MyGamma Class Reference

#include <Gamma.hh>

Collaboration diagram for MyGamma:

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

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

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

Detailed Description

Definition at line 46 of file Gamma.hh.

Constructor & Destructor Documentation

MyGamma()

MyGamma::MyGamma

(

)

Definition at line 37 of file Gamma.cc.

{}

~MyGamma()

MyGamma::~MyGamma

(

)

Definition at line 39 of file Gamma.cc.

{}

Member Function Documentation

Abs() [1/5]

static short MyGamma::Abs ( short  d )

inlinestaticprivate

Definition at line 62 of file Gamma.hh.

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

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Abs() [2/5]

static int MyGamma::Abs ( int  d )

inlinestaticprivate

Definition at line 63 of file Gamma.hh.

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

Abs() [3/5]

static long MyGamma::Abs ( long  d )

inlinestaticprivate

Definition at line 64 of file Gamma.hh.

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

Abs() [4/5]

static float MyGamma::Abs ( float  d )

inlinestaticprivate

Definition at line 65 of file Gamma.hh.

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

Abs() [5/5]

static double MyGamma::Abs ( double  d )

inlinestaticprivate

Definition at line 66 of file Gamma.hh.

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

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Exp()

static double MyGamma::Exp ( double  x )

inlinestaticprivate

Definition at line 69 of file Gamma.hh.

{ return std::exp(x); }

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GamCf()

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

private

Definition at line 76 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);
}

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Gamma() [1/2]

double MyGamma::Gamma

(

double

z

)

Definition at line 42 of file Gamma.cc.

{
  // Computation of gamma(z) for all z>0.
  //
  // The algorithm is based on the article by C.Lanczos [1] as denoted in
  // Numerical Recipes 2nd ed. on p. 207 (W.H.Press et al.).
  //
  // [1] C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86.
  //
  //--- Nve 14-nov-1998 UU-SAP Utrecht
  
  if (z<=0) return 0;
  
  double v = LnGamma(z);
  return std::exp(v);
}

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Gamma() [2/2]

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

Definition at line 60 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);
}

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GamSer()

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

private

Definition at line 116 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;
}

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LnGamma()

double MyGamma::LnGamma ( double  z )

staticprivate

Definition at line 147 of file Gamma.cc.

{
  // Computation of ln[gamma(z)] for all z>0.
  //
  // The algorithm is based on the article by C.Lanczos [1] as denoted in
  // Numerical Recipes 2nd ed. on p. 207 (W.H.Press et al.).
  //
  // [1] C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86.
  //
  // The accuracy of the result is better than 2e-10.
  //
  //--- Nve 14-nov-1998 UU-SAP Utrecht
  
  if (z<=0) return 0;
  
  // Coefficients for the series expansion
  double c[7] = { 2.5066282746310005, 76.18009172947146, -86.50532032941677
    ,24.01409824083091,  -1.231739572450155, 0.1208650973866179e-2
    ,-0.5395239384953e-5};
  
  double x   = z;
  double y   = x;
  double tmp = x+5.5;
  tmp = (x+0.5)*Log(tmp)-tmp;
  double ser = 1.000000000190015;
  for (int i=1; i<7; i++) {
    y   += 1;
    ser += c[i]/y;
  }
  double v = tmp+Log(c[0]*ser/x);
  return v;
}

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Log()

static double MyGamma::Log ( double  x )

inlinestaticprivate

Definition at line 68 of file Gamma.hh.

{ return std::log(x); }

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---

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

• Gamma.hh
• Gamma.cc