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authorValentin Popov <valentin@popov.link>2024-07-19 15:37:58 +0300
committerValentin Popov <valentin@popov.link>2024-07-19 15:37:58 +0300
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tree15afc392522a9e85dc3332235e311b7d39352ea9 /vendor/rand/src/distributions/gamma.rs
parent3d48cd3f81164bbfc1a755dc1d4a9a02f98c8ddd (diff)
downloadfparkan-a990de90fe41456a23e58bd087d2f107d321f3a1.tar.xz
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-// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
-// file at the top-level directory of this distribution and at
-// http://rust-lang.org/COPYRIGHT.
-//
-// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
-// option. This file may not be copied, modified, or distributed
-// except according to those terms.
-//
-// ignore-lexer-test FIXME #15679
-
-//! The Gamma and derived distributions.
-
-use self::GammaRepr::*;
-use self::ChiSquaredRepr::*;
-
-use {Rng, Open01};
-use super::normal::StandardNormal;
-use super::{IndependentSample, Sample, Exp};
-
-/// 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 [1] for
-/// `shape < 1`.
-///
-/// # Example
-///
-/// ```rust
-/// use rand::distributions::{IndependentSample, Gamma};
-///
-/// let gamma = Gamma::new(2.0, 5.0);
-/// let v = gamma.ind_sample(&mut rand::thread_rng());
-/// println!("{} is from a Gamma(2, 5) distribution", v);
-/// ```
-///
-/// [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](http://doi.acm.org/10.1145/358407.358414)
-#[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: 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: scale,
- c: 1. / (9. * d).sqrt(),
- d: d
- }
- }
-}
-
-impl Sample<f64> for Gamma {
- fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
-}
-impl Sample<f64> for GammaSmallShape {
- fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
-}
-impl Sample<f64> for GammaLargeShape {
- fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
-}
-
-impl IndependentSample<f64> for Gamma {
- fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
- match self.repr {
- Small(ref g) => g.ind_sample(rng),
- One(ref g) => g.ind_sample(rng),
- Large(ref g) => g.ind_sample(rng),
- }
- }
-}
-impl IndependentSample<f64> for GammaSmallShape {
- fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
- let Open01(u) = rng.gen::<Open01<f64>>();
-
- self.large_shape.ind_sample(rng) * u.powf(self.inv_shape)
- }
-}
-impl IndependentSample<f64> for GammaLargeShape {
- fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
- loop {
- let StandardNormal(x) = rng.gen::<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 Open01(u) = rng.gen::<Open01<f64>>();
-
- 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)`.
-///
-/// # Example
-///
-/// ```rust
-/// use rand::distributions::{ChiSquared, IndependentSample};
-///
-/// let chi = ChiSquared::new(11.0);
-/// let v = chi.ind_sample(&mut rand::thread_rng());
-/// println!("{} is from a χ²(11) distribution", v)
-/// ```
-#[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: repr }
- }
-}
-impl Sample<f64> for ChiSquared {
- fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
-}
-impl IndependentSample<f64> for ChiSquared {
- fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
- match self.repr {
- DoFExactlyOne => {
- // k == 1 => N(0,1)^2
- let StandardNormal(norm) = rng.gen::<StandardNormal>();
- norm * norm
- }
- DoFAnythingElse(ref g) => g.ind_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)`.
-///
-/// # Example
-///
-/// ```rust
-/// use rand::distributions::{FisherF, IndependentSample};
-///
-/// let f = FisherF::new(2.0, 32.0);
-/// let v = f.ind_sample(&mut rand::thread_rng());
-/// println!("{} is from an F(2, 32) distribution", v)
-/// ```
-#[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 Sample<f64> for FisherF {
- fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
-}
-impl IndependentSample<f64> for FisherF {
- fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
- self.numer.ind_sample(rng) / self.denom.ind_sample(rng) * self.dof_ratio
- }
-}
-
-/// The Student t distribution, `t(nu)`, where `nu` is the degrees of
-/// freedom.
-///
-/// # Example
-///
-/// ```rust
-/// use rand::distributions::{StudentT, IndependentSample};
-///
-/// let t = StudentT::new(11.0);
-/// let v = t.ind_sample(&mut rand::thread_rng());
-/// println!("{} is from a t(11) distribution", v)
-/// ```
-#[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 Sample<f64> for StudentT {
- fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
-}
-impl IndependentSample<f64> for StudentT {
- fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
- let StandardNormal(norm) = rng.gen::<StandardNormal>();
- norm * (self.dof / self.chi.ind_sample(rng)).sqrt()
- }
-}
-
-#[cfg(test)]
-mod test {
- use distributions::{Sample, IndependentSample};
- use super::{ChiSquared, StudentT, FisherF};
-
- #[test]
- fn test_chi_squared_one() {
- let mut chi = ChiSquared::new(1.0);
- let mut rng = ::test::rng();
- for _ in 0..1000 {
- chi.sample(&mut rng);
- chi.ind_sample(&mut rng);
- }
- }
- #[test]
- fn test_chi_squared_small() {
- let mut chi = ChiSquared::new(0.5);
- let mut rng = ::test::rng();
- for _ in 0..1000 {
- chi.sample(&mut rng);
- chi.ind_sample(&mut rng);
- }
- }
- #[test]
- fn test_chi_squared_large() {
- let mut chi = ChiSquared::new(30.0);
- let mut rng = ::test::rng();
- for _ in 0..1000 {
- chi.sample(&mut rng);
- chi.ind_sample(&mut rng);
- }
- }
- #[test]
- #[should_panic]
- fn test_chi_squared_invalid_dof() {
- ChiSquared::new(-1.0);
- }
-
- #[test]
- fn test_f() {
- let mut f = FisherF::new(2.0, 32.0);
- let mut rng = ::test::rng();
- for _ in 0..1000 {
- f.sample(&mut rng);
- f.ind_sample(&mut rng);
- }
- }
-
- #[test]
- fn test_t() {
- let mut t = StudentT::new(11.0);
- let mut rng = ::test::rng();
- for _ in 0..1000 {
- t.sample(&mut rng);
- t.ind_sample(&mut rng);
- }
- }
-}