示例#1
0
int main(int argc, char *argv[])
{
  int    Nnodes=16*16;              /* Total number of nodes in the problem.*/
                                    /* 'Nnodes' must be a perfect square.   */
  int    MaxMgLevels=6;             /* Maximum number of Multigrid Levels   */
  int    Nits_per_presmooth=1;      /* # of pre & post smoothings per level */
  double tolerance = 1.0e-8;        /* At convergence:                      */
                                    /*   ||r_k||_2 < tolerance ||r_0||_2    */
  int smoothPe_flag = ML_YES;       /* ML_YES: smooth tentative prolongator */
                                    /* ML_NO: don't smooth prolongator      */

  /***************************************************************************/
  /* Select Hiptmair relaxation subsmoothers for the nodal and edge problems */
  /* Choices include                                                         */
  /*   1) ML_Gen_Smoother_SymGaussSeidel: this corresponds to a processor    */
  /*      local version of symmetric Gauss-Seidel/SOR. The number of sweeps  */
  /*      can be set via either 'edge_its' or 'nodal_its'. The damping can   */
  /*      be set via 'edge_omega' or 'nodal_omega'. When set to ML_DDEFAULT, */
  /*      the damping is set to '1' on one processor. On multiple processors */
  /*      a lower damping value is set. This is needed to converge processor */
  /*      local SOR.                                                         */
  /*   2) ML_Gen_Smoother_Cheby: this corresponds to polynomial relaxation.    */
  /*      The degree of the polynomial is set via 'edge_its' or 'nodal_its'. */
  /*      If the degree is '-1', Marian Brezina's MLS polynomial is chosen.  */
  /*      Otherwise, a Chebyshev polynomial is used over high frequencies    */
  /*      [ lambda_max/alpha , lambda_max]. Lambda_max is computed. 'alpha'  */
  /*      is hardwired in this example to correspond to twice the ratio of   */
  /*      unknowns in the fine and coarse meshes.                            */
  /*                                                                         */
  /* Using 'hiptmair_type' (see comments below) it is also possible to choose*/
  /* when edge and nodal problems are relaxed within the Hiptmair smoother.  */
  /***************************************************************************/

  void  *edge_smoother=(void *)     /* Edge relaxation:                     */
               ML_Gen_Smoother_Cheby; /*   ML_Gen_Smoother_Cheby            */
                                    /*     ML_Gen_Smoother_SymGaussSeidel   */
  void *nodal_smoother=(void *)     /* Nodal relaxation                     */
               ML_Gen_Smoother_Cheby;/*     ML_Gen_Smoother_Cheby           */
                                    /*     ML_Gen_Smoother_SymGaussSeidel   */

  int  edge_its = 3;                /* Iterations or polynomial degree for  */
  int  nodal_its = 3;               /* edge/nodal subsmoothers.             */
  double nodal_omega = ML_DDEFAULT, /* SOR damping parameter for noda/edge  */
         edge_omega  = ML_DDEFAULT; /* subsmoothers (see comments above).   */
  int   hiptmair_type=HALF_HIPTMAIR;/* FULL_HIPTMAIR: each invokation       */
                                    /*     smoothes on edges, then nodes,   */
                                    /*     and then once again on edges.    */
                                    /* HALF_HIPTMAIR: each pre-invokation   */
                                    /*     smoothes on edges, then nodes.   */
                                    /*     Each post-invokation smoothes    */
                                    /*     on nodes then edges. .           */


  ML_Operator  *Tmat, *Tmat_trans, **Tmat_array, **Tmat_trans_array;
  ML           *ml_edges, *ml_nodes;
  ML_Aggregate *ag;
  int          Nfine_edge, Ncoarse_edge, Nfine_node, Ncoarse_node, Nlevels;
  int          level, coarsest_level, itmp;
  double       edge_coarsening_rate, node_coarsening_rate, *rhs, *xxx;
  void         **edge_args, **nodal_args;
  struct       user_partition Edge_Partition = {NULL, NULL,0,0}, 
                                Node_Partition = {NULL, NULL,0,0};
  struct Tmat_data Tmat_data;
int i, Ntotal;
 ML_Comm *comm;

  /* See Aztec User's Guide for information on these variables */

#ifdef AZTEC
  AZ_MATRIX    *Ke_mat, *Kn_mat;
  AZ_PRECOND   *Pmat = NULL;
  int          proc_config[AZ_PROC_SIZE], options[AZ_OPTIONS_SIZE];
  double       params[AZ_PARAMS_SIZE], status[AZ_STATUS_SIZE];
#endif


  /* get processor information (proc id & # of procs) and set ML's printlevel. */

#ifdef ML_MPI
  MPI_Init(&argc,&argv);
#endif
#ifdef AZTEC
  AZ_set_proc_config(proc_config, COMMUNICATOR);
#endif
  ML_Set_PrintLevel(10);   /* set ML's output level: 0 gives least output */

  /* Set the # of global nodes/edges and partition both the edges and the */
  /* nodes over the processors. NOTE: I believe we assume that if an edge */
  /* is assigned to a processor at least one of its nodes must be also    */
  /* assigned to that processor.                                          */

  Node_Partition.Nglobal = Nnodes;
  Edge_Partition.Nglobal = Node_Partition.Nglobal*2;
  Node_Partition.type = NODE;
  Edge_Partition.type = EDGE;
#define perxodic
#ifdef periodic
Node_Partition.Nglobal += 2; 
#endif
  partition_edges(&Edge_Partition);
  partition_nodes(&Node_Partition);
xxx = (double *) ML_allocate((Edge_Partition.Nlocal+100)*sizeof(double)); 
rhs = (double *) ML_allocate((Edge_Partition.Nlocal+100)*sizeof(double)); 
 for (i = 0; i < Edge_Partition.Nlocal + 100; i++) xxx[i] = -1.;
 for (i = 0; i < Edge_Partition.Nlocal; i++) xxx[i] = (double) 
        Edge_Partition.my_global_ids[i];

update_ghost_edges(xxx, (void *) &Edge_Partition);


  /* Create an empty multigrid hierarchy and set the 'MaxMGLevels-1'th   */
  /* level discretization within this hierarchy to the ML matrix         */
  /* representing Ke (Maxwell edge discretization).                      */

  ML_Create(&ml_edges, MaxMgLevels);
#ifdef AZTEC
  /* Build Ke as an Aztec matrix. Use built-in function AZ_ML_Set_Amat() */
  /* to convert to an ML matrix and put in hierarchy.                    */

  Ke_mat = user_Ke_build(&Edge_Partition);
  AZ_ML_Set_Amat(ml_edges, MaxMgLevels-1, Edge_Partition.Nlocal,
      		 Edge_Partition.Nlocal, Ke_mat, proc_config);
#else
  /* Build Ke directly as an ML matrix.                                  */

  ML_Init_Amatrix      (ml_edges, MaxMgLevels-1, Edge_Partition.Nlocal,
			Edge_Partition.Nlocal, &Edge_Partition);

  Ntotal = Edge_Partition.Nlocal;
  if (Edge_Partition.nprocs == 2) Ntotal += Edge_Partition.Nghost;
  ML_Set_Amatrix_Getrow(ml_edges, MaxMgLevels-1,  Ke_getrow, update_ghost_edges, Ntotal);
  ML_Set_Amatrix_Matvec(ml_edges, MaxMgLevels-1,  Ke_matvec);

#endif



  /* Build an Aztec matrix representing an auxiliary nodal PDE problem.  */
  /* This should be a variable coefficient Poisson problem (with unknowns*/
  /* at the nodes). The coefficients should be chosen to reflect the     */
  /* conductivity of the original edge problems.                         */
  /* Create an empty multigrid hierarchy. Convert the Aztec matrix to an */
  /* ML matrix and put it in the 'MaxMGLevels-1' level of the hierarchy. */
  /* Note it is possible to multiply T'*T for get this matrix though this*/
  /* will not incorporate material properties.                           */

  ML_Create(&ml_nodes, MaxMgLevels);

#ifdef AZTEC
  Kn_mat = user_Kn_build( &Node_Partition);
  AZ_ML_Set_Amat(ml_nodes, MaxMgLevels-1, Node_Partition.Nlocal, 
		 Node_Partition.Nlocal, Kn_mat, proc_config);
#else
  ML_Init_Amatrix      (ml_nodes, MaxMgLevels-1 , Node_Partition.Nlocal,
			Node_Partition.Nlocal, &Node_Partition);
  Ntotal = Node_Partition.Nlocal;
  if (Node_Partition.nprocs == 2) Ntotal += Node_Partition.Nghost;
  ML_Set_Amatrix_Getrow(ml_nodes, MaxMgLevels-1,  Kn_getrow, update_ghost_nodes, Ntotal);
#endif

  /* Build an ML matrix representing the null space of the PDE problem. */
  /* This should be a discrete gradient (nodes to edges).               */

#ifdef AZTEC
    Tmat = user_T_build (&Edge_Partition, &Node_Partition, 
  		   &(ml_nodes->Amat[MaxMgLevels-1]));
#else
    Tmat = ML_Operator_Create(ml_nodes->comm);
    Tmat_data.edge = &Edge_Partition;
    Tmat_data.node = &Node_Partition;
    Tmat_data.Kn   = &(ml_nodes->Amat[MaxMgLevels-1]);

    ML_Operator_Set_ApplyFuncData( Tmat,	Node_Partition.Nlocal,
				   Edge_Partition.Nlocal, ML_EMPTY, (void *) &Tmat_data, 
				   Edge_Partition.Nlocal, NULL, 0);
    ML_Operator_Set_Getrow( Tmat, ML_INTERNAL, Edge_Partition.Nlocal,Tmat_getrow);
    ML_Operator_Set_ApplyFunc(Tmat, ML_INTERNAL, Tmat_matvec);
  ML_Comm_Create( &comm);

  ML_CommInfoOP_Generate( &(Tmat->getrow->pre_comm), update_ghost_nodes, 
			  &Node_Partition,comm, Tmat->invec_leng, 
			  Node_Partition.Nghost);
#endif


  /********************************************************************/
  /* Set some ML parameters.                                          */
  /*------------------------------------------------------------------*/
	
  ML_Set_ResidualOutputFrequency(ml_edges, 1);
  ML_Set_Tolerance(ml_edges, 1.0e-8);
  ML_Aggregate_Create( &ag );
  ML_Aggregate_Set_CoarsenScheme_Uncoupled(ag);
  ML_Aggregate_Set_DampingFactor(ag, 0.0); /* must use 0 for maxwell */
  ML_Aggregate_Set_MaxCoarseSize(ag, 30);
  ML_Aggregate_Set_Threshold(ag, 0.0);


  /********************************************************************/
  /*                      Set up Tmat_trans                           */
  /*------------------------------------------------------------------*/

  Tmat_trans = ML_Operator_Create(ml_edges->comm);
  ML_Operator_Transpose_byrow(Tmat, Tmat_trans);


  Nlevels=ML_Gen_MGHierarchy_UsingReitzinger(ml_edges, &ml_nodes,MaxMgLevels-1,
					     ML_DECREASING,ag,Tmat,Tmat_trans, 
					     &Tmat_array,&Tmat_trans_array, 
					     smoothPe_flag, 1.5);

  /* Set the Hiptmair subsmoothers */

  if (nodal_smoother == (void *) ML_Gen_Smoother_SymGaussSeidel) {
    nodal_args = ML_Smoother_Arglist_Create(2);
    ML_Smoother_Arglist_Set(nodal_args, 0, &nodal_its);
    ML_Smoother_Arglist_Set(nodal_args, 1, &nodal_omega);
  }
  if (edge_smoother == (void *) ML_Gen_Smoother_SymGaussSeidel) {
    edge_args = ML_Smoother_Arglist_Create(2);
    ML_Smoother_Arglist_Set(edge_args, 0, &edge_its);
    ML_Smoother_Arglist_Set(edge_args, 1, &edge_omega);
  }
  if (nodal_smoother == (void *) ML_Gen_Smoother_Cheby) {
    nodal_args = ML_Smoother_Arglist_Create(2);
    ML_Smoother_Arglist_Set(nodal_args, 0, &nodal_its);
    Nfine_node = Tmat_array[MaxMgLevels-1]->invec_leng;
    Nfine_node = ML_gsum_int(Nfine_node, ml_edges->comm);
  }
  if (edge_smoother == (void *) ML_Gen_Smoother_Cheby) {
    edge_args = ML_Smoother_Arglist_Create(2);
    ML_Smoother_Arglist_Set(edge_args, 0, &edge_its);
    Nfine_edge = Tmat_array[MaxMgLevels-1]->outvec_leng;
    Nfine_edge = ML_gsum_int(Nfine_edge, ml_edges->comm);
  }

  /****************************************************
  * Set up smoothers for all levels but the coarsest. *
  ****************************************************/
  coarsest_level = MaxMgLevels - Nlevels;

  for (level = MaxMgLevels-1; level > coarsest_level; level--)
    {
      if (edge_smoother == (void *) ML_Gen_Smoother_Cheby) {
	Ncoarse_edge = Tmat_array[level-1]->outvec_leng;
	Ncoarse_edge = ML_gsum_int(Ncoarse_edge, ml_edges->comm);
	edge_coarsening_rate =  2.*((double) Nfine_edge)/ ((double) Ncoarse_edge);
	ML_Smoother_Arglist_Set(edge_args, 1, &edge_coarsening_rate);
	Nfine_edge = Ncoarse_edge;
      }
      if (nodal_smoother == (void *) ML_Gen_Smoother_Cheby) {
	Ncoarse_node = Tmat_array[level-1]->invec_leng;
	Ncoarse_node = ML_gsum_int(Ncoarse_node, ml_edges->comm);
	node_coarsening_rate =  2.*((double) Nfine_node)/ ((double) Ncoarse_node);
	ML_Smoother_Arglist_Set(nodal_args, 1, &node_coarsening_rate);
	Nfine_node = Ncoarse_node;
      }
      ML_Gen_Smoother_Hiptmair(ml_edges, level, ML_BOTH, Nits_per_presmooth,
			       Tmat_array, Tmat_trans_array, NULL, edge_smoother,
			       edge_args, nodal_smoother,nodal_args, hiptmair_type);
    }

  /*******************************************
  * Set up coarsest level smoother
  *******************************************/

  if (edge_smoother == (void *) ML_Gen_Smoother_Cheby) {
    edge_coarsening_rate = (double) Nfine_edge;
    ML_Smoother_Arglist_Set(edge_args, 1, &edge_coarsening_rate);
  }
  if (nodal_smoother == (void *) ML_Gen_Smoother_Cheby) {
    node_coarsening_rate = (double) Nfine_node;
    ML_Smoother_Arglist_Set(nodal_args,1,&node_coarsening_rate);
  }
  ML_Gen_CoarseSolverSuperLU( ml_edges, coarsest_level);
  

  /* Must be called before invoking the preconditioner */
  ML_Gen_Solver(ml_edges, ML_MGV, MaxMgLevels-1, coarsest_level); 



  /* Set the initial guess and the right hand side. Invoke solver */	

  xxx = (double *) ML_allocate(Edge_Partition.Nlocal*sizeof(double)); 
  ML_random_vec(xxx, Edge_Partition.Nlocal, ml_edges->comm);
  rhs = (double *) ML_allocate(Edge_Partition.Nlocal*sizeof(double)); 
  ML_random_vec(rhs, Edge_Partition.Nlocal, ml_edges->comm);

#ifdef AZTEC
  /* Choose the Aztec solver and criteria. Also tell Aztec that */
  /* ML will be supplying the preconditioner.                   */

  AZ_defaults(options, params);
  options[AZ_solver]   = AZ_fixed_pt;
  options[AZ_solver]   = AZ_gmres;
  options[AZ_kspace]   = 80;
  params[AZ_tol]       = tolerance;
  AZ_set_ML_preconditioner(&Pmat, Ke_mat, ml_edges, options); 
  options[AZ_conv] = AZ_noscaled;
  AZ_iterate(xxx, rhs, options, params, status, proc_config, Ke_mat, Pmat, NULL);
#else
  ML_Iterate(ml_edges, xxx, rhs);
#endif


  /* clean up. */

  ML_Smoother_Arglist_Delete(&nodal_args);
  ML_Smoother_Arglist_Delete(&edge_args);
  ML_Aggregate_Destroy(&ag);
  ML_Destroy(&ml_edges);
  ML_Destroy(&ml_nodes);
#ifdef AZTEC
  AZ_free((void *) Ke_mat->data_org);
  AZ_free((void *) Ke_mat->val);
  AZ_free((void *) Ke_mat->bindx);
  if (Ke_mat  != NULL) AZ_matrix_destroy(&Ke_mat);
  if (Pmat  != NULL) AZ_precond_destroy(&Pmat);
  if (Kn_mat != NULL) AZ_matrix_destroy(&Kn_mat);
#endif
  free(xxx);
  free(rhs);
  ML_Operator_Destroy(&Tmat);
  ML_Operator_Destroy(&Tmat_trans);
  ML_MGHierarchy_ReitzingerDestroy(MaxMgLevels-2, &Tmat_array, &Tmat_trans_array);

#ifdef ML_MPI
  MPI_Finalize();
#endif
		
  return 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;
	
}
示例#3
0
int main(int argc, char *argv[])
{
	int num_PDE_eqns=3, N_levels=3, nsmooth=1;

	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 */

  int    *data_org = NULL, *update = NULL, *external = NULL;
  int    *update_index = NULL, *extern_index = NULL;
  int    *cpntr = NULL;
  int    *bindx = NULL, N_update, iii;
  double *val = NULL;
	double *xxx, *rhs;

	AZ_MATRIX *Amat;
	AZ_PRECOND *Pmat = NULL;
	ML *ml;
	FILE *fp;
  int ch,i,j, Nrigid, *garbage;
   struct AZ_SCALING *scaling;
double solve_time, setup_time, start_time, *mode, *rigid;
ML_Aggregate *ag;
int  nblocks, *blocks;
char filename[80];
double alpha;
int one = 1;


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

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. */
	
  AZ_read_update(&N_update, &update, proc_config, N_grid_pts, num_PDE_eqns,
                 AZ_linear);
	
	
  AZ_read_msr_matrix(update, &val, &bindx, N_update, proc_config);

  AZ_transform(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();

AZ_defaults(options, params);
/*
scaling = AZ_scaling_create();
xxx = (double *) calloc( leng,sizeof(double));
rhs=(double *)calloc(leng,sizeof(double));
options[AZ_scaling] = AZ_sym_diag;
options[AZ_precond] = AZ_none;
options[AZ_max_iter] = 30;
options[AZ_keep_info] = 1;
AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, NULL, scaling); 
don't forget vector rescaling ...
free(xxx);
free(rhs);
*/
options[AZ_scaling] = AZ_none;
	



  ML_Create(&ml, N_levels);
			
			
  /* set up discretization matrix and matrix vector function */
	
  AZ_ML_Set_Amat(ml, N_levels-1, N_update, N_update, Amat, proc_config);
	
  ML_Aggregate_Create( &ag );

  Nrigid = 0;
if (proc_config[AZ_node] == 0) {
  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));
AZ_random_vector(rhs, data_org, proc_config);
  
  for (i = 0; i < Nrigid; i++) {
     sprintf(filename,"rigid_body_mode%d",i+1);
     AZ_input_msr_matrix(filename, update, &mode, &garbage, 
                         N_update, proc_config);


/*
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]);
*/
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);
printf("alpha1 is %e\n",alpha);
}
alpha = -AZ_gdot(N_update, mode, rhs, proc_config)/AZ_gdot(N_update, mode, mode, proc_config);
printf("alpha2 is %e\n",alpha);
daxpy_(&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_(&N_update, &alpha,  &(rigid[j*N_update]),  &one, rhs, &one);
printf("alpha4 is %e\n",alpha);
}


for (i = 0; i < Nrigid; i++) {
  alpha = -AZ_gdot(N_update, &(rigid[i*N_update]), rhs, proc_config);
  printf("alpha is %e\n",alpha);
}
  if (Nrigid != 0) {
     ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, Nrigid, rigid, N_update);
/*
     free(rigid);
*/
  }

	coarsest_level = ML_Gen_MGHierarchy_UsingAggregation(ml, N_levels-1, ML_DECREASING, ag);
	coarsest_level = N_levels - coarsest_level;
/*
ML_Operator_Print(&(ml->Pmat[N_levels-2]), "Pmat");
exit(1);
*/

	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--) {
j = 10;
if (level == N_levels-1) j = 10;
options[AZ_solver] = AZ_cg;
options[AZ_precond]=AZ_sym_GS; options[AZ_subdomain_solve]=AZ_icc;
/*
options[AZ_precond] = AZ_none;
*/
options[AZ_poly_ord] = 5;
ML_Gen_SmootherAztec(ml, level, options, params, proc_config, status,
j, ML_PRESMOOTHER,NULL);
ML_Gen_SmootherAztec(ml, level, options, params, proc_config, status,
j, ML_POSTSMOOTHER,NULL);
/*
		ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth,1.0);
		ML_Gen_Smoother_SymGaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth,1.0);
*/
/*
                nblocks = ML_Aggregate_Get_AggrCount( ag, level );
                ML_Aggregate_Get_AggrMap( ag, level, &blocks);
                ML_Gen_Smoother_VBlockSymGaussSeidel( ml , level, ML_BOTH, nsmooth, 1.0,
                                                 nblocks, blocks);
                ML_Gen_Smoother_VBlockSymGaussSeidel( ml , level, ML_POSTSMOOTHER, nsmooth, 1.0, 
                                                 nblocks, blocks);
*/
/*
                ML_Gen_Smoother_VBlockJacobi( ml , level, ML_PRESMOOTHER, nsmooth, .5,
                                                 nblocks, blocks);
                ML_Gen_Smoother_VBlockJacobi( ml , level, ML_POSTSMOOTHER, nsmooth,.5,
                                                 nblocks, blocks);
*/
/*
		ML_Gen_Smoother_GaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth);
		ML_Gen_Smoother_GaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth);    
*/
/* 
need to change this when num_pdes is different on different levels
*/
/*
if (level == N_levels-1) {
		ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth, 0.5, num_PDE_eqns);
		ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth, 0.5, num_PDE_eqns);
}
else {
		ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_PRESMOOTHER, nsmooth, 0.5, 2*num_PDE_eqns);
		ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_POSTSMOOTHER, nsmooth, 0.5, 2*num_PDE_eqns);
}
*/
/*
*/

/*
			ML_Gen_SmootherJacobi(ml , level, ML_PRESMOOTHER, nsmooth, .67);
			ML_Gen_SmootherJacobi(ml , level, ML_POSTSMOOTHER, nsmooth, .67 );
*/
		
		
	}
	
/*
	ML_Gen_CoarseSolverSuperLU( ml, coarsest_level);
*/
/*
ML_Gen_SmootherSymGaussSeidel(ml , coarsest_level, ML_PRESMOOTHER, 2*nsmooth,1.);
*/
/*
ML_Gen_SmootherBlockGaussSeidel(ml , level, ML_PRESMOOTHER, 50*nsmooth, 1.0, 2*num_PDE_eqns);
*/
ML_Gen_Smoother_BlockGaussSeidel(ml , level, ML_PRESMOOTHER, 2*nsmooth, 1.0, num_PDE_eqns);
		
	
	ML_Gen_Solver(ml, ML_MGV, N_levels-1, coarsest_level); 
	AZ_defaults(options, params);
	
        options[AZ_solver]   = AZ_GMRESR;
        options[AZ_scaling]  = AZ_none;
        options[AZ_precond]  = AZ_user_precond;
        options[AZ_conv]     = AZ_rhs;
        options[AZ_output]   = 1;
        options[AZ_max_iter] = 1500;
        options[AZ_poly_ord] = 5;
        options[AZ_kspace]   = 130;
        params[AZ_tol]       = 1.0e-8;
	
	AZ_set_ML_preconditioner(&Pmat, Amat, ml, options); 
setup_time = AZ_second() - start_time;
	
	xxx = (double *) malloc( leng*sizeof(double));

	
        /* Set rhs */
 
        fp = fopen("AZ_capture_rhs.dat","r");
        if (fp == NULL) {
           if (proc_config[AZ_node] == 0) printf("taking random vector for rhs\n");
/*
           AZ_random_vector(rhs, data_org, proc_config);
           AZ_reorder_vec(rhs, data_org, update_index, NULL);
           AZ_random_vector(xxx, data_org, proc_config);
           AZ_reorder_vec(xxx, data_org, update_index, NULL);
           Amat->matvec(xxx, rhs, Amat, proc_config);
*/
        }
        else {
           ch = getc(fp);
           if (ch == 'S') {
              while ( (ch = getc(fp)) != '\n') ;
           }
           else ungetc(ch,fp);
           for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++) 
              fscanf(fp,"%lf",&(rhs[i]));
           fclose(fp);
        }
	for (iii = 0; iii < leng; iii++) xxx[iii] = 0.0; 

        /* Set x */

        fp = fopen("AZ_capture_init_guess.dat","r");
        if (fp != NULL) {
           ch = getc(fp);
           if (ch == 'S') {
              while ( (ch = getc(fp)) != '\n') ;
           }
           else ungetc(ch,fp);
           for (i = 0; i < data_org[AZ_N_internal]+data_org[AZ_N_border]; i++)
              fscanf(fp,"%lf",&(xxx[i]));
           fclose(fp);
           options[AZ_conv] = AZ_expected_values;
        }

        /* 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_max_iter] = 40;
*/
           AZ_iterate(xxx, rhs, options, params, status, proc_config, Amat, Pmat, scaling); 
for (j = 0; j < Nrigid; j++) {
alpha = -AZ_gdot(N_update, xxx, &(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, xxx, &one);
printf("alpha5 is %e\n",alpha);
}
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);

   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);
   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;
	
}
示例#4
0
int main(int argc, char *argv[])
{
	int num_PDE_eqns=5, N_levels=3;
    /* int nsmooth=1; */

	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 */

  int    *data_org = NULL, *update = NULL, *external = NULL;
  int    *update_index = NULL, *extern_index = NULL;
  int    *cpntr = NULL;
  int    *bindx = NULL, N_update, iii;
  double *val = NULL;
	double *xxx, *rhs;

	AZ_MATRIX *Amat;
	AZ_PRECOND *Pmat = NULL;
	ML *ml;
	FILE *fp;
  int ch,i;
   struct AZ_SCALING *scaling;
double solve_time, setup_time, start_time;
ML_Aggregate *ag;
int *ivec;
#ifdef VBR_VERSION
ML_Operator *B, *C, *D;
int *vbr_cnptr, *vbr_rnptr, *vbr_indx, *vbr_bindx, *vbr_bnptr, total_blk_rows;
int total_blk_cols, blk_space, nz_space;
double *vbr_val;
struct ML_CSR_MSRdata *csr_data;
#endif


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

#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);

	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. */

  AZ_read_update(&N_update, &update, proc_config, N_grid_pts, num_PDE_eqns,
                 AZ_linear);

  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(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 );

#ifndef VBR_VERSION

  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];

#else

total_blk_rows = N_update/num_PDE_eqns;
total_blk_cols = total_blk_rows;
blk_space      = total_blk_rows*20;
nz_space       = blk_space*num_PDE_eqns*num_PDE_eqns;

vbr_cnptr = (int    *) ML_allocate(sizeof(int   )*(total_blk_cols+1));
vbr_rnptr = (int    *) ML_allocate(sizeof(int   )*(total_blk_cols+1));
vbr_bnptr = (int    *) ML_allocate(sizeof(int   )*(total_blk_cols+2));
vbr_indx  = (int    *) ML_allocate(sizeof(int   )*(blk_space+1));
vbr_bindx = (int    *) ML_allocate(sizeof(int   )*(blk_space+1));
vbr_val   = (double *) ML_allocate(sizeof(double)*(nz_space+1));

for (i = 0; i <= total_blk_cols; i++) vbr_cnptr[i] = num_PDE_eqns;

  AZ_msr2vbr(vbr_val, vbr_indx, vbr_rnptr,  vbr_cnptr, vbr_bnptr,
                vbr_bindx, bindx, val,
                total_blk_rows, total_blk_cols, blk_space,
                nz_space, -1);

  data_org[AZ_N_rows]  = data_org[AZ_N_internal] + data_org[AZ_N_border];
  data_org[AZ_N_int_blk]  = data_org[AZ_N_internal]/num_PDE_eqns;
  data_org[AZ_N_bord_blk] = data_org[AZ_N_bord_blk]/num_PDE_eqns;
  data_org[AZ_N_ext_blk]  = data_org[AZ_N_ext_blk]/num_PDE_eqns;
  data_org[AZ_matrix_type] = AZ_VBR_MATRIX;


  AZ_set_VBR(Amat, vbr_rnptr, vbr_cnptr, vbr_bnptr, vbr_indx, vbr_bindx,
             vbr_val, data_org, 0, NULL, AZ_LOCAL);

  Amat->matrix_type  = data_org[AZ_matrix_type];
#endif

  start_time = AZ_second();

  ML_Create(&ml, N_levels);
  ML_Set_PrintLevel(3);


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

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

  ML_Aggregate_Create( &ag );
  ML_Aggregate_Set_Threshold(ag,0.0);
  ML_Set_SpectralNormScheme_PowerMethod(ml);
/*
   To run SA:
     a) set damping factor to 1 and use power method
        ML_Aggregate_Set_DampingFactor(ag, 4./3.);
   To run NSA:
     a) set damping factor to 0
        ML_Aggregate_Set_DampingFactor(ag, 0.);
   To run NSR
     a) set damping factor to 1 and use power method
        ML_Aggregate_Set_DampingFactor(ag, 1.);
        ag->Restriction_smoothagg_transpose = ML_FALSE;
        ag->keep_agg_information=1;
        ag->keep_P_tentative=1;
     b) hack code so it calls the energy minimizing restriction
          line 2973 of ml_agg_genP.c
     c) turn on the NSR flag in ml_agg_energy_min.cpp
   To run Emin
     a) set min_eneryg = 2 and keep_agg_info = 1;
      ag->minimizing_energy=2;
      ag->keep_agg_information=1;
      ag->cheap_minimizing_energy = 0;
      ag->block_scaled_SA = 1;
*/
  ag->minimizing_energy=2;
  ag->keep_agg_information=1;
  ag->block_scaled_SA = 1;

  ML_Aggregate_Set_NullSpace(ag, num_PDE_eqns, num_PDE_eqns, NULL, N_update);
  ML_Aggregate_Set_MaxCoarseSize( ag, 20);

/*
ML_Aggregate_Set_RandomOrdering( ag );
ML_Aggregate_Set_DampingFactor(ag, .1);
ag->drop_tol_for_smoothing = 1.0e-3;
ML_Aggregate_Set_Threshold(ag, 1.0e-3);
ML_Aggregate_Set_MaxCoarseSize( ag, 300);
*/


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

	/* set up smoothers */

        AZ_defaults(options, params);

	for (level = N_levels-1; level > coarsest_level; level--) {
          /* This is the Aztec domain decomp/ilu smoother that we */
          /* usually use for this problem.                        */

/*
          options[AZ_precond] = AZ_dom_decomp;
          options[AZ_subdomain_solve] = AZ_ilut;
          params[AZ_ilut_fill] = 1.0;
          options[AZ_reorder] = 1;
          ML_Gen_SmootherAztec(ml, level, options, params,
                        proc_config, status, AZ_ONLY_PRECONDITIONER,
                        ML_PRESMOOTHER,NULL);
*/

          /*  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);

          parasails_thresh /= 4.;
          */


          /* This is the symmetric Gauss-Seidel smoothing. 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_SymGaussSeidel(ml,level,ML_PRESMOOTHER, nsmooth,1.);
	  ML_Gen_Smoother_SymGaussSeidel(ml,level,ML_POSTSMOOTHER,nsmooth,1.);
          */

          /* Block Gauss-Seidel with block size equal to #DOF per node.    */
          /* 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_BlockGaussSeidel(ml,level,ML_PRESMOOTHER,
                                           nsmooth,0.67, num_PDE_eqns);
	  ML_Gen_Smoother_BlockGaussSeidel(ml,level,ML_POSTSMOOTHER,
                                           nsmooth, 0.67, num_PDE_eqns);
          */


  	  ML_Gen_Smoother_SymBlockGaussSeidel(ml,level,ML_POSTSMOOTHER,
                                                1, 1.0, num_PDE_eqns);
	}

        ML_Gen_CoarseSolverSuperLU( ml, coarsest_level);
	ML_Gen_Solver(ml, ML_MGW, N_levels-1, coarsest_level);
	AZ_defaults(options, params);

        options[AZ_solver]   = AZ_gmres;
        options[AZ_scaling]  = AZ_none;
        options[AZ_precond]  = AZ_user_precond;
/*
        options[AZ_conv]     = AZ_r0;
*/
        options[AZ_output]   = 1;
        options[AZ_max_iter] = 1500;
        options[AZ_poly_ord] = 5;
        options[AZ_kspace]   = 130;
        params[AZ_tol]       = 1.0e-8;
/*
options[AZ_precond] = AZ_dom_decomp;
options[AZ_subdomain_solve] = AZ_ilut;
params[AZ_ilut_fill] = 2.0;
*/

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

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

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

        /* Set rhs */

        fp = fopen("AZ_capture_rhs.mat","r");
        if (fp == NULL) {
           if (proc_config[AZ_node] == 0) printf("taking random vector for rhs\n");
           AZ_random_vector(rhs, data_org, proc_config);
           AZ_reorder_vec(rhs, data_org, update_index, NULL);
        }
        else {
           fclose(fp);
	   ivec =(int *)malloc((leng+1)*sizeof(int));
           AZ_input_msr_matrix("AZ_capture_rhs.mat", update, &rhs, &ivec,
                                N_update, proc_config);
           free(ivec);
           AZ_reorder_vec(rhs, data_org, update_index, NULL);
        }

        /* Set x */

        fp = fopen("AZ_capture_init_guess.mat","r");
        if (fp != NULL) {
           fclose(fp);
	   ivec =(int *)malloc((leng+1)*sizeof(int));
           AZ_input_msr_matrix("AZ_capture_init_guess.mat",update, &xxx, &ivec,
                                N_update, proc_config);
           free(ivec);
           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);

   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;

}
示例#5
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;

}