Gnuplot data fit with log functions

Question

I would like to fit data with a function f(x), where f(x) = (K)(xlog(x) + (1-x)log(1-x)) + Ax*(1-x) + B*(x)*2(1-x)**2, and K, A, B are the fitted constants. And, is what I have until now, where green solid line is the fitted curve. Here is the Data and below my gnuplot script

f(x)= (K)*(x*log(x) + (1-x)*log(1-x)) + A*x*(1-x) + B*(x)**2*(1-x)**2
pl '1417.dat' u 1:2
fit f(x) '1417.dat' u 1:2 via K,A,B

Obtained K = 8116.63, A = 2.20, B=43692

I need to fit accurately at the minima regions, can anyone suggest how to fit with less deviation.

Your fit function is symmetric within the [0, 1] region. You can see this if you replace x by 1-x everywhere => your function will not change. In contrast, the data is not symmetric. So basically the fit function will not match the data. You should check the physical background of your data. Maybe a linear term (+C+D*x) might help? — maij
– maij, Commented Feb 18, 2021 at 11:20

theozh · Accepted Answer · 2021-02-18 13:36:04Z

2

I guess something must be "wrong" with your function/model (or with your data). If k(x), a(x), and b(x) are all symmetric functions to x=0.5, and so is f(x). How should the sum of 3 symmetric functions give an asymmetric function?

Code:

### impossible fitting
reset session

FILE = "SO/1417.dat"

k(x) = K*(x*log(x) + (1-x)*log(1-x))
a(x) = A*x*(1-x)
b(x) = B*x**2*(1-x)**2

f(x)= k(x) + a(x) + b(x)

set fit nolog
fit f(x) FILE u 1:2 via K,A,B

plot FILE u 1:2, k(x), a(x), b(x), f(x) lw 2 lc "red"
### end of code

Result:

answered Feb 18, 2021 at 13:36

theozh

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1 Comment

newstudent Over a year ago

thanks for your ans. yes, you are correct, I believe I need to add linear functions like, G1*x+G2*(1-x), where G1 and G2 are constants.

JJacquelin · Accepted Answer · 2021-02-19 07:58:03Z

1

For example the slightly different function below allows a better fitting :

Note that ln(x)ln(1-x) is exactly equal to zero at x=0 and x=1.

answered Feb 19, 2021 at 7:58

JJacquelin

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