Memoryless Weak Nonlinearity Composition
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(Difference between revisions)
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% zeta : memoryless weak power series z(x), first-order leading: [zeta_1, zeta_2 ... zeta_Nt] | % zeta : memoryless weak power series z(x), first-order leading: [zeta_1, zeta_2 ... zeta_Nt] | ||
% xi : memoryless weak power series y(z), first-order leading: [ xi_1, xi_2 ... xi_Nh] | % xi : memoryless weak power series y(z), first-order leading: [ xi_1, xi_2 ... xi_Nh] | ||
| - | % Mapping coefficients constituting nonlinearity composition zeta & xi are not commutative. | + | % Mapping coefficients, constituting nonlinearity composition, zeta & xi are not commutative. |
function y = composite2(zeta, xi, precision) | function y = composite2(zeta, xi, precision) | ||
if nargin < 3, precision = 34; end | if nargin < 3, precision = 34; end | ||
Current revision
% Compute composition y(z(x)) coefficients of x given mapping coefficients zeta & xi.
% zeta : memoryless weak power series z(x), first-order leading: [zeta_1, zeta_2 ... zeta_Nt]
% xi : memoryless weak power series y(z), first-order leading: [ xi_1, xi_2 ... xi_Nh]
% Mapping coefficients, constituting nonlinearity composition, zeta & xi are not commutative.
function y = composite2(zeta, xi, precision)
if nargin < 3, precision = 34; end
mp.Digits(precision); %Advanpix Multiprecision Toolbox
zeta = zeta(:)';
xi = xi(:)';
y = mp('0');
z_power = mp('1');
for power = 1:numel(xi)
z_power = conv(z_power, zeta);
term = [zeros(1,power-1,'mp'), xi(power)*z_power];
y = term + [y, zeros(1,numel(term)-numel(y),'mp')];
end
end