Foam::Math Namespace Reference

A namespace for various mathematical functions. More...

Functions
scalar	erfInv (const scalar y)
scalar	invIncGamma (const scalar a, const scalar P)
scalar	incGammaRatio_Q (const scalar a, const scalar x)
scalar	incGammaRatio_P (const scalar a, const scalar x)
scalar	incGamma_Q (const scalar a, const scalar x)
scalar	incGamma_P (const scalar a, const scalar x)

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

)

Definition at line 27 of file erfInv.C.

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

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

Here is the call graph for this function:

Here is the caller graph for this function:

invIncGamma()

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

Definition at line 85 of file invIncGamma.C.

References B, Foam::constant::physicoChemical::c1, Foam::constant::physicoChemical::c2, D, Foam::constant::mathematical::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().

Here is the call graph for this function:

Here is the caller graph for this function:

incGammaRatio_Q()

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

Definition at line 193 of file incGamma.C.

References Foam::constant::atomic::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, Foam::constant::mathematical::pi(), Foam::pow(), R, sigma(), Foam::sqrt(), Foam::sum(), WarningInFunction, x, and y.

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

Here is the call graph for this function:

Here is the caller graph for this function:

incGammaRatio_P()

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

Definition at line 431 of file incGamma.C.

References incGammaRatio_Q(), and x.

Referenced by incGamma_P().

Here is the call graph for this function:

Here is the caller graph for this function:

incGamma_Q()

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

Definition at line 437 of file incGamma.C.

References incGammaRatio_Q(), and x.

Here is the call graph for this function:

incGamma_P()

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

Definition at line 443 of file incGamma.C.

References incGammaRatio_P(), and x.

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

Here is the call graph for this function:

Here is the caller graph for this function: