scitbx::math::gamma Namespace Reference

The Gamma function and some of his/her friends. More...

Functions
template<typename FloatType>
FloatType	complete_lanczos (FloatType const &x)
	Factorial/Gamma function.
template<typename FloatType>
FloatType	complete_minimax (FloatType const &x)
	Minimax approach for arguments larger than 12.
template<typename FloatType>
FloatType	complete (FloatType const &x, bool minimax=true)
	Gamma function with automatic choice of the best approximation.
template<typename FloatType>
FloatType	incomplete_series (FloatType const &a, FloatType const &x, unsigned max_iterations=500)
	Incomplete gamma function using series expansion.
template<typename FloatType>
FloatType	incomplete_continued_fraction (FloatType const &a, FloatType const &x, unsigned max_iterations=500)
	Incomplete gamma function using continued fraction method.
template<typename FloatType>
FloatType	incomplete (FloatType const &a, FloatType const &x, unsigned max_iterations=500)
	Normalized form of incomplete gamma function.
template<typename FloatType>
FloatType	incomplete_complement (FloatType const &a, FloatType const &x, unsigned max_iterations=500)
	Complement of normalized form of incomplete gamma function.
template<typename FloatType>
FloatType	exponential_integral_e1z_lower_track (FloatType const &z)
template<typename FloatType>
FloatType	exponential_integral_e1z_upper_track (FloatType const &z)
template<typename FloatType>
FloatType	exponential_integral_e1z (FloatType const &z)

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Detailed Description

The Gamma function and some of his/her friends.

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Function Documentation

FloatType scitbx::math::gamma::complete_lanczos

(

FloatType const &

x

)

[inline]

Factorial/Gamma function.

Expression and coefficients obtained from: http://www.rskey.org/gamma.htm

Referenced by complete().

FloatType scitbx::math::gamma::complete_minimax

(

FloatType const &

x

)

[inline]

Minimax approach for arguments larger than 12.

http://www.netlib.no/netlib/specfun/gamma

References SCITBX_ASSERT.

Referenced by complete().

FloatType scitbx::math::gamma::exponential_integral_e1z

(

FloatType const &

z

)

[inline]

The exponential integral {z}^{} [-t] t^{-1} d t a modified form of AMS 55 5.1.56

References exponential_integral_e1z_lower_track(), exponential_integral_e1z_upper_track(), and SCITBX_ASSERT.

FloatType scitbx::math::gamma::exponential_integral_e1z_lower_track

(

FloatType const &

z

)

[inline]

The exponential integral {z}^{} [-t] t^{-1} d t a modified form of AMS 55 5.1.53

References SCITBX_ASSERT.

Referenced by exponential_integral_e1z().

FloatType scitbx::math::gamma::exponential_integral_e1z_upper_track

(

FloatType const &

z

)

[inline]

The exponential integral {z}^{} [-t] t^{-1} d t a modified form of AMS 55 5.1.56

References SCITBX_ASSERT.

Referenced by exponential_integral_e1z().

FloatType scitbx::math::gamma::incomplete	(	FloatType const &	a,
		FloatType const &	x,
		unsigned	max_iterations = 500
	)			[inline]

Normalized form of incomplete gamma function.

(1/(a))int_{0}^{x}exp(-t) t^{a-1} dt

References incomplete_continued_fraction(), incomplete_series(), and SCITBX_ASSERT.

Referenced by incomplete_complement().

FloatType scitbx::math::gamma::incomplete_complement	(	FloatType const &	a,
		FloatType const &	x,
		unsigned	max_iterations = 500
	)			[inline]

Complement of normalized form of incomplete gamma function.

1-(1/(a))int_{0}^{x}exp(-t) t^{a-1} dt

References incomplete().