% CHEB  compute D = differentiation matrix, x = Chebyshev grid
%
% Adapted from the code in chap. 6 of Trefethen, Spectral Methods in MATLAB,
% SIAM, 2000.  The grid runs from x=1 to x=-1.  cheb(N) corresponds to
% diffmat(N+1) in Chebfun apart from sign changes since the Chebfun
% grid runs from x=-1 to x=1.

  function [D,x] = cheb(N)
  if N==0, D=0; x=1; return, end
  x = cos(pi*(0:N)/N)'; 
  c = [2; ones(N-1,1); 2].*(-1).^(0:N)';
  D  = (c./c')./(x-x'+eye(N+1));    % off-diagonal entries
  D  = D - diag(sum(D,2));          % diagonal entries