How to fit data with custom function with two variables?

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Marek Balko on 25 Apr 2021
Hi,
I would ask How to fit data with custom function with two variables? I have data from measurements in two vectors, let's say Ra and Pr. I need to fit this data to equation: a*(Ra^(b))*(Pr^(c)) and extract the coeficients value. How can I do that? Thank you

You can minimize the error of your model to the data you want by optimizing the parameters. One alternative for it is, for example, by using fminsearch.
Ra = randn(100,1)*5; % Data you said you have
Pr = randn(100,1);
% I'm generating some example data
a = 0.5;
b = 0.1;
c = 0.35;
dataToFitModel = a*(Ra.^(b)).*(Pr.^(c)); % You didn't mention this data but you should have,
% otherwise it doesn't make sense to talk about fit
% Here you create a function to minimize the error between measurements and your model
fun = @(x) rms(dataToFitModel- ( x(1)*(Ra.^( x(2) )).*(Pr.^( x(3) )) ) )
fun = function_handle with value:
@(x)rms(dataToFitModel-(x(1)*(Ra.^(x(2))).*(Pr.^(x(3)))))
firstGuess = [0,0,0]; % Depending of your data you may need a start point close to the real answer
[x,fval] = fminsearch(fun,firstGuess);
aFromData = x(1)
aFromData = 0.5000
bFromData = x(2)
bFromData = 0.1000
cFromData = x(3)
cFromData = 0.3500
fval
fval = 4.6583e-05

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