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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

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