%
%   EIGENF2.M   Demo of Fourier Series Representation for f(x) = x(pi-x)
%
%   The goal here is to evaluate the infinite series expansion for 
%   f(x) = x(pi-x) in terms of sinusoids (i.e. a Fourier series expansion)
%
%   For normalized eigenfunctions, the coefficients and basis functions
%   are:
%      an = 4*sqrt(2/pi)/m^3     gn(x) = sqrt(2/pi)*sin(mx)  
%   with m = (2n-1)   and   n = 1, 2, ...
%
%   For unnormalized eigenfunctions, the coefficients and basis functions
%   are :
%      an = (8/pi)/m^3           gn(x) = sin(mx)          
%   with m = (2n-1)   and   n = 1, 2, ...
%
%   File prepared by J. R. White, UMass-Lowell (original Nov. 1997)
%     --> minor modifications (Aug. 1998)
%

%
%   getting started
      clear all, close all
%
%   set x domain
      Nx = 201;   x = linspace(0,pi,Nx);      c = 8/pi;
%
%   calc exact function 
      fe = x.*(pi-x);
%
%   calc Fourier Series approx
      fa = zeros(size(x));
      Max=100;   tol = 0.001;   mrerr = 1.0;   n = 0;
      while mrerr > tol   &    n < Max
        n = n+1;  m = 2*n-1;   
        ff = (c/m^3)*sin(m*x);   fa = fa + ff;
        rerr = ff(2:Nx-1)./fa(2:Nx-1);   mrerr = max(abs(rerr));
      end
%
%   plot curves
      plot(x,fe,'g-',x,fa,'r--'),grid
      r = axis;   r(2) = pi;   axis(r)
      title('Accuracy of Truncated Fourier Series for f(x) = x(pi-x)')
      ylabel('f(x)'), xlabel('x value')
      legend('Exact f(x)','Approx f(x)')
      gtext([num2str(n),' terms for convergence'])
%
%   end of demo
%