I'm trying to solve an implicit matrix equation with fsolve

I'm able to solve an implicit equation with fsolve:

    function y = brillouin(x,p)

      A=p(1); B=p(2);
      y=zeros(size(x));
      NN=length(x);
      opt=optimset('display','off');

      for i=1:NN
          y(i)=fsolve(@(y) y-tanh(A.*x(i)-B*y), 1e-9, opt);
      end
    end

I'm now trying to expand this to a vector y, with B being a matrix. Any help would be appreciated! Thanks.

Answer 1

[Matt J]

yet, and that is the problem, that the solutions, y(i,x) from fsolve are identical for each of the i=1:6.

That's because you are calling FSOLVE with a scalar initial point 1e-9. FSOLVE is therefore returning scalars.

If FSOLVE is supposed to be returning something in R^6, you must feed it an initial point that is in R^6.

Answer 2

[Matt J]

Your code should work as is, even if A and B are matrices instead of scalars.

[Matt J]

Oren Commented:

Thanks! alas, as the function is written now, y is a vector already, with a length the size of x. When i try to set B as a matrix, the multiplication B.*y is erroneous since y is a matrix the size of (size(b),size(x)).

[Matt J]

Couldn't understand any of that. Please execute at the command line

 >> whos A B x

in the case where A and B are matrix data, so that we can see how big everything is. Then tell us how many equations/unknowns will be processed in a single call to FSOLVE in this case.

[Oren]

Yes. My apologies, it works well: not producing what i would expected but the code does work. Thanks Matt J! I'm getting: "Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead. "

any ideas why ?

[Matt J]

Because you have more or fewer equations than unknowns.

Answer 3

[Oren]

Relocated to Comment by Matt J

Answer 4

[Oren]

Here is the problem: my function is y(x)=tanh(h*x-m*y) where m is a 6x6 matrix, h is 6x1 vector and x is a vector i define as x=0:0.1:2.5 . the solution for y=y(x) should be 6x length(x) (which in the case here is 6x26).

in order for the code to run, i use h=repmat(h,1,6); so that h and m have the same size (6x6).

the matrix m is defined as

m=[0 0 2 0 2 0; 0 0 0 2 0 2; 2 0 0 0 2 0; 0 2 0 0 0 2; 2 0 2 0 0 0; 0 2 0 2 0 0];

the vector h is

h=[0 1 0 1 0 1];

yet, and that is the problem, that the solutions, y(i,x) from fsolve are identical for each of the i=1:6. the code i use is the same as the above except:

y=zeros(6,NN);
h=repmat(h,1,6);
for i=1:NN   
    y(:,i)=fsolve(@(y) y-tanh(x(i)*h-m*y), 1e-9, opt);    
end

Thank you!