| [833] | 1 | //
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| 2 | // ********************************************************************
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| 3 | // * License and Disclaimer *
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| 4 | // * *
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of *
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and *
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| 7 | // * conditions of the Geant4 Software License, included in the file *
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These *
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| 9 | // * include a list of copyright holders. *
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| 10 | // * *
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| 11 | // * Neither the authors of this software system, nor their employing *
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| 12 | // * institutes,nor the agencies providing financial support for this *
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| 13 | // * work make any representation or warranty, express or implied, *
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| 14 | // * regarding this software system or assume any liability for its *
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| 15 | // * use. Please see the license in the file LICENSE and URL above *
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| 16 | // * for the full disclaimer and the limitation of liability. *
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| 17 | // * *
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| 18 | // * This code implementation is the result of the scientific and *
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| 19 | // * technical work of the GEANT4 collaboration. *
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| 20 | // * By using, copying, modifying or distributing the software (or *
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| 21 | // * any work based on the software) you agree to acknowledge its *
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| 22 | // * use in resulting scientific publications, and indicate your *
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| 23 | // * acceptance of all terms of the Geant4 Software license. *
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| 24 | // ********************************************************************
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| 25 | //
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| 26 | //
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| 27 | // $Id: G4DataInterpolation.hh,v 1.5 2006/06/29 18:59:29 gunter Exp $
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| [850] | 28 | // GEANT4 tag $Name: HEAD $
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| [833] | 29 | //
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| 30 | // Class description:
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| 31 | //
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| 32 | // The class consists of some methods for data interpolations and extrapolations.
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| 33 | // The methods based mainly on recommendations given in the book : An introduction to
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| 34 | // NUMERICAL METHODS IN C++, B.H. Flowers, Claredon Press, Oxford, 1995
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| 35 | //
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| 36 | // ------------------------------ Data members: ---------------------------------
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| 37 | //
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| 38 | // fArgument and fFunction - pointers to data table to be interpolated
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| 39 | // for y[i] and x[i] respectively
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| 40 | // fNumber - the corresponding table size
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| 41 | // ......
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| 42 | // G4DataInterpolation( G4double pX[], G4double pY[], G4int number )
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| 43 | //
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| 44 | // Constructor for initializing of fArgument, fFunction and fNumber data members:
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| 45 | // ......
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| 46 | // G4DataInterpolation( G4double pX[], G4double pY[], G4int number,
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| 47 | // G4double pFirstDerStart, G4double pFirstDerFinish )
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| 48 | //
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| 49 | // Constructor for cubic spline interpolation. It creates the array
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| 50 | // fSecondDerivative[0,...fNumber-1] which is used in this interpolation by
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| 51 | // the function:
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| 52 | // ....
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| 53 | // ~G4DataInterpolation()
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| 54 | //
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| 55 | // Destructor deletes dynamically created arrays for data members: fArgument,
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| 56 | // fFunction and fSecondDerivative, all have dimension of fNumber
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| 57 | //
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| 58 | // ------------------------------ Methods: ----------------------------------------
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| 59 | //
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| 60 | // G4double PolynomInterpolation(G4double pX, G4double& deltaY ) const
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| 61 | //
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| 62 | // This function returns the value P(pX), where P(x) is polynom of fNumber-1 degree
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| 63 | // such that P(fArgument[i]) = fFunction[i], for i = 0, ..., fNumber-1 .
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| 64 | // ........
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| 65 | // void PolIntCoefficient( G4double cof[]) const
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| 66 | //
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| 67 | // Given arrays fArgument[0,..,fNumber-1] and fFunction[0,..,fNumber-1] , this
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| 68 | // function calculates an array of coefficients. The coefficients don't provide
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| 69 | // usually (fNumber>10) better accuracy for polynom interpolation, as compared with
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| 70 | // PolynomInterpolation function. They could be used instead for derivate
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| 71 | // calculations and some other applications.
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| 72 | // .........
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| 73 | // G4double RationalPolInterpolation(G4double pX, G4double& deltaY ) const
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| 74 | //
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| 75 | // The function returns diagonal rational function (Bulirsch and Stoer algorithm
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| 76 | // of Neville type) Pn(x)/Qm(x) where P and Q are polynoms.
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| 77 | // Tests showed the method is not stable and hasn't advantage if compared with
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| 78 | // polynomial interpolation
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| 79 | // ................
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| 80 | // G4double CubicSplineInterpolation(G4double pX) const
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| 81 | //
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| 82 | // Cubic spline interpolation in point pX for function given by the table:
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| 83 | // fArgument, fFunction. The constructor, which creates fSecondDerivative, must be
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| 84 | // called before. The function works optimal, if sequential calls are in random
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| 85 | // values of pX.
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| 86 | // ..................
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| 87 | // G4double FastCubicSpline(G4double pX, G4int index) const
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| 88 | //
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| 89 | // Return cubic spline interpolation in the point pX which is located between
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| 90 | // fArgument[index] and fArgument[index+1]. It is usually called in sequence of
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| 91 | // known from external analysis values of index.
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| 92 | // .........
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| 93 | // G4int LocateArgument(G4double pX) const
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| 94 | //
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| 95 | // Given argument pX, returns index k, so that pX bracketed by fArgument[k] and
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| 96 | // fArgument[k+1]
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| 97 | // ......................
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| 98 | // void CorrelatedSearch( G4double pX, G4int& index ) const
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| 99 | //
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| 100 | // Given a value pX, returns a value 'index' such that pX is between fArgument[index]
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| 101 | // and fArgument[index+1]. fArgument MUST BE MONOTONIC, either increasing or
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| 102 | // decreasing. If index = -1 or fNumber, this indicates that pX is out of range.
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| 103 | // The value index on input is taken as the initial approximation for index on
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| 104 | // output.
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| 105 |
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| 106 | // --------------------------------- History: --------------------------------------
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| 107 | //
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| 108 | // 3.4.97 V.Grichine (Vladimir.Grichine@cern.ch)
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| 109 | //
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| 110 |
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| 111 |
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| 112 | #ifndef G4DATAINTERPOLATION_HH
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| 113 | #define G4DATAINTERPOLATION_HH
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| 114 |
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| 115 | #include "globals.hh"
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| 116 |
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| 117 | class G4DataInterpolation
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| 118 | {
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| 119 | public:
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| 120 | G4DataInterpolation( G4double pX[],
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| 121 | G4double pY[],
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| 122 | G4int number );
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| 123 |
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| 124 | // Constructor for cubic spline interpolation. It creates fSecond Deivative array
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| 125 | // as well as fArgument and fFunction
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| 126 |
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| 127 | G4DataInterpolation( G4double pX[],
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| 128 | G4double pY[],
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| 129 | G4int number,
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| 130 | G4double pFirstDerStart,
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| 131 | G4double pFirstDerFinish ) ;
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| 132 |
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| 133 | ~G4DataInterpolation() ;
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| 134 |
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| 135 | G4double PolynomInterpolation( G4double pX,
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| 136 | G4double& deltaY ) const ;
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| 137 |
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| 138 | void PolIntCoefficient( G4double cof[]) const ;
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| 139 |
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| 140 | G4double RationalPolInterpolation( G4double pX,
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| 141 | G4double& deltaY ) const ;
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| 142 |
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| 143 | G4double CubicSplineInterpolation( G4double pX ) const ;
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| 144 |
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| 145 | G4double FastCubicSpline( G4double pX,
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| 146 | G4int index ) const ;
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| 147 |
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| 148 | G4int LocateArgument( G4double pX ) const ;
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| 149 |
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| 150 | void CorrelatedSearch( G4double pX,
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| 151 | G4int& index ) const ;
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| 152 |
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| 153 | private:
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| 154 |
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| 155 | G4DataInterpolation(const G4DataInterpolation&);
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| 156 | G4DataInterpolation& operator=(const G4DataInterpolation&);
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| 157 |
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| 158 | private:
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| 159 | G4double* fArgument ;
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| 160 | G4double* fFunction ;
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| 161 | G4double* fSecondDerivative ;
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| 162 | G4int fNumber ;
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| 163 | } ;
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| 164 |
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| 165 | #endif
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