src/distributions/gamma.rs - platform/external/rust/crates/rand - Git at Google

 // 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::ChiSquaredRepr::*;
 use self::GammaRepr::*;

 use crate::distributions::normal::StandardNormal;
 use crate::distributions::{Distribution, Exp, Open01};
 use crate::Rng;

 /// 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 super::{Beta, ChiSquared, FisherF, StudentT};
     use crate::distributions::Distribution;

     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.);
     }
 }
	// 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::ChiSquaredRepr::*;
	use self::GammaRepr::*;

	use crate::distributions::normal::StandardNormal;
	use crate::distributions::{Distribution, Exp, Open01};
	use crate::Rng;

	/// 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 super::{Beta, ChiSquared, FisherF, StudentT};
	use crate::distributions::Distribution;

	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.);
	}
	}