Using fsolve to solve a set of equations with different constants every time

Hi guys, so I have used fsolve to sucessful solve the following four simultaneous non linear equations:

F(1)=x(1)*(i*(w1-d1)+k1)-g*x(3)*x(2)-sqrt(2*k1in)*alpha1in;

F(2)=x(2)*(-i*(w1-d1)+k1)-conj(g)*x(4)*x(1)-sqrt(2*k1in)*conj(alpha1in);

F(3)=x(3)*(i*(w3-d3)+k3)+(g/2)*x(1)^2-sqrt(2*k3in)*alpha3in

F(4)=x(4)*(i*(w3-d3)+k3)+(g/2)*x(2)^2-sqrt(2*k3in)*alpha3in

This is solving for x(i) in the way I want it to. The next step that I cannot seem to make work is that I want to find x(i) for multiple different w1 values. and record each x(i). I know how to record the x(i) for each different w1 if I can get there. I just don't know how to change w1 without changing it manually and recording the x(i). I want to do this for about 1000 w1 values so manually changing is not a great option. Any help would be greatly appreciated!

[Torsten]

Call fsolve 1000 times in a loop for your 1000 w1 values.

Answer 1

[Stephan]

Hi,

make a loop to vary w1 and pass it to fsolve by using one of the options in passing extra parameters.

An (incomplete) example would perhaps lok like this:

function x_all = main()
%Some code
d1 = 1;
k1 = 2;
g = 9.81;
w3 = 5;
k1in= 5;
alpha1in=10;
alpha3in=10;

x0 = zeros(1,4);

% Values for w1
w1_pool = 1:0.1:10;

% Preallocate result matrix
x_all = zeros(numel(w1_pool,numel(x0)));

% switch dispay off
options = optimoptions('fsolve','Display','off');

% Call fsolve in a loop
for k = 1 : numel(w1_pool)
    w1 = w1_pool(k);
    x_all(k,:) = fsolve(obj_fun,x0,options);
end

function F =  obj_fun(x)
F(1)=x(1)*(1i*(w1-d1)+k1)-g*x(3)*x(2)-sqrt(2*k1in)*alpha1in;
F(2)=x(2)*(-1i*(w1-d1)+k1)-conj(g)*x(4)*x(1)-sqrt(2*k1in)*conj(alpha1in);
F(3)=x(3)*(1i*(w3-d3)+k3)+(g/2)*x(1)^2-sqrt(2*k3in)*alpha3in;
F(4)=x(4)*(1i*(w3-d3)+k3)+(g/2)*x(2)^2-sqrt(2*k3in)*alpha3in;
end
end

Save this function as .m-file named the function Name(main.m in this example). Obtain the result by calling the function like this

result = main

Best regards

Stephan

[Lorcan Conlon]

Sorry Stephan, I am being told that F(1) does not have enough input arguments when I use this code. Have you any ideas what would cause this? Cheers, Lorcan

[Stephan]

could you provide your code?

[Torsten]

x_all(k,:) = fsolve( *@* obj_fun,x0,options);

d3, k3, k3in are undefined

x_all = zeros(numel(w1_pool),numel(x0));

[Stephan]

Thanks@Torsten!

- in addition to Torstens correction, i saw that i made a mistake - use:

x_all = zeros(numel(w1_pool),numel(x0));

instead of

x_all = zeros(numel(w1_pool,numel(x0)));

Also i did not define all the values for example k3, k3in, maybe you missed that part also...

So the corrected version of the code is:

function x_all = main()
%Some code
d1 = 1;
d3 = 1;
k1 = 2;
k3 = 3;
g = 9.81;
w3 = 5;
k1in= 5;
k3in= 4;
alpha1in=10;
alpha3in=10;

x0 = zeros(1,4);

% Values for w1
w1_pool = 1:1:10;

% Preallocate result matrix
x_all = zeros(numel(w1_pool),numel(x0))

% switch dispay off
options = optimoptions('fsolve','Display','off');

% Call fsolve in a loop
for k = 1 : numel(w1_pool)
    w1 = w1_pool(k);
    x_all(k,:) = fsolve(@obj_fun,x0,options);
end

function F =  obj_fun(x)
F(1)=x(1)*(1i*(w1-d1)+k1)-g*x(3)*x(2)-sqrt(2*k1in)*alpha1in;
F(2)=x(2)*(-1i*(w1-d1)+k1)-conj(g)*x(4)*x(1)-sqrt(2*k1in)*conj(alpha1in);
F(3)=x(3)*(1i*(w3-d3)+k3)+(g/2)*x(1)^2-sqrt(2*k3in)*alpha3in;
F(4)=x(4)*(1i*(w3-d3)+k3)+(g/2)*x(2)^2-sqrt(2*k3in)*alpha3in;
end
end

Sorry for the confusion...

[Lorcan Conlon]

Yes guys this is working now. Thanks very much!!

Answer 2

[Catherine Castiblanco]

Hello, I want to solve my function F(x) by using the command fzero with changing tau values. I took as a base the code of the recommended answer. I am struggling in determining the size of x0 and x_all for my case and I think is because of that matlab returns Error.Any help would be greatly appreciated!

My code is the following :

function x_all=main() 
r=0.03172;
s=0.333;
rho=0.001;
theta=0.715;
b=0.6;
x0=[0;1];

%values for tau
tau1_pool = 0.001:0.01:1;
%preallocate result matrix 
x_all = zeros(numel(x0),numel(tau1_pool))

% switch display off
%options = optimoptions('fzero','Display','off');

%Call fsolve in a loop
for i = 1 : numel(tau1_pool)
    tau1 = tau1_pool(i);
    x_all(1,i) = fzero(@obj_fun,x0);
end

function F = obj_fun(x)
F=(r*((1-tau1)*s*(x.^(1-s))*(1-theta))/(r-theta*(1-tau1)*s*x.^(1-s)))- rho -(x.^(s)/b)-r+(tau1/b);
end
end
%call the result by typing result=main