Gabriele Cosmo
117 lines
4.0 KiB
C++
117 lines
4.0 KiB
C++
//
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// ********************************************************************
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// * DISCLAIMER *
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// * *
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// * The following disclaimer summarizes all the specific disclaimers *
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// * of contributors to this software. The specific disclaimers,which *
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// * govern, are listed with their locations in: *
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// * http://cern.ch/geant4/license *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. *
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// * *
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// * This code implementation is the intellectual property of the *
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// * GEANT4 collaboration. *
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// * By copying, distributing or modifying the Program (or any work *
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// * based on the Program) you indicate your acceptance of this *
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// * statement, and all its terms. *
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// ********************************************************************
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//
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//
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// $Id: G4GaussLaguerreQ.cc,v 1.4 2001/07/11 10:00:41 gunter Exp $
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// GEANT4 tag $Name: geant4-05-00 $
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//
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#include "G4GaussLaguerreQ.hh"
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// ------------------------------------------------------------
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//
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// Constructor for Gauss-Laguerre quadrature method: integral from zero to
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// infinity of pow(x,alpha)*exp(-x)*f(x). The value of nLaguerre sets the accuracy.
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// The constructor creates arrays fAbscissa[0,..,nLaguerre-1] and
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// fWeight[0,..,nLaguerre-1] .
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//
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G4GaussLaguerreQ::G4GaussLaguerreQ( function pFunction,
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G4double alpha,
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G4int nLaguerre )
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: G4VGaussianQuadrature(pFunction)
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{
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const G4double tolerance = 1.0e-10 ;
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const G4int maxNumber = 12 ;
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G4int i, j, k ;
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G4double newton=0.;
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G4double newton1, temp1, temp2, temp3, temp, cofi ;
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fNumber = nLaguerre ;
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fAbscissa = new G4double[fNumber] ;
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fWeight = new G4double[fNumber] ;
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for(i=1;i<=fNumber;i++) // Loop over the desired roots
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{
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if(i == 1)
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{
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newton = (1.0 + alpha)*(3.0 + 0.92*alpha)/(1.0 + 2.4*fNumber + 1.8*alpha) ;
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}
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else if(i == 2)
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{
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newton += (15.0 + 6.25*alpha)/(1.0 + 0.9*alpha + 2.5*fNumber) ;
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}
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else
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{
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cofi = i - 2 ;
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newton += ((1.0+2.55*cofi)/(1.9*cofi) + 1.26*cofi*alpha/(1.0+3.5*cofi))*
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(newton - fAbscissa[i-3])/(1.0 + 0.3*alpha) ;
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}
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for(k=1;k<=maxNumber;k++)
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{
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temp1 = 1.0 ;
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temp2 = 0.0 ;
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for(j=1;j<=fNumber;j++)
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{
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temp3 = temp2 ;
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temp2 = temp1 ;
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temp1 = ((2*j - 1 + alpha - newton)*temp2 - (j - 1 + alpha)*temp3)/j ;
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}
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temp = (fNumber*temp1 - (fNumber +alpha)*temp2)/newton ;
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newton1 = newton ;
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newton = newton1 - temp1/temp ;
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if(fabs(newton - newton1) <= tolerance)
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{
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break ;
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}
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}
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if(k > maxNumber)
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{
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G4Exception("Too many iterations in Gauss-Laguerre constructor") ;
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}
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fAbscissa[i-1] = newton ;
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fWeight[i-1] = -exp(GammaLogarithm(alpha + fNumber) -
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GammaLogarithm((G4double)fNumber))/(temp*fNumber*temp2) ;
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}
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}
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// -----------------------------------------------------------------
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//
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// Gauss-Laguerre method for integration of pow(x,alpha)*exp(-x)*pFunction(x)
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// from zero up to infinity. pFunction is evaluated in fNumber points for which
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// fAbscissa[i] and fWeight[i] arrays were created in
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// G4VGaussianQuadrature(double,int) constructor
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G4double
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G4GaussLaguerreQ::Integral() const
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{
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G4int i ;
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G4double integral = 0.0 ;
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for(i=0;i<fNumber;i++)
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{
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integral += fWeight[i]*fFunction(fAbscissa[i]) ;
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}
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return integral ;
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}
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