How do I fit two equations that explain two parts of a curve?

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mdjupin 2015-2-17

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评论： mdjupin 2015-2-24

Hi,my equations are: y(t)={(a/b)*(1-exp(-b(x-x_start)),for x_start <= x < x_end %equ1 and {c*exp(-b(x-xend)),for x > x_end %equ2

Here I do not know a,b and c. The idea is that since both equations have b in common, I would like to know how fitting these equations I can get one single value for b. I already fitted these equations individually, but I obtained two values of b, which are different from each fit.

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John D'Errico 2015-2-17

I predict that your next question will be why is my curvefit not continuous at the break point? I.e., at x_end, the pair of functions will not be continuous.

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Sean de Wolski 2015-2-17

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https://ww2.mathworks.cn/matlabcentral/answers/178867-how-do-i-fit-two-equations-that-explain-two-parts-of-a-curve#answer_168283

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Break the data into two pieces and do the curve fit

xlow = x(x<x_end);
ylow = y*x<x_end);
xhigh = x(x>x_end); % Note you have nothing for x==x_end
yhigh = y(x>x_end);

Now do the curve fit - either with the Curve Fitting App, lsqcurvefit or fitnlm.

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Torsten 2015-2-23

在 MATLAB Online 中打开

You programmed it as

function call
xdata=[...];
ydata=[...];
xstart=...;
xend=...;
p0=[1 1 1];
p = lsqnonlin(@(p)myfun(xdata,ydata,xstart,xend,p),p0);
function F = myfun(xdata,ydata,xstart,xend,p)
for i=1:length(xdata)
if (xdata(i) >= xstart) && (xdata(i) < xend)
F(i) = ydata(i)-(p(1)/p(2))*(1-exp(-p(2)(xdata(i)-xstart)); 
else
F(i)=ydata(i)-(p(3)*exp(-p(2)(xdata(i)-xend));
end
end

Best wishes

Torsten.

mdjupin 2015-2-24

Thanks Torsten, this does work. I would advise not to use more than two equations, because the fitting get harder.

Cheers.

mdjupin

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Joep 2015-2-17

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在 MATLAB Online 中打开

This is very simple solution which works in some cases one thing you need to noticed is the 1-based indexing of matlab.

a=10; b=20; c=-1; d=-3;

for x=1:a
 t(x)=x;
 y(x)=c*x;
end
for x=a:b
 t(x)=t;
 y(x)=d*x.^2;
end
figure
plot(t,y)

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mdjupin 2015-2-17

Thanks Joep. Here I do not know a,b and c. The idea is that since both equations have b in common, I would like to know how fitting these equations I can get one single value for b. I already fitted these equations individually, but I obtained two values of b, which are different from each fit.

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