custom fitting to logarithmic fxn

Question

John Crane 2011-6-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/10174-custom-fitting-to-logarithmic-fxn

I need t fit a curve to some data. The equation is having form: level = A*(1- exp(-b*x))

where 'x' is independent variable. I need to find A and b values. Does any one know how to use lsqcurve fot or maybe something in the custom fitting tool box to accomplish this??

Thank You,

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Answer 1

bym 2011-6-25

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链接

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https://ww2.mathworks.cn/matlabcentral/answers/10174-custom-fitting-to-logarithmic-fxn#answer_14136

在 MATLAB Online 中打开

clc;clear;close
data = 2.*(1-exp(-.3.*(1:10)));
data = data + .5.*rand(1,10);
myfun = @(a,x)a(1).*(1-exp(a(2).*x));
plot(data,'bo');hold
a0 = [1.5,-.1];
ahat = lsqcurvefit(myfun,a0,(1:10),data);
plot(myfun(ahat,(1:10)),'g--')

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John Crane 2011-6-26

Thank you, this is great. I was wondering why you started a(2) with a negative number for this case? I ask because the independent axis for me will be time(t) and I would like to get a parameter(maybe calle beta) that would give a measurement of the growth of the curve to reach it's maximum? Or plateau?

Thanks

bym 2011-6-26

I set a(2) to negative because that was the form of your equation. If you set the starting point to a positive number in my example, you don't get a very satisfactory result. a(2) or b using your nomenclature is the parameter you are looking for, it is called the rate parameter http://en.wikipedia.org/wiki/Exponential_distribution

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