How to fit a function with mutiple variables

Hello everyone,

I have a problem related to the fitting of a function which contains multiple variables. I usually use the command lsqcurvefit to fit a function with only one varibales such as times (y = f(t)) but this time the function that I have to fit turns to this :

                             y = f(alpha*x,t)

x is a vector calculed from 2 look-up tables a and b. And we have a,b vary with times

                            t = [0 : 30 : 9000]

My goal is to find alpha for each value of a and b because later I want to create a look-up table of alpha that match with a and b. If I'm correct, it means at each step of times, I have to find an alpha that allows having a best fit of f with the curve between y(i) and y(i-1).

I tried to do this with a for loop but it doesn't work so I want to know your advises for my problem. May be I'm wrong from the beginning.

    a  = ([0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100])/100;
    b  = [-20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60] ; 
    x = interp2(a,b,x_out,a_measure,b_measure)  ;
    A = (1/Rth_int)+(1/Rth_ext) ;
    fitfun =@(alpha,times) (Temp_init-(A*Temp_ext+alpha*x.*(Imp.^2))/A).*exp(-(A*times)/(masse*Cp)+((Temp_ext*A+alpha*x.*(Imp.^2))/A);

May be I don't explain well the problem so if you guys have any questions please let me know. Thanks a lot.

Answer 1

[Jos (10584)]

So you're fitting a surface in 3D space, z = f(x,y)

Take a look here: http://uk.mathworks.com/help/curvefit/fit.html

[Tuan-Tu]

Thank for your answer but I'm not sure because my output parameter y is just a vector size 308*1. I tried to plot a surface in fonction of x and time but it doesn't work. You know how could I do this ? Thank you