Import Geant4 7.0.0 source tree

2016-06-09 11:11:55 +02:00
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+//
+// ********************************************************************
+// * DISCLAIMER                                                       *
+// *                                                                  *
+// * The following disclaimer summarizes all the specific disclaimers *
+// * of contributors to this software. The specific disclaimers,which *
+// * govern, are listed with their locations in:                      *
+// *   http://cern.ch/geant4/license                                  *
+// *                                                                  *
+// * Neither the authors of this software system, nor their employing *
+// * institutes,nor the agencies providing financial support for this *
+// * work  make  any representation or  warranty, express or implied, *
+// * regarding  this  software system or assume any liability for its *
+// * use.                                                             *
+// *                                                                  *
+// * This  code  implementation is the  intellectual property  of the *
+// * GEANT4 collaboration.                                            *
+// * By copying,  distributing  or modifying the Program (or any work *
+// * based  on  the Program)  you indicate  your  acceptance of  this *
+// * statement, and all its terms.                                    *
+// ********************************************************************
+//
+
+#include <math.h>
+#include <string.h>
+#include "Gamma.hh"
+
+MyGamma::MyGamma(){}
+
+MyGamma::~MyGamma(){}
+
+
+
+//______________________________________________________________________________
+double MyGamma::Gamma(double z)
+{
+	// 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);
+}
+
+//______________________________________________________________________________
+double MyGamma::Gamma(double a,double x)
+{   // 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);
+}
+
+//______________________________________________________________________________
+double MyGamma::GamCf(double a,double x)
+{
+	// 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);
+}
+
+//______________________________________________________________________________
+double MyGamma::GamSer(double a,double x)
+{
+	// 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;
+}
+
+
+double MyGamma::LnGamma(double z)
+{
+	// 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;
+}