MATLAB: Piecewise function in curve fitting toolbox using fittype

问题

Ignore the red fitted curve first. I'd like to get a curve to the blue datapoints. I know the first part (up to y~200 in this case) is linear, then a different curve (combination of two logarithmic curves but could also be approximated differently) and then it saturates at about 250 or 255. I tried it like this:

func = fittype('(x>=0 & x<=xTrans1).*(A*x+B)+(x>=xTrans1 & x<=xTrans2).*(C*x+D)+(x>=xTrans2).*E*255');
freg = fit(foundData(:,1), foundData(:,2), func);
plot(freg, foundData(:,1), foundData(:,2))

Okay obviously my fittype could be improved, but why is it actually THAT bad/wrong? I tried another simpler model:

func = fittype('(x>=0 & x<=xTrans1).*(A*x+B)+(x>=xTrans1).*(C*x+D)')
freg = fit(foundData(:,1), foundData(:,2), func);
plot(freg, foundData(:,1), foundData(:,2))

At least I'd expect there two be two linear functions, and what I get is:

Or is it only the plot which is wrong because the output of the fit is:

 General model:
 f_fit(x) = (x>=0 & x<=xTrans1).*(A*x+B)+(x>=xTrans1).*(C*x+D)
 Coefficients (with 95% confidence bounds):
   A =      0.6491
   B =      0.7317
   C =   0.0007511
   D =       143.5
   xTrans1 =       0.547

Which at least yields a good xTrans1 (but I can't see it in the plot)!

EDIT Thanks for pointing out the more clear way of programming the function to fit, I tried the following (three different linear functions with two transition points):

function y = singleRegression_ansatzfunktion(x,xtrans1,xtrans2,a,b,c,d,e,f)
y = zeros(size(x));

% 3 Geradengleichungen:
for i = 1:length(x)
    if x(i) < xtrans1
        y(i) = a + b.* x(i);
    elseif(x(i) < xtrans2)
        y(i) = c + d.* x(i);
    else
        y(i) = e + f.* x(i);
    end
end

Calling the fitter like that:

freg = fit(foundData(:,1), foundData(:,2), 'singleRegression_ansatzfunktion(x,xtrans1,xtrans2,a,b,c,d,e,f)');
plot(freg, foundData(:,1), foundData(:,2))

Resulting in:

 General model:
 f(x) = singleRegression_ansatzfunktion(x,xtrans1,xtrans2,a,b,c,d,e,f)
 Coefficients (with 95% confidence bounds):
   a =      0.7655
   b =      0.7952
   c =      0.1869
   d =      0.4898
   e =       159.2
   f =   0.0005512
   xtrans1 =      0.7094
   xtrans2 =      0.7547

!!!!Strange!!!!

EDIT2 When NOT letting MATLAB optimize the transition points but entering them myself like I shortly did in the cftool (should be the same like calling fit but was quicker to figure it out) via the custom equation:

(x>=0 & x<=2.9e4).*(A*x+B)+(x>2.9e4 & x<=1.3e5).*(B*x+D)+(x>1.3e5).*255

It worked pretty well. I don't know why MATLAB can't do this on his own but okay... There you go now as a result:

So at least I fixed it now but I still remain in doubt why MATLAB simply couldn't do this itself.

回答1:

Have you tried the approach in the fittype documentation page ("Fit Curve Defined by a File" example) i.e. define your function to fit in a file to see if it makes a difference?

The other approach I can think of would be to split your data in two (or more) different datasets and do two separate fits for each chunk (but that assumes you know a priori where the transition point(s) is/are or can work it/them out before fitting).

来源：https://stackoverflow.com/questions/20285780/matlab-piecewise-function-in-curve-fitting-toolbox-using-fittype

标签

matlab

plot

curve-fitting

linear-regression

least-squares