Since fsolve keeps giving me answers with a very small but non-zero imaginary part, which i really don’t want, I though about giving the derivative of my function. Is this a correct way to do it? Also, is there a way to tell the function not to go outside the reale line?

%g is a function that is defined by an equation. I know that is invertible
%and takes values between 0 and kappa.

function g = g(y, z, p, kappa, beta, mu, muz, sigma, sigmaz)

K = (mu^2/sigma^2)*0.5;
M = (sigmaz*mu)/sigma;
q = 1/(p-1);
alpha = (sqrt((beta-M-K)^2+4*K*(beta-muz))-beta+M+K)/(2*K);
C = beta-K*p/(1-p);
%function whose zero i need to find (with respect to w)
F = @(w) ((1-p)/C)*(kappa^q – w^q)+y+z-z*(w/kappa)^(alpha-1);
%its derivative with respect to w
J = @(w) ((1-p)/C)*(-q*(w^(q-1))) -z*((alpha-1)*w^(alpha-2))/(kappa^(alpha-1));
options = optimoptions(‘fsolve’, ‘SpecifyObjectiveGradient’, true);
fun = {F, J};
w0 = kappa/2;
g = fsolve(fun, w0, options);
endSince fsolve keeps giving me answers with a very small but non-zero imaginary part, which i really don’t want, I though about giving the derivative of my function. Is this a correct way to do it? Also, is there a way to tell the function not to go outside the reale line?

%g is a function that is defined by an equation. I know that is invertible
%and takes values between 0 and kappa.

function g = g(y, z, p, kappa, beta, mu, muz, sigma, sigmaz)

K = (mu^2/sigma^2)*0.5;
M = (sigmaz*mu)/sigma;
q = 1/(p-1);
alpha = (sqrt((beta-M-K)^2+4*K*(beta-muz))-beta+M+K)/(2*K);
C = beta-K*p/(1-p);
%function whose zero i need to find (with respect to w)
F = @(w) ((1-p)/C)*(kappa^q – w^q)+y+z-z*(w/kappa)^(alpha-1);
%its derivative with respect to w
J = @(w) ((1-p)/C)*(-q*(w^(q-1))) -z*((alpha-1)*w^(alpha-2))/(kappa^(alpha-1));
options = optimoptions(‘fsolve’, ‘SpecifyObjectiveGradient’, true);
fun = {F, J};
w0 = kappa/2;
g = fsolve(fun, w0, options);
end Since fsolve keeps giving me answers with a very small but non-zero imaginary part, which i really don’t want, I though about giving the derivative of my function. Is this a correct way to do it? Also, is there a way to tell the function not to go outside the reale line?

%g is a function that is defined by an equation. I know that is invertible
%and takes values between 0 and kappa.

function g = g(y, z, p, kappa, beta, mu, muz, sigma, sigmaz)

K = (mu^2/sigma^2)*0.5;
M = (sigmaz*mu)/sigma;
q = 1/(p-1);
alpha = (sqrt((beta-M-K)^2+4*K*(beta-muz))-beta+M+K)/(2*K);
C = beta-K*p/(1-p);
%function whose zero i need to find (with respect to w)
F = @(w) ((1-p)/C)*(kappa^q – w^q)+y+z-z*(w/kappa)^(alpha-1);
%its derivative with respect to w
J = @(w) ((1-p)/C)*(-q*(w^(q-1))) -z*((alpha-1)*w^(alpha-2))/(kappa^(alpha-1));
options = optimoptions(‘fsolve’, ‘SpecifyObjectiveGradient’, true);
fun = {F, J};
w0 = kappa/2;
g = fsolve(fun, w0, options);
end fsolve, complex values, jacobian MATLAB Answers — New Questions

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