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| <span id="814">814</span> |
| </pre><pre class="rust"><code><span class="comment">// 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. |
| |
| </span><span class="doccomment">//! The Gamma and derived distributions. |
| |
| </span><span class="comment">// We use the variable names from the published reference, therefore this |
| // warning is not helpful. |
| </span><span class="attribute">#![allow(clippy::many_single_char_names)] |
| |
| </span><span class="kw">use </span><span class="self">self</span>::ChiSquaredRepr::<span class="kw-2">*</span>; |
| <span class="kw">use </span><span class="self">self</span>::GammaRepr::<span class="kw-2">*</span>; |
| |
| <span class="kw">use </span><span class="kw">crate</span>::normal::StandardNormal; |
| <span class="kw">use </span>num_traits::Float; |
| <span class="kw">use crate</span>::{Distribution, Exp, Exp1, Open01}; |
| <span class="kw">use </span>rand::Rng; |
| <span class="kw">use </span>core::fmt; |
| <span class="attribute">#[cfg(feature = <span class="string">"serde1"</span>)] |
| </span><span class="kw">use </span>serde::{Serialize, Deserialize}; |
| |
| <span class="doccomment">/// 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`. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{Distribution, Gamma}; |
| /// |
| /// let gamma = Gamma::new(2.0, 5.0).unwrap(); |
| /// let v = gamma.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](https://doi.acm.org/10.1145/358407.358414) |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub struct </span>Gamma<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| repr: GammaRepr<F>, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Gamma::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>Error { |
| <span class="doccomment">/// `shape <= 0` or `nan`. |
| </span>ShapeTooSmall, |
| <span class="doccomment">/// `scale <= 0` or `nan`. |
| </span>ScaleTooSmall, |
| <span class="doccomment">/// `1 / scale == 0`. |
| </span>ScaleTooLarge, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>Error { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| Error::ShapeTooSmall => <span class="string">"shape is not positive in gamma distribution"</span>, |
| Error::ScaleTooSmall => <span class="string">"scale is not positive in gamma distribution"</span>, |
| Error::ScaleTooLarge => <span class="string">"scale is infinity in gamma distribution"</span>, |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">"std"</span>)))] |
| </span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>Error {} |
| |
| <span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">enum </span>GammaRepr<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| Large(GammaLargeShape<F>), |
| One(Exp<F>), |
| Small(GammaSmallShape<F>), |
| } |
| |
| <span class="comment">// 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. |
| |
| </span><span class="doccomment">/// 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. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">struct </span>GammaSmallShape<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| inv_shape: F, |
| large_shape: GammaLargeShape<F>, |
| } |
| |
| <span class="doccomment">/// Gamma distribution where the shape parameter is larger than 1. |
| /// |
| /// See `Gamma` for sampling from a Gamma distribution with general |
| /// shape parameters. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">struct </span>GammaLargeShape<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| scale: F, |
| c: F, |
| d: F, |
| } |
| |
| <span class="kw">impl</span><F> Gamma<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="doccomment">/// Construct an object representing the `Gamma(shape, scale)` |
| /// distribution. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>new(shape: F, scale: F) -> <span class="prelude-ty">Result</span><Gamma<F>, Error> { |
| <span class="kw">if </span>!(shape > F::zero()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::ShapeTooSmall); |
| } |
| <span class="kw">if </span>!(scale > F::zero()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::ScaleTooSmall); |
| } |
| |
| <span class="kw">let </span>repr = <span class="kw">if </span>shape == F::one() { |
| One(Exp::new(F::one() / scale).map_err(|<span class="kw">_</span>| Error::ScaleTooLarge)<span class="question-mark">?</span>) |
| } <span class="kw">else if </span>shape < F::one() { |
| Small(GammaSmallShape::new_raw(shape, scale)) |
| } <span class="kw">else </span>{ |
| Large(GammaLargeShape::new_raw(shape, scale)) |
| }; |
| <span class="prelude-val">Ok</span>(Gamma { repr }) |
| } |
| } |
| |
| <span class="kw">impl</span><F> GammaSmallShape<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>new_raw(shape: F, scale: F) -> GammaSmallShape<F> { |
| GammaSmallShape { |
| inv_shape: F::one() / shape, |
| large_shape: GammaLargeShape::new_raw(shape + F::one(), scale), |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><F> GammaLargeShape<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>new_raw(shape: F, scale: F) -> GammaLargeShape<F> { |
| <span class="kw">let </span>d = shape - F::from(<span class="number">1. </span>/ <span class="number">3.</span>).unwrap(); |
| GammaLargeShape { |
| scale, |
| c: F::one() / (F::from(<span class="number">9.</span>).unwrap() * d).sqrt(), |
| d, |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>Gamma<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">match </span><span class="self">self</span>.repr { |
| Small(<span class="kw-2">ref </span>g) => g.sample(rng), |
| One(<span class="kw-2">ref </span>g) => g.sample(rng), |
| Large(<span class="kw-2">ref </span>g) => g.sample(rng), |
| } |
| } |
| } |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>GammaSmallShape<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">let </span>u: F = rng.sample(Open01); |
| |
| <span class="self">self</span>.large_shape.sample(rng) * u.powf(<span class="self">self</span>.inv_shape) |
| } |
| } |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>GammaLargeShape<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="comment">// Marsaglia & Tsang method, 2000 |
| </span><span class="kw">loop </span>{ |
| <span class="kw">let </span>x: F = rng.sample(StandardNormal); |
| <span class="kw">let </span>v_cbrt = F::one() + <span class="self">self</span>.c * x; |
| <span class="kw">if </span>v_cbrt <= F::zero() { |
| <span class="comment">// a^3 <= 0 iff a <= 0 |
| </span><span class="kw">continue</span>; |
| } |
| |
| <span class="kw">let </span>v = v_cbrt * v_cbrt * v_cbrt; |
| <span class="kw">let </span>u: F = rng.sample(Open01); |
| |
| <span class="kw">let </span>x_sqr = x * x; |
| <span class="kw">if </span>u < F::one() - F::from(<span class="number">0.0331</span>).unwrap() * x_sqr * x_sqr |
| || u.ln() < F::from(<span class="number">0.5</span>).unwrap() * x_sqr + <span class="self">self</span>.d * (F::one() - v + v.ln()) |
| { |
| <span class="kw">return </span><span class="self">self</span>.d * v * <span class="self">self</span>.scale; |
| } |
| } |
| } |
| } |
| |
| <span class="doccomment">/// 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 |
| /// |
| /// ``` |
| /// use rand_distr::{ChiSquared, Distribution}; |
| /// |
| /// let chi = ChiSquared::new(11.0).unwrap(); |
| /// let v = chi.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a χ²(11) distribution", v) |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub struct </span>ChiSquared<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| repr: ChiSquaredRepr<F>, |
| } |
| |
| <span class="doccomment">/// Error type returned from `ChiSquared::new` and `StudentT::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub enum </span>ChiSquaredError { |
| <span class="doccomment">/// `0.5 * k <= 0` or `nan`. |
| </span>DoFTooSmall, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>ChiSquaredError { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| ChiSquaredError::DoFTooSmall => { |
| <span class="string">"degrees-of-freedom k is not positive in chi-squared distribution" |
| </span>} |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">"std"</span>)))] |
| </span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>ChiSquaredError {} |
| |
| <span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">enum </span>ChiSquaredRepr<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="comment">// 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. |
| </span>DoFExactlyOne, |
| DoFAnythingElse(Gamma<F>), |
| } |
| |
| <span class="kw">impl</span><F> ChiSquared<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="doccomment">/// Create a new chi-squared distribution with degrees-of-freedom |
| /// `k`. |
| </span><span class="kw">pub fn </span>new(k: F) -> <span class="prelude-ty">Result</span><ChiSquared<F>, ChiSquaredError> { |
| <span class="kw">let </span>repr = <span class="kw">if </span>k == F::one() { |
| DoFExactlyOne |
| } <span class="kw">else </span>{ |
| <span class="kw">if </span>!(F::from(<span class="number">0.5</span>).unwrap() * k > F::zero()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(ChiSquaredError::DoFTooSmall); |
| } |
| DoFAnythingElse(Gamma::new(F::from(<span class="number">0.5</span>).unwrap() * k, F::from(<span class="number">2.0</span>).unwrap()).unwrap()) |
| }; |
| <span class="prelude-val">Ok</span>(ChiSquared { repr }) |
| } |
| } |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>ChiSquared<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">match </span><span class="self">self</span>.repr { |
| DoFExactlyOne => { |
| <span class="comment">// k == 1 => N(0,1)^2 |
| </span><span class="kw">let </span>norm: F = rng.sample(StandardNormal); |
| norm * norm |
| } |
| DoFAnythingElse(<span class="kw-2">ref </span>g) => g.sample(rng), |
| } |
| } |
| } |
| |
| <span class="doccomment">/// 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 |
| /// |
| /// ``` |
| /// use rand_distr::{FisherF, Distribution}; |
| /// |
| /// let f = FisherF::new(2.0, 32.0).unwrap(); |
| /// let v = f.sample(&mut rand::thread_rng()); |
| /// println!("{} is from an F(2, 32) distribution", v) |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub struct </span>FisherF<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| numer: ChiSquared<F>, |
| denom: ChiSquared<F>, |
| <span class="comment">// denom_dof / numer_dof so that this can just be a straight |
| // multiplication, rather than a division. |
| </span>dof_ratio: F, |
| } |
| |
| <span class="doccomment">/// Error type returned from `FisherF::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub enum </span>FisherFError { |
| <span class="doccomment">/// `m <= 0` or `nan`. |
| </span>MTooSmall, |
| <span class="doccomment">/// `n <= 0` or `nan`. |
| </span>NTooSmall, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>FisherFError { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| FisherFError::MTooSmall => <span class="string">"m is not positive in Fisher F distribution"</span>, |
| FisherFError::NTooSmall => <span class="string">"n is not positive in Fisher F distribution"</span>, |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">"std"</span>)))] |
| </span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>FisherFError {} |
| |
| <span class="kw">impl</span><F> FisherF<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="doccomment">/// Create a new `FisherF` distribution, with the given parameter. |
| </span><span class="kw">pub fn </span>new(m: F, n: F) -> <span class="prelude-ty">Result</span><FisherF<F>, FisherFError> { |
| <span class="kw">let </span>zero = F::zero(); |
| <span class="kw">if </span>!(m > zero) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(FisherFError::MTooSmall); |
| } |
| <span class="kw">if </span>!(n > zero) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(FisherFError::NTooSmall); |
| } |
| |
| <span class="prelude-val">Ok</span>(FisherF { |
| numer: ChiSquared::new(m).unwrap(), |
| denom: ChiSquared::new(n).unwrap(), |
| dof_ratio: n / m, |
| }) |
| } |
| } |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>FisherF<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="self">self</span>.numer.sample(rng) / <span class="self">self</span>.denom.sample(rng) * <span class="self">self</span>.dof_ratio |
| } |
| } |
| |
| <span class="doccomment">/// The Student t distribution, `t(nu)`, where `nu` is the degrees of |
| /// freedom. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{StudentT, Distribution}; |
| /// |
| /// let t = StudentT::new(11.0).unwrap(); |
| /// let v = t.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a t(11) distribution", v) |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub struct </span>StudentT<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| chi: ChiSquared<F>, |
| dof: F, |
| } |
| |
| <span class="kw">impl</span><F> StudentT<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="doccomment">/// Create a new Student t distribution with `n` degrees of |
| /// freedom. |
| </span><span class="kw">pub fn </span>new(n: F) -> <span class="prelude-ty">Result</span><StudentT<F>, ChiSquaredError> { |
| <span class="prelude-val">Ok</span>(StudentT { |
| chi: ChiSquared::new(n)<span class="question-mark">?</span>, |
| dof: n, |
| }) |
| } |
| } |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>StudentT<F> |
| <span class="kw">where |
| </span>F: Float, |
| StandardNormal: Distribution<F>, |
| Exp1: Distribution<F>, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">let </span>norm: F = rng.sample(StandardNormal); |
| norm * (<span class="self">self</span>.dof / <span class="self">self</span>.chi.sample(rng)).sqrt() |
| } |
| } |
| |
| <span class="doccomment">/// The algorithm used for sampling the Beta distribution. |
| /// |
| /// Reference: |
| /// |
| /// R. C. H. Cheng (1978). |
| /// Generating beta variates with nonintegral shape parameters. |
| /// Communications of the ACM 21, 317-322. |
| /// https://doi.org/10.1145/359460.359482 |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">enum </span>BetaAlgorithm<N> { |
| BB(BB<N>), |
| BC(BC<N>), |
| } |
| |
| <span class="doccomment">/// Algorithm BB for `min(alpha, beta) > 1`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">struct </span>BB<N> { |
| alpha: N, |
| beta: N, |
| gamma: N, |
| } |
| |
| <span class="doccomment">/// Algorithm BC for `min(alpha, beta) <= 1`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">struct </span>BC<N> { |
| alpha: N, |
| beta: N, |
| delta: N, |
| kappa1: N, |
| kappa2: N, |
| } |
| |
| <span class="doccomment">/// The Beta distribution with shape parameters `alpha` and `beta`. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{Distribution, Beta}; |
| /// |
| /// let beta = Beta::new(2.0, 5.0).unwrap(); |
| /// let v = beta.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a Beta(2, 5) distribution", v); |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub struct </span>Beta<F> |
| <span class="kw">where |
| </span>F: Float, |
| Open01: Distribution<F>, |
| { |
| a: F, b: F, switched_params: bool, |
| algorithm: BetaAlgorithm<F>, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Beta::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub enum </span>BetaError { |
| <span class="doccomment">/// `alpha <= 0` or `nan`. |
| </span>AlphaTooSmall, |
| <span class="doccomment">/// `beta <= 0` or `nan`. |
| </span>BetaTooSmall, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>BetaError { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| BetaError::AlphaTooSmall => <span class="string">"alpha is not positive in beta distribution"</span>, |
| BetaError::BetaTooSmall => <span class="string">"beta is not positive in beta distribution"</span>, |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">"std"</span>)))] |
| </span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>BetaError {} |
| |
| <span class="kw">impl</span><F> Beta<F> |
| <span class="kw">where |
| </span>F: Float, |
| Open01: Distribution<F>, |
| { |
| <span class="doccomment">/// Construct an object representing the `Beta(alpha, beta)` |
| /// distribution. |
| </span><span class="kw">pub fn </span>new(alpha: F, beta: F) -> <span class="prelude-ty">Result</span><Beta<F>, BetaError> { |
| <span class="kw">if </span>!(alpha > F::zero()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(BetaError::AlphaTooSmall); |
| } |
| <span class="kw">if </span>!(beta > F::zero()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(BetaError::BetaTooSmall); |
| } |
| <span class="comment">// From now on, we use the notation from the reference, |
| // i.e. `alpha` and `beta` are renamed to `a0` and `b0`. |
| </span><span class="kw">let </span>(a0, b0) = (alpha, beta); |
| <span class="kw">let </span>(a, b, switched_params) = <span class="kw">if </span>a0 < b0 { |
| (a0, b0, <span class="bool-val">false</span>) |
| } <span class="kw">else </span>{ |
| (b0, a0, <span class="bool-val">true</span>) |
| }; |
| <span class="kw">if </span>a > F::one() { |
| <span class="comment">// Algorithm BB |
| </span><span class="kw">let </span>alpha = a + b; |
| <span class="kw">let </span>beta = ((alpha - F::from(<span class="number">2.</span>).unwrap()) |
| / (F::from(<span class="number">2.</span>).unwrap()<span class="kw-2">*</span>a<span class="kw-2">*</span>b - alpha)).sqrt(); |
| <span class="kw">let </span>gamma = a + F::one() / beta; |
| |
| <span class="prelude-val">Ok</span>(Beta { |
| a, b, switched_params, |
| algorithm: BetaAlgorithm::BB(BB { |
| alpha, beta, gamma, |
| }) |
| }) |
| } <span class="kw">else </span>{ |
| <span class="comment">// Algorithm BC |
| // |
| // Here `a` is the maximum instead of the minimum. |
| </span><span class="kw">let </span>(a, b, switched_params) = (b, a, !switched_params); |
| <span class="kw">let </span>alpha = a + b; |
| <span class="kw">let </span>beta = F::one() / b; |
| <span class="kw">let </span>delta = F::one() + a - b; |
| <span class="kw">let </span>kappa1 = delta |
| * (F::from(<span class="number">1. </span>/ <span class="number">18. </span>/ <span class="number">4.</span>).unwrap() + F::from(<span class="number">3. </span>/ <span class="number">18. </span>/ <span class="number">4.</span>).unwrap()<span class="kw-2">*</span>b) |
| / (a<span class="kw-2">*</span>beta - F::from(<span class="number">14. </span>/ <span class="number">18.</span>).unwrap()); |
| <span class="kw">let </span>kappa2 = F::from(<span class="number">0.25</span>).unwrap() |
| + (F::from(<span class="number">0.5</span>).unwrap() + F::from(<span class="number">0.25</span>).unwrap()/delta)<span class="kw-2">*</span>b; |
| |
| <span class="prelude-val">Ok</span>(Beta { |
| a, b, switched_params, |
| algorithm: BetaAlgorithm::BC(BC { |
| alpha, beta, delta, kappa1, kappa2, |
| }) |
| }) |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>Beta<F> |
| <span class="kw">where |
| </span>F: Float, |
| Open01: Distribution<F>, |
| { |
| <span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">let </span><span class="kw-2">mut </span>w; |
| <span class="kw">match </span><span class="self">self</span>.algorithm { |
| BetaAlgorithm::BB(algo) => { |
| <span class="kw">loop </span>{ |
| <span class="comment">// 1. |
| </span><span class="kw">let </span>u1 = rng.sample(Open01); |
| <span class="kw">let </span>u2 = rng.sample(Open01); |
| <span class="kw">let </span>v = algo.beta * (u1 / (F::one() - u1)).ln(); |
| w = <span class="self">self</span>.a * v.exp(); |
| <span class="kw">let </span>z = u1<span class="kw-2">*</span>u1 * u2; |
| <span class="kw">let </span>r = algo.gamma * v - F::from(<span class="number">4.</span>).unwrap().ln(); |
| <span class="kw">let </span>s = <span class="self">self</span>.a + r - w; |
| <span class="comment">// 2. |
| </span><span class="kw">if </span>s + F::one() + F::from(<span class="number">5.</span>).unwrap().ln() |
| >= F::from(<span class="number">5.</span>).unwrap() * z { |
| <span class="kw">break</span>; |
| } |
| <span class="comment">// 3. |
| </span><span class="kw">let </span>t = z.ln(); |
| <span class="kw">if </span>s >= t { |
| <span class="kw">break</span>; |
| } |
| <span class="comment">// 4. |
| </span><span class="kw">if </span>!(r + algo.alpha * (algo.alpha / (<span class="self">self</span>.b + w)).ln() < t) { |
| <span class="kw">break</span>; |
| } |
| } |
| }, |
| BetaAlgorithm::BC(algo) => { |
| <span class="kw">loop </span>{ |
| <span class="kw">let </span>z; |
| <span class="comment">// 1. |
| </span><span class="kw">let </span>u1 = rng.sample(Open01); |
| <span class="kw">let </span>u2 = rng.sample(Open01); |
| <span class="kw">if </span>u1 < F::from(<span class="number">0.5</span>).unwrap() { |
| <span class="comment">// 2. |
| </span><span class="kw">let </span>y = u1 * u2; |
| z = u1 * y; |
| <span class="kw">if </span>F::from(<span class="number">0.25</span>).unwrap() * u2 + z - y >= algo.kappa1 { |
| <span class="kw">continue</span>; |
| } |
| } <span class="kw">else </span>{ |
| <span class="comment">// 3. |
| </span>z = u1 * u1 * u2; |
| <span class="kw">if </span>z <= F::from(<span class="number">0.25</span>).unwrap() { |
| <span class="kw">let </span>v = algo.beta * (u1 / (F::one() - u1)).ln(); |
| w = <span class="self">self</span>.a * v.exp(); |
| <span class="kw">break</span>; |
| } |
| <span class="comment">// 4. |
| </span><span class="kw">if </span>z >= algo.kappa2 { |
| <span class="kw">continue</span>; |
| } |
| } |
| <span class="comment">// 5. |
| </span><span class="kw">let </span>v = algo.beta * (u1 / (F::one() - u1)).ln(); |
| w = <span class="self">self</span>.a * v.exp(); |
| <span class="kw">if </span>!(algo.alpha * ((algo.alpha / (<span class="self">self</span>.b + w)).ln() + v) |
| - F::from(<span class="number">4.</span>).unwrap().ln() < z.ln()) { |
| <span class="kw">break</span>; |
| }; |
| } |
| }, |
| }; |
| <span class="comment">// 5. for BB, 6. for BC |
| </span><span class="kw">if </span>!<span class="self">self</span>.switched_params { |
| <span class="kw">if </span>w == F::infinity() { |
| <span class="comment">// Assuming `b` is finite, for large `w`: |
| </span><span class="kw">return </span>F::one(); |
| } |
| w / (<span class="self">self</span>.b + w) |
| } <span class="kw">else </span>{ |
| <span class="self">self</span>.b / (<span class="self">self</span>.b + w) |
| } |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>test { |
| <span class="kw">use super</span>::<span class="kw-2">*</span>; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_chi_squared_one() { |
| <span class="kw">let </span>chi = ChiSquared::new(<span class="number">1.0</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">201</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| chi.sample(<span class="kw-2">&mut </span>rng); |
| } |
| } |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_chi_squared_small() { |
| <span class="kw">let </span>chi = ChiSquared::new(<span class="number">0.5</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">202</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| chi.sample(<span class="kw-2">&mut </span>rng); |
| } |
| } |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_chi_squared_large() { |
| <span class="kw">let </span>chi = ChiSquared::new(<span class="number">30.0</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">203</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| chi.sample(<span class="kw-2">&mut </span>rng); |
| } |
| } |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_chi_squared_invalid_dof() { |
| ChiSquared::new(-<span class="number">1.0</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_f() { |
| <span class="kw">let </span>f = FisherF::new(<span class="number">2.0</span>, <span class="number">32.0</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">204</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| f.sample(<span class="kw-2">&mut </span>rng); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_t() { |
| <span class="kw">let </span>t = StudentT::new(<span class="number">11.0</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">205</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| t.sample(<span class="kw-2">&mut </span>rng); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_beta() { |
| <span class="kw">let </span>beta = Beta::new(<span class="number">1.0</span>, <span class="number">2.0</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">201</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| beta.sample(<span class="kw-2">&mut </span>rng); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>test_beta_invalid_dof() { |
| Beta::new(<span class="number">0.</span>, <span class="number">0.</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_beta_small_param() { |
| <span class="kw">let </span>beta = Beta::<f64>::new(<span class="number">1e-3</span>, <span class="number">1e-3</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">206</span>); |
| <span class="kw">for </span>i <span class="kw">in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| <span class="macro">assert!</span>(!beta.sample(<span class="kw-2">&mut </span>rng).is_nan(), <span class="string">"failed at i={}"</span>, i); |
| } |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="rand_distr" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |