%{
Function gives the Maier-Saupe energy for auxiliary variables eta, mu, nu
for a one-dimensional interface
%}
function E = getE1D(x,eta,mu,nu,a,kappa2)
    dx = x(2) - x(1);
    M = length(eta);
    deta = zeros(1,M);
    dmu = zeros(1,M);
    dnu = zeros(1,M);
    for i=2:M-1
        deta(i) = (1/dx)*(eta(i+1)-eta(i-1));
        dmu(i) = (1/dx)*(mu(i+1)-mu(i-1));
        dnu(i) = (1/dx)*(nu(i+1)-nu(i-1));
    end
    f = -2*a*((1/3)*eta.^2 + mu.^2 + nu.^2) + 2*((1/3)*deta.^2 + dmu.^2 + dnu.^2) + kappa2*((4/9)*deta.^2 + dnu.^2);
    E = trapz(x,f);
end