function  true_flux_scp_qp_zoom (i_p, Exact)
% ZOOM version of true_flux_scp_qp_graph for text figure
% Copyright 2000 J.E. Akin. All rights reserved.
% under construction: requires analytic exact solution
% variable "ar" (analytic result) for "Exact" case number
%  ------------------------------------------------------
%  Matlab graph of i_p-th flux component value at mesh nodes
%   If i_p = 0, show RMS value
%  ------------------------------------------------------

% 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

  % fprintf ('Begin component value graph: \n')
  if ( nargin == 0 )
    i_p = 0 ; Exact = 0 ;
  end % if no arguments
  if ( nargin == 1 )
    Exact = 0 ;
  end % if 1 argument
  % fprintf ('Begin graph for exact case %g \n', Exact)

%    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)
  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)

%       Read new Gauss locations & flux component
  load el_qp_xyz_fluxes.tmp ; % x, du/dx

%       Set control data: number of gauss points
  npg = size(el_qp_xyz_fluxes,1) ; % quadrature pts w vectors
  if ( npg == 0 )
    error ('Error: missing file el_qp_xyz_fluxes.tmp')
  end % if error

% Gauss points are always inside the mesh geometry
  g_x  = el_qp_xyz_fluxes(:,1)  ; % position
  g_dx = el_qp_xyz_fluxes(:,2)  ; % flux

  load scp_node_ave_fluxes.tmp
  nr = size (scp_node_ave_fluxes, 1);
  if ( nr == 0 )
    error ('Error missing file scp_node_ave_fluxes.tmp')
  end % if error
  max_p = size (scp_node_ave_fluxes, 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 ) 
    error ('i_p > available data')
  end % if error

  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
  c_x (nod_per_el) = 0 ;        % Optional pre-allocation
  c_y (nod_per_el) = 0 ;        % Optional pre-allocation
  g_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) ;

%  add analytic points
   a_inc = (xmax-xmin)/(10*nt) ;
   ax = [xmin:a_inc:xmax] ;    % analytic points

  if ( i_p >= 1 )
    y = scp_node_ave_fluxes(:, i_p) ;
    if ( Exact == 9 ) % u" + U + x = 0, EBC, EBC
      ar = cos(ax)/sin(1) - 1.0;  % analytic result
    elseif ( Exact == 10 ) % u" + U + x = 0, EBC, NBC
      ar = cos(ax)/cos(1) - 1. ; % analytic result
    elseif ( Exact == 11 ) % u" + X^N = 0,  U(0)=0=U(1),
      N = input ('Enter source exponent N in Q = x^N ')
      ar = (1.-(N+2)*ax.^(N+1))/((N+1)*(N+2)) ; % analytic result
    else
      fprintf ('Unknown exact_case %g \n', Exact)
      error ('No solution given for Exact_Case number')
    end % if Exact
    % ar = (1. - (N+2)*ax.^(N+1))/((N+1)*(N+2)) ;% analytic result
    % ar = cos(ax)/sin(1) - 1.0;  % analytic result
    % ar = cos(ax)/cos(1) - 1.0;  % analytic result
  else % i_p = 0, get root mean sq
    for k = 1:np
      y (k) = sqrt ( sum (scp_node_ave_fluxes (k, 1:max_p).^2)) ;
    end % for k
    g_dx = abs(g_dx) ; % Gauss values
    if ( Exact == 9 ) % u" + U + x = 0, EBC, EBC
      ar = abs(cos(ax)/sin(1) - 1.0);  % analytic result
    elseif ( Exact == 10 ) % u" + U + x = 0, EBC, NBC
      ar = abs(cos(ax)/cos(1) - 1.) ; % analytic result
    elseif ( Exact == 11 ) % u" + X^N = 0,  U(0)=0=U(1),
      N = input ('Enter source exponentt N in Q = x^N ')
      ar = abs(1.-(N+2)*ax.^(N+1))/((N+1)*(N+2)) ; % analytic result
    else
      error ('No solution given for Exact_Case number')
    end % if Exact
    % ar = abs( (1. - (N+2)*ax.^(N+1))/((N+1)*(N+2)) );% analytic result
    % ar = abs( cos(ax)/sin(1) - 1.0) ;  % analytic result
    % ar = abs( cos(ax)/cos(1) - 1.0) ;  % analytic result
  end % if get RMS value

   maxa = max (ar)      ; mina = min (ar) ;

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

%    Initialize plots
   maxy = max (y)      ; miny = min (y) ;

% finalize axes
   ymax = max ([maxy, maxa])      ; ymin = min ([miny, mina]) ;
   if ( ymax == ymin )
     if ( abs (ymax) > 0 )
       ymax = ymax + abs (ymax)/20. ;
       ymin = ymin - abs (ymin)/20. ;
     end % if
   end % if
   clf                               % clear graphics
%b ymax= 0.25
%b ymin = -0.35
xmin = .15
xmax = .45
ymin = 0.03
ymax = 0.19
   axis ([xmin, xmax, ymin, ymax])   % set axes

   hold on                           % hold image for plots
   xlabel (['X, Near Element 2 (of ', ...
           int2str(nt),' Elements, ', int2str(np),' Nodes)'])
 % xlabel ('X, Node number at 45 deg, Element number at 90 deg')
   if ( i_p >= 1 )
     title(['Exact (dash), FEA SCP (solid), Gauss Point ', ...
            '(dash dot) Flux. Estimated Error (vertical)'])
   % title(['Exact (dash), FEA SCP (solid) & GPFlux Component\_', ...
   %        int2str(i_p),':   ', ...
   %        int2str(nt),' Elements, ', int2str(np),' Nodes'])
     ylabel (['Component ', int2str(i_p), ' (SCP max = ', ...
     num2str(V_X), ', min = ', num2str(V_N), ')'])
   else % i_p = 0, get root mean sq
     title(['RMS\_value of EXACT, SCP, GP Flux Component\_',int2str(i_p),':   ',...
       int2str(nt), ' Elements, ', int2str(np),' Nodes'])
     ylabel (['Flux Component\_', int2str(i_p), ...
     ' RMS Value (SCP max = ', num2str(V_X), ', min = ', num2str(V_N), ')'])
   end % if get RMS value

%      add analytic plot and Gauss plot
     plot (ax, ar, 'r--')
     plot (g_x, g_dx, 'ko')
%     for L2 element add constant flux line

%    Loop over all elements
  p_div = 20 ;
  p_er(1:2) = 0. ; p_x (1:2) = 0. ;
  x_c(p_div) = 0 ; cap(p_div) = 0 ;
  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
      t_y  = y (t_nodes) ;         % y at those nodes, only

%      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)
      plot (t_x, t_y)           % plot nod_per_el lines
      if ( nod_per_el == 2 ) % add qp constant line
        g_y (1) = g_dx (2*it) ;
        g_y (2) = g_dx (2*it) ;
        plot (t_x, g_y,'k-.')           % plot nod_per_el lines
      end % if horz line

% add vertical error lines
    p1 = min(t_x); p2 = max(t_x); p_dif=(p2 - p1);
    p_inc=p_dif/p_div ;
    j = 0;
    p_er(1) = g_dx (2*it) ; % constant qp
    for p = p1:p_inc:p2 % loop over points inside element
      p_x(1:2) = p ;
%-------------
      if ( i_p >= 1 )
        y = scp_node_ave_fluxes(:, i_p) ;
        if ( Exact == 9 ) % u" + U + x = 0, EBC, EBC
          p_ar = cos(p)/sin(1) - 1.0;  % analytic result
        elseif ( Exact == 10 ) % u" + U + x = 0, EBC, NBC
          p_ar = cos(p)/cos(1) - 1. ; % analytic result
        elseif ( Exact == 11 ) % u" + X^N = 0,  U(0)=0=U(1),
          N = input ('Enter source exponent N in Q = x^N ')
          p_ar = (1.-(N+2)*p^(N+1))/((N+1)*(N+2)) ; % analytic result
        else
          error ('No solution given for Exact_Case number')
        end % if Exact
      else % i_p = 0, get root mean sq
        for k = 1:np
          y (k) = sqrt ( sum (scp_node_ave_fluxes (k, 1:mp_p).^2)) ;
        end % for k
        if ( Exact == 9 ) % u" + U + x = 0, EBC, EBC
          p_ar = abs(cos(p)/sin(1) - 1.0);  % analytic result
        elseif ( Exact == 10 ) % u" + U + x = 0, EBC, NBC
          p_ar = abs(cos(p)/cos(1) - 1.) ; % analytic result
        elseif ( Exact == 11 ) % u" + X^N = 0,  U(0)=0=U(1),
          N = input ('Enter source exponentt N in Q = x^N ')
          p_ar = abs(1.-(N+2)*p^(N+1))/((N+1)*(N+2)) ; % analytic result
        else
          error ('No solution given for Exact_Case number')
        end % if Exact value
      end % if i_p = 0
%-------------
      %b p_ar = (1. - (N+2)*p^(N+1))/((N+1)*(N+2)) ;%
      %b p_ar = cos(p)/sin(1) - 1.0 ;  % analytic result
%      linear element interpolation
      h1 = (t_x(2) - p)/p_dif;
      p_el = h1*t_y(1) + (1. - h1)*t_y(2) ;
      %b er_el = (p_el - p_ar) ;
      p_er(2) = p_el ;
      % p_er(2) = p_ar ; %b er_el ;
      plot (p_x, p_er)          % plot vertical lines
      j = j + 1;
      %b x_c(j) = p ;
      %b cap(j) = er_el ;
    end % for pt in elem
    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', ['zoom_true_qp_flux_', int2str(i_p), '_1d'])
  hold off
y

  %b fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of true_flux_scp_qp_zoom