# multidimSampling¶

Example of sampling a multi-dim distribution using the DistSampler class NOTE: This tutorial must be run with ACLIC

Author: Lorenzo Moneta
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, August 17, 2022 at 09:34 AM.

In [1]:
using namespace ROOT::Math;


f

In [2]:
%%cpp -d
unction (a 4d gaussian)
#include "TMath.h"
#include "TF2.h"
#include "TStopwatch.h"
#include "Math/DistSampler.h"
#include "Math/DistSamplerOptions.h"
#include "Math/MinimizerOptions.h"
#include "Math/Factory.h"

#include "TKDTreeBinning.h"

#include "TTree.h"
#include "TFile.h"
#include "TMatrixDSym.h"
#include "TVectorD.h"
#include "TCanvas.h"
#include <cmath>

// Gauss ND function
// make a class in order to avoid constructing the
// matrices for every call
// This however requires that  the code must be compiled with ACLIC

bool debug = false;

// Define the GausND strcture
struct GausND {

TVectorD X;
TVectorD Mu;
TMatrixDSym CovMat;

GausND( int dim ) :
X(TVectorD(dim)),
Mu(TVectorD(dim)),
CovMat(TMatrixDSym(dim) )
{}

double operator() (double *x, double *p) {
// 4 parameters
int dim = X.GetNrows();
int k = 0;
for (int i = 0; i<dim; ++i) { X[i] = x[i] - p[k]; k++; }
for (int i = 0; i<dim; ++i) {
CovMat(i,i) = p[k]*p[k];
k++;
}
for (int i = 0; i<dim; ++i) {
for (int j = i+1; j<dim; ++j) {
// p now are the correlations N(N-1)/2
CovMat(i,j) = p[k]*sqrt(CovMat(i,i)*CovMat(j,j));
CovMat(j,i) = CovMat(i,j);
k++;
}
}
if (debug) {
X.Print();
CovMat.Print();
}

double det = CovMat.Determinant();
if (det <= 0) {
Fatal("GausND","Determinant is <= 0 det = %f",det);
CovMat.Print();
return 0;
}
double norm = std::pow( 2. * TMath::Pi(), dim/2) * sqrt(det);
// compute the gaussians
CovMat.Invert();
double fval  = std::exp( - 0.5 * CovMat.Similarity(X) )/ norm;

if (debug) {
std::cout << "det  " << det << std::endl;
std::cout << "norm " << norm << std::endl;
std::cout << "fval " << fval << std::endl;
}

return fval;
}
};

input_line_52:1:1: error: C++ requires a type specifier for all declarations
unction (a 4d gaussian)
^
input_line_52:1:10: error: use of undeclared identifier 'a'
unction (a 4d gaussian)
^
input_line_52:1:24: error: expected ';' after top level declarator
unction (a 4d gaussian)
^
;

In [3]:
const int N = 10000;
/*const int NBin = 1000;*/
const int DIM = 4;

double xmin[] = {-10,-10,-10, -10};
double xmax[] = { 10, 10, 10,  10};
double par0[] = { 1., -1., 2, 0, // the gaussian mu
1, 2, 1, 3, // the sigma
0.5,0.,0.,0.,0.,0.8 };  // the correlation

const int NPAR = DIM + DIM*(DIM+1)/2; // 14 in the 4d case


generate the sample

In [4]:
GausND gaus4d(4);
TF1 * f = new TF1("functionND",gaus4d,0,1,14);
f->SetParameters(par0);

double x0[] = {0,0,0,0};

input_line_54:2:2: error: unknown type name 'GausND'
GausND gaus4d(4);
^


for debugging

In [5]:
if (debug) f->EvalPar(x0,0);
debug = false;

TString name;
for (int i = 0; i < NPAR; ++i )  {
if (i < DIM) f->SetParName(i, name.Format("mu_%d",i+1) );
else if (i < 2*DIM) f->SetParName(i, name.Format("sig_%d",i-DIM+1) );
else if (i < 2*DIM) f->SetParName(i, name.Format("sig_%d",i-2*DIM+1) );
}

/*ROOT::Math::DistSamplerOptions::SetDefaultSampler("Foam");*/
DistSampler * sampler = Factory::CreateDistSampler();
if (sampler == 0) {
Info("multidimSampling","Default sampler %s is not available try with Foam ",
ROOT::Math::DistSamplerOptions::DefaultSampler().c_str() );
ROOT::Math::DistSamplerOptions::SetDefaultSampler("Foam");
}
sampler = Factory::CreateDistSampler();
if (sampler == 0) {
Error("multidimSampling","Foam sampler is not available - exit ");
return;
}

sampler->SetFunction(*f,DIM);
sampler->SetRange(xmin,xmax);
bool ret = sampler->Init();

std::vector<double> data1(DIM*N);
double v[DIM];
TStopwatch w;

if (!ret) {
Error("Sampler::Init","Error initializing unuran sampler");
return;
}

input_line_55:8:64: error: cannot initialize an array element of type 'void *' with an rvalue of type 'const int *'
else if (i < 2*DIM) f->SetParName(i, name.Format("sig_%d",i-DIM+1) );
^~~
input_line_55:9:66: error: cannot initialize an array element of type 'void *' with an rvalue of type 'const int *'
else if (i < 2*DIM) f->SetParName(i, name.Format("sig_%d",i-2*DIM+1) );
^~~
input_line_55:25:25: error: cannot initialize an array element of type 'void *' with an rvalue of type 'const int *'
sampler->SetFunction(*f,DIM);
^~~


generate the data

In [6]:
w.Start();
for (int i = 0; i < N; ++i) {
sampler->Sample(v);
for (int j = 0; j < DIM; ++j)
data1[N*j + i]     = v[j];
}
w.Stop();
w.Print();

input_line_56:6:13: error: cannot initialize an array element of type 'void *' with an rvalue of type 'const int *'
data1[N*j + i]     = v[j];
^


fill tree with data

In [7]:
TFile * file = new TFile("multiDimSampling.root","RECREATE");
double x[DIM];
TTree * t1 = new TTree("t1","Tree from Unuran");
t1->Branch("x",x,"x[4]/D");
for (int i = 0; i < N; ++i) {
for (int j = 0; j < DIM; ++j) {
x[j] = data1[i+N*j];
}
t1->Fill();
}

input_line_57:8:22: error: cannot initialize an array element of type 'void *' with an rvalue of type 'const int *'
x[j] = data1[i+N*j];
^


plot the data

In [8]:
t1->Draw("x[0]:x[1]:x[2]:x[3]","","candle");
TCanvas * c2 = new TCanvas();
c2->Divide(3,2);
int ic=1;
c2->cd(ic++);
t1->Draw("x[0]:x[1]");
c2->cd(ic++);
t1->Draw("x[0]:x[2]");
c2->cd(ic++);
t1->Draw("x[0]:x[3]");
c2->cd(ic++);
t1->Draw("x[1]:x[2]");
c2->cd(ic++);
t1->Draw("x[1]:x[3]");
c2->cd(ic++);
t1->Draw("x[2]:x[3]");

t1->Write();
file->Close();

input_line_59:2:3: error: use of undeclared identifier 't1'
(t1->Draw("x[0]:x[1]:x[2]:x[3]", "", "candle"))
^
Error in <HandleInterpreterException>: Error evaluating expression (t1->Draw("x[0]:x[1]:x[2]:x[3]", "", "candle"))
Execution of your code was aborted.


Draw all canvases

In [9]:
gROOT->GetListOfCanvases()->Draw()