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-// Copyright 2018 Developers of the Rand project.
-// Copyright 2013 The Rust Project Developers.
-//
-// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
-// option. This file may not be copied, modified, or distributed
-// except according to those terms.
-
-//! The Gamma and derived distributions.
-#![allow(deprecated)]
-
-use self::GammaRepr::*;
-use self::ChiSquaredRepr::*;
-
-use crate::Rng;
-use crate::distributions::normal::StandardNormal;
-use crate::distributions::{Distribution, Exp, Open01};
-
-/// The Gamma distribution `Gamma(shape, scale)` distribution.
-///
-/// The density function of this distribution is
-///
-/// ```text
-/// f(x) = x^(k - 1) * exp(-x / θ) / (Γ(k) * θ^k)
-/// ```
-///
-/// where `Γ` is the Gamma function, `k` is the shape and `θ` is the
-/// scale and both `k` and `θ` are strictly positive.
-///
-/// The algorithm used is that described by Marsaglia & Tsang 2000[^1],
-/// falling back to directly sampling from an Exponential for `shape
-/// == 1`, and using the boosting technique described in that paper for
-/// `shape < 1`.
-///
-/// [^1]: George Marsaglia and Wai Wan Tsang. 2000. "A Simple Method for
-/// Generating Gamma Variables" *ACM Trans. Math. Softw.* 26, 3
-/// (September 2000), 363-372.
-/// DOI:[10.1145/358407.358414](https://doi.acm.org/10.1145/358407.358414)
-#[deprecated(since="0.7.0", note="moved to rand_distr crate")]
-#[derive(Clone, Copy, Debug)]
-pub struct Gamma {
- repr: GammaRepr,
-}
-
-#[derive(Clone, Copy, Debug)]
-enum GammaRepr {
- Large(GammaLargeShape),
- One(Exp),
- Small(GammaSmallShape)
-}
-
-// These two helpers could be made public, but saving the
-// match-on-Gamma-enum branch from using them directly (e.g. if one
-// knows that the shape is always > 1) doesn't appear to be much
-// faster.
-
-/// Gamma distribution where the shape parameter is less than 1.
-///
-/// Note, samples from this require a compulsory floating-point `pow`
-/// call, which makes it significantly slower than sampling from a
-/// gamma distribution where the shape parameter is greater than or
-/// equal to 1.
-///
-/// See `Gamma` for sampling from a Gamma distribution with general
-/// shape parameters.
-#[derive(Clone, Copy, Debug)]
-struct GammaSmallShape {
- inv_shape: f64,
- large_shape: GammaLargeShape
-}
-
-/// Gamma distribution where the shape parameter is larger than 1.
-///
-/// See `Gamma` for sampling from a Gamma distribution with general
-/// shape parameters.
-#[derive(Clone, Copy, Debug)]
-struct GammaLargeShape {
- scale: f64,
- c: f64,
- d: f64
-}
-
-impl Gamma {
- /// Construct an object representing the `Gamma(shape, scale)`
- /// distribution.
- ///
- /// Panics if `shape <= 0` or `scale <= 0`.
- #[inline]
- pub fn new(shape: f64, scale: f64) -> Gamma {
- assert!(shape > 0.0, "Gamma::new called with shape <= 0");
- assert!(scale > 0.0, "Gamma::new called with scale <= 0");
-
- let repr = if shape == 1.0 {
- One(Exp::new(1.0 / scale))
- } else if shape < 1.0 {
- Small(GammaSmallShape::new_raw(shape, scale))
- } else {
- Large(GammaLargeShape::new_raw(shape, scale))
- };
- Gamma { repr }
- }
-}
-
-impl GammaSmallShape {
- fn new_raw(shape: f64, scale: f64) -> GammaSmallShape {
- GammaSmallShape {
- inv_shape: 1. / shape,
- large_shape: GammaLargeShape::new_raw(shape + 1.0, scale)
- }
- }
-}
-
-impl GammaLargeShape {
- fn new_raw(shape: f64, scale: f64) -> GammaLargeShape {
- let d = shape - 1. / 3.;
- GammaLargeShape {
- scale,
- c: 1. / (9. * d).sqrt(),
- d
- }
- }
-}
-
-impl Distribution<f64> for Gamma {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
- match self.repr {
- Small(ref g) => g.sample(rng),
- One(ref g) => g.sample(rng),
- Large(ref g) => g.sample(rng),
- }
- }
-}
-impl Distribution<f64> for GammaSmallShape {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
- let u: f64 = rng.sample(Open01);
-
- self.large_shape.sample(rng) * u.powf(self.inv_shape)
- }
-}
-impl Distribution<f64> for GammaLargeShape {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
- loop {
- let x = rng.sample(StandardNormal);
- let v_cbrt = 1.0 + self.c * x;
- if v_cbrt <= 0.0 { // a^3 <= 0 iff a <= 0
- continue
- }
-
- let v = v_cbrt * v_cbrt * v_cbrt;
- let u: f64 = rng.sample(Open01);
-
- let x_sqr = x * x;
- if u < 1.0 - 0.0331 * x_sqr * x_sqr ||
- u.ln() < 0.5 * x_sqr + self.d * (1.0 - v + v.ln()) {
- return self.d * v * self.scale
- }
- }
- }
-}
-
-/// The chi-squared distribution `χ²(k)`, where `k` is the degrees of
-/// freedom.
-///
-/// For `k > 0` integral, this distribution is the sum of the squares
-/// of `k` independent standard normal random variables. For other
-/// `k`, this uses the equivalent characterisation
-/// `χ²(k) = Gamma(k/2, 2)`.
-#[deprecated(since="0.7.0", note="moved to rand_distr crate")]
-#[derive(Clone, Copy, Debug)]
-pub struct ChiSquared {
- repr: ChiSquaredRepr,
-}
-
-#[derive(Clone, Copy, Debug)]
-enum ChiSquaredRepr {
- // k == 1, Gamma(alpha, ..) is particularly slow for alpha < 1,
- // e.g. when alpha = 1/2 as it would be for this case, so special-
- // casing and using the definition of N(0,1)^2 is faster.
- DoFExactlyOne,
- DoFAnythingElse(Gamma),
-}
-
-impl ChiSquared {
- /// Create a new chi-squared distribution with degrees-of-freedom
- /// `k`. Panics if `k < 0`.
- pub fn new(k: f64) -> ChiSquared {
- let repr = if k == 1.0 {
- DoFExactlyOne
- } else {
- assert!(k > 0.0, "ChiSquared::new called with `k` < 0");
- DoFAnythingElse(Gamma::new(0.5 * k, 2.0))
- };
- ChiSquared { repr }
- }
-}
-impl Distribution<f64> for ChiSquared {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
- match self.repr {
- DoFExactlyOne => {
- // k == 1 => N(0,1)^2
- let norm = rng.sample(StandardNormal);
- norm * norm
- }
- DoFAnythingElse(ref g) => g.sample(rng)
- }
- }
-}
-
-/// The Fisher F distribution `F(m, n)`.
-///
-/// This distribution is equivalent to the ratio of two normalised
-/// chi-squared distributions, that is, `F(m,n) = (χ²(m)/m) /
-/// (χ²(n)/n)`.
-#[deprecated(since="0.7.0", note="moved to rand_distr crate")]
-#[derive(Clone, Copy, Debug)]
-pub struct FisherF {
- numer: ChiSquared,
- denom: ChiSquared,
- // denom_dof / numer_dof so that this can just be a straight
- // multiplication, rather than a division.
- dof_ratio: f64,
-}
-
-impl FisherF {
- /// Create a new `FisherF` distribution, with the given
- /// parameter. Panics if either `m` or `n` are not positive.
- pub fn new(m: f64, n: f64) -> FisherF {
- assert!(m > 0.0, "FisherF::new called with `m < 0`");
- assert!(n > 0.0, "FisherF::new called with `n < 0`");
-
- FisherF {
- numer: ChiSquared::new(m),
- denom: ChiSquared::new(n),
- dof_ratio: n / m
- }
- }
-}
-impl Distribution<f64> for FisherF {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
- self.numer.sample(rng) / self.denom.sample(rng) * self.dof_ratio
- }
-}
-
-/// The Student t distribution, `t(nu)`, where `nu` is the degrees of
-/// freedom.
-#[deprecated(since="0.7.0", note="moved to rand_distr crate")]
-#[derive(Clone, Copy, Debug)]
-pub struct StudentT {
- chi: ChiSquared,
- dof: f64
-}
-
-impl StudentT {
- /// Create a new Student t distribution with `n` degrees of
- /// freedom. Panics if `n <= 0`.
- pub fn new(n: f64) -> StudentT {
- assert!(n > 0.0, "StudentT::new called with `n <= 0`");
- StudentT {
- chi: ChiSquared::new(n),
- dof: n
- }
- }
-}
-impl Distribution<f64> for StudentT {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
- let norm = rng.sample(StandardNormal);
- norm * (self.dof / self.chi.sample(rng)).sqrt()
- }
-}
-
-/// The Beta distribution with shape parameters `alpha` and `beta`.
-#[deprecated(since="0.7.0", note="moved to rand_distr crate")]
-#[derive(Clone, Copy, Debug)]
-pub struct Beta {
- gamma_a: Gamma,
- gamma_b: Gamma,
-}
-
-impl Beta {
- /// Construct an object representing the `Beta(alpha, beta)`
- /// distribution.
- ///
- /// Panics if `shape <= 0` or `scale <= 0`.
- pub fn new(alpha: f64, beta: f64) -> Beta {
- assert!((alpha > 0.) & (beta > 0.));
- Beta {
- gamma_a: Gamma::new(alpha, 1.),
- gamma_b: Gamma::new(beta, 1.),
- }
- }
-}
-
-impl Distribution<f64> for Beta {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
- let x = self.gamma_a.sample(rng);
- let y = self.gamma_b.sample(rng);
- x / (x + y)
- }
-}
-
-#[cfg(test)]
-mod test {
- use crate::distributions::Distribution;
- use super::{Beta, ChiSquared, StudentT, FisherF};
-
- const N: u32 = 100;
-
- #[test]
- fn test_chi_squared_one() {
- let chi = ChiSquared::new(1.0);
- let mut rng = crate::test::rng(201);
- for _ in 0..N {
- chi.sample(&mut rng);
- }
- }
- #[test]
- fn test_chi_squared_small() {
- let chi = ChiSquared::new(0.5);
- let mut rng = crate::test::rng(202);
- for _ in 0..N {
- chi.sample(&mut rng);
- }
- }
- #[test]
- fn test_chi_squared_large() {
- let chi = ChiSquared::new(30.0);
- let mut rng = crate::test::rng(203);
- for _ in 0..N {
- chi.sample(&mut rng);
- }
- }
- #[test]
- #[should_panic]
- fn test_chi_squared_invalid_dof() {
- ChiSquared::new(-1.0);
- }
-
- #[test]
- fn test_f() {
- let f = FisherF::new(2.0, 32.0);
- let mut rng = crate::test::rng(204);
- for _ in 0..N {
- f.sample(&mut rng);
- }
- }
-
- #[test]
- fn test_t() {
- let t = StudentT::new(11.0);
- let mut rng = crate::test::rng(205);
- for _ in 0..N {
- t.sample(&mut rng);
- }
- }
-
- #[test]
- fn test_beta() {
- let beta = Beta::new(1.0, 2.0);
- let mut rng = crate::test::rng(201);
- for _ in 0..N {
- beta.sample(&mut rng);
- }
- }
-
- #[test]
- #[should_panic]
- fn test_beta_invalid_dof() {
- Beta::new(0., 0.);
- }
-}
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