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Gabriele Cosmo
2020-06-26 10:23:25 +02:00
parent c02c370437
commit 67ba86d073
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source/global/HEPNumerics/include/G4DataInterpolation.hh
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// * acceptance of all terms of the Geant4 Software license. *
// ********************************************************************
//
//
// G4DataInterpolation
//
// Class description:
//
// The class consists of some methods for data interpolations and extrapolations.
// The methods based mainly on recommendations given in the book : An introduction to
// NUMERICAL METHODS IN C++, B.H. Flowers, Claredon Press, Oxford, 1995
//
// ------------------------------ Data members: ---------------------------------
//
// fArgument and fFunction - pointers to data table to be interpolated
// for y[i] and x[i] respectively
// fNumber - the corresponding table size
// ......
// G4DataInterpolation( G4double pX[], G4double pY[], G4int number )
//
// Constructor for initializing of fArgument, fFunction and fNumber data members:
// ......
// G4DataInterpolation( G4double pX[], G4double pY[], G4int number,
// G4double pFirstDerStart, G4double pFirstDerFinish )
//
// Constructor for cubic spline interpolation. It creates the array
// fSecondDerivative[0,...fNumber-1] which is used in this interpolation by
// the function:
// ....
// ~G4DataInterpolation()
//
// Destructor deletes dynamically created arrays for data members: fArgument,
// fFunction and fSecondDerivative, all have dimension of fNumber
//
// ------------------------------ Methods: ----------------------------------------
//
// G4double PolynomInterpolation(G4double pX, G4double& deltaY ) const
//
// This function returns the value P(pX), where P(x) is polynom of fNumber-1 degree
// such that P(fArgument[i]) = fFunction[i], for i = 0, ..., fNumber-1 .
// ........
// void PolIntCoefficient( G4double cof[]) const
//
// Given arrays fArgument[0,..,fNumber-1] and fFunction[0,..,fNumber-1] , this
// function calculates an array of coefficients. The coefficients don't provide
// usually (fNumber>10) better accuracy for polynom interpolation, as compared with
// PolynomInterpolation function. They could be used instead for derivate
// calculations and some other applications.
// .........
// G4double RationalPolInterpolation(G4double pX, G4double& deltaY ) const
//
// The function returns diagonal rational function (Bulirsch and Stoer algorithm
// of Neville type) Pn(x)/Qm(x) where P and Q are polynoms.
// Tests showed the method is not stable and hasn't advantage if compared with
// polynomial interpolation
// ................
// G4double CubicSplineInterpolation(G4double pX) const
//
// Cubic spline interpolation in point pX for function given by the table:
// fArgument, fFunction. The constructor, which creates fSecondDerivative, must be
// called before. The function works optimal, if sequential calls are in random
// values of pX.
// ..................
// G4double FastCubicSpline(G4double pX, G4int index) const
//
// Return cubic spline interpolation in the point pX which is located between
// fArgument[index] and fArgument[index+1]. It is usually called in sequence of
// known from external analysis values of index.
// .........
// G4int LocateArgument(G4double pX) const
//
// Given argument pX, returns index k, so that pX bracketed by fArgument[k] and
// fArgument[k+1]
// ......................
// void CorrelatedSearch( G4double pX, G4int& index ) const
//
// Given a value pX, returns a value 'index' such that pX is between fArgument[index]
// and fArgument[index+1]. fArgument MUST BE MONOTONIC, either increasing or
// decreasing. If index = -1 or fNumber, this indicates that pX is out of range.
// The value index on input is taken as the initial approximation for index on
// output.
// --------------------------------- History: --------------------------------------
//
// 3.4.97 V.Grichine (Vladimir.Grichine@cern.ch)
//
// The class consists of some methods for data interpolations and
// extrapolations. 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, 03.04.1997
// --------------------------------------------------------------------
#ifndef G4DATAINTERPOLATION_HH
#define G4DATAINTERPOLATION_HH
#define G4DATAINTERPOLATION_HH 1
#include "globals.hh"
class G4DataInterpolation
{
public:
G4DataInterpolation( G4double pX[],
G4double pY[],
G4int number );
public:
G4DataInterpolation(G4double pX[], G4double pY[], G4int number);
// Constructor for initializing data members.
// Constructor for cubic spline interpolation. It creates fSecond Deivative array
// as well as fArgument and fFunction
G4DataInterpolation( G4double pX[],
G4double pY[],
G4int number,
G4double pFirstDerStart,
G4double pFirstDerFinish ) ;
G4DataInterpolation(G4double pX[], G4double pY[], G4int number,
G4double pFirstDerStart, G4double pFirstDerFinish);
// Constructor for cubic spline interpolation. It creates fSecond Deivative
// array as well as fArgument and fFunction.
~G4DataInterpolation() ;
G4double PolynomInterpolation( G4double pX,
G4double& deltaY ) const ;
void PolIntCoefficient( G4double cof[]) const ;
~G4DataInterpolation();
// Destructor deletes dynamically created arrays for data members: fArgument,
// fFunction and fSecondDerivative, all have dimension of fNumber.
G4double RationalPolInterpolation( G4double pX,
G4double& deltaY ) const ;
G4DataInterpolation(const G4DataInterpolation&) = delete;
G4DataInterpolation& operator=(const G4DataInterpolation&) = delete;
// Copy constructor and assignement operator not allowed.
G4double CubicSplineInterpolation( G4double pX ) const ;
G4double PolynomInterpolation(G4double pX, G4double& deltaY) const;
// This function returns the value P(pX), where P(x) is polynom of fNumber-1
// degree such that P(fArgument[i]) = fFunction[i], for i = 0, ..., fNumber-1.
G4double FastCubicSpline( G4double pX,
G4int index ) const ;
void PolIntCoefficient(G4double cof[]) const;
// Given arrays fArgument[0,..,fNumber-1] and fFunction[0,..,fNumber-1], this
// function calculates an array of coefficients.
// The coefficients don't provide usually (fNumber>10) better accuracy for
// polynom interpolation, as compared with PolynomInterpolation() function.
// They could be used instead for derivate calculations and some other
// applications.
G4int LocateArgument( G4double pX ) const ;
void CorrelatedSearch( G4double pX,
G4int& index ) const ;
private:
G4double RationalPolInterpolation(G4double pX, G4double& deltaY) const;
// The function returns diagonal rational function (Bulirsch and Stoer
// algorithm of Neville type) Pn(x)/Qm(x) where P and Q are polynoms.
// Tests showed the method is not stable and hasn't advantage if compared
// with polynomial interpolation.
G4DataInterpolation(const G4DataInterpolation&);
G4DataInterpolation& operator=(const G4DataInterpolation&);
G4double CubicSplineInterpolation(G4double pX) const;
// Cubic spline interpolation in point pX for function given by the table:
// fArgument, fFunction. The constructor, which creates fSecondDerivative,
// must be called before. The function works optimal, if sequential calls
// are in random values of pX.
private:
G4double* fArgument ;
G4double* fFunction ;
G4double* fSecondDerivative ;
G4int fNumber ;
} ;
G4double FastCubicSpline(G4double pX, G4int index) const;
// Return cubic spline interpolation in the point pX which is located between
// fArgument[index] and fArgument[index+1]. It is usually called in sequence
// of known from external analysis values of index.
G4int LocateArgument(G4double pX) const;
// Given argument pX, returns index k, so that pX bracketed by fArgument[k]
// and fArgument[k+1].
void CorrelatedSearch(G4double pX, G4int& index) const;
// Given a value pX, returns a value 'index' such that pX is between
// fArgument[index] and fArgument[index+1]. fArgument MUST BE MONOTONIC,
// either increasing or decreasing. If index = -1 or fNumber, this indicates
// that pX is out of range. The value index on input is taken as the initial
// approximation for index on output.
private:
// pointers to data table to be interpolated for y[i] and x[i] respectively
G4double* fArgument = nullptr;
G4double* fFunction = nullptr;
G4double* fSecondDerivative = nullptr;
G4int fNumber = 0; // the corresponding table size
};
#endif