Fitting data with custom equation

Hi,

I have some datas to fit with by the following equation : d*atan(b*(x+a))+c . I've done it by the " curve fitting tool" how I can incorporate this process in a matlab script ? I'd like to obtain the parameter a,b,c,d as an answer.

Thanks.

Answer 1

[Stephan]

Hi,

you can use this code:

% Some data - replace it with yours (its from an earlier project)
x = [177600,961200, 2504000, 4997000, 8884000]';
y = [6.754, 24.416, 58.622, 107.980, 154.507]';

% Define Start points, fit-function and fit curve
x0 = [1 1 1 1]; 
fitfun = fittype( @(a,b,c,d,x) d*atan(b*(x+a))+c );
[fitted_curve,gof] = fit(x,y,fitfun,'StartPoint',x0)

% Save the coeffiecient values for a,b,c and d in a vector
coeffvals = coeffvalues(fitted_curve);

% Plot results
scatter(x, y, 'r+')
hold on
plot(x,fitted_curve(x))
hold off

Due to, that this code is taken from an older project and the values dont represent your function the result here is a very bad fit - but to show how it works with a custom function inside a script it should be good enough.

Best regards

Stephan

[Priodyuti Pradhan]

Thanks a lot for sharing! Really helpful!

[sandeep]

Is there a way to find the appropriate intial guess?

[Rekib Uddin]

Dear all,

How can we consider conditions in the custom equation....

e.g. y=-0.18 at x=0

Thanks and Regards

[Torsten]

You can insert the point in the custom equation thereby reducing the number of unknown parameters:

d*atan(b*(0+a)) + c  = -0.18
-> d*atan(b*a) + c = -0.18
-> c = -0.18 - d*atan(b*a)

Thus the modified custom equation to be fitted reads:

d*(atan(b*(x+a)) - atan(b*a)) - 0.18

which now has only 3 instead of 4 unknown parameters.

[Zeyu Ma]

Hi there, I wonder how to restrict the values of the parameters.

For example, force parameter a to be 0<a<1.

Thank you!

Answer 2

[Valrhona]

I have a question regarding the curve fitting tool itself.

How can I change the z=f(x,y) to f(x).

I cannot change the x, y, or z data in this curve fitting tool.

I would like to use a custom f(x) function (not f(x,y))

Many thanks!

[Koral Villalobos]

I need help with this too

[sandeep]

is there a way to find the appropriate intial guess?