multidimSampling.C

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/// \file
/// \ingroup tutorial_math
/// \notebook
/// Example of sampling a multi-dim distribution using the DistSampler class
/// NOTE: This tutorial must be run with ACLIC
///
/// \macro_image
/// \macro_code
///
/// \author Lorenzo Moneta

// function (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;
   }
};

// Use the Math namespace
using namespace ROOT::Math;

void multidimSampling() {


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

   double x0[] = {0,0,0,0};
   // for debugging
   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;
   }

   // generate the data
   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();

   // fill tree with data
   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();
   }

   // plot the data
   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();

}