Foam::Math Namespace Reference

A namespace for various mathematical functions. More...

Functions
scalar	erfInv (const scalar y)
	Inverse error function of a real-number argument.
scalar	invIncGamma (const scalar a, const scalar P)
	Inverse of regularised lower incomplete gamma function.
scalar	incGammaRatio_Q (const scalar a, const scalar x)
	Regularised upper incomplete gamma function.
scalar	incGammaRatio_P (const scalar a, const scalar x)
	Regularised lower incomplete gamma function.
scalar	incGamma_Q (const scalar a, const scalar x)
	Upper incomplete gamma function.
scalar	incGamma_P (const scalar a, const scalar x)
	Lower incomplete gamma function.

Detailed Description

A namespace for various mathematical functions.

Reference:

    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

Note

• The algorithm in invIncGamma is described in (DM:Sec. 4).
• The algorithm in incGammaRatio_Q is described in (DM:Sec. 3).
• The accuracy parameter IND is set to a value of 1.

Source files

• MathFunctions.H
• erfInv.C
• incGamma.C
• invIncGamma.C

Function Documentation

erfInv()

Foam::scalar erfInv

(

const scalar

y

)

Inverse error function of a real-number argument.

Parameters

y	Real-number argument at which to evaluate. Domain: (-1, 1)

Returns

The inverse of error function of y

Definition at line 29 of file erfInv.C.

References Foam::endl(), h, k, Foam::log(), Foam::mag(), Foam::nl, Foam::constant::mathematical::pi(), Foam::sqr(), Foam::sqrt(), WarningInFunction, x, and y.

Referenced by multiNormal::sample(), and normal::sample().

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invIncGamma()

Foam::scalar invIncGamma	(	const scalar	a,
		const scalar	P )

Inverse of regularised lower incomplete gamma function.

Parameters

a	Real-number argument. Domain: (0, infty]
P	Real-number argument. Domain: [0,1]

Definition at line 87 of file invIncGamma.C.

References B, D, e, Foam::endl(), Foam::constant::mathematical::Eu(), Foam::exp(), Foam::lgamma(), Foam::log(), Foam::mag(), Foam::max(), Foam::minimaxs(), Foam::pow(), s(), Foam::Sn(), Foam::sqr(), Foam::sqrt(), WarningInFunction, and y.

Referenced by massRosinRammler::sample().

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incGammaRatio_Q()

Foam::scalar incGammaRatio_Q	(	const scalar	a,
		const scalar	x )

Regularised upper incomplete gamma function.

Parameters

a	Real-number argument. Domain: (0, infty]
x	Real-number argument. Domain: [0, infty]

Definition at line 194 of file incGamma.C.

References alpha, Foam::calcPE15(), Foam::calcQE11(), Foam::calcQE16(), Foam::calcTE18(), Foam::endl(), Foam::erf(), Foam::erfc(), Foam::exp(), Foam::factorial(), H(), L, lambda(), Foam::log(), Foam::max(), n, phi, pi(), Foam::pow(), R, sigma(), Foam::sqrt(), Foam::sum(), WarningInFunction, x, and y.

Referenced by incGamma_Q(), incGammaRatio_P(), and LuoSvendsen::LuoSvendsen().

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incGammaRatio_P()

Foam::scalar incGammaRatio_P	(	const scalar	a,
		const scalar	x )

Regularised lower incomplete gamma function.

Parameters

a	Real-number argument. Domain: (0, infty]
x	Real-number argument. Domain: [0, infty]

Definition at line 432 of file incGamma.C.

References incGammaRatio_Q(), and x.

Referenced by incGamma_P().

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incGamma_Q()

Foam::scalar incGamma_Q	(	const scalar	a,
		const scalar	x )

Upper incomplete gamma function.

Parameters

a	Real-number argument. Domain: (0, infty]
x	Real-number argument. Domain: [0, infty]

Definition at line 438 of file incGamma.C.

References incGammaRatio_Q(), and x.

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incGamma_P()

Foam::scalar incGamma_P	(	const scalar	a,
		const scalar	x )

Lower incomplete gamma function.

Parameters

a	Real-number argument. Domain: (0, infty]
x	Real-number argument. Domain: [0, infty]

Definition at line 444 of file incGamma.C.

References incGammaRatio_P(), and x.

Referenced by RosinRammler::meanValue(), and massRosinRammler::sample().

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