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JMARKOV::JMarkovIntegrator Class Referenceabstract

Abstract base class for calculating the total probability (/m^2 target cross-section) for a photon from the source to hit the target (with a given, fixed number of scatterings) by Monte Carlo sampling the available nscat*3 dimensional phase space. More...

#include <JMarkovIntegrator.hh>

Inheritance diagram for JMARKOV::JMarkovIntegrator:
JMARKOV::JExperimentalIntegrator JMARKOV::JMarkovEnsembleIntegrator JMARKOV::JMarkovUniformIntegrator JMARKOV::JSourceTargetIntegrator JMARKOV::JMarkovEnsembleIntegrator1D JMARKOV::JMarkovEnsembleIntegrator3D

Public Member Functions

 JMarkovIntegrator ()
 standard constructor More...
 
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

virtual JPhotonPath generatePath (int nscat, double &winv)
 Generate a random photon path with a given number of scatterings. More...
 
virtual JPosition3D generatePosition (int nscat, int nv, double &winv)=0
 Generate a random position for vertex nv. More...
 

Detailed Description

Abstract base class for calculating the total probability (/m^2 target cross-section) for a photon from the source to hit the target (with a given, fixed number of scatterings) by Monte Carlo sampling the available nscat*3 dimensional phase space.

The sample distribution is implemented in derived classes.

Random numbers are drawn from gRandom.

Definition at line 39 of file JMarkovIntegrator.hh.

Constructor & Destructor Documentation

JMARKOV::JMarkovIntegrator::JMarkovIntegrator ( )
inline

standard constructor

Definition at line 43 of file JMarkovIntegrator.hh.

43 {}

Member Function Documentation

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

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 
)

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:779
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 
)

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 
)
inlineprotectedvirtual

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.
virtual JPosition3D JMARKOV::JMarkovIntegrator::generatePosition ( int  nscat,
int  nv,
double &  winv 
)
protectedpure virtual

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.

Implemented in JMARKOV::JExperimentalIntegrator, JMARKOV::JSourceTargetIntegrator, JMARKOV::JMarkovEnsembleIntegrator, and JMARKOV::JMarkovUniformIntegrator.


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