function u = my_hc2r(ubar)
%
% FFTWs HC2R transform: my_hc2r(my_r2hc(u)) = 2*N*u (2*N complex vector) 
%
N = length(ubar);       % we assume N is even
uhat = [ubar(1)+1i*0; ...
        ubar(2:N/2)+1i*ubar(N:-1:N/2+1+1); ...
        ubar(N/2+1)+1i*0];

    % find inverse fft and account for normalization constant (sans in FFTW)
u = N*ifft([uhat; flipud(conj(uhat(2:N/2)))],'symmetric');

         
        