How does TF1::GetRandom() work?

Newbie
1

Hi guys,

can anyone explain to me how TF1::GetRandom() exactly works when called?

I don’t know if it’s only me, but the explanation given in the source code is very foggy, or maybe too much condensed.

I will appreciate any kind of help

2

Hi,
the TF1::GetRandom()of the TF1 extract a number using the TF1 function as a p.d.f.
In example I defined the TF1 as

TF1 *f=new TF1("f","[0]*x*exp(-x)",0,20) and set the parameter [0] equal to 250

then i called 2000 times GetRandom to fill an histogram

for( int i=0;i<2000;i++)h->Fill(f->GetRandom())

and the result is the plot attached.(choosing the right scaling factors, the TF1 overlap with the histogram perfectly)

Cheers,
Stefano

pdf_vsHist
pdf_vsHist.png1352×934 49.4 KB

1 Like
3

Hi Stefano,

Sorry for the misunderstanding, but with my questions I meant: “How does GetRandom() can give you random numbers following the function shape?”

The explanation given in the source file is the following:
The distribution contained in the function fname (TF1) is integrated over the channel contents.
It is normalized to 1. For each bin the integral is approximated by a parabola. The parabola coefficients are stored as non persistent data members Getting one random number implies:

  • Generating a random number between 0 and 1 (say r1)
  • Look in which bin in the normalized integral r1 corresponds to
  • Evaluate the parabolic curve in the selected bin to find the corresponding X value.

This is what is not clear to me about GetRandom()

Thank you so much

4

Sorry for the late answer and the misunderstanding,
When you want to generate a random number according to a specific distribution, you have
to apply the Inverse transform sampling

  • normalize the area of the distribution
  • build the cumulative distribution (CDF), basically you integrate the the normalized function.
  • the cumulative distribution for how is defined, span the y-axis the range [0,1] and is monotonically increasing
  • randomly choose a number r1 between 0 and 1, you choose the y of the CDF, then to this y correspond only one x, and this x is distributed as the function you defined.

In simple case, as exponential distribution you are able to do all this analitically and obtain

x = log(1-r1)/(−λ)

otherwise you have to do everything numerically with some approximation, and it is what root do.

I hope everything is understandable .

S

1 Like
5

Ok that’s clear, but what about the parabola mentioned in the description?

6

It’s just for the approximation of the cumulative and to easily compute the x from the y

7

Ok thank you, problem solved :smiley: