JMARKOV::JExponentialGenerator Class Reference

Implementation of the JGenerator interface. More...

#include <JMarkovGenerator.hh>

Inheritance diagram for JMARKOV::JExponentialGenerator:

Public Member Functions
	JExponentialGenerator (double _r1, double _r2, double _L)
	Constructor. More...
double	getWeight (JPosition3D pos)
	return the weight (=probability density dP/dV) for the given position. More...
JPosition3D	getPosition ()
	Return a randomly generated position. More...
double	getR ()
double	getWeight (double r)

Protected Member Functions
double	getIntegrand (double r)
double	getInvertedIntegrand (double x)
	return value y such that getIntegrand(y) = x More...

Protected Attributes
double	r1
double	r2
double	L
double	C
double	ximin
double	ximax

Detailed Description

Implementation of the JGenerator interface.

Generates positions according to an exponential distribution, around the origin, i.e. with probability density

rho( vec x ) = alpha * exp(-r/l)

for given l. The minimal and maximal values of r are given by r1 and r2, respectively.

Definition at line 276 of file JMarkovGenerator.hh.

Constructor & Destructor Documentation

JMARKOV::JExponentialGenerator::JExponentialGenerator ( double  _r1, double  _r2, double  _L  )

inline

Constructor.

_r1 and _r2 are the minimal and maximal allowed value of r. _L is the length scale.

Definition at line 285 of file JMarkovGenerator.hh.

                                                               :
      r1(_r1), r2(_r2), L(_L) 
    {
      // normalization factor
      ximin = getIntegrand(r1) ;
      ximax = getIntegrand(r2) ;
      C = ximax-ximin ;
    }

Member Function Documentation

double JMARKOV::JExponentialGenerator::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 294 of file JMarkovGenerator.hh.

                                        {
      return getWeight( pos.getLength() ) ;
    }

JPosition3D JMARKOV::JExponentialGenerator::getPosition ( )

inlinevirtual

Return a randomly generated position.

Implements JMARKOV::JGenerator.

Definition at line 298 of file JMarkovGenerator.hh.

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

double JMARKOV::JExponentialGenerator::getR ( )

inline

Definition at line 305 of file JMarkovGenerator.hh.

                  {
      // generate integrand value
      double xi = gRandom->Uniform(ximin,ximax) ;
      // find matching value of r
      return getInvertedIntegrand(xi) ;
    }

double JMARKOV::JExponentialGenerator::getWeight ( double  r )

inline

Definition at line 312 of file JMarkovGenerator.hh.

                                 {
      return exp(-r/L) / C ;
    }

double JMARKOV::JExponentialGenerator::getIntegrand ( double  r )

inlineprotected

Definition at line 319 of file JMarkovGenerator.hh.

                                    {
      return -4*M_PI*L*exp(-r/L)*(2*L*L+2*L*r+r*r) ;
    }

double JMARKOV::JExponentialGenerator::getInvertedIntegrand ( double  x )

inlineprotected

return value y such that getIntegrand(y) = x

Definition at line 324 of file JMarkovGenerator.hh.

                                            {
      const double precision = 1e-10 ;
      // using the bisection algorithm
      double rl = r1 ;
      double vl = getIntegrand(rl)-x ;
      double rr = r2 ;
      double vr = getIntegrand(rr)-x ;
      double rc ;
      double vc ;

      while( rr-rl > precision ) {
        rc = 0.5*(rl+rr) ;
        vc = getIntegrand(rc)-x ;
        if( (vc>0) == (vr>0) ) {
          // must be in left half
          rr = rc ;
          vr = vc ;
        } else {
          // must be in right half
          rl = rc ;
          vl = vc ;
        }
      }
      return rc ;
    }

Member Data Documentation

double JMARKOV::JExponentialGenerator::r1

protected

Definition at line 350 of file JMarkovGenerator.hh.

double JMARKOV::JExponentialGenerator::r2

protected

Definition at line 351 of file JMarkovGenerator.hh.

double JMARKOV::JExponentialGenerator::L

protected

Definition at line 352 of file JMarkovGenerator.hh.

double JMARKOV::JExponentialGenerator::C

protected

Definition at line 353 of file JMarkovGenerator.hh.

double JMARKOV::JExponentialGenerator::ximin

protected

Definition at line 354 of file JMarkovGenerator.hh.

double JMARKOV::JExponentialGenerator::ximax

protected

Definition at line 355 of file JMarkovGenerator.hh.

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

• JMarkovGenerator.hh