EVALUATE_FNL

function Fnl = evaluate_Fnl(obj,z)

This function evaluates the nonlinearity at input state z in a dynamical system object in the first-order form using either the tensor based

$\mathbf{F(z)} = \sum_{i>2} \mathbf{F}_i \mathbf{z}^{\otimes i}$

or the multi-index based notation

$\mathbf{F(z)} = \sum_{\mathbf{m} \in \bf{N}^N} \mathbf{F}_\mathbf{m} \mathbf{z}^{\mathbf{m}}$

switch obj.order
    case 1
        Fnl = zeros(obj.N,1);
        degree = length(obj.F);
        switch obj.Options.notation
            case 'tensor'
                for j = 2:degree
                    % expand_tensor does not support vectorization
                    % Fnl = Fnl + expand_tensor(obj.F{j},z);
                    Fj  = tensor_to_multi_index(obj.F{j});
                    Fnl = Fnl + expand_multiindex(Fj,z);
                end
            case 'multiindex'
                for j = 2:degree
                    Fnl = Fnl + expand_multiindex(obj.F(j),z);
                end
        end

    case 2
        [x, xd] = deal(z(1:obj.n,:),z(obj.n+1:obj.N,:));
        nt = size(x,2);
        fnl = obj.compute_fnl(x,xd);
        Fnl = [-fnl;
                sparse(obj.n,nt)];
end