MathFunctions.H

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License
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Namespace
    Foam::Math
 
Description
    A namespace for various mathematical functions.
 
    Reference:
    \verbatim
        Inverse error function (tag:W):
            Winitzki, S. (2008).
            A handy approximation for the error function and its inverse.
            A lecture note obtained through private communication.
            URL:https://sites.google.com/site/winitzki/sergei-winitzkis-files
            (Retrieved on: 16 Feb 2021).
 
        Incomplete gamma functions (tag:DM):
            DiDonato, A. R., & Morris Jr, A. H. (1986).
            Computation of the incomplete gamma
            function ratios and their inverse.
            ACM Transactions on Mathematical Software (TOMS), 12(4), 377-393.
            DOI:10.1145/22721.23109
    \endverbatim
 
Note
  - The algorithm in \c invIncGamma is described in (DM:Sec. 4).
  - The algorithm in \c incGammaRatio_Q is described in (DM:Sec. 3).
  - The accuracy parameter \c IND is set to a value of 1.
 
SourceFiles
    erfInv.C
    incGamma.C
    invIncGamma.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef MathFunctions_H
#define MathFunctions_H
 
#include "scalar.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
/*---------------------------------------------------------------------------*\
                        Namespace Math Declaration
\*---------------------------------------------------------------------------*/
 
namespace Math
{
 
//- Inverse error function of a real-number argument
//  \param y Real-number argument at which to evaluate. Domain: (-1, 1)
//  \return The inverse of error function of y
scalar erfInv(const scalar y);
 
 
// Incomplete gamma functions
 
//- Inverse of regularised lower incomplete gamma function
//  \param a Real-number argument. Domain: (0, infty]
//  \param P Real-number argument. Domain: [0,1]
scalar invIncGamma(const scalar a, const scalar P);
 
//- Regularised upper incomplete gamma function
//  \param a Real-number argument. Domain: (0, infty]
//  \param x Real-number argument. Domain: [0, infty]
scalar incGammaRatio_Q(const scalar a, const scalar x);
 
//- Regularised lower incomplete gamma function
//  \param a Real-number argument. Domain: (0, infty]
//  \param x Real-number argument. Domain: [0, infty]
scalar incGammaRatio_P(const scalar a, const scalar x);
 
//- Upper incomplete gamma function
//  \param a Real-number argument. Domain: (0, infty]
//  \param x Real-number argument. Domain: [0, infty]
scalar incGamma_Q(const scalar a, const scalar x);
 
//- Lower incomplete gamma function
//  \param a Real-number argument. Domain: (0, infty]
//  \param x Real-number argument. Domain: [0, infty]
scalar incGamma_P(const scalar a, const scalar x);
 
 
} // End namespace Math
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //