How to fit data with custom function with two variables?

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

Answer 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