function  ave_est_exact_norms ()
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab graph of error estimate   value at mesh nodes
%  ------------------------------------------------------

% c_x    = x coordinates of nod_per_el line element
% msh_typ_nodes   = connectivity list for elements, nt x nod_per_el
% loop   = corners for nod_per_el line element
% nod_per_el = Nodes per element
% np     = Number of Points
% nt     = Number of elements
% pre_e  = Element items before connectivity list
  pre_e  = 0 ;
% pre_p  = Nodal items before coordinates
  pre_p = 1;
% msh_bc_xyz = Nodal coordinates (with preceeding data)
% t_x    = x coordinates of nod_per_el corners

%    Read coordinate file and connectivity file
%    integer bc code, real xy pairs for np points (pre_p = 1)
  load msh_bc_xyz.tmp ;  

%    Set control data: number of points
  np = size (msh_bc_xyz,1) ;   % number of nodal points  
  fprintf ('Read %g mesh coordinate pairs \n', np)
  ns = size (msh_bc_xyz,2) - pre_p ;   % space dimension
  if ( ns ~= 1)
    error ('This is not a 1D mesh')
  end % if not 1D data
  x (np)      = 0.       ;       % pre-allocate array x
  y (np)      = 0.       ;       % pre-allocate array y
  yE(np)      = 0.       ;       % pre-allocate array y
  
%    Set control data: number elements
  load  msh_typ_nodes.tmp ; % nod_per_el nodes per element
  nt = size (msh_typ_nodes,1) ;          % number of elements in mesh 
  nod_per_el = size (msh_typ_nodes,2) - pre_e -1 ; % nodes per elem
  fprintf ('Read %g elements connections \n', nt)

  load pt_ave_ex_error.tmp
  nr = size (pt_ave_ex_error, 1);
  if ( nr == 0 )
    error ('Error missing file pt_ave_ex_error.tmp')
  end % if error
  max_p = size (pt_ave_ex_error, 2) ; % number of columns
  fprintf ('Read %g nodal exact error norms \n', nr)
  y = pt_ave_ex_error ;

%    Cite max, min values
  [V_X, L_X] = max (y) ;
  [V_N, L_N] = min (y) ;
  fprintf ('Max value is %g at node %g \n', V_X, L_X)
  fprintf ('Min value is %g at node %g \n', V_N, L_N)
  null (1:np) = V_N ;

  load pt_ave_error_est.tmp
  nr = size (pt_ave_error_est, 1);
  if ( nr == 0 )
    error ('Error missing file pt_ave_error_est.tmp')
  end % if error
  max_p = size (pt_ave_error_est, 2) ; % number of columns
  fprintf ('Read %g nodal estimate error norms \n', nr)
  yE = pt_ave_error_est ;

%    Cite max, min values
  [VE_X, LE_X] = max (yE) ;
  [VE_N, LE_N] = min (yE) ;
  fprintf ('Max value is %g at node %g \n', VE_X, LE_X)
  fprintf ('Min value is %g at node %g \n', VE_N, LE_N)

  t_nodes (nod_per_el) = 0 ;    % Optional pre-allocation
  t_x (nod_per_el) = 0 ;        % Optional pre-allocation
  t_y (nod_per_el) = 0 ;        % Optional pre-allocation
  c_x (nod_per_el) = 0 ;        % Optional pre-allocation
  c_y (nod_per_el) = 0 ;        % Optional pre-allocation

%                set constants
  loop = [1:nod_per_el] ; % default to sequential order

  % msh_bc_xyz has: pre_p items then: x, y
  x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column


%    Initialize plots
   xmax = max (x)        ; xmin = min (x) ;
   ymax = max (y)         ; ymin = min (y)  ;
   Emax = max (yE)         ; Emin = min (yE)  ;
   ymax = max (Emax, ymax)  ; ymin = min (Emin, ymin)  ;
% ymax=50
   if ( ymax == ymin )
     if ( abs (ymax) > 0 )
       ymax = ymax + abs (ymax)/20. ;
       ymin = ymin - abs (ymin)/20. ;
     end % if
   end % if
   clf                               % clear graphics
   axis ([xmin, xmax, ymin, ymax])   % set axes

   hold on                           % hold image for plots
   xlabel ('X, Node number at 45 deg, Element number at 90 deg')
   title(['FEA Estimated & Exact Nodal Energy Norm Error, % * 100: ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])
   ylabel (['Error Norm (o - Exact max = ', ...
   num2str(V_X), ', min = ', num2str(V_N), ')'])

%    Loop over all elements
  for it = 1:nt  ;

%      Extract element connectivity 
    t_nodes = msh_typ_nodes (it, (pre_e+2):(nod_per_el+pre_e+1)); 

%      Skip point elements, if any
    if ( all (t_nodes) ) % then valid line

%      Extract element coordinates & values
      t_x  = x (t_nodes) ;         % x at those nodes, only
      t_y  = y (t_nodes) ;         % y at those nodes, only

%      Plot the element number
      x_bar = sum (t_x' )/nod_per_el ;
      t_text = sprintf ('   (%g)', it);  % offset # from pt
      text (x_bar, V_N, t_text, 'Rotation', 90) % incline
      plot (x_bar, V_N, 'k+')

%      Plot this element (if non-sequential use loop)
      plot (t_x, t_y)           % plot nod_per_el lines
      t_y = yE (t_nodes) ;
      plot (t_x, t_y, 'k--')
      plot (t_x, t_y, 'ko')
    end % if zero in connectivity
  end % for over all elements

% plot node points on axis
  for i = 1:np
    t_text = sprintf ('   %g', i);  % offset # from pt
    text (x(i), null(i), t_text, 'Rotation', 45) % incline
  end % for all
  plot (x, null, 'k*')
  grid
 
% label max min points 
  % plot (x(L_X), y(L_X), 'kx')
  % plot (x(L_N), y(L_N), 'ko')
  v_text = sprintf ('---min') ;
  text  (x(L_N), V_N, v_text) ;
  v_text = sprintf ('---max') ;
  text  (x(L_X), V_X, [v_text]) ;

%       -depsc -tiff            % for an eps version
  %b print ('-dpsc', ['ave_est_exact_norms'])
  hold off
  %b v_text = ['Created ave_est_exact_norms.ps'] ;
  %b fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of ave_est_exact_norms