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

4 次查看（过去 30 天）
mdjupin
mdjupin 2015-2-17
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.
  1 个评论
John D'Errico
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.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Sean de Wolski
Sean de Wolski 2015-2-17
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.
  7 个评论
显示 5更早的评论
Torsten
Torsten 2015-2-23
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
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

请先登录，再进行评论。

更多回答（1 个）

Joep
Joep 2015-2-17
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)
  1 个评论
mdjupin
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.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Fit Postprocessing 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by