Gabriele Cosmo
165 lines
5.5 KiB
C++
165 lines
5.5 KiB
C++
// This code implementation is the intellectual property of
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// the GEANT4 collaboration.
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//
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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 statement,
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// and all its terms.
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//
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// $Id: G4ChebyshevApproximation.hh,v 1.2 1999/11/16 17:30:55 gcosmo Exp $
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// GEANT4 tag $Name: geant4-01-00 $
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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:
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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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// 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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// 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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protected:
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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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