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Geant4/global/HEPNumerics/include/G4ChebyshevApproximation.hh

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  //
  // 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
  
  // Author: V.Grichine, 24.04.1997
  // --------------------------------------------------------------------
  #ifndef G4CHEBYSHEVAPPROXIMATION_HH
  #define G4CHEBYSHEVAPPROXIMATION_HH 1
  
  #include "globals.hh"
  
  using function = G4double (*)(G4double);
  
  class G4ChebyshevApproximation
  {
   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, 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, G4double a, G4double b, G4int n);
    // Constructor for creation of Chebyshev coefficients for integral
    // from pFunction.
  
    ~G4ChebyshevApproximation();
    // Destructor deletes the array of Chebyshev coefficients
  
    G4ChebyshevApproximation(const G4ChebyshevApproximation&) = delete;
    G4ChebyshevApproximation& operator=(const G4ChebyshevApproximation&) = delete;
    // Copy constructor and assignment operator not allowed.
  
    G4double GetChebyshevCof(G4int number) const;
    // Access function for Chebyshev coefficients
  
    G4double ChebyshevEvaluation(G4double x) const;
    // Evaluate the value of fFunction at the point x via the Chebyshev
    // coefficients fChebyshevCof[0,...,fNumber-1]
  
    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
  
    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