function  TISE_C2_L2_graph (i_p, mode)
% Copyright 2000 J.E. Akin. All rights reserved.
% under construction: requires analytic exact solution
%  ------------------------------------------------------
%  Matlab graph of i_p-th component value at mesh nodes
%  for a mesh of 3 node quintic Hermite line elements
%   i_p = 1 is solution, = 2 is solution slope
%   mode > 0 then is eigenvector to be scaled
%  ------------------------------------------------------

% 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

% UNDER_CONSTRUCTION
  if ( nargin == 0 )
    i_p = 1 ;  mode = 0 ;
  elseif ( nargin == 1 )
    mode = 0 ;
  end % if no arguments

%    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 coordinates \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)
  if ( nod_per_el ~= 2 )
    error ('This is not a mesh of 2 node line elements')
  end % if 

  load node_results.tmp
  nr = size (node_results, 1);
  if ( nr == 0 )
    error ('Error missing file node_results.tmp')
  end % if error
  max_p = size (node_results, 2) ; % number of columns
  fprintf ('Read %g nodal solution values \n', nr)
  fprintf ('     with %g components each \n', max_p)
  if ( i_p > max_p ) 
    fprintf ('Data requested for component i_p = %g \n', i_p)
    error ('i_p > available data')
  end % if error

  H (2)       = 0. ;
  HC2 (6)     = 0. ;
  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
  t_dy (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) ;

  if ( mode > 0 ) % scale the eigenvector
    [Big, Loc] = max ( abs (node_results(:, 1)) ) ;
    node_results = node_results ./ node_results(Loc, 1) ;
  end % if mode
  y  = node_results(:, 1) ;
  dy = node_results(:, 2) ;
  d2y = node_results(:, 3) ;
  ysq = y .^2 ;

%%    Cite max, min values
  %[V_X, L_X] = max (y) ;
  %[V_N, L_N] = min (y) ;

%    Initialize plots
   if ( i_p == 1 )
     maxy = max (y)      ; miny = min (y) ;
     maxysq = max (ysq)      ; minysq = min (ysq) ;
   end % if
   if ( i_p == 2 )
     maxy = max (dy)      ; miny = min (dy) ;
   end % if
   if ( i_p == 3 )
     maxy = max (d2y)      ; miny = min (d2y) ;
   end % if

% finalize axes
   ymax = maxy ; ymin = miny ;
       ymax = ymax + abs (ymax)/5.0 ;
       ymin = ymin - abs (ymin)/5.0 ;

   clf                               % clear graphics
%b ymin=-0.7
   axis ([xmin, xmax, ymin, ymax])   % set axes

   hold on                           % hold image for plots
   xlabel (['X, Node at 45 deg (', int2str(nod_per_el), ...
     ' per element), Element at 90 deg'])
   if ( i_p == 1 )
     title(['TISE Qunitic C2 FEA Waveform from:  ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])    
     [V_X, L_X] = max (y) ;
     [V_N, L_N] = min (y) ;
     ylabel (['Y Value, solid (',num2str(V_N), ' to ', ...
              num2str(V_X), '), Y ^2 dashed'])
   elseif (i_p == 2 )
     title(['TISE Qunitic C2 FEA Waveform Slope from:  ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])    
     [V_X, L_X] = max (dy) ;
     [V_N, L_N] = min (dy) ;
     ylabel (['Y Slope Value, solid (',num2str(V_N), ' to ', ...
              num2str(V_X), ')'])
   elseif (i_p == 3 )
     title(['TISE Qunitic C2 FEA Waveform Curvature from:  ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])    
     [V_X, L_X] = max (d2y) ;
     [V_N, L_N] = min (d2y) ;
     ylabel (['Y" Value, solid (',num2str(V_N), ' to ', ...
              num2str(V_X), ')'])
   end % i_p
  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 ;

%    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
      A = abs(t_x(2) - t_x(1)) ;
      t_y  = y (t_nodes) ;         % y at those nodes, only
      t_dy  = dy (t_nodes) ;         % dy at those nodes, only
      t_d2y  = d2y (t_nodes) ;         % dy at those nodes, only
      D (1:3:6) = t_y ;
      D (2:3:6) = t_dy ;
      D (3:3:6) = t_d2y ;
      t_ysq = t_y .^2 ;
      if ( i_p == 1 )
        plot (t_x, t_y, 'ko')        % plot nodal value symbols
      elseif ( i_p == 2 )
        plot (t_x, t_dy, 'ko')        % plot nodal value symbols
      elseif ( i_p == 3 )
        plot (t_x, t_d2y, 'ko')        % plot nodal value symbols
      end % if

%      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+')
      %b text (x_bar, 0.0, t_text, 'Rotation', 90) % incline
      %b plot (x_bar, 0.0, 'k+')

%      Plot this element (if non-sequential use loop)
    %  % c_x  = t_x (loop) ;       % x for nod_per_el line element
    %  % c_y  = t_y (loop) ;       % values at nodes
    %  % plot (c_x, c_y)           % plot nod_per_el lines
    %  plot (t_x, t_y)           % plot nod_per_el lines

%      Loop over local points on the quadratic polynomial element
      n_poly = ceil ( 95 / nt) ;
      for k = 1: (n_poly + 1) % points in parametric space
%          get element parametric interpolation functions
         R  = (k - 1)/n_poly ;   % on 0 to 1
         R3 = R*R*R ;
%        H = ELEMENT SHAPE FUNCTIONS
%        LOCAL NODE COORD. ARE 0,+1    1----------2
         H (1) = 1. - R  ;       
         H (2) = R ;
         x_el (k) = H * t_x ;  % true x value
%
        if ( i_p == 1 )
          HC2 (1) = 1 - 10*R3 + 15*R3*R - 6*R3*R*R ;
          HC2 (2) = (R - 6*R3 + 8*R3*R - 3*R3*R*R)*A ;
          HC2 (3) = (R*R - 3*R3 + 3*R3*R - R3*R*R)*A*A/2 ;
          HC2 (4) = 10*R3 - 15*R3*R + 6*R3*R*R ;
          HC2 (5) = (7*R3*R - 3*R3*R*R - 4*R3)*A ;
          HC2 (6) = (R3 - 2*R3*R + R3*R*R)*A*A/2 ;
          y_el (k) = HC2 * D' ;  % true y value
%
       elseif (i_p == 2 )
         DHC2 (1) = 30 * (2 * R3 - R * R - R3 * R) / A ;
         DHC2 (2) = 1 - 18 * R * R + 32 * R3 - 15 * R3 * R ;
         DHC2 (3) = 0.5*(2 * R - 9 * R * R + 12 * R3 - 5 * R3 * R)*A ;
         DHC2 (4) = 30 * R * R * (1 - 2 * R + R * R) / A ;
         DHC2 (5) = 28 * R3 - 15 * R3 * R - 12 * R * R ;
         DHC2 (6) = 0.5 * R * R * (3 - 8 * R + 5 * R * R) * A ;
         dy_el (k) = DHC2 * D' ;  % true y value
% 
       elseif ( i_p == 3)
         D2HC2 (1) = 30 * (6 * R^2 - 2 * R - 4 * R3) / A^2 ;
         D2HC2 (2) = ( - 36 * R + 96 * R * R - 60 * R3) / A ;
         D2HC2 (3) = 0.5 * (2 - 18 * R + 36 * R * R - 20 * R3) ;
         D2HC2 (4) = 30 * (2 * R - 6 * R * R + 4 * R3) / A^2 ;
         D2HC2 (5) = (84 * R * R - 60 * R3 - 24 * R) / A ;
         D2HC2 (6) = 0.5 * (6 * R - 24 * R * R + 20 * R3) ;
         d2y_el (k) = D2HC2 * D' ;  % true y value
       end % if i_p
      end % for k
      if ( i_p == 1 )
        plot (x_el, y_el)
        ysq_el = y_el .^2 ;
        plot (x_el, ysq_el,'k--')
      elseif ( i_p == 2 )
        plot (x_el, dy_el)
%       ysq_el = dy_el .^2 ;
%       plot (x_el, ysq_el,'k--')
      elseif ( i_p == 3 )
        plot (x_el, d2y_el)
%       ysq_el = d2y_el .^2 ;
%       plot (x_el, ysq_el,'k--')
      end % if
    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')
  %b v_text = sprintf ('---min') ;
  %b text  (x(L_N), V_N, v_text) ;
  %b v_text = sprintf ('---max') ;
  %b text  (x(L_X), V_X, [v_text]) ;

%       -depsc -tiff            % for an eps version
  %b print ('-dpsc', ['true_L3_TISE_', int2str(i_p), '_graph'])
  hold off
  %b v_text = ['Created true_L3_TISE_', int2str(i_p), '_graph.ps'] ;
  %b fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of TISE_C2_L2_graph