function y = solve_two_boundaries(fname, y, x, params, y_index, nze, periods, y_kmin_l, y_kmax_l, is_linear, Block_Num, y_kmin, maxit_, solve_tolf, lambda, cutoff, simulation_method)
% Computes the deterministic simulation of a block of equation containing
% both lead and lag variables using relaxation methods 
%
% INPUTS
%   fname               [string]        name of the file containing the block
%                                       to simulate
%   y                   [matrix]        All the endogenous variables of the model
%   x                   [matrix]        All the exogenous variables of the model
%   params              [vector]        All the parameters of the model
%   y_index             [vector of int] The index of the endogenous variables of
%                                       the block
%   nze                 [integer]       number of non-zero elements in the
%                                       jacobian matrix
%   periods             [integer]       number of simulation periods
%   y_kmin_l            [integer]       maximum number of lag in the block
%   y_kmax_l            [integer]       maximum number of lead in the block
%   is_linear           [integer]       if is_linear=1 the block is linear
%                                       if is_linear=0 the block is not linear
%   Block_Num           [integer]       block number
%   y_kmin              [integer]       maximum number of lag in the model
%   maxit_              [integer]       maximum number of iteration in Newton
%   solve_tolf          [double]        convergence criteria
%   lambda              [double]        initial value of step size in
%   Newton
%   cutoff              [double]        cutoff to correct the direction in Newton in case
%                                       of singular jacobian matrix
%   simulation_method   [integer]       linear solver method used in the
%                                       Newton algorithm : 
%                                            - 0 sprse LU
%                                            - 2 GMRES
%                                            - 3 BicGStab
%
% OUTPUTS
%   y                   [matrix]        All endogenous variables of the model      
%  
% ALGORITHM
%   Newton with LU or GMRES or BicGstab
%    
% SPECIAL REQUIREMENTS
%   none.
%  

% Copyright (C) 1996-2008 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.

  global oo_;
  cvg=0;
  iter=0;
  Per_u_=0;
  g2 = [];
  g3 = [];
  Blck_size=size(y_index,2);
  correcting_factor=0.01;
  luinc_tol=1e-10;
  max_resa=1e100;
  Jacobian_Size=Blck_size*(y_kmin+y_kmax_l +periods);
  g1=spalloc( Blck_size*periods, Jacobian_Size, nze*periods);
  reduced = 0;
  while ~(cvg==1 | iter>maxit_),
    [r, g1, g2, g3, b]=feval(fname, y, x, params, periods, 0, y_kmin, Blck_size);
    g1a=g1(:, y_kmin*Blck_size+1:(periods+y_kmin)*Blck_size);
    %disp(['size(g1)=' int2str(size(g1))]);
    %disp(['g1(:,' int2str(1:y_kmin_l*Blck_size) ')']);
    %disp(['g1(:,' int2str((periods+y_kmin_l)*Blck_size+1:(periods+y_kmin_l+y_kmax_l)*Blck_size) ')']);
    b = b' -g1(:, 1:y_kmin_l*Blck_size)*reshape(y(1+y_kmin-y_kmin_l:y_kmin,y_index)',1,y_kmin_l*Blck_size)'-g1(:, (periods+y_kmin_l)*Blck_size+1:(periods+y_kmin_l+y_kmax_l)*Blck_size)*reshape(y(periods+y_kmin+1:periods+y_kmin+y_kmax_l,y_index)',1,y_kmax_l*Blck_size)';
    if(~isreal(r))
      max_res=(-(max(max(abs(r))))^2)^0.5;
    else
      max_res=max(max(abs(r)));
    end;
    if(~isreal(max_res) | isnan(max_res))
      cvg = 0;
    elseif(is_linear & iter>0)
      cvg = 1;
    else
      cvg=(max_res<solve_tolf);
    end;
    if(~cvg)
      if(iter>0)
        if(~isreal(max_res) | isnan(max_res) | (max_resa<max_res && iter>1))
          if(isnan(max_res))
            detJ=det(g1aa);
            if(abs(detJ)<1e-7)
              max_factor=max(max(abs(g1aa)));
              ze_elem=sum(diag(g1aa)<cutoff);
              disp([num2str(full(ze_elem),'%d') ' elements on the Jacobian diagonal are below the cutoff (' num2str(cutoff,'%f') ')']);
              if(correcting_factor<max_factor)
                correcting_factor=correcting_factor*4;
                disp(['The Jacobain matrix is singular, det(Jacobian)=' num2str(detJ,'%f') '.']);
                disp(['    trying to correct the Jacobian matrix:']);
                disp(['    correcting_factor=' num2str(correcting_factor,'%f') ' max(Jacobian)=' num2str(full(max_factor),'%f')]);
                dx = (g1aa+correcting_factor*speye(periods*Blck_size))\ba- ya;
                y(1+y_kmin:periods+y_kmin,y_index)=reshape((ya_save+lambda*dx)',length(y_index),periods)';
                continue;
              else
                disp('The singularity of the jacobian matrix could not be corrected');
                return;
              end;
            end;
          elseif(lambda>1e-8)
            lambda=lambda/2;
            reduced = 1;
            disp(['reducing the path length: lambda=' num2str(lambda,'%f')]);
            y(1+y_kmin:periods+y_kmin,y_index)=reshape((ya_save+lambda*dx)',length(y_index),periods)';
            continue;
          else
            if(cutoff == 0)
              fprintf('Error in simul: Convergence not achieved in block %d, after %d iterations.\n Increase "options_.maxit_".\n',Block_Num, iter);
            else
              fprintf('Error in simul: Convergence not achieved in block %d, after %d iterations.\n Increase "options_.maxit_" or set "cutoff=0" in model options.\n',Block_Num, iter);
            end;
            oo_.deterministic_simulation.status = 0;
            oo_.deterministic_simulation.error = max_res;
            oo_.deterministic_simulation.iterations = iter;
            oo_.deterministic_simulation.block(Block_Num).status = 0;% Convergency failed.
            oo_.deterministic_simulation.block(Block_Num).error = max_res;
            oo_.deterministic_simulation.block(Block_Num).iterations = iter;
            return;
          end;
        else
          if(lambda<1)
            lambda=max(lambda*2, 1);
          end;
        end;
      end;
      ya = reshape(y(y_kmin+1:y_kmin+periods,y_index)',1,periods*Blck_size)';
      ya_save=ya;
      g1aa=g1a;
      ba=b;
      max_resa=max_res;
      if(simulation_method==0),
        dx = g1a\b- ya;
        ya = ya + lambda*dx;
        y(1+y_kmin:periods+y_kmin,y_index)=reshape(ya',length(y_index),periods)';
      elseif(simulation_method==2),
        flag1=1;
        while(flag1>0)
          [L1, U1]=luinc(g1a,luinc_tol);
          [za,flag1] = gmres(g1a,b,Blck_size,1e-6,Blck_size*periods,L1,U1);
          if (flag1>0 | reduced)
            if(flag1==1)
              disp(['Error in simul: No convergence inside GMRES after ' num2str(periods*10,'%6d') ' iterations, in block' num2str(Block_Size,'%3d')]);
            elseif(flag1==2)
              disp(['Error in simul: Preconditioner is ill-conditioned, in block' num2str(Block_Size,'%3d')]);
            elseif(flag1==3)
              disp(['Error in simul: GMRES stagnated (Two consecutive iterates were the same.), in block' num2str(Block_Size,'%3d')]);
            end;
            luinc_tol = luinc_tol/10;
            reduced = 0;
          else
            dx = za - ya;
            ya = ya + lambda*dx;
            y(1+y_kmin:periods+y_kmin,y_index)=reshape(ya',length(y_index),periods)';
          end;
        end;
      elseif(simulation_method==3),
        flag1=1;
        while(flag1>0)
          [L1, U1]=luinc(g1a,luinc_tol);
          [za,flag1] = bicgstab(g1a,b,1e-7,Blck_size*periods,L1,U1);
          if (flag1>0 | reduced)
            if(flag1==1)
              disp(['Error in simul: No convergence inside BICGSTAB after ' num2str(periods*10,'%6d') ' iterations, in block' num2str(Block_Size,'%3d')]);
            elseif(flag1==2)
              disp(['Error in simul: Preconditioner is ill-conditioned, in block' num2str(Block_Size,'%3d')]);
            elseif(flag1==3)
              disp(['Error in simul: GMRES stagnated (Two consecutive iterates were the same.), in block' num2str(Block_Size,'%3d')]);
            end;
            luinc_tol = luinc_tol/10;
            reduced = 0;
          else
            dx = za - ya;
            ya = ya + lambda*dx;
            y(1+y_kmin:periods+y_kmin,y_index)=reshape(ya',length(y_index),periods)';
          end;
        end;
      end;
    end
    iter=iter+1;
    disp(['iteration: ' num2str(iter,'%d') ' error: ' num2str(max_res,'%e')]);
  end;
  if (iter>maxit_)
    disp(['No convergence after ' num2str(iter,'%4d') ' iterations in Block ' num2str(Block_Num,'%d')]);
    oo_.deterministic_simulation.status = 0;
    oo_.deterministic_simulation.error = max_res;
    oo_.deterministic_simulation.iterations = iter;
    oo_.deterministic_simulation.block(Block_Num).status = 0;% Convergency failed.
    oo_.deterministic_simulation.block(Block_Num).error = max_res;
    oo_.deterministic_simulation.block(Block_Num).iterations = iter;
    return;
  end
  oo_.deterministic_simulation.status = 1;
  oo_.deterministic_simulation.error = max_res;
  oo_.deterministic_simulation.iterations = iter;
  oo_.deterministic_simulation.block(Block_Num).status = 1;% Convergency obtained.
  oo_.deterministic_simulation.block(Block_Num).error = max_res;
  oo_.deterministic_simulation.block(Block_Num).iterations = iter;
  return;