function  exact_node_flux_vectors (length)
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab plot of 2-D exact flux vectors at the mesh nodes
%  ------------------------------------------------------

% c_x    = x coordinates of nod_per_el line polygon
% c_y    = y coordinates of nod_per_el line polygon
% inc_e  = increment in element numbers on plot, if > 0
% inc_p  = increment in node numbers on plot, if > 0
% msh_typ_nodes   = connectivity list for elements, nt x nod_per_el
% loop   = corners for nod_per_el line polygon
% lab_p  = 1, if node points are circled
  lab_p  = 0;
% length = maximum length of arrows, in scaled x,y units
% 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
% t_y    = y coordinates of nod_per_el corners
% x_bar  = x-centroid of each element
% xy     = Coordinates of points, np x 2
% y_bar  = y-centroid of each element

%                set constants
  if ( nargin == 0 )
    length = 0.3 ;   % the max length on paper
  end % if

%    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)
% fprintf ('       x        y \n')
  
%    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 element
  fprintf ('Read %g elements connections \n', nt)

%       Read new Gauss locations & flux     components
  load exact_node_flux.tmp ; % x, y, du/dx, du/dy at qp

%       Set control data: number of gauss points
  npg = size(exact_node_flux,1) ; % quadrature pts w vectors
  if ( npg == 0 )
    error ('Error: missing file exact_node_flux.tmp')
  end % if error
  fprintf ('Read %g nodal flux sets \n', npg)
  nf = size(exact_node_flux,2) ;  % flux components
  if ( nf ~= 2 ) % vectors not meaningful
    fprintf ('Read %g flux components instead of 2 \n', nf)
    fprintf ('Use contour_el_fluxes or smooth_el_fluxes instead \n')
    error ('Error: These are not vector data')
  end % if vector data

  x (np)      = 0.       ;       % pre-allocate array x
  y (np)      = 0.       ;       % pre-allocate array y
  x_bar (nt)  = 0.       ;       % pre-allocate array x_bar
  y_bar (nt)  = 0.       ;       % pre-allocate array y_bar
  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 + 1) = 0 ;    % Optional pre-allocation
  c_y (nod_per_el + 1) = 0 ;    % Optional pre-allocation
  loop (nod_per_el + 1) = 0 ;   % Optional pre-allocation

  g_dx(npg)  = 0.       ;       % pre-allocate flux     array
  g_dy(npg)  = 0.       ;       % pre-allocate flux     array
  g_sq(npg)  = 0.       ;       % pre-allocate magnitude array

%    Mesh Range Alone
  % msh_bc_xyz has: pre_p items then: x, y
  x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column of xy
  y = msh_bc_xyz (1:np, (pre_p+2)) ; % extract y column of xy

  gxmax = max (x)      ; gxmin = min (x) ;
  gymax = max (y)      ; gymin = min (y) ;
  gxdiff = gxmax - gxmin ; gydiff = gymax - gymin ;
  if ( gydiff == 0.0 )
    gydiff = 0.5 ; % allow for 1-D mesh (with y == 0)
  end % if no y coordinates

%     FE Flux Values
  d_x(2) = 0. ; d_y(2)  = 0. ; % vector ends on paper
  g_dx = exact_node_flux(:,1)  ; % flux    
  g_dy = exact_node_flux(:,2)  ; % flux    
  g_sq = sqrt (g_dx.^2 + g_dy.^2) ;
  big  = max (g_sq)  ; % magnitude

  largest = 1.e-6;
%     Scale flux     vectors
  if ( big > largest ) largest = big;
  g_sq  = g_sq*length/largest ; % flux     scaled  %b

%     convert flux vector end to scaled paper positioin
  g_dx = x + length * g_dx /big ; % flux component end position 
  g_dy = y + length * g_dy /big ; % flux component end position

% Gauss points are always inside the mesh geometry, BUT
% the ends of the scaled flux vector often is not. Check those
% end points for plot scaling
  fxmax = max (g_dx)      ; fxmin = min (g_dx) ;
  fymax = max (g_dy)      ; fymin = min (g_dy) ;

%     Scale everything
  xmax = max([gxmax, fxmax]); xmin = min([gxmin, fxmin]);
  ymax = max([gymax, fymax]); ymin = min([gymin, fymin]);

  clf                               % clear graphics
  axis ([xmin, xmax, ymin, ymax])   % set axes
  axis ('equal')                    % true shape style
  hold on                           % hold image for plots
  grid                              % add grid dots
  xlabel ('X')                      % add label
  ylabel ('Y')                      % add label
  title  (['Exact 2-D Flux Vectors', ...
   ' at ', int2str(np),' Nodes (', int2str(nt),' Elements),', ...
   ' max = ', num2str(largest)])     % add title
  %title  (['Exact Nodal 2-D Flux Vectors, max = ', ...
              %num2str(largest)])     % add title

%      Select element type details
  [loop] = get_El_Loop (nod_per_el) ;

%      Plot input mesh points & label them
  if (lab_p == 1)                   % plot all points
    plot (x, y, 'b.')               % mark each node
  end % if show labels

%    Show 20 nodes and 10 elements
  inc_p = floor(np/20) ; inc_e = floor(nt/10) ;
  if (inc_p == 0 ) 
    inc_p = np - 1 ;
  end % if inc_p
  if (inc_e == 0 ) 
    inc_e = nt - 1 ;
  end % if inc_e
%    Show all if a small mesh
  if ( np <= 20 )
    inc_p = 1 ;
  end % if np
  if ( nt <= 10 )
    inc_e = 1 ;
  end % if nt

  if (inc_p > 0)                      % plot node numbers
    for i = 1:inc_p:np                % convert to string
      p_text = sprintf ('  %g', i);   % offset # from pt
      text (x(i), y(i), p_text)       % plot pt number
    end % for all points
  end % if show labels
  disp (' ')

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

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

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

%      Get the centroid
    x_bar (it) = sum (t_x' )/nod_per_el ;
    y_bar (it) = sum (t_y' )/nod_per_el ;

%      Plot this polygon
    c_x  = t_x (loop) ;       % x for nod_per_el line polygon
    c_y  = t_y (loop) ;       % y for nod_per_el line polygon
    plot (c_x, c_y, 'b-')     % plot nod_per_el lines, in blue
  end % for over all elements
%
%    Finish the plots with polygon numbers
  if (inc_e > 0)                     % plot elem number, inclined
    % plot (x_bar, y_bar, 'g.')        % centroid of each element
    for i = 1:inc_e:nt               % convert to string
      t_text = sprintf ('  %g', i);  % offset # from pt
      text (x_bar(i), y_bar(i), t_text, 'Rotation', 45) % incline
    end % for all polygons
  end % if show labels

%  ---------------- Now add the vectors to the mesh --------------

%      Plot flux     arrows at Gauss point
      for ig = 1:npg
%            FE values
        d_x(1) = x(ig)  ; d_y(1) = y(ig) ; % vector start point
        d_x(2) = g_dx(ig) ; % vector end position
        d_y(2) = g_dy(ig) ; % vector end position
        plot (d_x, d_y, 'k-')       % black line
        plot (d_x(2), d_y(2), 'r.') % red end point

      end % for Gauss pts

%       -depsc -tiff            % for an eps version
  %bprint -dpsc exact_node_flux_vectors
  hold off
%bfprintf ('Created file exact_node_flux_vectors.ps \n')
end