How do I fit two equations that explain two parts of a curve?
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mdjupin
el 17 de Feb. de 2015
Comentada: mdjupin
el 24 de Feb. de 2015
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 comentario
John D'Errico
el 17 de Feb. de 2015
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.
Respuesta aceptada
Sean de Wolski
el 17 de Feb. de 2015
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 comentarios
Torsten
el 23 de Feb. de 2015
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.
Más respuestas (1)
Joep
el 17 de Feb. de 2015
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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