function  exact_and_fe_node_flux_vec (mesh, length)
% NOTE Fourier sign changes below
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  plot 2-D exact and SCP average flux vectors at the nodes
%  ------------------------------------------------------
% mesh   = 1, show mesh lines, =0 omit
% length = maximum length of arrows, in scaled x,y units

% 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;
% 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 )
    mesh   = 1   ;   % show mesh
    length = 0.3 ;   % the max length on paper
  elseif ( nargin == 1 )
     length = 0.3
  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 exact node flux components
  load exact_node_flux.tmp ; % du/dx, du/dy at nodes

%       Set control data: number of nodes
  npg = size(exact_node_flux,1) ; % pts w vectors
  if ( npg == 0 )
    error ('Error: missing file exact_node_flux.tmp')
  end % if error
  fprintf ('Read %g nodal exact 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

%       Read new SCP node flux components
  load scp_node_ave_fluxes.tmp ; % du/dx, du/dy at nodes

%       Set control data: number of nodes
  npgs = size(scp_node_ave_fluxes,1) ; % pts w vectors
  if ( npgs == 0 )
    error ('Error: missing file scp_node_ave_fluxes.tmp')
  end % if error
  fprintf ('Read %g nodal SCP flux sets \n', npgs)
  nfs = size(scp_node_ave_fluxes,2) ;  % flux components
  if ( nfs ~= 2 ) % vectors not meaningful
    fprintf ('Read %g flux components instead of 2 \n', nfs)
    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

  e_dx(npg)  = 0.       ;       % pre-allocate flux     array
  e_dy(npg)  = 0.       ;       % pre-allocate flux     array
  e_sq(npg)  = 0.       ;       % pre-allocate magnitude array


  s_dx(npg)  = 0.       ;       % pre-allocate flux     array
  s_dy(npg)  = 0.       ;       % pre-allocate flux     array
  s_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

%     Exact Flux Values
% Fourier sign change
  d_x(2) = 0. ; d_y(2)  = 0. ; % vector ends on paper
  e_dx = -exact_node_flux(:,1)  ; % flux    
  e_dy = -exact_node_flux(:,2)  ; % flux    
  e_sq = sqrt (e_dx.^2 + e_dy.^2) ;
  big_e  = max (e_sq)  ; % magnitude

  largest = 1.e-6; % avoid division by zero
  if ( big_e > largest ) 
    largest = big_e;
  end % if

%     SCP Flux Values
% Fouried sign change
  s_dx = -scp_node_ave_fluxes(:,1)  ; % flux    
  s_dy = -scp_node_ave_fluxes(:,2)  ; % flux    
  s_sq = sqrt (s_dx.^2 + s_dy.^2) ;
  big_s  = max (s_sq)  ; % magnitude

  if ( big_s > largest ) 
    largest = big_s;
  end % if

%     Scale exact flux vectors
  e_sq  = e_sq*length/largest ; % flux     scaled  %b
%     Scale SCP flux vectors
  s_sq  = s_sq*length/largest ; % flux     scaled  %b

%     convert flux vector end to scaled paper positioin
  s_dx = x + length * s_dx /largest ; % flux component end position 
  s_dy = y + length * s_dy /largest ; % flux component end position
  e_dx = x + length * e_dx /largest ; % flux component end position 
  e_dy = y + length * e_dy /largest ; % flux component end position

% Node points are always on the mesh geometry, BUT
% the ends of the scaled flux vector often is not. Check those
% end points for plot scaling
  fxmax = max (e_dx)      ; fxmin = min (e_dx) ;
  fymax = max (e_dy)      ; fymin = min (e_dy) ;
  sxmax = max (s_dx)      ; sxmin = min (s_dx) ;
  symax = max (s_dy)      ; symin = min (s_dy) ;

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

  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: ', int2str(nt),' Elements'])
  ylabel (['Y: ', int2str(np),' Nodes (', ...
          int2str(nod_per_el), ' per Element) '])
  title (['Nodal 2-D Fluxes; Exact (solid, max = ', ...
          num2str(big_e), ') & FEA SCP (dash, max = ', ...
          num2str(big_s), ')' ])

%      Select element type details
  [loop] = get_El_Loop (nod_per_el) ;
%
%      Plot input mesh points & label them
  if (mesh == 0)                   % plot all points
    plot (x, y, 'g+')               % 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
inc_p=0 ;
inc_e=0 ;
  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 (' ')

  if ( mesh == 1)
%    Loop over all elements, plot mesh
    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
%      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
  end % if plot mesh
 
%    Finish the plots with polygon numbers
  if (inc_e > 0)                     % plot elem number, inclined
    for it = 1:inc_e:nt               % convert to string
%      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  = sum (t_x' )/nod_per_el ;
      y_bar  = sum (t_y' )/nod_per_el ;
      t_text = sprintf ('  %g', it);  % offset # from pt
      text (x_bar, y_bar, t_text, 'Rotation', 45) % incline
      plot (x_bar, y_bar, 'g.')        % centroid of each element
    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
%             exact vector
        d_x(2) = e_dx(ig) ; % vector end position
        d_y(2) = e_dy(ig) ; % vector end position
        plot (d_x, d_y, 'r-')       % red line
        plot (d_x(2), d_y(2), 'r.') % red end point
%            SCP average vector
        d_x(2) = s_dx(ig) ; % vector end position
        d_y(2) = s_dy(ig) ; % vector end position
        plot (d_x, d_y, 'k--')       % black dash line
        plot (d_x(2), d_y(2), 'k.') % black end point
      end % for Gauss pts

%       -depsc -tiff            % for an eps version
  %b print -dpsc exact_and_scp_2d_vectors
  hold off
%b fprintf ('Created file exact_and_scp_2d_vectors.ps \n')
% end