function [x,fail] = cobweb(g,x,eps,N,xmin,xmax,ymin,ymax)
%
%  On entry :
%    g         function defining the x = g(x);
%    x         start point for the fixed-point iteration;
%    eps       accuracy requirement: stops when two consecutive
%              approximations in the sequence are
%    N         maximal number of allowed iterations;
%    xmin      minimal value for x to view the graph;
%    xmax      maximal value for x to view the graph;
%    ymin      minimal value for g(x) to view the graph;
%    ymax      maximal value for g(x) to view the graph.
%
%  On return :
%    x         last approximation in the sequence;
%    fail      0 means success, 1 means failure.
%
%  Example : 
%    >> cobweb('myfun',0.3,1.0e-6,10,0.1,10,0,10)
%
fprintf('illustration of fixed-point iteration...\n');
xr = xmin:0.1:xmax;           % sample range to plot
yr = feval(g,xr);             % evaluate at the samples
figure;                       % new figure window
axis([xmin xmax ymin ymax]);  % adjust the scale
hold on;                      % overlay plot
plot(xr,yr);                  % plot the function y = g(x)
plot(xr,xr);                  % plot the diagonal y = x
for i = 1:N                   % perform N iterations                
  y = feval(g,x);             % y = g(x)
  plot([x x],[x y],'g--');    % vertical line
  plot([x y],[y y],'r--');    % horizontal line
  fprintf('  x = %e, y = %e, |x-y| = %e\n', x, y, abs(x-y));
  if (abs(x-y) < eps)
     fprintf('succeeded after %d steps\n', i);
     x = y;
     fail = 0;
     return;                  % terminate with success
  end;
  x = y;                    
end;
fail = 1;                     % terminate with failure