// // ******************************************************************** // * License and Disclaimer * // * * // * The Geant4 software is copyright of the Copyright Holders of * // * the Geant4 Collaboration. It is provided under the terms and * // * conditions of the Geant4 Software License, included in the file * // * LICENSE and available at http://cern.ch/geant4/license . These * // * include a list of copyright holders. * // * * // * 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. Please see the license in the file LICENSE and URL above * // * for the full disclaimer and the limitation of liability. * // * * // * This code implementation is the result of the scientific and * // * technical work of the GEANT4 collaboration. * // * By using, copying, modifying or distributing the software (or * // * any work based on the software) you agree to acknowledge its * // * use in resulting scientific publications, and indicate your * // * acceptance of all terms of the Geant4 Software license. * // ******************************************************************** // // // $Id$ // // Class description: // // Class for Gauss-Legendre integration method // Roots of ortogonal polynoms and corresponding weights are calculated based on // iteration method (by bisection Newton algorithm). Constant values for initial // approximations were derived from the book: M. Abramowitz, I. Stegun, Handbook // of mathematical functions, DOVER Publications INC, New York 1965 ; chapters 9, // 10, and 22 . // // ------------------------- CONSTRUCTORS: ------------------------------- // // Constructor for GaussLegendre quadrature method. The value nLegendre set the // accuracy required, i.e the number of points where the function pFunction will // be evaluated during integration. The constructor creates the arrays for // abscissas and weights that used in Gauss-Legendre quadrature method. // The values a and b are the limits of integration of the pFunction. // // G4GaussLegendreQ( function pFunction, // G4int nLegendre ) // // -------------------------- METHODS: --------------------------------------- // // Returns the integral of the function to be pointed by fFunction between a and b, // by 2*fNumber point Gauss-Legendre integration: the function is evaluated exactly // 2*fNumber Times at interior points in the range of integration. Since the weights // and abscissas are, in this case, symmetric around the midpoint of the range of // integration, there are actually only fNumber distinct values of each. // // G4double Integral(G4double a, G4double b) const // // ----------------------------------------------------------------------- // // Returns the integral of the function to be pointed by fFunction between a and b, // by ten point Gauss-Legendre integration: the function is evaluated exactly // ten Times at interior points in the range of integration. Since the weights // and abscissas are, in this case, symmetric around the midpoint of the range of // integration, there are actually only five distinct values of each // // G4double // QuickIntegral(G4double a, G4double b) const // // --------------------------------------------------------------------- // // Returns the integral of the function to be pointed by fFunction between a and b, // by 96 point Gauss-Legendre integration: the function is evaluated exactly // ten Times at interior points in the range of integration. Since the weights // and abscissas are, in this case, symmetric around the midpoint of the range of // integration, there are actually only five distinct values of each // // G4double // AccurateIntegral(G4double a, G4double b) const // ------------------------------- HISTORY -------------------------------- // // 13.05.97 V.Grichine (Vladimir.Grichine@cern.chz0 #ifndef G4GAUSSLEGENDREQ_HH #define G4GAUSSLEGENDREQ_HH #include "G4VGaussianQuadrature.hh" class G4GaussLegendreQ : public G4VGaussianQuadrature { public: explicit G4GaussLegendreQ( function pFunction ) ; G4GaussLegendreQ( function pFunction, G4int nLegendre ) ; // Methods G4double Integral(G4double a, G4double b) const ; G4double QuickIntegral(G4double a, G4double b) const ; G4double AccurateIntegral(G4double a, G4double b) const ; private: G4GaussLegendreQ(const G4GaussLegendreQ&); G4GaussLegendreQ& operator=(const G4GaussLegendreQ&); }; #endif