MyGamma Class Reference

#include <Gamma.hh>

Public Member Functions
double	Gamma (double a, double x)
double	Gamma (double z)
	MyGamma ()
	~MyGamma ()

Private Member Functions
double	GamCf (double a, double x)
double	GamSer (double a, double x)

Static Private Member Functions
static double	Abs (double d)
static float	Abs (float d)
static int	Abs (int d)
static long	Abs (long d)
static short	Abs (short d)
static double	Exp (double x)
static double	LnGamma (double z)
static double	Log (double x)

Detailed Description

Definition at line 45 of file Gamma.hh.

Constructor & Destructor Documentation

MyGamma()

MyGamma::MyGamma

(

)

Definition at line 36 of file Gamma.cc.

{}

~MyGamma()

MyGamma::~MyGamma

(

)

Definition at line 38 of file Gamma.cc.

{}

Member Function Documentation

Abs() [1/5]

static double MyGamma::Abs ( double  d )

inlinestaticprivate

Definition at line 65 of file Gamma.hh.

{ return (d > 0) ? d : -d; }

Abs() [2/5]

static float MyGamma::Abs ( float  d )

inlinestaticprivate

Definition at line 64 of file Gamma.hh.

{ return (d > 0) ? d : -d; }

Abs() [3/5]

static int MyGamma::Abs ( int  d )

inlinestaticprivate

Definition at line 62 of file Gamma.hh.

{ return (d > 0) ? d : -d; }

Abs() [4/5]

static long MyGamma::Abs ( long  d )

inlinestaticprivate

Definition at line 63 of file Gamma.hh.

{ return (d > 0) ? d : -d; }

Abs() [5/5]

static short MyGamma::Abs ( short  d )

inlinestaticprivate

Definition at line 61 of file Gamma.hh.

{ return (d > 0) ? d : -d; }

Referenced by GamCf(), and GamSer().

Exp()

static double MyGamma::Exp ( double  x )

inlinestaticprivate

Definition at line 68 of file Gamma.hh.

{ return std::exp(x); }

Referenced by GamCf(), and GamSer().

GamCf()

double MyGamma::GamCf ( double  a, double  x  )

private

Definition at line 66 of file Gamma.cc.

{
  // Computation of the incomplete gamma function P(a,x)
  // via its continued fraction representation.
  //
  // The algorithm is based on the formulas and code as denoted in
  // Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).
  //
  //--- Nve 14-nov-1998 UU-SAP Utrecht
  
  int itmax    = 100;      // Maximum number of iterations
  double eps   = 3.e-7;    // Relative accuracy
  double fpmin = 1.e-30;   // Smallest double value allowed here
  
  if (a <= 0 || x <= 0) return 0;
  
  double gln = LnGamma(a);
  double b   = x+1-a;
  double c   = 1/fpmin;
  double d   = 1/b;
  double h   = d;
  double an,del;
  for (int i=1; i<=itmax; i++) {
    an = double(-i)*(double(i)-a);
    b += 2;
    d  = an*d+b;
    if (Abs(d) < fpmin) d = fpmin;
    c = b+an/c;
    if (Abs(c) < fpmin) c = fpmin;
    d   = 1/d;
    del = d*c;
    h   = h*del;
    if (Abs(del-1) < eps) break;
    //if (i==itmax) cout << "*GamCf(a,x)* a too large or itmax too small" << endl;
  }
  double v = Exp(-x+a*Log(x)-gln)*h;
  return (1-v);
}

References Abs(), G4InuclParticleNames::an, eps, Exp(), LnGamma(), and Log().

Referenced by Gamma().

Gamma() [1/2]

double MyGamma::Gamma	(	double	a,
		double	x
	)

Definition at line 50 of file Gamma.cc.

{
  // Computation of the incomplete gamma function P(a,x)
  //
  // The algorithm is based on the formulas and code as denoted in
  // Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).
  //
  //--- Nve 14-nov-1998 UU-SAP Utrecht
  
  if (a <= 0 || x <= 0) return 0;
  
  if (x < (a+1)) return GamSer(a,x);
  else           return GamCf(a,x);
}

References GamCf(), and GamSer().

Gamma() [2/2]

double MyGamma::Gamma

(

double

z

)

Definition at line 41 of file Gamma.cc.

{
  if (z <= 0)
      return 0;
 
  return std::tgamma(z);
}

Referenced by GVFlashShowerParameterisation::gam().

GamSer()

double MyGamma::GamSer ( double  a, double  x  )

private

Definition at line 106 of file Gamma.cc.

{
  // Computation of the incomplete gamma function P(a,x)
  // via its series representation.
  //
  // The algorithm is based on the formulas and code as denoted in
  // Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).
  //
  //--- Nve 14-nov-1998 UU-SAP Utrecht
  
  int itmax  = 100;   // Maximum number of iterations
  double eps = 3.e-7; // Relative accuracy
  
  if (a <= 0 || x <= 0) return 0;
  
  double gln = LnGamma(a);
  double ap  = a;
  double sum = 1/a;
  double del = sum;
  for (int n=1; n<=itmax; n++) {
    ap  += 1;
    del  = del*x/ap;
    sum += del;
    if (MyGamma::Abs(del) < Abs(sum*eps)) break;
    //if (n==itmax) cout << "*GamSer(a,x)* a too large or itmax too small" << endl;
  }
  double v = sum*Exp(-x+a*Log(x)-gln);
  return v;
}

References Abs(), G4InuclParticleNames::ap, eps, Exp(), LnGamma(), Log(), and CLHEP::detail::n.

Referenced by Gamma().

LnGamma()

double MyGamma::LnGamma ( double  z )

staticprivate

Definition at line 137 of file Gamma.cc.

{
  if (z <= 0)
      return 0;
 
  return std::lgamma(z);
}

Referenced by GamCf(), and GamSer().

Log()

static double MyGamma::Log ( double  x )

inlinestaticprivate

Definition at line 67 of file Gamma.hh.

{ return std::log(x); }

Referenced by GamCf(), and GamSer().

---

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

• source/parameterisations/gflash/include/Gamma.hh
• source/parameterisations/gflash/src/Gamma.cc