Gabriele Cosmo
237 lines
11 KiB
C++
237 lines
11 KiB
C++
//
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// ********************************************************************
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// * License and Disclaimer *
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// * *
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// * The Geant4 software is copyright of the Copyright Holders of *
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// * the Geant4 Collaboration. It is provided under the terms and *
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// * conditions of the Geant4 Software License, included in the file *
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// * LICENSE and available at http://cern.ch/geant4/license . These *
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// * include a list of copyright holders. *
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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. Please see the license in the file LICENSE and URL above *
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// * for the full disclaimer and the limitation of liability. *
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// * *
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// * This code implementation is the result of the scientific and *
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// * technical work of the GEANT4 collaboration. *
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// * By using, copying, modifying or distributing the software (or *
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// * any work based on the software) you agree to acknowledge its *
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// * use in resulting scientific publications, and indicate your *
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// * acceptance of all terms of the Geant4 Software license. *
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// ********************************************************************
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//
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//
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// $Id: G4GaussLegendreQ.cc 69546 2013-05-08 09:50:34Z gcosmo $
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//
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#include "G4GaussLegendreQ.hh"
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#include "G4PhysicalConstants.hh"
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G4GaussLegendreQ::G4GaussLegendreQ( function pFunction )
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: G4VGaussianQuadrature(pFunction)
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{
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}
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// --------------------------------------------------------------------------
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//
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// Constructor for GaussLegendre quadrature method. The value nLegendre sets
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// the accuracy required, i.e the number of points where the function pFunction
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// will be evaluated during integration. The constructor creates the arrays for
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// abscissas and weights that are used in Gauss-Legendre quadrature method.
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// The values a and b are the limits of integration of the pFunction.
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// nLegendre MUST BE EVEN !!!
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G4GaussLegendreQ::G4GaussLegendreQ( function pFunction,
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G4int nLegendre )
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: G4VGaussianQuadrature(pFunction)
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{
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const G4double tolerance = 1.6e-10 ;
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G4int k = nLegendre ;
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fNumber = (nLegendre + 1)/2 ;
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if(2*fNumber != k)
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{
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G4Exception("G4GaussLegendreQ::G4GaussLegendreQ()", "InvalidCall",
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FatalException, "Invalid nLegendre argument !") ;
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}
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G4double newton0=0.0, newton1=0.0,
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temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0 ;
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fAbscissa = new G4double[fNumber] ;
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fWeight = new G4double[fNumber] ;
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for(G4int i=1;i<=fNumber;i++) // Loop over the desired roots
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{
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newton0 = std::cos(pi*(i - 0.25)/(k + 0.5)) ; // Initial root
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do // approximation
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{ // loop of Newton's method
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temp1 = 1.0 ;
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temp2 = 0.0 ;
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for(G4int j=1;j<=k;j++)
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{
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temp3 = temp2 ;
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temp2 = temp1 ;
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temp1 = ((2.0*j - 1.0)*newton0*temp2 - (j - 1.0)*temp3)/j ;
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}
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temp = k*(newton0*temp1 - temp2)/(newton0*newton0 - 1.0) ;
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newton1 = newton0 ;
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newton0 = newton1 - temp1/temp ; // Newton's method
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}
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while(std::fabs(newton0 - newton1) > tolerance) ;
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fAbscissa[fNumber-i] = newton0 ;
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fWeight[fNumber-i] = 2.0/((1.0 - newton0*newton0)*temp*temp) ;
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}
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}
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// --------------------------------------------------------------------------
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//
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// Returns the integral of the function to be pointed by fFunction between a
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// and b, by 2*fNumber point Gauss-Legendre integration: the function is
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// evaluated exactly 2*fNumber times at interior points in the range of
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// integration. Since the weights and abscissas are, in this case, symmetric
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// around the midpoint of the range of integration, there are actually only
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// fNumber distinct values of each.
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G4double
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G4GaussLegendreQ::Integral(G4double a, G4double b) const
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{
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G4double xMean = 0.5*(a + b),
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xDiff = 0.5*(b - a),
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integral = 0.0, dx = 0.0 ;
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for(G4int i=0;i<fNumber;i++)
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{
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dx = xDiff*fAbscissa[i] ;
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integral += fWeight[i]*(fFunction(xMean + dx) + fFunction(xMean - dx)) ;
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}
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return integral *= xDiff ;
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}
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// --------------------------------------------------------------------------
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//
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// Returns the integral of the function to be pointed by fFunction between a
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// and b, by ten point Gauss-Legendre integration: the function is evaluated
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// exactly ten times at interior points in the range of integration. Since the
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// weights and abscissas are, in this case, symmetric around the midpoint of
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// the range of integration, there are actually only five distinct values of
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// each.
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G4double
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G4GaussLegendreQ::QuickIntegral(G4double a, G4double b) const
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{
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// From Abramowitz M., Stegan I.A. 1964 , Handbook of Math... , p. 916
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static const G4double abscissa[] = { 0.148874338981631, 0.433395394129247,
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0.679409568299024, 0.865063366688985,
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0.973906528517172 } ;
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static const G4double weight[] = { 0.295524224714753, 0.269266719309996,
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0.219086362515982, 0.149451349150581,
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0.066671344308688 } ;
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G4double xMean = 0.5*(a + b),
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xDiff = 0.5*(b - a),
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integral = 0.0, dx = 0.0 ;
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for(G4int i=0;i<5;i++)
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{
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dx = xDiff*abscissa[i] ;
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integral += weight[i]*(fFunction(xMean + dx) + fFunction(xMean - dx)) ;
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}
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return integral *= xDiff ;
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}
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// -------------------------------------------------------------------------
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//
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// Returns the integral of the function to be pointed by fFunction between a
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// and b, by 96 point Gauss-Legendre integration: the function is evaluated
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// exactly ten times at interior points in the range of integration. Since the
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// weights and abscissas are, in this case, symmetric around the midpoint of
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// the range of integration, there are actually only five distinct values of
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// each.
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G4double
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G4GaussLegendreQ::AccurateIntegral(G4double a, G4double b) const
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{
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// From Abramowitz M., Stegan I.A. 1964 , Handbook of Math... , p. 919
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static const
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G4double abscissa[] = {
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0.016276744849602969579, 0.048812985136049731112,
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0.081297495464425558994, 0.113695850110665920911,
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0.145973714654896941989, 0.178096882367618602759, // 6
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0.210031310460567203603, 0.241743156163840012328,
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0.273198812591049141487, 0.304364944354496353024,
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0.335208522892625422616, 0.365696861472313635031, // 12
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0.395797649828908603285, 0.425478988407300545365,
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0.454709422167743008636, 0.483457973920596359768,
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0.511694177154667673586, 0.539388108324357436227, // 18
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0.566510418561397168404, 0.593032364777572080684,
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0.618925840125468570386, 0.644163403784967106798,
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0.668718310043916153953, 0.692564536642171561344, // 24
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0.715676812348967626225, 0.738030643744400132851,
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0.759602341176647498703, 0.780369043867433217604,
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0.800308744139140817229, 0.819400310737931675539, // 30
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0.837623511228187121494, 0.854959033434601455463,
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0.871388505909296502874, 0.886894517402420416057,
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0.901460635315852341319, 0.915071423120898074206, // 36
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0.927712456722308690965, 0.939370339752755216932,
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0.950032717784437635756, 0.959688291448742539300,
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0.968326828463264212174, 0.975939174585136466453, // 42
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0.982517263563014677447, 0.988054126329623799481,
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0.992543900323762624572, 0.995981842987209290650,
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0.998364375863181677724, 0.999689503883230766828 // 48
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} ;
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static const
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G4double weight[] = {
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0.032550614492363166242, 0.032516118713868835987,
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0.032447163714064269364, 0.032343822568575928429,
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0.032206204794030250669, 0.032034456231992663218, // 6
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0.031828758894411006535, 0.031589330770727168558,
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0.031316425596862355813, 0.031010332586313837423,
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0.030671376123669149014, 0.030299915420827593794, // 12
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0.029896344136328385984, 0.029461089958167905970,
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0.028994614150555236543, 0.028497411065085385646,
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0.027970007616848334440, 0.027412962726029242823, // 18
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0.026826866725591762198, 0.026212340735672413913,
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0.025570036005349361499, 0.024900633222483610288,
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0.024204841792364691282, 0.023483399085926219842, // 24
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0.022737069658329374001, 0.021966644438744349195,
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0.021172939892191298988, 0.020356797154333324595,
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0.019519081140145022410, 0.018660679627411467385, // 30
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0.017782502316045260838, 0.016885479864245172450,
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0.015970562902562291381, 0.015038721026994938006,
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0.014090941772314860916, 0.013128229566961572637, // 36
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0.012151604671088319635, 0.011162102099838498591,
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0.010160770535008415758, 0.009148671230783386633,
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0.008126876925698759217, 0.007096470791153865269, // 42
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0.006058545504235961683, 0.005014202742927517693,
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0.003964554338444686674, 0.002910731817934946408,
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0.001853960788946921732, 0.000796792065552012429 // 48
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} ;
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G4double xMean = 0.5*(a + b),
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xDiff = 0.5*(b - a),
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integral = 0.0, dx = 0.0 ;
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for(G4int i=0;i<48;i++)
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{
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dx = xDiff*abscissa[i] ;
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integral += weight[i]*(fFunction(xMean + dx) + fFunction(xMean - dx)) ;
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}
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return integral *= xDiff ;
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}
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