Modified Stiffness Evaluation Procedure for SSM computation

Contents

function [v_out] = StEP(F,vectors, m, nl_order)
        

StEP

This function performs an adjusted version of STEP for SSM computations.

[multis,multi_idcs,multi_multiplicities] = unique(m.','rows');
num_vecs = size(multis,1);

% order of nonlinear function
switch nl_order

    case 1

        v1 = vectors{1};
        v_out = 1/2 * ( F(v1) - F(-v1));

    case 2

        v1 = vectors{1};
        v2 = vectors{2};
        % Process for getting quadratic coefficients from nonlinearity

        % Evaluate complex input via real vector inputs to nonlinearity
        F2 = @(v) (1i*F(real(v)+imag(v)) +(1-1i)*F(real(v)) - (1+1i)*F(imag(v)));

        if num_vecs == 1
            % Same vector is input twice
            v_out = 1/2 * ( F2(v1) + F2(-v1));

        else
            % Two different vectors are input
            v_out = 1/4 * ( F2(v1+v2) + F2(-v1-v2) - F2(v1-v2) - F2(-v1+v2) );

        end
    case 3

        % Evaluate complex input via real vector inputs to nonlinearity
        F3 = @(v)  2*F(real(v)) + (-1+1i)/2*F(real(v)+imag(v)) - (1+1i)/2*F(real(v)-imag(v)) -2i*F(imag(v));

        H = @(v)  1/2 * (F3(v)-F3(-v)); % Cubic function

        if num_vecs == 1
            v1 = vectors{1};

            % All three input vectors are the same
            v_out = H(v1);

        elseif num_vecs == 2
            % Two of the input vectors are the same

            % check which vector is input twice
            if sum(1==multi_multiplicities ) == 2
                v1 = vectors{multi_idcs(1)};
                v2 = vectors{multi_idcs(2)};
            else
                v1 = vectors{multi_idcs(2)};
                v2 = vectors{multi_idcs(1)};
            end

            v_out = 1/2 * (H(v1+v2) - H(v1-v2)) - H(v2);



        else
            v1 = vectors{1};
            v2 = vectors{2};
            v3 = vectors{3};
            % All input vectors are the same
            v_out = H(v1+v2+v3) - H(v1+v2) - H(v1+v3) - H(v2+v3) + H(v1) + H(v2) + H(v3);

        end

end
        

Published with MATLAB® R2023a