HankelFunction.cc File Reference

#include <TMath.h>
#include "GeneratorInterface/Hydjet2Interface/interface/HankelFunction.h"

Go to the source code of this file.

Enumerations
enum	{ kNe = 2, kNCoeff = 9 }

Functions
double	BesselI0 (double x)
double	BesselI1 (double x)
double	HankelK0 (double x)
double	HankelK1 (double x)
double	HankelKn (int n, double x)

Variables
const double	i0Coefficient [kNCoeff][kNe]
const double	i1Coefficient [kNCoeff][kNe]
const double	k0Coefficient [kNCoeff][kNe]
const double	k1Coefficient [kNCoeff][kNe]

Enumeration Type Documentation

anonymous enum

Enumerator
kNe
kNCoeff

Definition at line 14 of file HankelFunction.cc.

{kNe = 2, kNCoeff = 9};

Function Documentation

double BesselI0

(

double

x

)

Definition at line 72 of file HankelFunction.cc.

References Abs(), create_public_lumi_plots::ax, i0Coefficient, p1, p2, p3, p4, q1, q2, and detailsBasic3DVector::y.

Referenced by gen::Hydjet2Hadronizer::CharmEnhancementFactor(), and HankelK0().

                          { 
  //  (C) Copr. 1986-92 Numerical Recipes Software +7.
  //compute Bessel function of zeroth order
  
  const double p1 = i0Coefficient[0][0];
  const double p2 = i0Coefficient[1][0];
  const double p3 = i0Coefficient[2][0];
  const double p4 = i0Coefficient[3][0];
  const double p5 = i0Coefficient[4][0];
  const double p6 = i0Coefficient[5][0];
  const double p7 = i0Coefficient[6][0];
  
  const double q1 = i0Coefficient[0][1];
  const double q2 = i0Coefficient[1][1];
  const double q3 = i0Coefficient[2][1];
  const double q4 = i0Coefficient[3][1];
  const double q5 = i0Coefficient[4][1];
  const double q6 = i0Coefficient[5][1];
  const double q7 = i0Coefficient[6][1];
  const double q8 = i0Coefficient[7][1];
  const double q9 = i0Coefficient[8][1];

  double i0 = 0.;

  if(TMath::Abs(x) < 3.75) {
    double y = (x / 3.75) * (x / 3.75);
    i0 =  p1 + y * (p2 + y * (p3 + y * (p4 + y * (p5 + y * (p6 + y * p7)))));
  } 
  else {
    double ax = TMath::Abs(x);
    double y = 3.75 / ax;
    i0 = (TMath::Exp(ax)/TMath::Sqrt(ax))*(q1 + y*(q2 + y*(q3 + y*(q4 + y*(q5 + y*(q6 + y*(q7 + y*(q8 + y*q9))))))));
  }
  
  return i0;
}

double BesselI1

(

double

x

)

Definition at line 109 of file HankelFunction.cc.

References Abs(), create_public_lumi_plots::ax, i1Coefficient, p1, p2, p3, p4, q1, q2, and detailsBasic3DVector::y.

Referenced by gen::Hydjet2Hadronizer::CharmEnhancementFactor(), and HankelK1().

                          {
  //  (C) Copr. 1986-92 Numerical Recipes Software +7.
  //compute Bessel function of first order

  const double p1 = i1Coefficient[0][0];
  const double p2 = i1Coefficient[1][0];
  const double p3 = i1Coefficient[2][0];
  const double p4 = i1Coefficient[3][0];
  const double p5 = i1Coefficient[4][0];
  const double p6 = i1Coefficient[5][0];
  const double p7 = i1Coefficient[6][0];

  const double q1 = i1Coefficient[0][1];
  const double q2 = i1Coefficient[1][1];
  const double q3 = i1Coefficient[2][1];
  const double q4 = i1Coefficient[3][1];
  const double q5 = i1Coefficient[4][1];
  const double q6 = i1Coefficient[5][1];
  const double q7 = i1Coefficient[6][1];
  const double q8 = i1Coefficient[7][1];
  const double q9 = i1Coefficient[8][1];

  double i1 = 0.;

  if (TMath::Abs(x) < 3.75) {
    double y = (x / 3.75) * (x / 3.75);
    i1 = x * (p1 + y * (p2 + y * (p3 + y * (p4 + y * (p5 + y * (p6 + y * p7))))));
  } 
  else {
    double ax = TMath::Abs(x);
    double y = 3.75/ax;
    i1 = (TMath::Exp(ax)/TMath::Sqrt(ax))*(q1 + y*(q2 + y*(q3 + y*(q4 + y*(q5 + y*(q6 + y*(q7 + y*(q8 + y*q9))))))));
    if(x < 0.) i1 = -i1;
  }

  return i1;
}

double HankelK0

(

double

x

)

Definition at line 147 of file HankelFunction.cc.

References BesselI0(), SiStripMonitorClusterAlca_cfi::k0, k0Coefficient, p1, p2, p3, p4, q1, q2, x, and detailsBasic3DVector::y.

Referenced by HankelKn().

                          { 
  const double p1 = k0Coefficient[0][0];
  const double p2 = k0Coefficient[1][0];
  const double p3 = k0Coefficient[2][0];
  const double p4 = k0Coefficient[3][0];
  const double p5 = k0Coefficient[4][0];
  const double p6 = k0Coefficient[5][0];
  const double p7 = k0Coefficient[6][0];

  const double q1 = k0Coefficient[0][1];
  const double q2 = k0Coefficient[1][1];
  const double q3 = k0Coefficient[2][1];
  const double q4 = k0Coefficient[3][1];
  const double q5 = k0Coefficient[4][1];
  const double q6 = k0Coefficient[5][1];
  const double q7 = k0Coefficient[6][1];

  double k0 = 0.;
  if(x <= 2.0) {
    double y = x * x / 4.0;
    k0 = (-TMath::Log(x/2.0)*BesselI0(x)) + (p1 + y*(p2 + y*(p3 + y*(p4 + y*(p5 + y*(p6 + y*p7))))));
  } 
  else {
    double y = (2.0 / x);
    k0 = (TMath::Exp(-x)/TMath::Sqrt(x))*(q1 + y*(q2 + y*(q3 + y*(q4 + y*(q5 + y*(q6 + y*q7))))));
  }

  return k0;
}

double HankelK1

(

double

x

)

Definition at line 177 of file HankelFunction.cc.

References BesselI1(), k1Coefficient, p1, p2, p3, p4, q1, q2, x, and detailsBasic3DVector::y.

Referenced by HankelKn(), and GrandCanonical::ParticleEnergyDensity().

                          { 
  //  (C) Copr. 1986-92 Numerical Recipes Software +7.
  // compute modified Hankel function of the first order
  const double p1 = k1Coefficient[0][0];
  const double p2 = k1Coefficient[1][0];
  const double p3 = k1Coefficient[2][0];
  const double p4 = k1Coefficient[3][0];
  const double p5 = k1Coefficient[4][0];
  const double p6 = k1Coefficient[5][0];
  const double p7 = k1Coefficient[6][0];

  const double q1 = k1Coefficient[0][1];
  const double q2 = k1Coefficient[1][1];
  const double q3 = k1Coefficient[2][1];
  const double q4 = k1Coefficient[3][1];
  const double q5 = k1Coefficient[4][1];
  const double q6 = k1Coefficient[5][1];
  const double q7 = k1Coefficient[6][1];

  double k1 = 0.;

  if(x <= 2.0) { 
    double y = x * x / 4.0;
    k1 = (TMath::Log(x/2.0)*BesselI1(x)) + (1.0/x)*(p1 + y*(p2 + y*(p3 + y*(p4 + y*(p5 + y*(p6 + y*p7))))));
  } 
  else {
    double y = 2.0 / x;
    k1 = (TMath::Exp(-x)/TMath::Sqrt(x))*(q1 + y*(q2 + y*(q3 + y*(q4 + y*(q5 + y*(q6 + y*q7))))));
  }

  return k1;
}

double HankelKn	(	int	n,
		double	x
	)

Definition at line 210 of file HankelFunction.cc.

References trackerHits::c, HankelK0(), HankelK1(), gen::k, kp, and x.

Referenced by GrandCanonical::ParticleEnergyDensity(), NAStrangeDensity::ParticleNumberDensity(), and GrandCanonical::ParticleNumberDensity().

                                 {
  //  (C) Copr. 1986-92 Numerical Recipes Software +7.
  // compute modified Hankel function of the first order
  if(n < 2) throw "Bad argument n in Kn";

  double tox = 2.0 / x;
  double km = HankelK0(x);
  double k = HankelK1(x);
  double kp = 0.;
  
  for(int c = 1; c <= n-1; ++c) {
    kp = km + c * tox * k;
    km = k;
    k = kp;
  }

  return k;
}

Variable Documentation

const double i0Coefficient[kNCoeff][kNe]

Initial value:

= 
  {
    
    {1.0,        0.39894228},
    {3.5156229,  0.01328592},
    {3.0899424,  0.00225319},
    {1.2067492, -0.00157565},
    {0.2659732,  0.00916281},
    {0.0360768, -0.02057706},
    {0.0045813,  0.02635537},
    {0.,        -0.01647633},
    {0.,         0.00392377}
  }

Definition at line 16 of file HankelFunction.cc.

Referenced by BesselI0().

const double i1Coefficient[kNCoeff][kNe]

Initial value:

=
  {
    
    {0.5,         0.39894228},
    {0.87890594, -0.03988024},
    {0.51498869, -0.00362018},
    {0.15084934,  0.00163801},
    {0.02658733, -0.01031555},
    {0.00301532,  0.02282967},
    {0.00032411, -0.02895312},
    {0.,          0.01787654},
    {0.,         -0.00420059}
  }

Definition at line 30 of file HankelFunction.cc.

Referenced by BesselI1().

const double k0Coefficient[kNCoeff][kNe]

Initial value:

=
  {
    
    {-0.57721566, 1.25331414},   
    {0.42278420, -0.07832358}, 
    {0.23069756,  0.02189568}, 
    {0.03488590, -0.01062446}, 
    {0.00262698,  0.00587872}, 
    {0.00010750, -0.00251540}, 
    {0.0000074,   0.00053208}, 
    {0.,          0.        }, 
    {0.,          0.        }
  }

Definition at line 44 of file HankelFunction.cc.

Referenced by HankelK0().

const double k1Coefficient[kNCoeff][kNe]

Initial value:

=
  {
    
    {1.0,          1.25331414},   
    {0.15443144,   0.23498619}, 
    {-0.67278579, -0.03655620}, 
    {-0.18156897,  0.01504268}, 
    {-0.01919402, -0.00780353}, 
    {-0.00110404,  0.00325614}, 
    {-0.00004686, -0.00068245}, 
    { 0.,          0.        }, 
    { 0.,          0.        }
  }

Definition at line 58 of file HankelFunction.cc.

Referenced by HankelK1().