How to fit data with custom function with two variables?

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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

Answers (1)

Thiago Henrique Gomes Lobato
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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