function  true_qp_flux_er_sq_graph (i_p, Exact)
% Copyright 2000 J.E. Akin. All rights reserved.
% under construction: requires analytic exact solution
% variable "p_ar" (analytic result) for "Exact" case number
%  ------------------------------------------------------
%  Matlab graph of i_p-th component value at mesh nodes
%   If i_p = 0, show RMS value
%  ------------------------------------------------------

% 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

  fprintf ('Begin component value graph: \n')
  if ( nargin == 0 )
    i_p = 0 ; Exact = 0 ;
  end % if no arguments
  if ( nargin == 1 )
    Exact = 0 ;
  end % if 1 argument
  fprintf ('Begin graph for exact case %g \n', Exact)

%    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
  
%    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 el_qp_xyz_fluxes.tmp     
  nr = size (el_qp_xyz_fluxes, 1);  % rows
  ngp = nr/nt ; % gauss points
  if ( nr == 0 )
    error ('Error missing file el_qp_xyz_fluxes.tmp')
  end % if error
  max_p = size (el_qp_xyz_fluxes, 2) ; % number of columns
  fprintf ('Read %g element flux values \n', nt)
  fprintf ('     at %g quadrature pts  \n', ngp)  
  %if ( i_p > max_p ) 
    %error ('i_p > available data')
  %end % if error

  x (np)      = 0.       ;       % pre-allocate array x
  y (np)      = 0.       ;       % pre-allocate array y
  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
  xmax = max (x)      ; xmin = min (x) ;

%%  add analytic points
%   a_inc = (xmax-xmin)/(10*nt) ;
%   ax = [xmin:a_inc:xmax] ;    % analytic points

%    Cite max, min values
  [V_X, L_X] = max (el_qp_xyz_fluxes(:, 2));
  [V_N, L_N] = min (el_qp_xyz_fluxes(:, 2));
  fprintf ('Max flux is %g at elem %g \n', V_X, round(L_X/2))
  fprintf ('Min flux is %g at elem %g \n', V_N, round(L_N/2))
  null (1:np) = 0.0 ;

%    Initialize plots
   % maxy = max (y)      ; miny = min (y) ;
   % maxe = max (error)      ; mine = min (error) ;

ymin=-0.10
ymax= 0.10  % manual set
%% finalize axes
%   %ymax = max ([maxy, maxa])      ; ymin = min ([miny, mina]) ;
%   if ( ymax == ymin )
%     if ( abs (ymax) > 0 )
%       ymax = ymax + abs (ymax)/20. ;
%       ymin = ymin - abs (ymin)/20. ;
%     end % if
%   end % if
%   diff = ymax - ymin ;
%   ymax = ymax + abs (diff)/20. ;
%    ymin = ymin - abs (diff)/20. ;
   clf                               % clear graphics
   axis ([xmin, xmax, ymin, ymax])   % set axes

   hold on                           % hold image for plots
   xlabel ('X, Node number at 45 deg')
   if ( i_p >= 1 )
     title(['Exact Error in Element Flux Component\_', int2str(i_p),':   ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])
     ylabel ('Error in Flux ')
   else % i_p = 0, get root mean sq
     title(['Exact Error in RMS\_value of Element Flux Component\_', ...
       int2str(i_p),':   ', int2str(nt), ' Elements, ', ...
       int2str(np),' Nodes'])
     ylabel ('Flux RMS Error ')
   end % if get RMS value

%    Loop over all elements
  p_div = 20 ;
  p_er(1:2) = 0.  ;
  p_x (1:2) = 0. ;
  x_c(p_div) = 0 ; cap(p_div) = 0 ;
  for it = 1:nt  ;
      p_el = el_qp_xyz_fluxes(2*it, 2) ;

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

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

%      Plot this element (if non-sequential use loop)
    p1 = min(t_x); p2 = max(t_x); p_dif=(p2 - p1);
    p_inc=p_dif/p_div;
    j = 0;
    for p = p1:p_inc:p2 % loop over points inside element
      p_x(1:2) = p ;
%-------------
      if ( i_p >= 1 )
        if ( Exact == 9 ) % u" + U + x = 0, EBC, EBC
          p_ar = cos(p)/sin(1) - 1.0;  % analytic result
        elseif ( Exact == 10 ) % u" + U + x = 0, EBC, NBC
          p_ar = cos(p)/cos(1) - 1. ; % analytic result
        elseif ( Exact == 11 ) % u" + X^N = 0,  U(0)=0=U(1),
          N = input ('Enter source exponent N in Q = x^N ')
          p_ar = (1.-(N+2)*p^(N+1))/((N+1)*(N+2)) ; % analytic result
        else
          error ('No solution given for Exact_Case number')
        end % if Exact
      else % i_p = 0, get root mean sq
        if ( Exact == 9 ) % u" + U + x = 0, EBC, EBC
          p_ar = abs(cos(p)/sin(1) - 1.0);  % analytic result
        elseif ( Exact == 10 ) % u" + U + x = 0, EBC, NBC
          p_ar = abs(cos(p)/cos(1) - 1.) ; % analytic result
        elseif ( Exact == 11 ) % u" + X^N = 0,  U(0)=0=U(1),
          N = input ('Enter source exponentt N in Q = x^N ')
          p_ar = abs(1.-(N+2)*p^(N+1))/((N+1)*(N+2)) ; % analytic result
        else
          error ('No solution given for Exact_Case number')
        end % if Exact value
      end % if i_p = 0
%-------------
      % p_ar = (1. - (N+2)*p^(N+1))/((N+1)*(N+2)) ;% analytic result
      % p_ar = cos(p)/sin(1) - 1.0 ;  % analytic result
%      linear element interpolation
      % h1 = (t_x(2) - p)/p_dif; 
      % p_el = h1*t_y(1) + (1. - h1)*t_y(2) ;
      er_el = (p_el - p_ar) ;
      p_er(2) = er_el ;
      plot (p_x, p_er)          % plot vertical lines
      j = j + 1;
      x_c(j) = p ;
      cap(j) = er_el ; 
    end % for pt in elem
    plot (x_c, cap, 'r-') % capline
  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 
% 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
  print ('-dpsc', ['true_qp_flux_error_', int2str(i_p), '_graph'])
  hold off
  v_text = ['Created true_qp_flux_error_', int2str(i_p), '_graph.ps'] ;
  fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of true_qp_flux_er_sq_graph