How to find a variable in a function that mostly match a set of data points

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KEDI YAN 2020-7-29

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编辑： Star Strider 2020-8-3

I have a one-variable function and a set of data points. The variable of the function is x.

If I mannuly change the variable from 1.0 to 3.0, the function's result will be closer to the data points I have as shown in the pictures below.

I was wondering what kind of MATLAB function I can use to automatically find the best value of x to match the function to the data points the most?

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Wilmer Alexander - Conferencista en Automatización y Robótica más influyente en Iberoamérica 2020-7-30

Thanks for asking. If possible. I remain at your disposal for any questions.

Gracias por preguntar. Si es posible. Quedo a su disposición para cualquier consulta.

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Star Strider 2020-7-30

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First, I would experiment with fminsearch, since it uses a derivative-free approach. With one parameter, this should not be difficult.

For more difficult problems, I tend to favor the ga function. I have no idea how difficult your problem is.

With either of those, the function you would use would be something like this:

fcn = @(x) norm(ydata(:) - yourFunction(x,xdata(:));

This would be easier to respond to with the function and the data.

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KEDI YAN 2020-7-30

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Hi Star,

I was, at the begining, trying to use fminsearch, but didn't really understand how to use it. Below is my MATLAB script. The variable x I mentioned in my question is actually Rp2, the function I mentioned is S21, and the data points I mentioned is S21_real.

You can mannuly try different value of Rp2 to match the function results to the data points. How do I use the fminsearch to automatically find the best Rp2 then?

clear
clc
wo = 2*pi*13.56*10^6;
Rsource = 50; Rload = 50;
Rp1 = 0.2; Rp4 = 0.2
L1 = 106e-9; L4 = 106e-9;
C1 = 1/(wo^2*L1); C4 = 1/(wo^2*L4);
Rp2 = 1.6; % The only variable is Rp2
Rp3 = Rp2; 
L2 = 1.84e-6; L3 = 1.84e-6;
C2 = 1/(wo^2*L2); C3 = 1/(wo^2*L3);
d23_array = []; S21_array = []; i = 0;
S21_real = [0.028 0.066 0.126 0.237 0.339 0.468 0.589 0.631 0.596 0.519 0.447 ...
    0.367 0.305 0.249 0.209]; % The data points
for d23=10e-3:10e-3:150e-3
    i = i+1;
    Z11 = Rp1+Rsource+1i*wo*L1-1i/(wo*C1);
    Z22 = Rp2+1i*wo*L2-1i/(wo*C2);
    Z33 = Rp3+1i*wo*L3-1i/(wo*C3);
    Z44 = Rp4+Rload+1i*wo*L4-1i/(wo*C4);
    M12 = MI_loop_spiral_50mm_Ben();
    M34 = MI_loop_spiral_50mm_Ben();
    M23 = MI_Tx_Rx_Ben(d23);
    Z12 = 1i*wo*M12;
    Z34 = 1i*wo*M34;
    Z23 = 1i*wo*M23;
    % VL/VS
    Numerator = Z12*Z23*Z34*Rload;
    Denominator = -Z11*Z22*Z33*Z44-Z12^2*Z34^2+Z11*Z22*Z34^2+Z11*Z44*Z23^2+Z33*Z44*Z12^2;
    VL_over_Vs = Numerator./Denominator;
    S21 = 2*VL_over_Vs*(Rsource/Rload)^0.5; % The function
    d23_array(i) = d23;
    S21_array(i) = abs(S21);
end
plot(d23_array,S21_array,'r-o');
hold on
plot(d23_array,S21_real,'bd');
hold off
legend('Function','Data Points')

KEDI YAN 2020-8-2

Sorry about the late response.

Could you sort of exlain how you feed Rp2 to fminsearch and how you used the output from the fminsearch?

Star Strider 2020-8-3

编辑：Star Strider 2020-8-3

在 MATLAB Online 中打开

I did something like this:

function b = Rp2_fcn(Rp2)
wo = 2*pi*13.56*10^6;
Rsource = 50; Rload = 50;
Rp1 = 0.2; Rp4 = 0.2
L1 = 106e-9; L4 = 106e-9;
C1 = 1/(wo^2*L1); C4 = 1/(wo^2*L4);
% Rp2 = 1.6; % The only variable is Rp2
Rp3 = Rp2; 
L2 = 1.84e-6; L3 = 1.84e-6;
C2 = 1/(wo^2*L2); C3 = 1/(wo^2*L3);
d23_array = []; S21_array = []; i = 0;
S21_real = [0.028 0.066 0.126 0.237 0.339 0.468 0.589 0.631 0.596 0.519 0.447 ...
    0.367 0.305 0.249 0.209]; % The data points
for d23=10e-3:10e-3:150e-3
    i = i+1;
    Z11 = Rp1+Rsource+1i*wo*L1-1i/(wo*C1);
    Z22 = Rp2+1i*wo*L2-1i/(wo*C2);
    Z33 = Rp3+1i*wo*L3-1i/(wo*C3);
    Z44 = Rp4+Rload+1i*wo*L4-1i/(wo*C4);
    M12 = MI_loop_spiral_50mm_Ben();
    M34 = MI_loop_spiral_50mm_Ben();
    M23 = MI_Tx_Rx_Ben(d23);
    Z12 = 1i*wo*M12;
    Z34 = 1i*wo*M34;
    Z23 = 1i*wo*M23;
    % VL/VS
    Numerator = Z12*Z23*Z34*Rload;
    Denominator = -Z11*Z22*Z33*Z44-Z12^2*Z34^2+Z11*Z22*Z34^2+Z11*Z44*Z23^2+Z33*Z44*Z12^2;
    VL_over_Vs = Numerator./Denominator;
    S21 = 2*VL_over_Vs*(Rsource/Rload)^0.5; % The function
    d23_array(i) = d23;
    S21_array(i) = abs(S21);
end
b = norm(S21_array - S21_real);
end

I remember making other changes in the code to make it more efficient, however I do not remember what they were.

the fminsearch call was essentially:

Rp2 = fminsearch(Rp2_fcn, rand);

EDIT — (3 Aug 2020 at 19:08)

Corrected typographical errors.

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