JMARKOV::JMagicalDistribution Class Reference

The 'magical distributions' are a class of distributions. More...

#include <JMarkovGenerator.hh>

Inheritance diagram for JMARKOV::JMagicalDistribution:

Public Member Functions
	JMagicalDistribution (unsigned int _N, double _lambda)
	~JMagicalDistribution ()
JPosition3D	getPosition ()
	Return a randomly generated position.
double	getWeight (JPosition3D pos)
	return the weight (=probability density dP/dV) for the given position.

Protected Attributes
unsigned int	N
double	lambda
JExpRsqInvGenerator	gen
TH1F *	h

Detailed Description

The 'magical distributions' are a class of distributions.

The magical distribution of degree N is the distribution of the distance to the origin after taking N random steps where the step size r is drawn from an "exponential inverse r-squared" 1/r^2 exp(-r/lambda) distribution, which is the base behaviour for scattering

Note that it seems to satisfy the property (for lambda = 1 ) mean = -0.5 + sqrt( (1+8*n)/4 )

Definition at line 192 of file JMarkovGenerator.hh.

Constructor & Destructor Documentation

JMagicalDistribution()

JMARKOV::JMagicalDistribution::JMagicalDistribution ( unsigned int _N, double _lambda )

inline

Definition at line 196 of file JMarkovGenerator.hh.

                                                            : N(_N), lambda(_lambda), gen(1) {
      const int nbins = 1000 ;
      const double xmax = 100 ;
      const int nsamples = 10000000 ;
      h = new TH1F("h","",nbins,0,xmax) ;
      for( int i=0 ; i<nsamples ; ++i ) {
        JPosition3D pos = gen.getPosition() ;
        for( unsigned int n=1 ; n<N ; ++n ) pos += gen.getPosition() ;
        double r = pos.getLength() ;
        h->Fill(r) ;
      }
      h->Scale( 1.0/h->Integral("width") ) ;
    }

~JMagicalDistribution()

JMARKOV::JMagicalDistribution::~JMagicalDistribution ( )

inline

Definition at line 210 of file JMarkovGenerator.hh.

                            {
      delete h ;
    }

Member Function Documentation

getPosition()

JPosition3D JMARKOV::JMagicalDistribution::getPosition ( )

inlinevirtual

Return a randomly generated position.

Implements JMARKOV::JGenerator.

Definition at line 214 of file JMarkovGenerator.hh.

                              {
      double r = h->GetRandom() ;
      double x,y,z ;
      gRandom->Sphere(x,y,z,r) ;
      return JPosition3D(x,y,z) ;
    }

getWeight()

double JMARKOV::JMagicalDistribution::getWeight ( JPosition3D pos )

inlinevirtual

return the weight (=probability density dP/dV) for the given position.

When the generator is properly normalized, the integral of this quantity over the whole space is 1.

Implements JMARKOV::JGenerator.

Definition at line 221 of file JMarkovGenerator.hh.

                                        {
      double r =  pos.getLength() ;
      Int_t bin = h->FindBin(r) ;
      return h->GetBinContent(bin)/(r*r) ;
    }

Member Data Documentation

N

unsigned int JMARKOV::JMagicalDistribution::N

protected

Definition at line 229 of file JMarkovGenerator.hh.

lambda

double JMARKOV::JMagicalDistribution::lambda

protected

Definition at line 230 of file JMarkovGenerator.hh.

gen

JExpRsqInvGenerator JMARKOV::JMagicalDistribution::gen

protected

Definition at line 231 of file JMarkovGenerator.hh.

h

TH1F* JMARKOV::JMagicalDistribution::h

protected

Definition at line 232 of file JMarkovGenerator.hh.

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The documentation for this class was generated from the following file:

• JMarkovGenerator.hh