| <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/sunhe/incubator-teaclave/third_party/rust-sgx-sdk/sgx_rand/src/distributions/gamma.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>gamma.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../../sgx_rand/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../sgx_rand/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </pre><pre class="rust"><code><span class="comment">// Licensed to the Apache Software Foundation (ASF) under one |
| // or more contributor license agreements. See the NOTICE file |
| // distributed with this work for additional information |
| // regarding copyright ownership. The ASF licenses this file |
| // to you under the Apache License, Version 2.0 (the |
| // "License"); you may not use this file except in compliance |
| // with the License. You may obtain a copy of the License at |
| // |
| // http://www.apache.org/licenses/LICENSE-2.0 |
| // |
| // Unless required by applicable law or agreed to in writing, |
| // software distributed under the License is distributed on an |
| // "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY |
| // KIND, either express or implied. See the License for the |
| // specific language governing permissions and limitations |
| // under the License.. |
| |
| </span><span class="doccomment">//! The Gamma and derived distributions. |
| |
| </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">super</span>::normal::StandardNormal; |
| <span class="kw">use super</span>::{Exp, IndependentSample, Sample}; |
| <span class="kw">use crate</span>::{Open01, Rng}; |
| |
| <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 \[1\] for |
| /// `shape < 1`. |
| /// |
| /// # Example |
| /// |
| /// ```rust |
| /// use sgx_rand::distributions::{IndependentSample, Gamma}; |
| /// |
| /// let gamma = Gamma::new(2.0, 5.0); |
| /// let v = gamma.ind_sample(&mut sgx_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) |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">pub struct </span>Gamma { |
| repr: GammaRepr, |
| } |
| |
| <span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">enum </span>GammaRepr { |
| Large(GammaLargeShape), |
| One(Exp), |
| Small(GammaSmallShape), |
| } |
| |
| <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)] |
| </span><span class="kw">struct </span>GammaSmallShape { |
| inv_shape: f64, |
| large_shape: GammaLargeShape, |
| } |
| |
| <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)] |
| </span><span class="kw">struct </span>GammaLargeShape { |
| scale: f64, |
| c: f64, |
| d: f64, |
| } |
| |
| <span class="kw">impl </span>Gamma { |
| <span class="doccomment">/// Construct an object representing the `Gamma(shape, scale)` |
| /// distribution. |
| /// |
| /// Panics if `shape <= 0` or `scale <= 0`. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>new(shape: f64, scale: f64) -> Gamma { |
| <span class="macro">assert!</span>(shape > <span class="number">0.0</span>, <span class="string">"Gamma::new called with shape <= 0"</span>); |
| <span class="macro">assert!</span>(scale > <span class="number">0.0</span>, <span class="string">"Gamma::new called with scale <= 0"</span>); |
| |
| <span class="kw">let </span>repr = <span class="kw">if </span>(shape - <span class="number">1.0</span>).abs() < f64::EPSILON { |
| One(Exp::new(<span class="number">1.0 </span>/ scale)) |
| } <span class="kw">else if </span>shape < <span class="number">1.0 </span>{ |
| Small(GammaSmallShape::new_raw(shape, scale)) |
| } <span class="kw">else </span>{ |
| Large(GammaLargeShape::new_raw(shape, scale)) |
| }; |
| Gamma { repr } |
| } |
| } |
| |
| <span class="kw">impl </span>GammaSmallShape { |
| <span class="kw">fn </span>new_raw(shape: f64, scale: f64) -> GammaSmallShape { |
| GammaSmallShape { |
| inv_shape: <span class="number">1. </span>/ shape, |
| large_shape: GammaLargeShape::new_raw(shape + <span class="number">1.0</span>, scale), |
| } |
| } |
| } |
| |
| <span class="kw">impl </span>GammaLargeShape { |
| <span class="kw">fn </span>new_raw(shape: f64, scale: f64) -> GammaLargeShape { |
| <span class="kw">let </span>d = shape - <span class="number">1. </span>/ <span class="number">3.</span>; |
| GammaLargeShape { |
| scale, |
| c: <span class="number">1. </span>/ (<span class="number">9. </span>* d).sqrt(), |
| d, |
| } |
| } |
| } |
| |
| <span class="kw">impl </span>Sample<f64> <span class="kw">for </span>Gamma { |
| <span class="kw">fn </span>sample<R: Rng>(<span class="kw-2">&mut </span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="self">self</span>.ind_sample(rng) |
| } |
| } |
| <span class="kw">impl </span>Sample<f64> <span class="kw">for </span>GammaSmallShape { |
| <span class="kw">fn </span>sample<R: Rng>(<span class="kw-2">&mut </span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="self">self</span>.ind_sample(rng) |
| } |
| } |
| <span class="kw">impl </span>Sample<f64> <span class="kw">for </span>GammaLargeShape { |
| <span class="kw">fn </span>sample<R: Rng>(<span class="kw-2">&mut </span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="self">self</span>.ind_sample(rng) |
| } |
| } |
| |
| <span class="kw">impl </span>IndependentSample<f64> <span class="kw">for </span>Gamma { |
| <span class="kw">fn </span>ind_sample<R: Rng>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="kw">match </span><span class="self">self</span>.repr { |
| Small(<span class="kw-2">ref </span>g) => g.ind_sample(rng), |
| One(<span class="kw-2">ref </span>g) => g.ind_sample(rng), |
| Large(<span class="kw-2">ref </span>g) => g.ind_sample(rng), |
| } |
| } |
| } |
| <span class="kw">impl </span>IndependentSample<f64> <span class="kw">for </span>GammaSmallShape { |
| <span class="kw">fn </span>ind_sample<R: Rng>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="kw">let </span>Open01(u) = rng.gen::<Open01<f64>>(); |
| |
| <span class="self">self</span>.large_shape.ind_sample(rng) * u.powf(<span class="self">self</span>.inv_shape) |
| } |
| } |
| <span class="kw">impl </span>IndependentSample<f64> <span class="kw">for </span>GammaLargeShape { |
| <span class="kw">fn </span>ind_sample<R: Rng>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="kw">loop </span>{ |
| <span class="kw">let </span>StandardNormal(x) = rng.gen::<StandardNormal>(); |
| <span class="kw">let </span>v_cbrt = <span class="number">1.0 </span>+ <span class="self">self</span>.c * x; |
| <span class="kw">if </span>v_cbrt <= <span class="number">0.0 </span>{ |
| <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>Open01(u) = rng.gen::<Open01<f64>>(); |
| |
| <span class="kw">let </span>x_sqr = x * x; |
| <span class="kw">if </span>u < <span class="number">1.0 </span>- <span class="number">0.0331 </span>* x_sqr * x_sqr |
| || u.ln() < <span class="number">0.5 </span>* x_sqr + <span class="self">self</span>.d * (<span class="number">1.0 </span>- 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 |
| /// |
| /// ```rust |
| /// use sgx_rand::distributions::{ChiSquared, IndependentSample}; |
| /// |
| /// let chi = ChiSquared::new(11.0); |
| /// let v = chi.ind_sample(&mut sgx_rand::thread_rng()); |
| /// println!("{} is from a χ²(11) distribution", v) |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">pub struct </span>ChiSquared { |
| repr: ChiSquaredRepr, |
| } |
| |
| <span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">enum </span>ChiSquaredRepr { |
| <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), |
| } |
| |
| <span class="kw">impl </span>ChiSquared { |
| <span class="doccomment">/// Create a new chi-squared distribution with degrees-of-freedom |
| /// `k`. Panics if `k < 0`. |
| </span><span class="kw">pub fn </span>new(k: f64) -> ChiSquared { |
| <span class="kw">let </span>repr = <span class="kw">if </span>(k - <span class="number">1.0</span>).abs() < f64::EPSILON { |
| DoFExactlyOne |
| } <span class="kw">else </span>{ |
| <span class="macro">assert!</span>(k > <span class="number">0.0</span>, <span class="string">"ChiSquared::new called with `k` < 0"</span>); |
| DoFAnythingElse(Gamma::new(<span class="number">0.5 </span>* k, <span class="number">2.0</span>)) |
| }; |
| ChiSquared { repr } |
| } |
| } |
| <span class="kw">impl </span>Sample<f64> <span class="kw">for </span>ChiSquared { |
| <span class="kw">fn </span>sample<R: Rng>(<span class="kw-2">&mut </span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="self">self</span>.ind_sample(rng) |
| } |
| } |
| <span class="kw">impl </span>IndependentSample<f64> <span class="kw">for </span>ChiSquared { |
| <span class="kw">fn </span>ind_sample<R: Rng>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <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>StandardNormal(norm) = rng.gen::<StandardNormal>(); |
| norm * norm |
| } |
| DoFAnythingElse(<span class="kw-2">ref </span>g) => g.ind_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 |
| /// |
| /// ```rust |
| /// use sgx_rand::distributions::{FisherF, IndependentSample}; |
| /// |
| /// let f = FisherF::new(2.0, 32.0); |
| /// let v = f.ind_sample(&mut sgx_rand::thread_rng()); |
| /// println!("{} is from an F(2, 32) distribution", v) |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">pub struct </span>FisherF { |
| numer: ChiSquared, |
| denom: ChiSquared, |
| <span class="comment">// denom_dof / numer_dof so that this can just be a straight |
| // multiplication, rather than a division. |
| </span>dof_ratio: f64, |
| } |
| |
| <span class="kw">impl </span>FisherF { |
| <span class="doccomment">/// Create a new `FisherF` distribution, with the given |
| /// parameter. Panics if either `m` or `n` are not positive. |
| </span><span class="kw">pub fn </span>new(m: f64, n: f64) -> FisherF { |
| <span class="macro">assert!</span>(m > <span class="number">0.0</span>, <span class="string">"FisherF::new called with `m < 0`"</span>); |
| <span class="macro">assert!</span>(n > <span class="number">0.0</span>, <span class="string">"FisherF::new called with `n < 0`"</span>); |
| |
| FisherF { |
| numer: ChiSquared::new(m), |
| denom: ChiSquared::new(n), |
| dof_ratio: n / m, |
| } |
| } |
| } |
| <span class="kw">impl </span>Sample<f64> <span class="kw">for </span>FisherF { |
| <span class="kw">fn </span>sample<R: Rng>(<span class="kw-2">&mut </span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="self">self</span>.ind_sample(rng) |
| } |
| } |
| <span class="kw">impl </span>IndependentSample<f64> <span class="kw">for </span>FisherF { |
| <span class="kw">fn </span>ind_sample<R: Rng>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="self">self</span>.numer.ind_sample(rng) / <span class="self">self</span>.denom.ind_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 |
| /// |
| /// ```rust |
| /// use sgx_rand::distributions::{StudentT, IndependentSample}; |
| /// |
| /// let t = StudentT::new(11.0); |
| /// let v = t.ind_sample(&mut sgx_rand::thread_rng()); |
| /// println!("{} is from a t(11) distribution", v) |
| /// ``` |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">pub struct </span>StudentT { |
| chi: ChiSquared, |
| dof: f64, |
| } |
| |
| <span class="kw">impl </span>StudentT { |
| <span class="doccomment">/// Create a new Student t distribution with `n` degrees of |
| /// freedom. Panics if `n <= 0`. |
| </span><span class="kw">pub fn </span>new(n: f64) -> StudentT { |
| <span class="macro">assert!</span>(n > <span class="number">0.0</span>, <span class="string">"StudentT::new called with `n <= 0`"</span>); |
| StudentT { |
| chi: ChiSquared::new(n), |
| dof: n, |
| } |
| } |
| } |
| <span class="kw">impl </span>Sample<f64> <span class="kw">for </span>StudentT { |
| <span class="kw">fn </span>sample<R: Rng>(<span class="kw-2">&mut </span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="self">self</span>.ind_sample(rng) |
| } |
| } |
| <span class="kw">impl </span>IndependentSample<f64> <span class="kw">for </span>StudentT { |
| <span class="kw">fn </span>ind_sample<R: Rng>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> f64 { |
| <span class="kw">let </span>StandardNormal(norm) = rng.gen::<StandardNormal>(); |
| norm * (<span class="self">self</span>.dof / <span class="self">self</span>.chi.ind_sample(rng)).sqrt() |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="sgx_rand" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
