Gabriele Cosmo
183 lines
7.2 KiB
C++
183 lines
7.2 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: G4ChebyshevApproximation.hh,v 1.6 2006/06/29 18:59:26 gunter Exp $
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// GEANT4 tag $Name: geant4-09-01 $
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//
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// Class description:
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//
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// Class creating the Chebyshev approximation for a function pointed by fFunction
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// data member. The Chebyshev polinom approximation provides an efficient evaluation
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// of minimax polynomial, which (among all polynomials of the same degree) has the
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// smallest maximum deviation from the true function.
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// The methods based mainly on recommendations given in the book : An introduction to
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// NUMERICAL METHODS IN C++, B.H. Flowers, Claredon Press, Oxford, 1995
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//
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// ------------------------- MEMBER DATA ------------------------------------
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//
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// function fFunction - pointer to a function considered
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// G4int fNumber - number of Chebyshev coefficients
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// G4double* fChebyshevCof - array of Chebyshev coefficients
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// G4double fMean = (a+b)/2 - mean point of interval
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// G4double fDiff = (b-a)/2 - half of the interval value
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//
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// ------------------------ CONSTRUCTORS ----------------------------------
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//
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// Constructor for initialisation of the class data members. It creates the array
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// fChebyshevCof[0,...,fNumber-1], fNumber = n ; which consists of Chebyshev
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// coefficients describing the function pointed by pFunction. The values a and b
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// fixe the interval of validity of Chebyshev approximation.
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//
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// G4ChebyshevApproximation( function pFunction,
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// G4int n,
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// G4double a,
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// G4double b )
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//
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// --------------------------------------------------------------------
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//
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// Constructor for creation of Chebyshev coefficients for m-derivative
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// from pFunction. The value of m ! MUST BE ! < n , because the result
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// array of fChebyshevCof will be of (n-m) size. There is a definite dependence
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// between the proper selection of n, m, a and b values to get better accuracy
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// of the derivative value.
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//
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// G4ChebyshevApproximation( function pFunction,
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// G4int n,
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// G4int m,
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// G4double a,
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// G4double b )
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//
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// ------------------------------------------------------
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//
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// Constructor for creation of Chebyshev coefficients for integral
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// from pFunction.
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//
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// G4ChebyshevApproximation( function pFunction,
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// G4double a,
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// G4double b,
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// G4int n )
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//
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// ---------------------------------------------------------------
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//
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// Destructor deletes the array of Chebyshev coefficients
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//
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// ~G4ChebyshevApproximation()
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//
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// ----------------------------- METHODS ----------------------------------
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//
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// Access function for Chebyshev coefficients
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//
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// G4double GetChebyshevCof(G4int number) const
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//
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// --------------------------------------------------------------
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//
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// Evaluate the value of fFunction at the point x via the Chebyshev coefficients
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// fChebyshevCof[0,...,fNumber-1]
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//
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// G4double ChebyshevEvaluation(G4double x) const
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//
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// ------------------------------------------------------------------
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//
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// Returns the array derCof[0,...,fNumber-2], the Chebyshev coefficients of the
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// derivative of the function whose coefficients are fChebyshevCof
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//
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// void DerivativeChebyshevCof(G4double derCof[]) const
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//
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// ------------------------------------------------------------------------
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//
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// This function produces the array integralCof[0,...,fNumber-1] , the Chebyshev
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// coefficients of the integral of the function whose coefficients are
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// fChebyshevCof. The constant of integration is set so that the integral vanishes
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// at the point (fMean - fDiff)
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//
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// void IntegralChebyshevCof(G4double integralCof[]) const
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// --------------------------- HISTORY --------------------------------------
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//
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// 24.04.97 V.Grichine ( Vladimir.Grichine@cern.ch )
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#ifndef G4CHEBYSHEVAPPROXIMATION_HH
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#define G4CHEBYSHEVAPPROXIMATION_HH
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#include "globals.hh"
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typedef G4double (*function)(G4double) ;
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class G4ChebyshevApproximation
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{
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public: // with description
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G4ChebyshevApproximation( function pFunction,
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G4int n,
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G4double a,
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G4double b ) ;
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//
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// Constructor for creation of Chebyshev coefficients for m-derivative
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// from pFunction. The value of m ! MUST BE ! < n , because the result
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// array of fChebyshevCof will be of (n-m) size.
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G4ChebyshevApproximation( function pFunction,
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G4int n,
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G4int m,
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G4double a,
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G4double b ) ;
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//
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// Constructor for creation of Chebyshev coefficients for integral
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// from pFunction.
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G4ChebyshevApproximation( function pFunction,
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G4double a,
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G4double b,
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G4int n ) ;
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~G4ChebyshevApproximation() ;
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// Access functions
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G4double GetChebyshevCof(G4int number) const ;
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// Methods
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G4double ChebyshevEvaluation(G4double x) const ;
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void DerivativeChebyshevCof(G4double derCof[]) const ;
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void IntegralChebyshevCof(G4double integralCof[]) const ;
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private:
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G4ChebyshevApproximation(const G4ChebyshevApproximation&);
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G4ChebyshevApproximation& operator=(const G4ChebyshevApproximation&);
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private:
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function fFunction ;
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G4int fNumber ;
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G4double* fChebyshevCof ;
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G4double fMean ;
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G4double fDiff ;
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};
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#endif
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