/******************************************************************************
 * Copyright 1998-2019 Lawrence Livermore National Security, LLC and other
 * HYPRE Project Developers. See the top-level COPYRIGHT file for details.
 *
 * SPDX-License-Identifier: (Apache-2.0 OR MIT)
 ******************************************************************************/

/******************************************************************************
 *
 * LGMRES lgmres 
 *
 *****************************************************************************/

#include "krylov.h"
#include "_hypre_utilities.h"

/*--------------------------------------------------------------------------
 * hypre_LGMRESFunctionsCreate
 *--------------------------------------------------------------------------*/

hypre_LGMRESFunctions *
hypre_LGMRESFunctionsCreate(
   void *       (*CAlloc)        ( size_t count, size_t elt_size,HYPRE_Int location ),
   HYPRE_Int    (*Free)          ( void *ptr ),
   HYPRE_Int    (*CommInfo)      ( void  *A, HYPRE_Int   *my_id,
                                   HYPRE_Int   *num_procs ),
   void *       (*CreateVector)  ( void *vector ),
   void *       (*CreateVectorArray)  ( HYPRE_Int size, void *vectors ),
   HYPRE_Int    (*DestroyVector) ( void *vector ),
   void *       (*MatvecCreate)  ( void *A, void *x ),
   HYPRE_Int    (*Matvec)        ( void *matvec_data, HYPRE_Complex alpha, void *A,
                                   void *x, HYPRE_Complex beta, void *y ),
   HYPRE_Int    (*MatvecDestroy) ( void *matvec_data ),
   HYPRE_Real   (*InnerProd)     ( void *x, void *y ),
   HYPRE_Int    (*CopyVector)    ( void *x, void *y ),
   HYPRE_Int    (*ClearVector)   ( void *x ),
   HYPRE_Int    (*ScaleVector)   ( HYPRE_Complex alpha, void *x ),
   HYPRE_Int    (*Axpy)          ( HYPRE_Complex alpha, void *x, void *y ),
   HYPRE_Int    (*PrecondSetup)  ( void *vdata, void *A, void *b, void *x ),
   HYPRE_Int    (*Precond)       ( void *vdata, void *A, void *b, void *x )
   )
{
   hypre_LGMRESFunctions * lgmres_functions;
   lgmres_functions = (hypre_LGMRESFunctions *)
      CAlloc( 1, sizeof(hypre_LGMRESFunctions), HYPRE_MEMORY_HOST );

   lgmres_functions->CAlloc = CAlloc;
   lgmres_functions->Free = Free;
   lgmres_functions->CommInfo = CommInfo; /* not in PCGFunctionsCreate */
   lgmres_functions->CreateVector = CreateVector;
   lgmres_functions->CreateVectorArray = CreateVectorArray; /* not in PCGFunctionsCreate */
   lgmres_functions->DestroyVector = DestroyVector;
   lgmres_functions->MatvecCreate = MatvecCreate;
   lgmres_functions->Matvec = Matvec;
   lgmres_functions->MatvecDestroy = MatvecDestroy;
   lgmres_functions->InnerProd = InnerProd;
   lgmres_functions->CopyVector = CopyVector;
   lgmres_functions->ClearVector = ClearVector;
   lgmres_functions->ScaleVector = ScaleVector;
   lgmres_functions->Axpy = Axpy;
/* default preconditioner must be set here but can be changed later... */
   lgmres_functions->precond_setup = PrecondSetup;
   lgmres_functions->precond       = Precond;

   return lgmres_functions;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESCreate
 *--------------------------------------------------------------------------*/
 
void *
hypre_LGMRESCreate( hypre_LGMRESFunctions *lgmres_functions )
{
   hypre_LGMRESData *lgmres_data;
 
   lgmres_data = hypre_CTAllocF(hypre_LGMRESData, 1, lgmres_functions, HYPRE_MEMORY_HOST);

   lgmres_data->functions = lgmres_functions;
 
   /* set defaults */
   (lgmres_data -> k_dim)          = 20;
   (lgmres_data -> tol)            = 1.0e-06;
   (lgmres_data -> cf_tol)         = 0.0;
   (lgmres_data -> a_tol)          = 0.0; /* abs. residual tol */
   (lgmres_data -> min_iter)       = 0;
   (lgmres_data -> max_iter)       = 1000;
   (lgmres_data -> rel_change)     = 0;
   (lgmres_data -> stop_crit)      = 0; /* rel. residual norm */
   (lgmres_data -> converged)      = 0;
   (lgmres_data -> precond_data)   = NULL;
   (lgmres_data -> print_level)    = 0;
   (lgmres_data -> logging)        = 0;
   (lgmres_data -> p)              = NULL;
   (lgmres_data -> r)              = NULL;
   (lgmres_data -> w)              = NULL;
   (lgmres_data -> w_2)            = NULL;
   (lgmres_data -> matvec_data)    = NULL;
   (lgmres_data -> norms)          = NULL;
   (lgmres_data -> log_file_name)  = NULL;
 
 /* lgmres specific */
   (lgmres_data -> aug_dim)         = 2;
   (lgmres_data -> approx_constant) = 1;


   return (void *) lgmres_data;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESDestroy
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESDestroy( void *lgmres_vdata )
{
	hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;
   HYPRE_Int i;
 
   if (lgmres_data)
   {
      hypre_LGMRESFunctions *lgmres_functions = lgmres_data->functions;
      if ( (lgmres_data->logging>0) || (lgmres_data->print_level) > 0 )
      {
         if ( (lgmres_data -> norms) != NULL )
            hypre_TFreeF( lgmres_data -> norms, lgmres_functions );
      }
 
      if ( (lgmres_data -> matvec_data) != NULL )
         (*(lgmres_functions->MatvecDestroy))(lgmres_data -> matvec_data);
 
      if ( (lgmres_data -> r) != NULL )
         (*(lgmres_functions->DestroyVector))(lgmres_data -> r);
      if ( (lgmres_data -> w) != NULL )
         (*(lgmres_functions->DestroyVector))(lgmres_data -> w);
      if ( (lgmres_data -> w_2) != NULL )
         (*(lgmres_functions->DestroyVector))(lgmres_data -> w_2);


      if ( (lgmres_data -> p) != NULL )
      {
         for (i = 0; i < (lgmres_data -> k_dim+1); i++)
         {
            if ( (lgmres_data -> p)[i] != NULL )
	       (*(lgmres_functions->DestroyVector))( (lgmres_data -> p) [i]);
         }
         hypre_TFreeF( lgmres_data->p, lgmres_functions );
      }

      /* lgmres mod */
      if ( (lgmres_data -> aug_vecs) != NULL )
      {
         for (i = 0; i < (lgmres_data -> aug_dim + 1); i++)
         {
            if ( (lgmres_data -> aug_vecs)[i] != NULL )
	       (*(lgmres_functions->DestroyVector))( (lgmres_data -> aug_vecs) [i]);
         }
         hypre_TFreeF( lgmres_data->aug_vecs, lgmres_functions );
      }
      if ( (lgmres_data -> a_aug_vecs) != NULL )
      {
         for (i = 0; i < (lgmres_data -> aug_dim); i++)
         {
            if ( (lgmres_data -> a_aug_vecs)[i] != NULL )
	       (*(lgmres_functions->DestroyVector))( (lgmres_data -> a_aug_vecs) [i]);
         }
         hypre_TFreeF( lgmres_data->a_aug_vecs, lgmres_functions );
      }
      /*---*/

      hypre_TFreeF(lgmres_data->aug_order, lgmres_functions);
      


      hypre_TFreeF( lgmres_data, lgmres_functions );
      hypre_TFreeF( lgmres_functions, lgmres_functions );
   }
 
   return hypre_error_flag;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESGetResidual
 *--------------------------------------------------------------------------*/

HYPRE_Int hypre_LGMRESGetResidual( void *lgmres_vdata, void **residual )
{
   /* returns a pointer to the residual vector */

   hypre_LGMRESData  *lgmres_data     = (hypre_LGMRESData *)lgmres_vdata;
   *residual = lgmres_data->r;
   return hypre_error_flag;
   
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESSetup
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetup( void *lgmres_vdata,
                  void *A,
                  void *b,
                  void *x         )
{
   hypre_LGMRESData *lgmres_data     = (hypre_LGMRESData *)lgmres_vdata;
   hypre_LGMRESFunctions *lgmres_functions = lgmres_data->functions;

   HYPRE_Int            k_dim            = (lgmres_data -> k_dim);
   HYPRE_Int            max_iter         = (lgmres_data -> max_iter);
   HYPRE_Int          (*precond_setup)(void*,void*,void*,void*) = (lgmres_functions->precond_setup);
   void          *precond_data     = (lgmres_data -> precond_data);

   HYPRE_Int            rel_change       = (lgmres_data -> rel_change);
   
  /* lgmres mod */
   HYPRE_Int            aug_dim          = (lgmres_data -> aug_dim);  

   
 
   (lgmres_data -> A) = A;
 
   /*--------------------------------------------------
    * The arguments for NewVector are important to
    * maintain consistency between the setup and
    * compute phases of matvec and the preconditioner.
    *--------------------------------------------------*/
 
   if ((lgmres_data -> p) == NULL)
	   (lgmres_data -> p) = (void**)(*(lgmres_functions->CreateVectorArray))(k_dim+1,x);
   if ((lgmres_data -> r) == NULL)
      (lgmres_data -> r) = (*(lgmres_functions->CreateVector))(b);
   if ((lgmres_data -> w) == NULL)
      (lgmres_data -> w) = (*(lgmres_functions->CreateVector))(b);
 
   if (rel_change)
   {  
      if ((lgmres_data -> w_2) == NULL)
         (lgmres_data -> w_2) = (*(lgmres_functions->CreateVector))(b);
   }
 
   /* lgmres mod */
   if ((lgmres_data -> aug_vecs) == NULL)
      (lgmres_data -> aug_vecs) = (void**)(*(lgmres_functions->CreateVectorArray))(aug_dim+1,x); /* one extra */
   if ((lgmres_data -> a_aug_vecs) == NULL)
      (lgmres_data -> a_aug_vecs) = (void**)(*(lgmres_functions->CreateVectorArray))(aug_dim,x);
   if ((lgmres_data -> aug_order) == NULL)
      (lgmres_data -> aug_order) = hypre_CTAllocF(HYPRE_Int,aug_dim,lgmres_functions, HYPRE_MEMORY_HOST);
   /*---*/


   if ((lgmres_data -> matvec_data) == NULL)
      (lgmres_data -> matvec_data) = (*(lgmres_functions->MatvecCreate))(A, x);
 
   precond_setup(precond_data, A, b, x);
 
   /*-----------------------------------------------------
    * Allocate space for log info
    *-----------------------------------------------------*/
 
   if ( (lgmres_data->logging)>0 || (lgmres_data->print_level) > 0 )
   {
      if ((lgmres_data -> norms) == NULL)
         (lgmres_data -> norms) = hypre_CTAllocF(HYPRE_Real, max_iter + 1,lgmres_functions, HYPRE_MEMORY_HOST);
   }
   if ( (lgmres_data->print_level) > 0 ) {
      if ((lgmres_data -> log_file_name) == NULL)
		  (lgmres_data -> log_file_name) = (char*)"gmres.out.log";
   }
 
   return hypre_error_flag;
}
 
/*--------------------------------------------------------------------------
 * hypre_LGMRESSolve

   Note: no rel. change capability

 *-------------------------------------------------------------------------*/

HYPRE_Int
hypre_LGMRESSolve(void  *lgmres_vdata,
                 void  *A,
                 void  *b,
		 void  *x)
{
   hypre_LGMRESData  *lgmres_data   = (hypre_LGMRESData *)lgmres_vdata;
   hypre_LGMRESFunctions *lgmres_functions = lgmres_data->functions;
   HYPRE_Int 		     k_dim        = (lgmres_data -> k_dim);
   HYPRE_Int               min_iter     = (lgmres_data -> min_iter);
   HYPRE_Int 		     max_iter     = (lgmres_data -> max_iter);
   HYPRE_Real 	     r_tol        = (lgmres_data -> tol);
   HYPRE_Real 	     cf_tol       = (lgmres_data -> cf_tol);
   HYPRE_Real        a_tol        = (lgmres_data -> a_tol);
   void             *matvec_data  = (lgmres_data -> matvec_data);

   void             *r            = (lgmres_data -> r);
   void             *w            = (lgmres_data -> w);
   

   void            **p            = (lgmres_data -> p);

   /* lgmres  mod*/
   void          **aug_vecs       = (lgmres_data ->aug_vecs);
   void          **a_aug_vecs     = (lgmres_data ->a_aug_vecs);
   HYPRE_Int            *aug_order      = (lgmres_data->aug_order);
   HYPRE_Int             aug_dim        = (lgmres_data -> aug_dim);
   HYPRE_Int             approx_constant=  (lgmres_data ->approx_constant);
   HYPRE_Int             it_arnoldi, aug_ct, it_total, ii, order, it_aug;
   HYPRE_Int             spot = 0;
   HYPRE_Real      tmp_norm, r_norm_last;
   /*---*/

   HYPRE_Int 	           (*precond)(void*,void*,void*,void*)   = (lgmres_functions -> precond);
   HYPRE_Int 	            *precond_data = (HYPRE_Int*)(lgmres_data -> precond_data);

   HYPRE_Int             print_level    = (lgmres_data -> print_level);
   HYPRE_Int             logging        = (lgmres_data -> logging);

   HYPRE_Real     *norms          = (lgmres_data -> norms);
   
   HYPRE_Int        break_value = 0;
   HYPRE_Int	      i, j, k;
   HYPRE_Real *rs, **hh, *c, *s; 
   HYPRE_Int        iter; 
   HYPRE_Int        my_id, num_procs;
   HYPRE_Real epsilon, gamma, t, r_norm, b_norm, den_norm;
   
   HYPRE_Real epsmac = 1.e-16; 
   HYPRE_Real ieee_check = 0.;

   HYPRE_Real cf_ave_0 = 0.0;
   HYPRE_Real cf_ave_1 = 0.0;
   HYPRE_Real weight;
   HYPRE_Real r_norm_0;


   /* We are not checking rel. change for now... */
   

   (lgmres_data -> converged) = 0;
   /*-----------------------------------------------------------------------
    * With relative change convergence test on, it is possible to attempt
    * another iteration with a zero residual. This causes the parameter
    * alpha to go NaN. The guard_zero_residual parameter is to circumvent
    * this. Perhaps it should be set to something non-zero (but small).
    *-----------------------------------------------------------------------*/

   (*(lgmres_functions->CommInfo))(A,&my_id,&num_procs);
   if ( logging>0 || print_level>0 )
   {
      norms          = (lgmres_data -> norms);
      /* not used yet      log_file_name  = (lgmres_data -> log_file_name);*/
      /* fp = fopen(log_file_name,"w"); */
   }

   /* initialize work arrays  - lgmres includes aug_dim*/
   rs = hypre_CTAllocF(HYPRE_Real,k_dim+1+aug_dim,lgmres_functions, HYPRE_MEMORY_HOST);
   c = hypre_CTAllocF(HYPRE_Real,k_dim+aug_dim,lgmres_functions, HYPRE_MEMORY_HOST);
   s = hypre_CTAllocF(HYPRE_Real,k_dim+aug_dim,lgmres_functions, HYPRE_MEMORY_HOST);


   
  /* lgmres mod. - need non-modified hessenberg to avoid aug_dim matvecs */
   hh = hypre_CTAllocF(HYPRE_Real*,k_dim+aug_dim+1,lgmres_functions, HYPRE_MEMORY_HOST);
   for (i=0; i < k_dim+aug_dim+1; i++)
   {	
   	hh[i] = hypre_CTAllocF(HYPRE_Real,k_dim+aug_dim,lgmres_functions, HYPRE_MEMORY_HOST); 
   }
   
   (*(lgmres_functions->CopyVector))(b,p[0]);

   /* compute initial residual */
   (*(lgmres_functions->Matvec))(matvec_data,-1.0, A, x, 1.0, p[0]);

   b_norm = sqrt((*(lgmres_functions->InnerProd))(b,b));

   /* Since it is does not diminish performance, attempt to return an error flag
      and notify users when they supply bad input. */
   if (b_norm != 0.) ieee_check = b_norm/b_norm; /* INF -> NaN conversion */
   if (ieee_check != ieee_check)
   {
      /* ...INFs or NaNs in input can make ieee_check a NaN.  This test
         for ieee_check self-equality works on all IEEE-compliant compilers/
         machines, c.f. page 8 of "Lecture Notes on the Status of IEEE 754"
         by W. Kahan, May 31, 1996.  Currently (July 2002) this paper may be
         found at http://HTTP.CS.Berkeley.EDU/~wkahan/ieee754status/IEEE754.PDF */
      if (logging > 0 || print_level > 0)
      {
        hypre_printf("\n\nERROR detected by Hypre ... BEGIN\n");
        hypre_printf("ERROR -- hypre_LGMRESSolve: INFs and/or NaNs detected in input.\n");
        hypre_printf("User probably placed non-numerics in supplied b.\n");
        hypre_printf("Returning error flag += 101.  Program not terminated.\n");
        hypre_printf("ERROR detected by Hypre ... END\n\n\n");
      }
      hypre_error(HYPRE_ERROR_GENERIC);
      return hypre_error_flag;
   }

   r_norm = sqrt((*(lgmres_functions->InnerProd))(p[0],p[0]));
   r_norm_0 = r_norm;

   /* Since it is does not diminish performance, attempt to return an error flag
      and notify users when they supply bad input. */
   if (r_norm != 0.) ieee_check = r_norm/r_norm; /* INF -> NaN conversion */
   if (ieee_check != ieee_check)
   {
      /* ...INFs or NaNs in input can make ieee_check a NaN.  This test
         for ieee_check self-equality works on all IEEE-compliant compilers/
         machines, c.f. page 8 of "Lecture Notes on the Status of IEEE 754"
         by W. Kahan, May 31, 1996.  Currently (July 2002) this paper may be
         found at http://HTTP.CS.Berkeley.EDU/~wkahan/ieee754status/IEEE754.PDF */
      if (logging > 0 || print_level > 0)
      {
        hypre_printf("\n\nERROR detected by Hypre ... BEGIN\n");
        hypre_printf("ERROR -- hypre_LGMRESSolve: INFs and/or NaNs detected in input.\n");
        hypre_printf("User probably placed non-numerics in supplied A or x_0.\n");
        hypre_printf("Returning error flag += 101.  Program not terminated.\n");
        hypre_printf("ERROR detected by Hypre ... END\n\n\n");
      }
      hypre_error(HYPRE_ERROR_GENERIC);
      return hypre_error_flag;
   }

   if ( logging>0 || print_level > 0)
   {
      norms[0] = r_norm;
      if ( print_level>1 && my_id == 0 )
      {
  	 hypre_printf("L2 norm of b: %e\n", b_norm);
         if (b_norm == 0.0)
            hypre_printf("Rel_resid_norm actually contains the residual norm\n");
         hypre_printf("Initial L2 norm of residual: %e\n", r_norm);
      
      }
   }
   iter = 0;

   if (b_norm > 0.0)
   {
/* convergence criterion |r_i|/|b| <= accuracy if |b| > 0 */
     den_norm= b_norm;
   }
   else
   {
/* convergence criterion |r_i|/|r0| <= accuracy if |b| = 0 */
     den_norm= r_norm;
   };

  /* convergence criteria: |r_i| <= max( a_tol, r_tol * den_norm)
      den_norm = |r_0| or |b|
      note: default for a_tol is 0.0, so relative residual criteria is used unless
            user specifies a_tol, or sets r_tol = 0.0, which means absolute
            tol only is checked  */
      
   epsilon = hypre_max(a_tol,r_tol*den_norm);
   
   /* so now our stop criteria is |r_i| <= epsilon */
 

   if ( print_level>1 && my_id == 0 )
   {
      if (b_norm > 0.0)
         {hypre_printf("=============================================\n\n");
          hypre_printf("Iters     resid.norm     conv.rate  rel.res.norm\n");
          hypre_printf("-----    ------------    ---------- ------------\n");
      
          }

      else
         {hypre_printf("=============================================\n\n");
          hypre_printf("Iters     resid.norm     conv.rate\n");
          hypre_printf("-----    ------------    ----------\n");
      
          };
   }

   
   
/*lgmres initialization */
   for (ii=0; ii<aug_dim; ii++) {
      aug_order[ii] = 0;
   }
   aug_ct = 0; /* number of aug. vectors available */



   /* outer iteration cycle */
   while (iter < max_iter)
   {
   /* initialize first term of hessenberg system */

	rs[0] = r_norm;
        if (r_norm == 0.0)
        {
           hypre_TFreeF(c,lgmres_functions); 
           hypre_TFreeF(s,lgmres_functions); 
           hypre_TFreeF(rs,lgmres_functions);
           for (i=0; i < k_dim+aug_dim+1; i++) {
              hypre_TFreeF(hh[i],lgmres_functions);
           }

           hypre_TFreeF(hh,lgmres_functions); 
	   return hypre_error_flag;
           
	}

        /* see if we are already converged and 
           should print the final norm and exit */
	if (r_norm <= epsilon && iter >= min_iter) 
        {
           (*(lgmres_functions->CopyVector))(b,r);
           (*(lgmres_functions->Matvec))(matvec_data,-1.0,A,x,1.0,r);
           r_norm = sqrt((*(lgmres_functions->InnerProd))(r,r));
           if (r_norm  <= epsilon)
           {
              if ( print_level>1 && my_id == 0)
              {
                 hypre_printf("\n\n");
                 hypre_printf("Final L2 norm of residual: %e\n\n", r_norm);
              }
              break;
              }
           else
              if ( print_level>0 && my_id == 0)
                 hypre_printf("false convergence 1\n");
           
	}
        
      	t = 1.0 / r_norm;
        r_norm_last = r_norm;
	
        (*(lgmres_functions->ScaleVector))(t,p[0]);
	i = 0;

        /* lgmres mod: determine number of arnoldi steps to take */
        /* if approx_constant then we keep the space the same size
           even if we don't have the full number of aug vectors yet*/
        if (approx_constant) {
           it_arnoldi = k_dim - aug_ct;
        } else {
           it_arnoldi = k_dim - aug_dim; 
        }
        it_total =  it_arnoldi + aug_ct;
        it_aug = 0; /* keep track of augmented iterations */


        /***RESTART CYCLE (right-preconditioning) ***/
        while (i < it_total && iter < max_iter)
	{
           i++;
           iter++;
           (*(lgmres_functions->ClearVector))(r);


           /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */ 
           if ( i <= it_arnoldi) 
           { /* Arnoldi */
              precond(precond_data, A, p[i-1], r);
              (*(lgmres_functions->Matvec))(matvec_data, 1.0, A, r, 0.0, p[i]);
           } else 
           { /*lgmres aug step */
              it_aug ++;
              order = i - it_arnoldi - 1; /* which aug step (note i starts at 1) - aug order number at 0*/ 
              for (ii=0; ii<aug_dim; ii++) 
              {
                 if (aug_order[ii] == order) 
                 {
                    spot = ii;
                    break; /* must have this because there will be duplicates before aug_ct = aug_dim */ 
                 }  
              }
              /* copy a_aug_vecs[spot] to p[i] */ 
              (*(lgmres_functions->CopyVector))(a_aug_vecs[spot],p[i]);
              
              /*note: an alternate implementation choice would be to only save the AUGVECS and
                not A_AUGVEC and then apply the PC here to the augvec */
           }
           /*---*/

           /* modified Gram_Schmidt */
           for (j=0; j < i; j++)
           {
              hh[j][i-1] = (*(lgmres_functions->InnerProd))(p[j],p[i]);
              (*(lgmres_functions->Axpy))(-hh[j][i-1],p[j],p[i]);
           }
           t = sqrt((*(lgmres_functions->InnerProd))(p[i],p[i]));
           hh[i][i-1] = t;	
           if (t != 0.0)
           {
              t = 1.0/t;
              (*(lgmres_functions->ScaleVector))(t,p[i]);
           }


           /* done with modified Gram_schmidt and Arnoldi step.
              update factorization of hh */
           for (j = 1; j < i; j++)
           {
              t = hh[j-1][i-1];
              hh[j-1][i-1] = s[j-1]*hh[j][i-1] + c[j-1]*t;
              hh[j][i-1] = -s[j-1]*t + c[j-1]*hh[j][i-1];
           }
           t= hh[i][i-1]*hh[i][i-1];
           t+= hh[i-1][i-1]*hh[i-1][i-1];
           gamma = sqrt(t);
           if (gamma == 0.0) gamma = epsmac;
           c[i-1] = hh[i-1][i-1]/gamma;
           s[i-1] = hh[i][i-1]/gamma;
           rs[i] = -hh[i][i-1]*rs[i-1];
           rs[i]/=  gamma;
           rs[i-1] = c[i-1]*rs[i-1];
           /* determine residual norm */
           hh[i-1][i-1] = s[i-1]*hh[i][i-1] + c[i-1]*hh[i-1][i-1];
           r_norm = fabs(rs[i]);

           /* print ? */
           if ( print_level>0 )
           {
              norms[iter] = r_norm;
              if ( print_level>1 && my_id == 0 )
              {
                 if (b_norm > 0.0)
                    hypre_printf("% 5d    %e    %f   %e\n", iter, 
                           norms[iter],norms[iter]/norms[iter-1],
                           norms[iter]/b_norm);
                 else
                    hypre_printf("% 5d    %e    %f\n", iter, norms[iter],
                           norms[iter]/norms[iter-1]);
              }
           }
           /*convergence factor tolerance */
           if (cf_tol > 0.0)
           {
              cf_ave_0 = cf_ave_1;
              cf_ave_1 = pow( r_norm / r_norm_0, 1.0/(2.0*iter));
              
              weight   = fabs(cf_ave_1 - cf_ave_0);
              weight   = weight / hypre_max(cf_ave_1, cf_ave_0);
              weight   = 1.0 - weight;
#if 0
              hypre_printf("I = %d: cf_new = %e, cf_old = %e, weight = %e\n",
                     i, cf_ave_1, cf_ave_0, weight );
#endif
              if (weight * cf_ave_1 > cf_tol) 
              {
                 break_value = 1;
                 break;
              }
           }
           /* should we exit the restart cycle? (conv. check) */
           if (r_norm <= epsilon && iter >= min_iter)
           {
                 break;
           }
           

	} /*** end of restart cycle ***/

	/* now compute solution, first solve upper triangular system */

	if (break_value) break;
	
	rs[i-1] = rs[i-1]/hh[i-1][i-1];
	for (k = i-2; k >= 0; k--)
	{
           t = 0.0;
           for (j = k+1; j < i; j++)
           {
              t -= hh[k][j]*rs[j];
           }
           t+= rs[k];
           rs[k] = t/hh[k][k];
	}
        /* form linear combination of p's to get solution */
        /* put the new aug_vector in aug_vecs[aug_dim]  - a temp position*/	
        /* i = number of iterations */  
        /* it_aug = number of augmented iterations */ 
        /* it_arnoldi = number of arnoldi iterations */


        /*check if exited early before all arnoldi its */
        if (it_arnoldi > i) it_arnoldi = i; 


        if (!it_aug)
        {
           (*(lgmres_functions->CopyVector))(p[i-1],w);
           (*(lgmres_functions->ScaleVector))(rs[i-1],w);
           for (j = i-2; j >=0; j--)
              (*(lgmres_functions->Axpy))(rs[j], p[j], w);
        }
        else /* need some of the augvecs */
        {
           (*(lgmres_functions->CopyVector))(p[0],w);
           (*(lgmres_functions->ScaleVector))(rs[0],w);

           /* reg. arnoldi directions */  
           for (j = 1; j < it_arnoldi; j++) /*first one already done */
           {
              (*(lgmres_functions->Axpy))(rs[j], p[j], w);
           }
            
           /* augment directions */
           for (ii=0; ii<it_aug; ii++) 
           {
              for (j=0; j<aug_dim; j++) 
              {
                 if (aug_order[j] == ii) 
                 {
                    spot = j;
                    break; /* must have this because there will be
                            * duplicates before aug_ct = aug_dim */ 
                 }  
              }
              (*(lgmres_functions->Axpy))(rs[it_arnoldi+ii], aug_vecs[spot], w);
           }
        }


        /* grab the new aug vector before the prec*/
        (*(lgmres_functions->CopyVector))(w,aug_vecs[aug_dim]);
        
	(*(lgmres_functions->ClearVector))(r);
	/* find correction (in r) (un-wind precond.)*/
        precond(precond_data, A, w, r);

        /* update current solution x (in x) */
	(*(lgmres_functions->Axpy))(1.0,r,x);
         

        /* check for convergence by evaluating the actual residual */
	if (r_norm <= epsilon && iter >= min_iter) 
        {
           /* calculate actual residual norm*/
           (*(lgmres_functions->CopyVector))(b,r);
           (*(lgmres_functions->Matvec))(matvec_data,-1.0,A,x,1.0,r);
           r_norm = sqrt( (*(lgmres_functions->InnerProd))(r,r) );
           
           if (r_norm <= epsilon)
           {
              if ( print_level>1 && my_id == 0 )
              {
                 hypre_printf("\n\n");
                 hypre_printf("Final L2 norm of residual: %e\n\n", r_norm);
              }
              (lgmres_data -> converged) = 1;
              break;
           }
           else /* conv. has not occurred, according to true residual */ 
           {
              if ( print_level>0 && my_id == 0)
                 hypre_printf("false convergence 2\n");
              (*(lgmres_functions->CopyVector))(r,p[0]);
              i = 0;
           }
	} /* end of convergence check */
        
        /* compute residual vector and continue loop */

        /* copy r0 (not scaled) to w*/  
	(*(lgmres_functions->CopyVector))(p[0],w);
	(*(lgmres_functions->ScaleVector))(r_norm_last,w);


	for (j=i ; j > 0; j--)
	{
           rs[j-1] = -s[j-1]*rs[j];
           rs[j] = c[j-1]*rs[j];
	}
        
        if (i) (*(lgmres_functions->Axpy))(rs[i]-1.0,p[i],p[i]);
        for (j=i-1 ; j > 0; j--)
           (*(lgmres_functions->Axpy))(rs[j],p[j],p[i]);
        
        if (i)
        {
           (*(lgmres_functions->Axpy))(rs[0]-1.0,p[0],p[0]);
           (*(lgmres_functions->Axpy))(1.0,p[i],p[0]);
        }

        /* lgmres mod */  
        /* collect aug vector and A*augvector for future restarts -
           only if we will be restarting (i.e. this cycle performed it_total
           iterations). ordering starts at 0.*/
        if (aug_dim > 0) 
        {
           if (!aug_ct) 
           {
              spot = 0;
              aug_ct++;
           } 
           else if (aug_ct < aug_dim) 
           {
              spot = aug_ct;
              aug_ct++;
           } 
           else 
           { /* truncate - already have aug_dim number of vectors*/
              for (ii=0; ii<aug_dim; ii++) 
              {
                 if (aug_order[ii] == (aug_dim-1)) 
                 {
                    spot = ii;
                 }  
              }
           } 
           /* aug_vecs[aug_dim] contains new aug vector */
           (*(lgmres_functions->CopyVector))(aug_vecs[aug_dim], aug_vecs[spot]);
           /*need to normalize */
           tmp_norm = sqrt((*(lgmres_functions->InnerProd))(aug_vecs[spot], aug_vecs[spot]));
           
           tmp_norm = 1.0/tmp_norm;
           (*(lgmres_functions->ScaleVector))(tmp_norm ,aug_vecs[spot]);
           
           /*set new aug vector to order 0  - move all others back one */
           for (ii=0; ii < aug_dim; ii++) 
           {
              aug_order[ii]++;
           } 
           aug_order[spot] = 0; 

           /*now add the A*aug vector to A_AUGVEC(spot) - this is
            * independ. of preconditioning type*/
           /* A*augvec = V*H*y  = r0-rm   (r0 is in w and rm is in p[0])*/
           (*(lgmres_functions->CopyVector))( w, a_aug_vecs[spot]);
           (*(lgmres_functions->ScaleVector))(- 1.0, a_aug_vecs[spot]); /* -r0*/
           (*(lgmres_functions->Axpy))(1.0, p[0],a_aug_vecs[spot]); /* rm - r0 */
           (*(lgmres_functions->ScaleVector))(-tmp_norm, a_aug_vecs[spot]); /* r0-rm /norm */
           
        }
        
   } /* END of iteration while loop */
        

   if ( print_level>1 && my_id == 0 )
          hypre_printf("\n\n"); 

   (lgmres_data -> num_iterations) = iter;
   if (b_norm > 0.0)
      (lgmres_data -> rel_residual_norm) = r_norm/b_norm;
   if (b_norm == 0.0)
      (lgmres_data -> rel_residual_norm) = r_norm;

   if (iter >= max_iter && r_norm > epsilon && epsilon > 0) hypre_error(HYPRE_ERROR_CONV);
   

   hypre_TFreeF(c,lgmres_functions); 
   hypre_TFreeF(s,lgmres_functions); 
   hypre_TFreeF(rs,lgmres_functions);

   for (i=0; i < k_dim+1+aug_dim; i++)
   {	
   	hypre_TFreeF(hh[i],lgmres_functions);
   }
   hypre_TFreeF(hh,lgmres_functions); 

   return hypre_error_flag;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESSetKDim, hypre_LGMRESGetKDim
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetKDim( void   *lgmres_vdata,
                    HYPRE_Int   k_dim )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

   
   (lgmres_data -> k_dim) = k_dim;
 
   return hypre_error_flag;
   
}

HYPRE_Int
hypre_LGMRESGetKDim( void   *lgmres_vdata,
                    HYPRE_Int * k_dim )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *k_dim = (lgmres_data -> k_dim);
 
   return hypre_error_flag;
}
/*--------------------------------------------------------------------------
 * hypre_LGMRESSetAugDim
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetAugDim( void   *lgmres_vdata,
                    HYPRE_Int   aug_dim )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;
 
   if (aug_dim < 0) aug_dim = 0; /* must be positive */
 
   if (aug_dim > (lgmres_data -> k_dim) -1) /* must be be <= (restart size-1) */
   {
      while (aug_dim > (lgmres_data -> k_dim) -1)
      {
         aug_dim--;
      }

      aug_dim = (((0)<(aug_dim)) ? (aug_dim) : (0));

   }
   (lgmres_data -> aug_dim) = aug_dim;
 
   return hypre_error_flag;
}
HYPRE_Int
hypre_LGMRESGetAugDim( void   *lgmres_vdata,
                       HYPRE_Int * aug_dim )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *aug_dim = (lgmres_data -> aug_dim);
 
   return hypre_error_flag;
}



/*--------------------------------------------------------------------------
 * hypre_LGMRESSetTol, hypre_LGMRESGetTol
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetTol( void   *lgmres_vdata,
                   HYPRE_Real  tol       )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> tol) = tol;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetTol( void   *lgmres_vdata,
                   HYPRE_Real  * tol      )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *tol = (lgmres_data -> tol);
 
   return hypre_error_flag;
}
/*--------------------------------------------------------------------------
 * hypre_LGMRESSetAbsoluteTol, hypre_LGMRESGetAbsoluteTol
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetAbsoluteTol( void   *lgmres_vdata,
                   HYPRE_Real  a_tol       )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> a_tol) = a_tol;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetAbsoluteTol( void   *lgmres_vdata,
                   HYPRE_Real  * a_tol      )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *a_tol = (lgmres_data -> a_tol);
 
   return hypre_error_flag;
}
/*--------------------------------------------------------------------------
 * hypre_LGMRESSetConvergenceFactorTol, hypre_LGMRESGetConvergenceFactorTol
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetConvergenceFactorTol( void   *lgmres_vdata,
                   HYPRE_Real  cf_tol       )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> cf_tol) = cf_tol;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetConvergenceFactorTol( void   *lgmres_vdata,
                   HYPRE_Real * cf_tol       )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *cf_tol = (lgmres_data -> cf_tol);
 
   return hypre_error_flag;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESSetMinIter, hypre_LGMRESGetMinIter
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetMinIter( void *lgmres_vdata,
                       HYPRE_Int   min_iter  )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> min_iter) = min_iter;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetMinIter( void *lgmres_vdata,
                       HYPRE_Int * min_iter  )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *min_iter = (lgmres_data -> min_iter);
 
   return hypre_error_flag;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESSetMaxIter, hypre_LGMRESGetMaxIter
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetMaxIter( void *lgmres_vdata,
                       HYPRE_Int   max_iter  )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> max_iter) = max_iter;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetMaxIter( void *lgmres_vdata,
                       HYPRE_Int * max_iter  )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *max_iter = (lgmres_data -> max_iter);
 
   return hypre_error_flag;
}


/*--------------------------------------------------------------------------
 * hypre_LGMRESSetStopCrit, hypre_LGMRESGetStopCrit
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetStopCrit( void   *lgmres_vdata,
                        HYPRE_Int  stop_crit       )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> stop_crit) = stop_crit;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetStopCrit( void   *lgmres_vdata,
                        HYPRE_Int * stop_crit       )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *stop_crit = (lgmres_data -> stop_crit);
 
   return hypre_error_flag;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESSetPrecond
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESSetPrecond( void  *lgmres_vdata,
						HYPRE_Int  (*precond)(void*,void*,void*,void*),
						HYPRE_Int  (*precond_setup)(void*,void*,void*,void*),
                       void  *precond_data )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;
   hypre_LGMRESFunctions *lgmres_functions = lgmres_data->functions;

 
   (lgmres_functions -> precond)        = precond;
   (lgmres_functions -> precond_setup)  = precond_setup;
   (lgmres_data -> precond_data)   = precond_data;
 
   return hypre_error_flag;
}
 
/*--------------------------------------------------------------------------
 * hypre_LGMRESGetPrecond
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESGetPrecond( void         *lgmres_vdata,
                       HYPRE_Solver *precond_data_ptr )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *precond_data_ptr = (HYPRE_Solver)(lgmres_data -> precond_data);
 
   return hypre_error_flag;
}
 
/*--------------------------------------------------------------------------
 * hypre_LGMRESSetPrintLevel, hypre_LGMRESGetPrintLevel
 *--------------------------------------------------------------------------*/

HYPRE_Int
hypre_LGMRESSetPrintLevel( void *lgmres_vdata,
                        HYPRE_Int   level)
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> print_level) = level;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetPrintLevel( void *lgmres_vdata,
                        HYPRE_Int * level)
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *level = (lgmres_data -> print_level);
 
   return hypre_error_flag;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESSetLogging, hypre_LGMRESGetLogging
 *--------------------------------------------------------------------------*/

HYPRE_Int
hypre_LGMRESSetLogging( void *lgmres_vdata,
                      HYPRE_Int   level)
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   (lgmres_data -> logging) = level;
 
   return hypre_error_flag;
}

HYPRE_Int
hypre_LGMRESGetLogging( void *lgmres_vdata,
                      HYPRE_Int * level)
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *level = (lgmres_data -> logging);
 
   return hypre_error_flag;
}

/*--------------------------------------------------------------------------
 * hypre_LGMRESGetNumIterations
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESGetNumIterations( void *lgmres_vdata,
                             HYPRE_Int  *num_iterations )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *num_iterations = (lgmres_data -> num_iterations);
 
   return hypre_error_flag;
}
 
/*--------------------------------------------------------------------------
 * hypre_LGMRESGetConverged
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESGetConverged( void *lgmres_vdata,
                             HYPRE_Int  *converged )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *converged = (lgmres_data -> converged);
 
   return hypre_error_flag;
}
 
/*--------------------------------------------------------------------------
 * hypre_LGMRESGetFinalRelativeResidualNorm
 *--------------------------------------------------------------------------*/
 
HYPRE_Int
hypre_LGMRESGetFinalRelativeResidualNorm( void   *lgmres_vdata,
                                         HYPRE_Real *relative_residual_norm )
{
   hypre_LGMRESData *lgmres_data = (hypre_LGMRESData *)lgmres_vdata;

 
   *relative_residual_norm = (lgmres_data -> rel_residual_norm);
   
   return hypre_error_flag;
} 
