Nonautonomous conjugate relations

Contents

function [redConj,mapConj] = nonAut_conj_red(kappa_set,F_kappa)
        

NONAUT_CONJ_RED

This function detects complex conjugate relations between forcing. For instance, when kappa_set = [1,-1,2,3,-3] and F_kappa = [1;1;2;3;4], it will return redConj = [1,3,4,5] with mapConj = {[1 2],3,4,5}

[redConj,mapConj] = NONAUT_CONJ_RED(kappa_set,F_kappa)

See also: NONAUT_1STORDER_LEADTERMS, NONAUT_2NDORDER_LEADTERMS

redConj = [];
mapConj = [];
assert(numel(kappa_set)==numel(unique(kappa_set)),'there exist redundancy in kappa of external forcing');
kappa = kappa_set;
while ~isempty(kappa)
    ka = kappa(1);
    ka_redConj = find(kappa_set==ka);
    redConj = [redConj;ka_redConj];
    % find the conjugate one if it exists
    ka_conj = find(kappa_set==-ka);
    if ~isempty(ka_conj) && norm(conj(F_kappa(:,ka_redConj))-F_kappa(:,ka_conj))<1e-6*norm(F_kappa(:,ka_conj))
        mapConj = [mapConj, {[ka_redConj,ka_conj]}];
        kappa = setdiff(kappa,[ka,-ka],'stable');
    else
        mapConj = [mapConj, {ka_redConj}];
        kappa = setdiff(kappa,ka,'stable');
    end
end
        

end
        

Published with MATLAB® R2023a