Solving a system of equations in matlab

I'm trying to solve a system of equations in matlab that is parametrized in A. The equations are: x^2+Ay^2=12 x*y=3 and A is parametrized from 1/3 to 3.

my solution thus far:

I created a function file to solve for x and y x=x(1) and y=x(2)

function F = functionfile(x,A) F(1)=x(1).*x(1)- A.*(x(2).*x(2)) -12; F(2)=x(1).*x(2)-3; end

and I solve it in my main file:

x0=[1;1]; A=2; options=optimset('Display','off'); x=fsolve(@functionfile,x0,options,A);

My problem is, when I try to make A a vector of 1/3:1/3:3, it returns an error message that doesn't occur when I give A a single value. How do I fix this problem?

Answer 1

[Sven]

Hi E,

There's a main issue that causes your problem here. Firstly, imagine that you had got inside your function functionfile with x=[1;1] and A=1/3:1/3:3. You would hit the very first line which is:

F(1)=x(1).*x(1)- A.*(x(2).*x(2)) -12;

Do you see how this cannot work? The output on the right-hand side is a 1-by-9 array, but you're trying to put it all into the single element F(1).

A couple of hints:

1. You can put a breakpoint on the first line of your functionfile and check this out yourself (because MATLAB errors inside optimisations like fsolve are a little difficult to track down)
2. You can format your code in the question above to make it a bit easier to read (your question is actually a good one... it's just a little squashed)
3. Can you explain what kind of answer you expect when A is a vector? Perhaps you'd just like to loop over each element of A and solve it independently?

A = 1/3:1/3:3
x = zeros(2,length(A))
for i = 1:length(A)
  x(:,i) = fsolve(@tmpfunc,x0,options,A(i));
end

Hope this answered your question.

Answer 2

[E]

Thank you! I should have thought of the loop idea! That was exactly what I needed to do!