Power curve fitting in gnuplot for redundant values

问题

I am trying to fit the power curve into my data with following gnuplot code.

set termoption enhanced
f(x) = a*x**b;
fit f(x) 'data.txt' via a,b
plot 'data.txt' with points title 'data points', \
f(x) with lines title sprintf('power fit curve f(x) = %.2f·x^{%.2f}', a, b)

It works fine for non-redundant data for x axis. (no repeats).

But for following type of data: It is fitting the curve only to points of first x value i.e. 1, (Starred). and not to the whole dataset.

Data:

1   2194*
1   2675*  
1   1911*  
2   966  
2   1122  
2   951  
2   1356  
3   935  
3   934  
4   851  
4   886  
4   849  
4   597  

回答1:

You must set appropriate starting values for a and b, because nonlinear fitting usually does not have one unique minimum. If you don't specify any starting values, 1 is assumed, which goes in the completely wrong direction in your case.

So, with the following script

set termoption enhanced
f(x) = a*x**b
b = -1
a = 2000
fit f(x) 'data.txt' via a,b
plot 'data.txt' with points title 'data points', \
     f(x) with lines title sprintf('power fit curve f(x) = %.2f·x^{%.2f}', a, b)

you get a proper fit:

来源：https://stackoverflow.com/questions/18712839/power-curve-fitting-in-gnuplot-for-redundant-values