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Gabriele Cosmo
2020-06-26 10:23:25 +02:00
parent c02c370437
commit 67ba86d073
1871 changed files with 174422 additions and 131884 deletions
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source/global/HEPNumerics/include/G4ChebyshevApproximation.hh
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// * acceptance of all terms of the Geant4 Software license. *
// ********************************************************************
//
//
// G4ChebyshevApproximation
//
// Class description:
//
// Class creating the Chebyshev approximation for a function pointed by fFunction
// data member. The Chebyshev polinom approximation provides an efficient evaluation
// of minimax polynomial, which (among all polynomials of the same degree) has the
// smallest maximum deviation from the true function.
// The methods based mainly on recommendations given in the book : An introduction to
// NUMERICAL METHODS IN C++, B.H. Flowers, Claredon Press, Oxford, 1995
//
// ------------------------- MEMBER DATA ------------------------------------
//
// function fFunction - pointer to a function considered
// G4int fNumber - number of Chebyshev coefficients
// G4double* fChebyshevCof - array of Chebyshev coefficients
// G4double fMean = (a+b)/2 - mean point of interval
// G4double fDiff = (b-a)/2 - half of the interval value
//
// ------------------------ CONSTRUCTORS ----------------------------------
//
// Constructor for initialisation of the class data members. It creates the array
// fChebyshevCof[0,...,fNumber-1], fNumber = n ; which consists of Chebyshev
// coefficients describing the function pointed by pFunction. The values a and b
// fixe the interval of validity of Chebyshev approximation.
//
// G4ChebyshevApproximation( function pFunction,
// G4int n,
// G4double a,
// G4double b )
//
// Class creating the Chebyshev approximation for a function pointed by
// fFunction data member. The Chebyshev polinom approximation provides an
// efficient evaluation of minimax polynomial, which (among all polynomials of
// the same degree) has the smallest maximum deviation from the true function.
// The methods based mainly on recommendations given in the book : An
// introduction to NUMERICAL METHODS IN C++, B.H. Flowers, Claredon Press,
// Oxford, 1995
// Author: V.Grichine, 24.04.1997
// --------------------------------------------------------------------
//
// Constructor for creation of Chebyshev coefficients for m-derivative
// from pFunction. The value of m ! MUST BE ! < n , because the result
// array of fChebyshevCof will be of (n-m) size. There is a definite dependence
// between the proper selection of n, m, a and b values to get better accuracy
// of the derivative value.
//
// G4ChebyshevApproximation( function pFunction,
// G4int n,
// G4int m,
// G4double a,
// G4double b )
//
// ------------------------------------------------------
//
// Constructor for creation of Chebyshev coefficients for integral
// from pFunction.
//
// G4ChebyshevApproximation( function pFunction,
// G4double a,
// G4double b,
// G4int n )
//
// ---------------------------------------------------------------
//
// Destructor deletes the array of Chebyshev coefficients
//
// ~G4ChebyshevApproximation()
//
// ----------------------------- METHODS ----------------------------------
//
// Access function for Chebyshev coefficients
//
// G4double GetChebyshevCof(G4int number) const
//
// --------------------------------------------------------------
//
// Evaluate the value of fFunction at the point x via the Chebyshev coefficients
// fChebyshevCof[0,...,fNumber-1]
//
// G4double ChebyshevEvaluation(G4double x) const
//
// ------------------------------------------------------------------
//
// Returns the array derCof[0,...,fNumber-2], the Chebyshev coefficients of the
// derivative of the function whose coefficients are fChebyshevCof
//
// void DerivativeChebyshevCof(G4double derCof[]) const
//
// ------------------------------------------------------------------------
//
// This function produces the array integralCof[0,...,fNumber-1] , the Chebyshev
// coefficients of the integral of the function whose coefficients are
// fChebyshevCof. The constant of integration is set so that the integral vanishes
// at the point (fMean - fDiff)
//
// void IntegralChebyshevCof(G4double integralCof[]) const
// --------------------------- HISTORY --------------------------------------
//
// 24.04.97 V.Grichine ( Vladimir.Grichine@cern.ch )
#ifndef G4CHEBYSHEVAPPROXIMATION_HH
#define G4CHEBYSHEVAPPROXIMATION_HH
#define G4CHEBYSHEVAPPROXIMATION_HH 1
#include "globals.hh"
typedef G4double (*function)(G4double) ;
typedef G4double (*function)(G4double);
class G4ChebyshevApproximation
{
public: // with description
public:
G4ChebyshevApproximation(function pFunction, G4int n, G4double a, G4double b);
// Constructor for creation of Chebyshev coefficients for m-derivative
// from pFunction. The value of m ! MUST BE ! < n , because the result
// array of fChebyshevCof will be of (n-m) size.
// It creates the array fChebyshevCof[0,...,fNumber-1], fNumber = n ;
// which consists of Chebyshev coefficients describing the function pointed
// by pFunction. The values a and b fixe the interval of validity of
// Chebyshev approximation.
G4ChebyshevApproximation( function pFunction,
G4int n,
G4double a,
G4double b ) ;
//
// Constructor for creation of Chebyshev coefficients for m-derivative
// from pFunction. The value of m ! MUST BE ! < n , because the result
// array of fChebyshevCof will be of (n-m) size.
G4ChebyshevApproximation(function pFunction, G4int n, G4int m, G4double a,
G4double b);
// Constructor for creation of Chebyshev coefficients for m-derivative
// from pFunction. The value of m ! MUST BE ! < n , because the result
// array of fChebyshevCof will be of (n-m) size. There is a definite
// dependence between the proper selection of n, m, a and b values to get
// better accuracy of the derivative value.
G4ChebyshevApproximation( function pFunction,
G4int n,
G4int m,
G4double a,
G4double b ) ;
//
// Constructor for creation of Chebyshev coefficients for integral
// from pFunction.
G4ChebyshevApproximation(function pFunction, G4double a, G4double b, G4int n);
// Constructor for creation of Chebyshev coefficients for integral
// from pFunction.
G4ChebyshevApproximation( function pFunction,
G4double a,
G4double b,
G4int n ) ;
~G4ChebyshevApproximation();
// Destructor deletes the array of Chebyshev coefficients
~G4ChebyshevApproximation() ;
// Access functions
G4double GetChebyshevCof(G4int number) const ;
// Methods
G4ChebyshevApproximation(const G4ChebyshevApproximation&) = delete;
G4ChebyshevApproximation& operator=(const G4ChebyshevApproximation&) = delete;
// Copy constructor and assignment operator not allowed.
G4double ChebyshevEvaluation(G4double x) const ;
void DerivativeChebyshevCof(G4double derCof[]) const ;
void IntegralChebyshevCof(G4double integralCof[]) const ;
private:
G4double GetChebyshevCof(G4int number) const;
// Access function for Chebyshev coefficients
G4ChebyshevApproximation(const G4ChebyshevApproximation&);
G4ChebyshevApproximation& operator=(const G4ChebyshevApproximation&);
G4double ChebyshevEvaluation(G4double x) const;
// Evaluate the value of fFunction at the point x via the Chebyshev
// coefficients fChebyshevCof[0,...,fNumber-1]
private:
void DerivativeChebyshevCof(G4double derCof[]) const;
// Returns the array derCof[0,...,fNumber-2], the Chebyshev coefficients
// of the derivative of the function whose coefficients are fChebyshevCof
function fFunction ;
G4int fNumber ;
G4double* fChebyshevCof ;
G4double fMean ;
G4double fDiff ;
void IntegralChebyshevCof(G4double integralCof[]) const;
// This function produces the array integralCof[0,...,fNumber-1] , the
// Chebyshev coefficients of the integral of the function whose coefficients
// are fChebyshevCof. The constant of integration is set so that the integral
// vanishes at the point (fMean - fDiff)
private:
function fFunction; // pointer to a function considered
G4int fNumber; // number of Chebyshev coefficients
G4double* fChebyshevCof; // array of Chebyshev coefficients
G4double fMean; // (a+b)/2 - mean point of interval
G4double fDiff; // (b-a)/2 - half of the interval value
};
#endif