Is this a correct way to use fsolve?

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Salvatore Bianco
Salvatore Bianco 2024-7-15
编辑： Torsten 2024-7-15
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

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Torsten
Torsten 2024-7-15
编辑：Torsten 2024-7-15
Solve in w^2 instead of w - then there shouldn't be imaginary parts in the solution:
F = @(w) ((1-p)/C)*(kappa^q - (w^2)^q)+y+z-z*(w^2/kappa)^(alpha-1);
instead of
F = @(w) ((1-p)/C)*(kappa^q - w^q)+y+z-z*(w/kappa)^(alpha-1);
Don't forget to take the square of g before exiting the function:
...
g = fsolve(fun, w0, options);
g = g^2;
end
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Salvatore Bianco
Salvatore Bianco 2024-7-15
Sorry, I just edited it. I did not use g^2 since I am now solving for q^2. So when I do find it, I take the square root so I have g?
Salvatore Bianco
Salvatore Bianco 2024-7-15
Sorry, I think the summer heat is hitting my brain, now I got it.

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