Solving Nonlinear Matrix Equation

I have an equation of the form

where A= positive definite symmetrix matrix (2 by 2), X is data matrix of dimensions (N by 2) and mu is a vector (1 by 2). Ki are scaler values and P is a constant. I want to use fsolve to solve for mu.

I am using the script as below

K_values in the code is an array that contains the values of each Ki.

data in the code is a ( N by 2 ) matrix of values that is passed on to the script below

The matrix A is calculated before running the script. The only unknown is the vector mu.

fsolve returns an error: Not enough input arguments

Any insight into solving this is highly appreciated.

syms X [length(data) 2]
syms mu [1 2]
syms K
T=subs(trace(inv(A)*(X-mu)'*(X-mu))^(P),X,data);
L1=subs(K*T,{K},{[K_values]});
fun1=matlabFunction(sum(L1));
mu0=[1;1];
options = optimoptions('fsolve','Display','none');
mu=fsolve(fun1,mu0,options);

Answer 1

[Walter Roberson]

fun1=matlabFunction(sum(L1));

That is going to produce a function with two inputs, mu1 and mu2. fsolve() only provides one input as a vector.

fun1=matlabFunction(sum(L1), 'vars', {mu} );

[AAQIB PEERZADA]

Thanks for the reply Mr. Walter. Defining fun1 as you suggested solves the equation with the following warning however,

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead.

Can you offer any insights into this warning message?

Thanks again for your time,

[Walter Roberson]

https://www.mathworks.com/help/optim/ug/choosing-the-algorithm.html#bsbwxrw

When I scan over the default algorithm at https://www.mathworks.com/help/optim/ug/equation-solving-algorithms.html#f51372 the use of the \ operator hints to me that your function needs to return a square matrix to solve the equations properly but I could be misreading.

The default algorithm was chosen because it was designed for nonlinear problems. However it is not always appropriate. To avoid seeing warning message, pass an options structure telling the code to use a different algorithm.

[AAQIB PEERZADA]

Thanks Mr. Walter. It is now clear to me. Appreciate your help.