JMARKOV::JExperimentalIntegrator Class Reference

In this implementation of the JMarkovIntegrator interface, the sample distribution is built up out of correlated path vertices. More...

#include <JMarkovIntegrator.hh>

Inheritance diagram for JMARKOV::JExperimentalIntegrator:

Public Member Functions
	JExperimentalIntegrator (double _lambda)
	constructor. More...
	~JExperimentalIntegrator ()
vector< double >	integrate (int N, int nscat, JSourceModel *src, JScatteringModel *sm, JTargetModel *trg, double lambda_abs)
	Integrate with N samples. More...
vector< double >	dummy_integrate (int N, int nscat, JSourceModel *src, JScatteringModel *sm, JTargetModel *trg, double lambda_abs)
	Integrate a test function with N samples. More...
vector< JPhotonPath >	get_diagnostic_ensemble (int N, int nscat, JSourceModel *src, JScatteringModel *sm, JTargetModel *trg, double lambda_abs)
	Return photon paths generated with the generatePath method. More...

Protected Member Functions
JPosition3D	generatePosition (int nscat, int nv, double &winv)
	dummy implementation More...
JPhotonPath	generatePath (int nscat, double &winv, JPosition3D source_pos, JPosition3D target_pos)
JPosition3D	getFirstScatteringVertex (int nscat, JPosition3D src_pos, JPosition3D trg_pos, double &winv)
	recursive function to randomly generate the first scattering vertex for isotropic scattering from a source to a target More...
virtual JPhotonPath	generatePath (int nscat, double &winv)
	Generate a random photon path with a given number of scatterings. More...

Protected Attributes
JExpRsqInvGenerator	gen

Detailed Description

In this implementation of the JMarkovIntegrator interface, the sample distribution is built up out of correlated path vertices.

lambda is the effective length scale defined as:

1/lambda := 1/lambda_scat + 1/lambda_abs

Definition at line 633 of file JMarkovIntegrator.hh.

Constructor & Destructor Documentation

JMARKOV::JExperimentalIntegrator::JExperimentalIntegrator ( double  _lambda )

inline

constructor.

Definition at line 639 of file JMarkovIntegrator.hh.

: gen(_lambda) {}

JMARKOV::JExperimentalIntegrator::~JExperimentalIntegrator ( )

inline

Definition at line 641 of file JMarkovIntegrator.hh.

{}

Member Function Documentation

JPosition3D JMARKOV::JExperimentalIntegrator::generatePosition ( int  nscat, int  nv, double &  winv  )

inlineprotectedvirtual

dummy implementation

Implements JMARKOV::JMarkovIntegrator.

Definition at line 646 of file JMarkovIntegrator.hh.

                                                                    {
      return JPosition3D(0,0,0) ;
    } ;

JPhotonPath JMARKOV::JExperimentalIntegrator::generatePath ( int  nscat, double &  winv, JPosition3D  source_pos, JPosition3D  target_pos  )

inlineprotected

Definition at line 650 of file JMarkovIntegrator.hh.

                                                                                                        {
      JPhotonPath p(nscat) ;
      p.front() = source_pos ;
      p.back()  = target_pos ;
      double _winv = 1 ;

      for( int nv=1 ; nv<=nscat ; ++nv ) {
        double __winv ;
        p[nv] = getFirstScatteringVertex(nscat+1-nv,p[nv-1],p.back(),__winv ) ;
        _winv *= __winv ;
      }
      winv = _winv ;
      return p ;
    }

JPosition3D JMARKOV::JExperimentalIntegrator::getFirstScatteringVertex ( int  nscat, JPosition3D  src_pos, JPosition3D  trg_pos, double &  winv  )

inlineprotected

recursive function to randomly generate the first scattering vertex for isotropic scattering from a source to a target

Definition at line 671 of file JMarkovIntegrator.hh.

                                                                                                              {
      double _winv = 1 ;
      if( nscat == 0 ) {
        winv = 1 ;
        return trg_pos ;
      }
      if( gRandom->Integer(2) == 0 ) {
        src_pos = getFirstScatteringVertex(nscat-1,src_pos,trg_pos,_winv) ;
      }
      JPosition3D pos = gen.getPosition() ;
      winv = 1.0 / gen.getWeight(pos) ;
      return src_pos + pos ;
    }

vector< double > JMARKOV::JMarkovIntegrator::integrate ( int  N, int  nscat, JSourceModel *  src, JScatteringModel *  sm, JTargetModel *  trg, double  lambda_abs  )

inherited

Integrate with N samples.

Returns a vector with the contribution to the integral of each sample. The mean of those values is the estimate of the result of the integral, while the distribution itself can be used to estimate the stability of the result. In this distribution, you want to avoid

• long tails (because they make the result unstable)
• small contributions (because it means that parts of the parameter space are being oversampled, so it is less efficient) This can be achieved by tuning the sample distribution to the problem at hand.

Definition at line 130 of file JMarkovIntegrator.hh.

                                                                                                                                               {
    vector<double> contributions(N,-1) ;

    for( int i=0 ; i<N ; ++i ) {
      double winv ;
      JPhotonPath p = generatePath(nscat,winv) ;

      double rho = getPhotonPathProbabilityDensity(p,src,sm,trg,lambda_abs) ;
      contributions[i] = rho * winv ; 
    }
    return contributions ;
  }

vector< double > JMARKOV::JMarkovIntegrator::dummy_integrate ( int  N, int  nscat, JSourceModel *  src, JScatteringModel *  sm, JTargetModel *  trg, double  lambda_abs  )

inherited

Integrate a test function with N samples.

This can be used as a sanity check for derived classes of JMarkovIntegrator.

The integral should yield 1 when the complete relevant part of the volume is taken into account. If it does not, it may be a sign that the implementation is not correct.

Returns a vector with the contribution to the integral of each sample.

Definition at line 143 of file JMarkovIntegrator.hh.

                                                                                                                                                     {
    vector<double> contributions(N,-1) ;

    for( int i=0 ; i<N ; ++i ) {
      const double r = 10 ;
      double winv ;
      JPhotonPath p = generatePath(nscat,winv) ;
      double rho = 1.0/(4.0/3.0*M_PI*r*r*r) ;
      if( p[1].getLength()>r ) rho = 0 ;
      contributions[i] = rho * winv ; 
    }
    return contributions ;
  }

vector< JPhotonPath > JMARKOV::JMarkovIntegrator::get_diagnostic_ensemble ( int  N, int  nscat, JSourceModel *  src, JScatteringModel *  sm, JTargetModel *  trg, double  lambda_abs  )

inherited

Return photon paths generated with the generatePath method.

This can be used to identify the parts of parameter space that are over- or undersampled in a given problem so that the integrator may be optimized to handle those better.

Definition at line 157 of file JMarkovIntegrator.hh.

                                                                                                                                                                  {
    vector<JPhotonPath> paths ;

    for( int i=0 ; i<N ; ++i ) {
      double winv ;
      JPhotonPath p = generatePath(nscat,winv) ;
      paths.push_back(p) ;
    }
    return paths ;
  }

virtual JPhotonPath JMARKOV::JMarkovIntegrator::generatePath ( int  nscat, double &  winv  )

inlineprotectedvirtualinherited

Generate a random photon path with a given number of scatterings.

winv must be set to the inverted probability density to generate this particular path.

Definition at line 94 of file JMarkovIntegrator.hh.

                                                                {
      // this default implementation assumes that the vertex positions
      // are completely uncorrelated
      JPhotonPath p(nscat) ;
      double _winv = 1 ;
      for( int nv=0 ; nv<nscat+2 ; ++nv ) {
        double part_winv ;
        p[nv] = generatePosition( nscat, nv, part_winv ) ;
        _winv *= part_winv ;
      }
      winv = _winv ;
      return p ;
    }

Member Data Documentation

JExpRsqInvGenerator JMARKOV::JExperimentalIntegrator::gen

protected

Definition at line 685 of file JMarkovIntegrator.hh.

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

• JMarkovIntegrator.hh