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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:
JMARKOV::JMarkovIntegrator

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< JPhotonPathget_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.

639 : gen(_lambda) {}
JMARKOV::JExperimentalIntegrator::~JExperimentalIntegrator ( )
inline

Definition at line 641 of file JMarkovIntegrator.hh.

641 {}

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.

646  {
647  return JPosition3D(0,0,0) ;
648  } ;
JPhotonPath JMARKOV::JExperimentalIntegrator::generatePath ( int  nscat,
double &  winv,
JPosition3D  source_pos,
JPosition3D  target_pos 
)
inlineprotected

Definition at line 650 of file JMarkovIntegrator.hh.

650  {
651  JPhotonPath p(nscat) ;
652  p.front() = source_pos ;
653  p.back() = target_pos ;
654  double _winv = 1 ;
655 
656  for( int nv=1 ; nv<=nscat ; ++nv ) {
657  double __winv ;
658  p[nv] = getFirstScatteringVertex(nscat+1-nv,p[nv-1],p.back(),__winv ) ;
659  _winv *= __winv ;
660  }
661  winv = _winv ;
662  return p ;
663  }
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 s...
A photon path.
Definition: JPhotonPath.hh:38
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.

671  {
672  double _winv = 1 ;
673  if( nscat == 0 ) {
674  winv = 1 ;
675  return trg_pos ;
676  }
677  if( gRandom->Integer(2) == 0 ) {
678  src_pos = getFirstScatteringVertex(nscat-1,src_pos,trg_pos,_winv) ;
679  }
680  JPosition3D pos = gen.getPosition() ;
681  winv = 1.0 / gen.getWeight(pos) ;
682  return src_pos + pos ;
683  }
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 s...
double getWeight(JPosition3D pos)
return the weight (=probability density dP/dV) for the given position.
JPosition3D getPosition()
Return a randomly generated position.
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.

130  {
131  vector<double> contributions(N,-1) ;
132 
133  for( int i=0 ; i<N ; ++i ) {
134  double winv ;
135  JPhotonPath p = generatePath(nscat,winv) ;
136 
137  double rho = getPhotonPathProbabilityDensity(p,src,sm,trg,lambda_abs) ;
138  contributions[i] = rho * winv ;
139  }
140  return contributions ;
141  }
A photon path.
Definition: JPhotonPath.hh:38
then JShowerPostfit f $INPUT_FILE o $OUTPUT_FILE N
virtual JPhotonPath generatePath(int nscat, double &winv)
Generate a random photon path with a given number of scatterings.
double getPhotonPathProbabilityDensity(JPhotonPath &p, JSourceModel *src, JScatteringModel *sm, JTargetModel *trg, double lambda_abs)
Return the probability density for a photon path with the given ingredients.
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.

143  {
144  vector<double> contributions(N,-1) ;
145 
146  for( int i=0 ; i<N ; ++i ) {
147  const double r = 10 ;
148  double winv ;
149  JPhotonPath p = generatePath(nscat,winv) ;
150  double rho = 1.0/(4.0/3.0*M_PI*r*r*r) ;
151  if( p[1].getLength()>r ) rho = 0 ;
152  contributions[i] = rho * winv ;
153  }
154  return contributions ;
155  }
A photon path.
Definition: JPhotonPath.hh:38
then JShowerPostfit f $INPUT_FILE o $OUTPUT_FILE N
data_type r[M+1]
Definition: JPolint.hh:758
virtual JPhotonPath generatePath(int nscat, double &winv)
Generate a random photon path with a given number of scatterings.
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.

157  {
158  vector<JPhotonPath> paths ;
159 
160  for( int i=0 ; i<N ; ++i ) {
161  double winv ;
162  JPhotonPath p = generatePath(nscat,winv) ;
163  paths.push_back(p) ;
164  }
165  return paths ;
166  }
A photon path.
Definition: JPhotonPath.hh:38
then JShowerPostfit f $INPUT_FILE o $OUTPUT_FILE N
virtual JPhotonPath generatePath(int nscat, double &winv)
Generate a random photon path with a given number of scatterings.
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.

94  {
95  // this default implementation assumes that the vertex positions
96  // are completely uncorrelated
97  JPhotonPath p(nscat) ;
98  double _winv = 1 ;
99  for( int nv=0 ; nv<nscat+2 ; ++nv ) {
100  double part_winv ;
101  p[nv] = generatePosition( nscat, nv, part_winv ) ;
102  _winv *= part_winv ;
103  }
104  winv = _winv ;
105  return p ;
106  }
A photon path.
Definition: JPhotonPath.hh:38
virtual JPosition3D generatePosition(int nscat, int nv, double &winv)=0
Generate a random position for vertex nv.

Member Data Documentation

JExpRsqInvGenerator JMARKOV::JExperimentalIntegrator::gen
protected

Definition at line 685 of file JMarkovIntegrator.hh.


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