRESMOOTHER,
                                                  nsmooth, 1., nblocks, blocks);
      ML_Gen_Smoother_VBlockSymGaussSeidelSequential(ml, level, ML_POSTSMOOTHER,
                                                  nsmooth, 1., nblocks, blocks);
      free(blocks);
*/

      /* Block Jacobi Smoothing */
      /*
      nblocks = ml->Amat[level].invec_leng/num_PDE_eqns;
      blocks = (int *) ML_allocate(sizeof(int)*N_update);
      for (i =0; i < ml->Amat[level].invec_leng; i++)
         blocks[i] = i/num_PDE_eqns;

      ML_Gen_Smoother_VBlockJacobi(ml , level, ML_BOTH, nsmooth,
                                   ML_ONE_STEP_CG, nblocks, blocks);
      free(blocks);
      */

      /* Jacobi Smoothing                                                 */
     /*

      ML_Gen_Smoother_Jacobi(ml , level, ML_PRESMOOTHER, nsmooth, ML_ONE_STEP_CG);
      ML_Gen_Smoother_Jacobi(ml , level, ML_POSTSMOOTHER, nsmooth,ML_ONE_STEP_CG);
     */



      /*  This does a block Gauss-Seidel (not true GS in parallel)        */
      /*  where each processor has 'nblocks' blocks.                      */
      /*
      nblocks = 250;
      ML_Gen_Blocks_Metis(ml, level, &nblocks, &blocks);
      ML_Gen_Smoother_VBlockJacobi(ml , level, ML_BOTH, nsmooth,ML_ONE_STEP_CG,
                                        nblocks, blocks);
      free(blocks);
      */
      num_PDE_eqns = 6;
   }
   /* Choose coarse grid solver: mls, superlu, symGS, or Aztec */

   /*
   ML_Gen_Smoother_Cheby(ml, coarsest_level, ML_BOTH, 30., nsmooth);
   ML_Gen_CoarseSolverSuperLU( ml, coarsest_level);
   */
   /*
   ML_Gen_Smoother_SymGaussSeidel(ml , coarsest_level, ML_BOTH, nsmooth,1.);
   */

   old_prec = options[AZ_precond];
   old_sol  = options[AZ_solver];
   old_tol  = params[AZ_tol];
   params[AZ_tol] = 1.0e-9;
   params[AZ_tol] = 1.0e-5;
   options[AZ_precond] = AZ_Jacobi;
   options[AZ_solver]  = AZ_cg;
   options[AZ_poly_ord] = 1;
   options[AZ_conv] = AZ_r0;
   options[AZ_orth_kvecs] = AZ_TRUE;

   j = AZ_gsum_int(ml->Amat[coarsest_level].outvec_leng, proc_config);

   options[AZ_keep_kvecs] = j - 6;
   options[AZ_max_iter] =  options[AZ_keep_kvecs];

   ML_Gen_SmootherAztec(ml, coarsest_level, options, params,
            proc_config, status, options[AZ_keep_kvecs], ML_PRESMOOTHER, NULL);

   options[AZ_conv] = AZ_noscaled;
   options[AZ_keep_kvecs] = 0;
   options[AZ_orth_kvecs] = 0;
   options[AZ_precond] = old_prec;
   options[AZ_solver] = old_sol;
   params[AZ_tol] = old_tol;

   /*   */


#ifdef RST_MODIF
   ML_Gen_Solver(ml, ML_MGV, N_levels-1, coarsest_level);
#else
#ifdef	MB_MODIF
   ML_Gen_Solver(ml, ML_SAAMG,   N_levels-1, coarsest_level);
#else
   ML_Gen_Solver(ml, ML_MGFULLV, N_levels-1, coarsest_level);
#endif
#endif

   options[AZ_solver]   = AZ_GMRESR;
         options[AZ_solver]   = AZ_cg;
   options[AZ_scaling]  = AZ_none;
   options[AZ_precond]  = AZ_user_precond;
   options[AZ_conv]     = AZ_r0;
   options[AZ_conv] = AZ_noscaled;
   options[AZ_output]   = 1;
   options[AZ_max_iter] = 500;
   options[AZ_poly_ord] = 5;
   options[AZ_kspace]   = 40;
   params[AZ_tol]       = 4.8e-6;

   AZ_set_ML_preconditioner(&Pmat, Amat, ml, options);
   setup_time = AZ_second() - start_time;

   /* Set rhs */

   fp = fopen("AZ_capture_rhs.dat","r");
   if (fp == NULL) {
      AZ_random_vector(rhs, data_org, proc_config);
      if (proc_config[AZ_node] == 0) printf("taking random vector for rhs\n");
      for (i = 0; i < -N_update; i++) {
        rhs[i] = (double) update[i]; rhs[i] = 7.;
      }
   }
   else {
      if (proc_config[AZ_node]== 0) printf("reading rhs guess from file\n");
      AZ_input_msr_matrix("AZ_capture_rhs.dat", update, &rhs, &garbage,
			  N_update, proc_config);
      free(garbage);
   }
   AZ_reorder_vec(rhs, data_org, update_index, NULL);

   printf("changing rhs by multiplying with A\n");
  Amat->matvec(rhs, xxx, Amat, proc_config);
  for (i = 0; i < N_update; i++) rhs[i] = xxx[i];

   fp = fopen("AZ_capture_init_guess.dat","r");
   if (fp != NULL) {
      fclose(fp);
      if (proc_config[AZ_node]== 0) printf("reading initial guess from file\n");
      AZ_input_msr_matrix("AZ_capture_init_guess.dat", update, &xxx, &garbage,
      			  N_update, proc_config);
      free(garbage);


      xxx = (double *) realloc(xxx, sizeof(double)*(
					 Amat->data_org[AZ_N_internal]+
					 Amat->data_org[AZ_N_border] +
					 Amat->data_org[AZ_N_external]));
   }
   AZ_reorder_vec(xxx, data_org, update_index, NULL);

   /* if Dirichlet BC ... put the answer in */

/*
   for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++) {
      if ( (val[i] > .99999999) && (val[i] < 1.0000001))
         xxx[i] = rhs[i];
   }
*/

   fp = fopen("AZ_no_multilevel.dat","r");
   scaling = AZ_scaling_create();
   start_time = AZ_second();


   if (fp != NULL) {
      fclose(fp);
      options[AZ_precond] = AZ_none;
      options[AZ_scaling] = AZ_sym_diag;
      options[AZ_ignore_scaling] = AZ_TRUE;

      options[AZ_keep_info] = 1;
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);

/*
      options[AZ_pre_calc] = AZ_reuse;
      options[AZ_conv] = AZ_expected_values;
      if (proc_config[AZ_node] == 0)
              printf("\n-------- Second solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
      if (proc_config[AZ_node] == 0)
              printf("\n-------- Third solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling);
*/
   }
   else {
      options[AZ_keep_info] = 1;
      options[AZ_conv] = AZ_noscaled;
      options[AZ_conv] = AZ_r0;
      params[AZ_tol] = 1.0e-7;
      /* ML_Iterate(ml, xxx, rhs); */
alpha = sqrt(AZ_gdot(N_update, xxx, xxx, proc_config));
printf("init guess = %e\n",alpha);
alpha = sqrt(AZ_gdot(N_update, rhs, rhs, proc_config));
printf("rhs = %e\n",alpha);
#ifdef SCALE_ME
	ML_MSR_scalerhs(rhs, scaling_vect, data_org[AZ_N_internal] +
                    data_org[AZ_N_border]);
	ML_MSR_scalesol(xxx, scaling_vect, data_org[AZ_N_internal] +
			data_org[AZ_N_border]);
#endif

max_diag = 0.;
min_diag = 1.e30;
max_sum  = 0.;
for (i = 0; i < N_update; i++) {
   if (Amat->val[i] < 0.) printf("woops negative diagonal A(%d,%d) = %e\n",
				 i,i,Amat->val[i]);
   if (Amat->val[i] > max_diag) max_diag = Amat->val[i];
   if (Amat->val[i] < min_diag) min_diag = Amat->val[i];
   sum = fabs(Amat->val[i]);
   for (j = Amat->bindx[i]; j < Amat->bindx[i+1]; j++) {
      sum += fabs(Amat->val[j]);
   }
   if (sum > max_sum) max_sum = sum;
}
printf("Largest diagonal = %e, min diag = %e large abs row sum = %e\n",
max_diag, min_diag, max_sum);

      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);

      options[AZ_pre_calc] = AZ_reuse;
      options[AZ_conv] = AZ_expected_values;
/*
      if (proc_config[AZ_node] == 0)
              printf("\n-------- Second solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
      if (proc_config[AZ_node] == 0)
              printf("\n-------- Third solve with improved convergence test -----\n");
      AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling);
*/
   }
   solve_time = AZ_second() - start_time;

   if (proc_config[AZ_node] == 0)
      printf("Solve time = %e, MG Setup time = %e\n", solve_time, setup_time);
   if (proc_config[AZ_node] == 0)
     printf("Printing out a few entries of the solution ...\n");

   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 7) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 23) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 47) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 101) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}
   j = AZ_gsum_int(7, proc_config); /* sync processors */
   for (j=0;j<Amat->data_org[AZ_N_internal]+ Amat->data_org[AZ_N_border];j++)
     if (update[j] == 171) {printf("solution(gid = %d) = %10.4e\n",
			      update[j],xxx[update_index[j]]); fflush(stdout);}


   ML_Aggregate_Destroy(&ag);
   ML_Destroy(&ml);
   AZ_free((void *) Amat->data_org);
   AZ_free((void *) Amat->val);
   AZ_free((void *) Amat->bindx);
   AZ_free((void *) update);
   AZ_free((void *) external);
   AZ_free((void *) extern_index);
   AZ_free((void *) update_index);
   AZ_scaling_destroy(&scaling);
   if (Amat  != NULL) AZ_matrix_destroy(&Amat);
   if (Pmat  != NULL) AZ_precond_destroy(&Pmat);
   free(xxx);
   free(rhs);


#ifdef HAVE_MPI
  MPI_Finalize();
#endif

  return 0;

}