How solve linear equations

Hi everyone, I am working on a PhD assignement.

I need to solve a linear equation using matlab. The equation is listed below:

(Rb)^2*(xi)^2 + (Rb)^2*(X0)^2 + (Rb)^2*(xi)*(X0) + (Ra)^2*(yi)^2 + (Ra)^2*(Y0)^2 - (Ra)^2*(yi)*(Y0) - (Ra)^2*(Rb)^2 = 0;

I have 20 values of xi and yi, and I need to get the answers for X0, Y0, Ra, and Rb.

The examples on found on the internet are very simple linear equations which I am not so sure how to do it in my case.

Thank you!

[John D'Errico]

This is NOT a linear equation. Calling it linear will not make it so. IF I decided to call it a unicorn would that be true too?

[Bjorn Gustavsson]

Do you try to fit parameters of an ellipse to some set of points [xi,yi]? If so search for that on the file exchange. Also for your research experience, first rewrite your equation into a more readable form, I had to look long and hard to see what it is (might be?). One of the primary steps in problem-solving is to put the problem (equations) into as clear and clean form as possible.

[Cong Liu]

https://ww2.mathworks.cn/matlabcentral/answers/599119-how-solve-linear-equations#comment_1022635

Hi Bjorn Gustavsson

Thank you for the response. yes, I am trying to fit parameters of an ellipse. I have a set of xi, yi data colllected from my experiment. Now I am trying to fit them into an sllipse. But first thing first, I need to calcualte the parameters.

Sorry I am new to this. What is the file exchange and how can it help me?

[Bjorn Gustavsson]

You will find a link to the file exchange in the top-left drop-down text-menu. It is a repository of all sorts of additional functions and toolboxes for matlab. You will find a lot of useful stuff on there, never avoid looking for solutions to your problems there, even if you dont find an exact full solution you will, almost guaranteed, find something that takes you a large step of the way. In addition to that, from your question it seems that you should spend a day or two to work through the getting started and introduction stuff on the site. Here's the direct link to the file exchange: fileexchange

Answer 1

[Alan Stevens]

Here is one way of structuring your problem:

% Set initial values for Ra, Rb, X0, Y0
Guess = [Ra, Rb, X0, Y0];  % Use them to create initial guess

% Call solver with input arguments of Guess and the xi and yi data values.
[Values, Fval] = fminsearch(@fn,Guess,[],xi,yi); 

% Extract values
Ra = Values(1);
Rb = Values(2);
X0 = Values(3);
Y0 = Values(4);


function F = fn(Guess,xi,yi)

         Ra = Guess(1);
         Rb = Guess(2);
         X0 = Guess(3);
         Y0 = Guess(4);
         F1 = (Rb)^2*(xi).^2 + (Rb)^2*(X0)^2 + (Rb)^2*(xi)*(X0) ...
             + (Ra)^2*(yi).^2 + (Ra)^2*(Y0)^2 - (Ra)^2*(yi)*(Y0) ...
             - (Ra)^2*(Rb)^2; 
         F = F1'*F1;  % Assuming xi and yi are column vectors.

end