fitting a function of three output

Hi everyone!

I need you advise on fitting coefficientts of a function that output 3 valus:

E = calcE(N, Ds, Dd, k), where E is a vector: E(1), E(2), E(3)

Ds, Dd and k are know. I need to find the set of N, where N is a vector N(1),N(2),N(3), that result E1,2,3 that is equal to a given e: e(1), e(2), e(3).

I tied:

function N1 = calcN(Ds, Dd, k, e)
b0 = [1, 1, 1];
fun = @(N)calcE(N,Ds, Dd,k)./e;
N1 = lsqcurvefit(fun,b0, N, e);
end

tryig to force E ./ e =1

But did't work...

with calcE

function E = calcE(N,Ds, Dd,k)

S(1) = -sqrt((1-N(1)^2-N(2)^2) / (1-N(2)^2+(N(1)^2)*((((k^2) * (1-N(1)^2))/N(2)^2)+2*k)));
S(2) = (S(1)*N(1)*k/N(2));
S(3) = -sqrt(1-S(1)^2 - S(2)^2);

E(1) = sqrt((N(1)*Dd(1))^2 + (S(1)*Ds(1))^2);
E(2) = sign(k)*sqrt((N(2)*Dd(2))^2 + (S(2)*Ds(2))^2);
E(3) = sqrt((N(3)*Ds(3))^2 + (S(3)*Dd(3))^2);

end

Thanks!

Nadav

Answer 1

[MULI]

Hi Nadav,

I understand you are trying to get optimized values of (N) which are used to compute vector (E) that should match with target vector (e).

The function "lsqcurvefit” is designed to minimize the difference between function's outputs and target values. It is typically more effective to minimize the absolute or squared differences than trying to make each ratio equal to 1.

Below is the modified code which you can try:

function N_opt = calcN(Ds, Dd, k, e) 

    b0 = [1, 1, 1]; % Initial guess for the N vector 

    % Objective function: modeled E based on N, Ds, Dd, k 

    fun = @(N, xdata) calcE(N, Ds, Dd, k); % x is not used in calcE but is required by lsqcurvefit syntax 

    % Use lsqcurvefit to find the N that minimizes the difference between calcE's output and e 

    N_opt = lsqcurvefit(fun, b0, [], e); % xdata is set to [] since it's not used 

end 

You may refer to this documentation for more information and examples related to “lsqcurvefit”.

https://www.mathworks.com/help/releases/R2020a/optim/ug/lsqcurvefit.html

Hope this answers your query!