Trait Gamma 

pub trait Gamma
where
    Self: Sized,
{
    // Required methods
    fn gamma(self) -> Self;
    fn digamma(self) -> Self;
    fn trigamma(&self) -> Self;
    fn inc_gamma(self, p: Self) -> Self;
    fn ln_gamma(self) -> (Self, i32);
}

Gamma functions.

Required Methods

fn gamma(self) -> Self

Compute the gamma function.

fn digamma(self) -> Self

Compute the real-valued digamma function.

The formula is as follows:

       d ln(Γ(p))
ψ(p) = ----------
           dp

where Γ is the gamma function. The computation is based on an approximation as described in the reference below.

Examples

use special::Gamma;

const EULER_MASCHERONI: f64 = 0.57721566490153286060651209008240243104215933593992;
assert!((1.0.digamma() + EULER_MASCHERONI).abs() < 1e-15);

References

1. M. J. Beal, Variational algorithms for approximate Bayesian inference. University of London, 2003, pp. 265–266.

fn trigamma(&self) -> Self

Compute the trigamma function.

The implementation is based on a Julia implementation.

fn inc_gamma(self, p: Self) -> Self

Compute the regularized lower incomplete gamma function.

The formula is as follows:

          γ(x, p)    1   x
P(x, p) = ------- = ---- ∫ t^(p - 1) e^(-t) dt
           Γ(p)     Γ(p) 0

where γ is the incomplete lower gamma function, and Γ is the complete gamma function.

The implementation is based on a C implementation by John Burkardt. The original algorithm was published in Applied Statistics and is known as Algorithm AS 239.

fn ln_gamma(self) -> (Self, i32)

Compute the natural logarithm of the gamma function.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl Gamma for f32

fn gamma(self) -> Self

fn digamma(self) -> Self

fn trigamma(&self) -> Self

fn inc_gamma(self, p: Self) -> Self

fn ln_gamma(self) -> (Self, i32)

impl Gamma for f64

fn gamma(self) -> Self

fn digamma(self) -> Self

fn trigamma(&self) -> Self

fn inc_gamma(self, p: Self) -> Self

fn ln_gamma(self) -> (Self, i32)

Implementors