function  quiver_exact_node_flux (scale, inc_v) % default (1.0, 1)
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  plot of 2-D FE ave flux vectors at mesh node pts, omit mesh
%  ------------------------------------------------------

% 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
% inc_v  = increment in vector plot, default = 1
% msh_typ_nodes   = connectivity list for elements, nt x nod_per_el
% 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)
% scale  = standard Matlab scale argument, default 1.0
% 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
  if ( nargin == 0 )
    scale = 1.  ;   % the default scale
    inc_v = 1   ;
  elseif ( nargin == 1 )
    inc_v = 1   ;
  end % if
  fprintf ('Using a scale of %g and vector increment of %g \n', ...
            scale, inc_v)

%    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

% 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_x  = x (1:inc_v:np)            ; % position
  g_y  = y (1:inc_v:np)            ; % position
  g_dx = exact_node_flux(:,1)  ; % flux    
  g_dy = exact_node_flux(:,2)  ; % flux    
  g_sq = sqrt (g_dx.^2 + g_dy.^2) ;
  [big, N_big]  = max (g_sq)  ; % magnitude

  g_dx = - g_dx ; g_dy = -g_dy ; % Fourier law sign change
  fprintf ('Using Fourier law sign change \n')

% largest = 0.0  ;
%     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]);
%  xmax = gxmax ; xmin = gxmin ;
%  ymax = gymax ; ymin = gymin ;

% xmax = gxmax + gxdiff/10 ; ymax = gymax + gydiff/10 ; % keep
% xmin = gxmin - gxdiff/10 ; ymin = gymin - gydiff/10 ; % keep
  xmax = gxmax + gxdiff/20 ; ymax = gymax + gydiff/20 ;
  xmin = gxmin - gxdiff/20 ; ymin = gymin - gydiff/20 ;

  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 Coordinate at ', int2str(np),' Nodes (', ...
          int2str(nod_per_el),' per Element)'])
  ylabel (['Y Coordinate on ', int2str(nt),' Elements'])
  title (['Exact Nodal 2-D Flux Vectors, max = ', ...
          num2str(big), ' (at ', int2str(N_big),')'])

%%      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/10) ; inc_e = floor(nt/5) ;
  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
  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

%  ---------------- Now add the vectors to the mesh --------------
  quiver (g_x, g_y, g_dx, g_dy, scale)

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