Generate random samples from a user-defined distribution¶

Author: Lukas Breitwieser
In this tutorial we demonstrate how to create a random number generator that draws samples from a user-defined distribution.

Let's start by setting up BioDynaMo notebooks

In [1]:
%jsroot on
gROOT->LoadMacro("${BDMSYS}/etc/rootlogon.C");

INFO: Created simulation object 'simulation' with UniqueName='simulation'.

We have to create a TCanvas object to draw results in this notebook.

In [2]:
TCanvas c("", "", 400, 300);
c.SetGrid();

Let's assume that we want to generate random numbers from a student-t distribution.
Class Random does not provide a direct function for that.
Therefore, we use the user-defined distribution feature Random::GetUserDefinedDistRng1D.
Fortunately, ROOT already provides a function called tdistribution_pdf that we can use.
Have a look at the following two links for more math functions: TMath and statistical functions

In [3]:
auto* random = simulation.GetRandom();
auto distribution = [](const double* x, const double* param) { 
    return ROOT::Math::tdistribution_pdf(*x, 1.0); 
};
auto udd_rng = random->GetUserDefinedDistRng1D(distribution, {}, -5, 10);

The returned random number generator has a function to draw the distribution.

In [4]:
udd_rng.Draw();
c.Draw();

In the next step we want to verify that the created random number generator follows the specified distribution.
Therefore, we create a histogram with 100 bins in the range [-5, 10] and fill it with 10000 samples.

In [5]:
TH1F h("","", 100, -5, 10);
for (int i = 0; i < 10000; ++i){
    auto rndm_sample = udd_rng.Sample();
    h.Fill(rndm_sample);
}

Let's draw the result:

In [6]:
h.SetFillColor(kBlue-10);
h.Draw();
c.Draw();

As we can see from the last figure the samples from our random number generator fit our distribution.