creating for loop in fzero

Dear all, I want to plot "z" vs. "kappa" where kappa is changing from 1 to 0. this is my @ff function:

function y = f(x)

y = (1/pi)*((0.1*x)-(((sqrt((1+x)./2)).*exp(1).^-(6*(sqrt(2*0.1*(1+x))))))*(kappa*(sqrt((1-x)/(1+x)))-(sqrt((1+x)/(1-x)))));

after that using fzero I want to find "z" for every single kappa in the region in order to get the plotted data:

fun = @ff; % function

x0 = 0; % initial interval

z = fzero(fun,x0);

now how can I create a loop to change kappa from 1 to 0 and get "z" for each of them on my plot. many Thanks in Advance,

Answer 1

[Star Strider]

Try this:

f = @(x,kappa) (1/pi)*((0.1*x)-(((sqrt((1+x)./2)).*exp(-(6*(sqrt(2*0.1*(1+x))))))).*(kappa*(sqrt((1-x)./(1+x)))-(sqrt((1+x)./(1-x)))));

N = 10;                                             % Length Of ‘kappa’ Vector
kappa = linspace(0, 1, N);

for k1 = 1:N
    z(k1) = fzero(@(x) f(x, kappa(k1)), 1E-3);
end

figure(1)
plot(kappa, z)
xlabel('\kappa')
ylabel('z(\kappa)')
grid

[fartash2020]

Hi again,

Now for this same equation. my Kappa is constant Kappa=0.1 I add "Delta_E" and "Lambda" to the equation and I want them to change( which I have written below). This time I want to draw a mesh plot for (Z, lambda, Delta_E). I would highly appreciate if you help me correct it:

kd = 6 ;

kappa = 0.1 ;

f = @(x,lambda) ((Delta_E)+(lambda*x)-(((sqrt((1+x)./2)).*exp(1).^(-(kd*(sqrt(2*lambda*(1+x))))))).*(kappa*(sqrt((1-x)./(1+x)))-(sqrt((1+x)./(1-x)))));

N = 100;

lambda = linspace(0.05,0.25, N);

Delta_E= linspace(0.1,0.35, N);

for k1 = 1:N

    z(k1) = fzero(@(x) f(x, lambda(k1)), 1E-3);

end

figure(1)

mesh(lambda,Delta_E, z)

xlabel('\lambda')

ylabel('\delta E')

zlabel('Z')

grid

[Star Strider]

I am not certain what you are doing. If you want to find the zeros of a bivariate function, I would use the contour function. See the documentation on contour for details.

However yours is trivariate in ‘lambda’, ‘Delta_E’ and ‘x’, so that might not work. You could do a nested loop through ‘lambda’ and ‘Delta_E’ using fzero. That might be the only way to approach this.

[fartash2020]

Thanks Star Strider, but how can I create a nested loop?

[Star Strider]

Try this:

N = 100;
kd = 6;
kappa = 0.1;
lambda = linspace(0.05,0.25, N);
Delta_E = linspace(0.1,0.35, N);
[Lm,DE] = meshgrid(lambda, Delta_E);

f = @(x,lambda,Delta_E) ((Delta_E)+(lambda*x)-(((sqrt((1+x)./2)).*exp(-(kd*(sqrt(2*lambda*(1+x))))))).*(kappa*(sqrt((1-x)./(1+x)))-(sqrt((1+x)./(1-x)))));

for k1 = 1:length(lambda)
    for k2 = 1:length(Delta_E)
        z(k1,k2) = fzero(@(x) f(x,lambda(k1),Delta_E(k2)), rand);
    end
end

figure(1)
mesh(lambda, Delta_E, z)

You might find it worthwhile to plot the absolute value of ‘z’, because the results are complex when they are not NaN, although the plot itself reveals little.