Gnuplot fitting

Question

I want to fit the following data:

70  0.0429065
100 0.041212
150 0.040117
200 0.035018
250 0.024366
300 0.02017
350 0.018255
400 0.015368

to the following function which is combination of an exponantial and a gaussian functions:

$ f(x)= a1*(a2* exp(-x/T2e)+ exp(-(x/T2g)**2))

$ fit f(x) 'data' via a1,a2,T2e,T2g

But it keeps giving me the following results:

a1              = 0.0720021        +/- 0.04453      (61.84%)
a2              = 0.310022         +/- 0.9041       (291.6%)
T2e             = 63291.7          +/- 2.029e+07    (3.206e+04%)
T2g             = 252.79           +/- 32.36        (12.8%)

While when I try to fit it separetly to

$ g(x)=b* exp(-(x/T2g)**2)

$ fit g(x) 'data' via b,T2g

I get

b               = 0.0451053        +/- 0.001598     (3.542%)
T2g             = 359.359          +/- 16.89        (4.701%)

and

$ S(x)=S0* exp(-x/T2e)

$ fit S(x) 'data' via S0,T2e

gives:

S0              = 0.057199         +/- 0.003954     (6.913%)
T2e              = 319.257          +/- 38.17        (11.96%)

I already tried to set the initial values but it didn't change the results.

Does anybody know what is wrong? Thank you,

please provide your full code (ideally, as copy & paste code) which will make it much more time saving for others to reproduce. Are you sure that this function can be a good fit at all? There are not too many datapoints and no clear feature, i.e. gaussian peak and exponential tail. — theozh, Mar 20 '19 at 18:53
$S(x)=S0* exp(-x/T2e) $g(x)=b* exp(-(x/T2g)**2) $ fit S(x) 'data' via S0,T2e $ fit g(x) 'data' via b,T2g I think since each function separately fits with good approximation, the sum of them should also fit. — Kassik, Mar 20 '19 at 19:07

theozh · Accepted Answer · 2019-03-20T20:17:00.257

Ok, you can see an exponential decay with a hump which could be a Gaussian. The approach, how I got to a fit: first, exclude the datapoints 100 and 150 and fit the exponental and then set a Gaussian approximately at 170. You probably don't get a good fit, because at least the Gaussian peak is shifted by some value x1.

With the code:

 ### fitting 
reset session

$Data <<EOD
70  0.0429065
100 0.041212
150 0.040117
200 0.035018
250 0.024366
300 0.02017
350 0.018255
400 0.015368
EOD

a = 0.055
T2e = 310

b = 0.008
x1 = 170
T2g = 54

Exponential(x) = a*exp(-x/T2e)
Gaussian(x) = b*exp(-((x-x1)/T2g)**2)

f(x) = Exponential(x) + Gaussian(x)
fit f(x) $Data u 1:2 via a,b,x1,T2e,T2g

plot $Data u 1:2 w lp pt 7, f(x) lc rgb "red"
### end of code

You'll get:

a               = 0.0535048        +/- 0.00183      (3.42%)
b               = 0.00833589       +/- 0.001006     (12.06%)
x1              = 170.356          +/- 5.664        (3.325%)
T2e             = 315.114          +/- 12.94        (4.106%)
T2g             = 54.823           +/- 12.13        (22.12%)

Gnuplot fitting

1 Answers1