function  biggs_time_hist (i_p, save, p_max) 
% exact solution for FEA node 3, Biggs node 2
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab time-history of i_p-th component value at mesh node
%   If i_p = 0, show RMS value, save = time group number
%   p_max = N_G_DOF number of nodal parameters
%  ------------------------------------------------------

% 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

  %b fprintf ('Begin component value graph: \n')
  if ( nargin == 1 )
     save = 1 ; p_max = 1 ;
  elseif ( nargin == 0 )
    i_p = 1 ; save = 1 ; p_max = 1 ;
  end % if no arguments
  if ( save < 10 )
    file = ['node_history_00',  int2str(save)];
  elseif ( save < 100 )
    file = ['node_history_0',  int2str(save)];
  else
    file = ['node_history_',  int2str(save)];
  end % if
  filename = [file, '.tmp']
  fid= fopen(filename, 'r') ;

  %b load node_history_001.tmp ;  
  history = fscanf (fid, '%g  \n', [(p_max+2),inf]) ;
  node_history = history' ;
  load Biggs_exact_y2.tmp
  X2 = Biggs_exact_y2(:, 2) ;
  Y2 = Biggs_exact_y2(:, 3) ;
  Y2dot = Biggs_exact_y2(:, 4);
  Y2dd  = Biggs_exact_y2(:, 5);

%    Set control data: number of points
  np = size (node_history,1) ;   % number of nodal points  
  fprintf ('Read %g time-history sets \n', np)
  max_p = size (node_history,2) - pre_p -1 ;   % space dimension
  fprintf ('with %g nodal dof values  \n', max_p)
  node = node_history (1, 1) ;
  fprintf ('for node number %g \n', node)
  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
  
  x = node_history (1:np, (pre_p+1)) ; % extract x column

  if ( i_p >= 1 )
    y = node_history(:, i_p+2) ;
  else % i_p = 0, get root mean sq
    for k = 1:np
      y (k) = sqrt(sum (node_history (k, 3:(2+max_p)).^2));
    end % for k
  end % if get RMS value

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

%    Initialize plots
   xmax = max (x)      ; xmin = min (x) ;
   ymax = max (y)      ; ymin = min (y) ;
   if ( ymax == ymin )
     if ( abs (ymax) > 0 )
       ymax = ymax + abs (ymax)/20. ;
       ymin = ymin - abs (ymin)/20. ;
     end % if
   end % if
if ( i_p ==1 )
ymax=1.4
ymin=-1.4
end
if (i_p == 2 )
ymax=60
ymin=-60
end
if (i_p == 3 )
ymax=4000
ymin=-4000
end

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

   hold on                           % hold image for plots
   xlabel ('Time')
   if ( i_p >= 1 )
    %title(['FEA Time-History for Component\_', int2str(i_p) ])  
     title(['FEA Time-History for Component\_', int2str(i_p), ...
            ' at Node ', int2str(node) ])
     ylabel (['Component ', int2str(i_p), ' (max = ', ...
     num2str(V_X), ', min = ', num2str(V_N), ')'])
   else % i_p = 0, get root mean sq
     title(['FEA RMS\_value Time-History at Node ', int2str(node)']) 
     ylabel (['FEA Solution RMS Value (max = ', ...
     num2str(V_X), ', min = ', num2str(V_N), ')'])
   end % if get RMS value

% plot node values         
   plot (x, y, 'k-')
   %b plot (x, y, 'ko')
   if ( i_p == 1 )
     plot (X2,Y2,'b--')
   end % if
   if ( i_p == 2 )
     plot (X2,Y2dot,'b--')
   end % if
   if ( i_p == 3 )
     plot (X2,Y2dd,'b--')
   end % if
  grid
 
  legend (['Numerical'], ['Biggs exact'])
% label max min points 
  %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', ['node_', int2str(i_p), '_hist'])
  hold off
  %b v_text = ['Created node_', int2str(i_p), '_hist.ps'] ;
  %b fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of biggs_time_hist