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<!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 `/home/runner/.cargo/registry/src/github.com-1ecc6299db9ec823/rand_distr-0.3.0/src/poisson.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>poisson.rs - source</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css" disabled ><link rel="stylesheet" type="text/css" href="../../ayu.css" disabled ><script id="default-settings"></script><script src="../../storage.js"></script><script src="../../crates.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="https://www.rust-lang.org/favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc source"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu" role="button">☰</div><a href='../../rand_distr/index.html'><div class='logo-container'><img src='https://www.rust-lang.org/logos/rust-logo-128x128-blk.png' alt='logo'></div></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!" aria-haspopup="menu"><img src="../../brush.svg" width="18" height="18" alt="Pick another theme!"></button><div id="theme-choices" role="menu"></div></div><nav class="sub"><form class="search-form"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" disabled autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><button type="button" class="help-button">?</button>
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</pre><div class="example-wrap"><pre class="rust ">
<span class="comment">// Copyright 2018 Developers of the Rand project.</span>
<span class="comment">// Copyright 2016-2017 The Rust Project Developers.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="doccomment">//! The Poisson distribution.</span>
<span class="kw">use</span> <span class="ident">num_traits</span>::{<span class="ident">Float</span>, <span class="ident">FloatConst</span>};
<span class="kw">use</span> <span class="kw">crate</span>::{<span class="ident">Cauchy</span>, <span class="ident">Distribution</span>, <span class="ident">Standard</span>};
<span class="kw">use</span> <span class="ident">rand</span>::<span class="ident">Rng</span>;
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">fmt</span>;
<span class="doccomment">/// The Poisson distribution `Poisson(lambda)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This distribution has a density function:</span>
<span class="doccomment">/// `f(k) = lambda^k * exp(-lambda) / k!` for `k >= 0`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use rand_distr::{Poisson, Distribution};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let poi = Poisson::new(2.0).unwrap();</span>
<span class="doccomment">/// let v = poi.sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from a Poisson(2) distribution", v);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Poisson</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">Float</span> <span class="op">+</span> <span class="ident">FloatConst</span>, <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>
{
<span class="ident">lambda</span>: <span class="ident">F</span>,
<span class="comment">// precalculated values</span>
<span class="ident">exp_lambda</span>: <span class="ident">F</span>,
<span class="ident">log_lambda</span>: <span class="ident">F</span>,
<span class="ident">sqrt_2lambda</span>: <span class="ident">F</span>,
<span class="ident">magic_val</span>: <span class="ident">F</span>,
}
<span class="doccomment">/// Error type returned from `Poisson::new`.</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
<span class="kw">pub</span> <span class="kw">enum</span> <span class="ident">Error</span> {
<span class="doccomment">/// `lambda <= 0` or `nan`.</span>
<span class="ident">ShapeTooSmall</span>,
}
<span class="kw">impl</span> <span class="ident">fmt</span>::<span class="ident">Display</span> <span class="kw">for</span> <span class="ident">Error</span> {
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt</span>::<span class="ident">Formatter</span><span class="op"><</span><span class="lifetime">'_</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt</span>::<span class="prelude-ty">Result</span> {
<span class="ident">f</span>.<span class="ident">write_str</span>(<span class="kw">match</span> <span class="self">self</span> {
<span class="ident">Error</span>::<span class="ident">ShapeTooSmall</span> <span class="op">=</span><span class="op">></span> <span class="string">"lambda is not positive in Poisson distribution"</span>,
})
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="kw">impl</span> <span class="ident">std</span>::<span class="ident">error</span>::<span class="ident">Error</span> <span class="kw">for</span> <span class="ident">Error</span> {}
<span class="kw">impl</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> <span class="ident">Poisson</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">Float</span> <span class="op">+</span> <span class="ident">FloatConst</span>, <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>
{
<span class="doccomment">/// Construct a new `Poisson` with the given shape parameter</span>
<span class="doccomment">/// `lambda`.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">lambda</span>: <span class="ident">F</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Poisson</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>, <span class="ident">Error</span><span class="op">></span> {
<span class="kw">if</span> <span class="op">!</span>(<span class="ident">lambda</span> <span class="op">></span> <span class="ident">F</span>::<span class="ident">zero</span>()) {
<span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error</span>::<span class="ident">ShapeTooSmall</span>);
}
<span class="kw">let</span> <span class="ident">log_lambda</span> <span class="op">=</span> <span class="ident">lambda</span>.<span class="ident">ln</span>();
<span class="prelude-val">Ok</span>(<span class="ident">Poisson</span> {
<span class="ident">lambda</span>,
<span class="ident">exp_lambda</span>: (<span class="op">-</span><span class="ident">lambda</span>).<span class="ident">exp</span>(),
<span class="ident">log_lambda</span>,
<span class="ident">sqrt_2lambda</span>: (<span class="ident">F</span>::<span class="ident">from</span>(<span class="number">2.0</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">lambda</span>).<span class="ident">sqrt</span>(),
<span class="ident">magic_val</span>: <span class="ident">lambda</span> <span class="op">*</span> <span class="ident">log_lambda</span> <span class="op">-</span> <span class="kw">crate</span>::<span class="ident">utils</span>::<span class="ident">log_gamma</span>(<span class="ident">F</span>::<span class="ident">one</span>() <span class="op">+</span> <span class="ident">lambda</span>),
})
}
}
<span class="kw">impl</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Poisson</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>
<span class="kw">where</span> <span class="ident">F</span>: <span class="ident">Float</span> <span class="op">+</span> <span class="ident">FloatConst</span>, <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>
{
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-</span><span class="op">></span> <span class="ident">F</span> {
<span class="comment">// using the algorithm from Numerical Recipes in C</span>
<span class="comment">// for low expected values use the Knuth method</span>
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">lambda</span> <span class="op"><</span> <span class="ident">F</span>::<span class="ident">from</span>(<span class="number">12.0</span>).<span class="ident">unwrap</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">result</span> <span class="op">=</span> <span class="ident">F</span>::<span class="ident">zero</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">p</span> <span class="op">=</span> <span class="ident">F</span>::<span class="ident">one</span>();
<span class="kw">while</span> <span class="ident">p</span> <span class="op">></span> <span class="self">self</span>.<span class="ident">exp_lambda</span> {
<span class="ident">p</span> <span class="op">=</span> <span class="ident">p</span><span class="kw-2">*</span><span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">F</span><span class="op">></span>();
<span class="ident">result</span> <span class="op">=</span> <span class="ident">result</span> <span class="op">+</span> <span class="ident">F</span>::<span class="ident">one</span>();
}
<span class="ident">result</span> <span class="op">-</span> <span class="ident">F</span>::<span class="ident">one</span>()
}
<span class="comment">// high expected values - rejection method</span>
<span class="kw">else</span> {
<span class="comment">// we use the Cauchy distribution as the comparison distribution</span>
<span class="comment">// f(x) ~ 1/(1+x^2)</span>
<span class="kw">let</span> <span class="ident">cauchy</span> <span class="op">=</span> <span class="ident">Cauchy</span>::<span class="ident">new</span>(<span class="ident">F</span>::<span class="ident">zero</span>(), <span class="ident">F</span>::<span class="ident">one</span>()).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">result</span>;
<span class="kw">loop</span> {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">comp_dev</span>;
<span class="kw">loop</span> {
<span class="comment">// draw from the Cauchy distribution</span>
<span class="ident">comp_dev</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">cauchy</span>);
<span class="comment">// shift the peak of the comparison ditribution</span>
<span class="ident">result</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">sqrt_2lambda</span> <span class="op">*</span> <span class="ident">comp_dev</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">lambda</span>;
<span class="comment">// repeat the drawing until we are in the range of possible values</span>
<span class="kw">if</span> <span class="ident">result</span> <span class="op">></span><span class="op">=</span> <span class="ident">F</span>::<span class="ident">zero</span>() {
<span class="kw">break</span>;
}
}
<span class="comment">// now the result is a random variable greater than 0 with Cauchy distribution</span>
<span class="comment">// the result should be an integer value</span>
<span class="ident">result</span> <span class="op">=</span> <span class="ident">result</span>.<span class="ident">floor</span>();
<span class="comment">// this is the ratio of the Poisson distribution to the comparison distribution</span>
<span class="comment">// the magic value scales the distribution function to a range of approximately 0-1</span>
<span class="comment">// since it is not exact, we multiply the ratio by 0.9 to avoid ratios greater than 1</span>
<span class="comment">// this doesn't change the resulting distribution, only increases the rate of failed drawings</span>
<span class="kw">let</span> <span class="ident">check</span> <span class="op">=</span> <span class="ident">F</span>::<span class="ident">from</span>(<span class="number">0.9</span>).<span class="ident">unwrap</span>()
<span class="op">*</span> (<span class="ident">F</span>::<span class="ident">one</span>() <span class="op">+</span> <span class="ident">comp_dev</span> <span class="op">*</span> <span class="ident">comp_dev</span>)
<span class="op">*</span> (<span class="ident">result</span> <span class="op">*</span> <span class="self">self</span>.<span class="ident">log_lambda</span>
<span class="op">-</span> <span class="kw">crate</span>::<span class="ident">utils</span>::<span class="ident">log_gamma</span>(<span class="ident">F</span>::<span class="ident">one</span>() <span class="op">+</span> <span class="ident">result</span>)
<span class="op">-</span> <span class="self">self</span>.<span class="ident">magic_val</span>)
.<span class="ident">exp</span>();
<span class="comment">// check with uniform random value - if below the threshold, we are within the target distribution</span>
<span class="kw">if</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">F</span><span class="op">></span>() <span class="op"><</span><span class="op">=</span> <span class="ident">check</span> {
<span class="kw">break</span>;
}
}
<span class="ident">result</span>
}
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="ident">test</span> {
<span class="kw">use</span> <span class="kw">super</span>::<span class="kw-2">*</span>;
<span class="kw">fn</span> <span class="ident">test_poisson_avg_gen</span><span class="op"><</span><span class="ident">F</span>: <span class="ident">Float</span> <span class="op">+</span> <span class="ident">FloatConst</span><span class="op">></span>(<span class="ident">lambda</span>: <span class="ident">F</span>, <span class="ident">tol</span>: <span class="ident">F</span>)
<span class="kw">where</span> <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>
{
<span class="kw">let</span> <span class="ident">poisson</span> <span class="op">=</span> <span class="ident">Poisson</span>::<span class="ident">new</span>(<span class="ident">lambda</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="kw">crate</span>::<span class="ident">test</span>::<span class="ident">rng</span>(<span class="number">123</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sum</span> <span class="op">=</span> <span class="ident">F</span>::<span class="ident">zero</span>();
<span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
<span class="ident">sum</span> <span class="op">=</span> <span class="ident">sum</span> <span class="op">+</span> <span class="ident">poisson</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
}
<span class="kw">let</span> <span class="ident">avg</span> <span class="op">=</span> <span class="ident">sum</span> <span class="op">/</span> <span class="ident">F</span>::<span class="ident">from</span>(<span class="number">1000.0</span>).<span class="ident">unwrap</span>();
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">avg</span> <span class="op">-</span> <span class="ident">lambda</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="ident">tol</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_poisson_avg</span>() {
<span class="ident">test_poisson_avg_gen</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>(<span class="number">10.0</span>, <span class="number">0.5</span>);
<span class="ident">test_poisson_avg_gen</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>(<span class="number">15.0</span>, <span class="number">0.5</span>);
<span class="ident">test_poisson_avg_gen</span>::<span class="op"><</span><span class="ident">f32</span><span class="op">></span>(<span class="number">10.0</span>, <span class="number">0.5</span>);
<span class="ident">test_poisson_avg_gen</span>::<span class="op"><</span><span class="ident">f32</span><span class="op">></span>(<span class="number">15.0</span>, <span class="number">0.5</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_poisson_invalid_lambda_zero</span>() {
<span class="ident">Poisson</span>::<span class="ident">new</span>(<span class="number">0.0</span>).<span class="ident">unwrap</span>();
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_poisson_invalid_lambda_neg</span>() {
<span class="ident">Poisson</span>::<span class="ident">new</span>(<span class="op">-</span><span class="number">10.0</span>).<span class="ident">unwrap</span>();
}
}
</pre></div>
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