y=phys2cheb(f);

function y=phys2cheb(f);

% Written by Mike Watson, November 29
% takes a real vector from physical space f defined on a grid [-1,1] and 
% outputs it's normalized Chebyshev spectral coefficients y

N=length(f)-1;
f_even=[f;flipud(f(2:N))];  % create an even extension of f;

F=real(fft(f_even));  %perform a discrete cosine transform (DCT);

if N > 1
   y=(1/N).*F(1:N+1);
   y(1)=y(1)/2;
   y(N+1)=y(N+1)/2;
else
    y=f;
end