JMARKOV::JSourceTargetIntegrator Class Reference

In this implementation of the JMarkovIntegrator interface, the sample distribution is built up out of three components: More...

#include <JMarkovIntegrator.hh>

Inheritance diagram for JMARKOV::JSourceTargetIntegrator:

Public Member Functions
	JSourceTargetIntegrator (double Rsing, JPosition3D src_pos, JPosition3D trg_pos, double fraction_exp, double Lexp, double Rexp)
	constructor. More...
	~JSourceTargetIntegrator ()
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
virtual JPosition3D	generatePosition (int nscat, int nv, double &winv)
	Generate a random position for vertex nv. More...
virtual JPhotonPath	generatePath (int nscat, double &winv)
	Generate a random photon path with a given number of scatterings. More...

Protected Attributes
JExponentialGenerator	gen_exp
JSingularityGenerator	gen_s1
JSingularityGenerator	gen_s2
JGenerator *	gen_exp_shift
JTripleGenerator *	gen

Detailed Description

In this implementation of the JMarkovIntegrator interface, the sample distribution is built up out of three components:

• a 1/r^2 distribution centered around the source
• a 1/r^2 distribution centered around the target
• an exponential distribution around the point directly between the source and the target

Definition at line 582 of file JMarkovIntegrator.hh.

Constructor & Destructor Documentation

JMARKOV::JSourceTargetIntegrator::JSourceTargetIntegrator ( double  Rsing, JPosition3D  src_pos, JPosition3D  trg_pos, double  fraction_exp, double  Lexp, double  Rexp  )

inline

constructor.

Arguments:

• position of the source
• position of the target
• the fraction of points that is drawn from the exponential distribution
• the minimal radius of the exp. distr.
• the maximal radius of the exp. distr.
• the length parameter of the exp. distr.
• the maximal radius for the 1/r^2 distributions

Definition at line 597 of file JMarkovIntegrator.hh.

                                                                                                                                     : gen_exp(0,Rexp,Lexp), gen_s1(Rsing,src_pos), gen_s2(Rsing,trg_pos) {
      JPosition3D cnt_pos = 0.5*(src_pos+trg_pos) ;
      gen_exp_shift = new JShiftedGenerator(&gen_exp,cnt_pos) ;
      double fraction_sing = 0.5*(1-fraction_exp) ;
      gen = new JTripleGenerator( fraction_sing, &gen_s1, fraction_sing, &gen_s2, fraction_exp, gen_exp_shift ) ;
    }

JMARKOV::JSourceTargetIntegrator::~JSourceTargetIntegrator ( )

inline

Definition at line 604 of file JMarkovIntegrator.hh.

                               {
      delete gen_exp_shift ;
      delete gen ;
    }

Member Function Documentation

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

inlineprotectedvirtual

Generate a random position for vertex nv.

nv = 1 is the first scattering vertex, nv = 2 is the second scattering vertex etc.

So we require that 0 < nv <= nscat

winv has to be set to 1 over the probability density for this particular position. NOTE: this only works when the positions of each vertex are UNCORRELATED to each other (as in the default implementation of generatePath. If they are not, this method can be given a dummy implementation and be ignored.

Implements JMARKOV::JMarkovIntegrator.

Definition at line 611 of file JMarkovIntegrator.hh.

                                                                            {
      JPosition3D pos = gen->getPosition() ;
      winv = 1.0/gen->getWeight(pos) ;
      return 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

JExponentialGenerator JMARKOV::JSourceTargetIntegrator::gen_exp

protected

Definition at line 617 of file JMarkovIntegrator.hh.

JSingularityGenerator JMARKOV::JSourceTargetIntegrator::gen_s1

protected

Definition at line 618 of file JMarkovIntegrator.hh.

JSingularityGenerator JMARKOV::JSourceTargetIntegrator::gen_s2

protected

Definition at line 619 of file JMarkovIntegrator.hh.

JGenerator* JMARKOV::JSourceTargetIntegrator::gen_exp_shift

protected

Definition at line 620 of file JMarkovIntegrator.hh.

JTripleGenerator* JMARKOV::JSourceTargetIntegrator::gen

protected

Definition at line 621 of file JMarkovIntegrator.hh.

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

• JMarkovIntegrator.hh