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</pre><pre class="rust"><code><span class="comment">// Copyright 2021 Developers of the Rand project.
//
// Licensed under the Apache License, Version 2.0 &lt;LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0&gt; or the MIT license
// &lt;LICENSE-MIT or https://opensource.org/licenses/MIT&gt;, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
</span><span class="doccomment">//! The Gumbel distribution.
</span><span class="kw">use crate</span>::{Distribution, OpenClosed01};
<span class="kw">use </span>core::fmt;
<span class="kw">use </span>num_traits::Float;
<span class="kw">use </span>rand::Rng;
<span class="doccomment">/// Samples floating-point numbers according to the Gumbel distribution
///
/// This distribution has density function:
/// `f(x) = exp(-(z + exp(-z))) / σ`, where `z = (x - μ) / σ`,
/// `μ` is the location parameter, and `σ` the scale parameter.
///
/// # Example
/// ```
/// use rand::prelude::*;
/// use rand_distr::Gumbel;
///
/// let val: f64 = thread_rng().sample(Gumbel::new(0.0, 1.0).unwrap());
/// println!(&quot;{}&quot;, val);
/// ```
</span><span class="attribute">#[derive(Clone, Copy, Debug)]
#[cfg_attr(feature = <span class="string">&quot;serde1&quot;</span>, derive(serde::Serialize, serde::Deserialize))]
</span><span class="kw">pub struct </span>Gumbel&lt;F&gt;
<span class="kw">where
</span>F: Float,
OpenClosed01: Distribution&lt;F&gt;,
{
location: F,
scale: F,
}
<span class="doccomment">/// Error type returned from `Gumbel::new`.
</span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)]
</span><span class="kw">pub enum </span>Error {
<span class="doccomment">/// location is infinite or NaN
</span>LocationNotFinite,
<span class="doccomment">/// scale is not finite positive number
</span>ScaleNotPositive,
}
<span class="kw">impl </span>fmt::Display <span class="kw">for </span>Error {
<span class="kw">fn </span>fmt(<span class="kw-2">&amp;</span><span class="self">self</span>, f: <span class="kw-2">&amp;mut </span>fmt::Formatter&lt;<span class="lifetime">&#39;_</span>&gt;) -&gt; fmt::Result {
f.write_str(<span class="kw">match </span><span class="self">self </span>{
Error::ScaleNotPositive =&gt; <span class="string">&quot;scale is not positive and finite in Gumbel distribution&quot;</span>,
Error::LocationNotFinite =&gt; <span class="string">&quot;location is not finite in Gumbel distribution&quot;</span>,
})
}
}
<span class="attribute">#[cfg(feature = <span class="string">&quot;std&quot;</span>)]
#[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">&quot;std&quot;</span>)))]
</span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>Error {}
<span class="kw">impl</span>&lt;F&gt; Gumbel&lt;F&gt;
<span class="kw">where
</span>F: Float,
OpenClosed01: Distribution&lt;F&gt;,
{
<span class="doccomment">/// Construct a new `Gumbel` distribution with given `location` and `scale`.
</span><span class="kw">pub fn </span>new(location: F, scale: F) -&gt; <span class="prelude-ty">Result</span>&lt;Gumbel&lt;F&gt;, Error&gt; {
<span class="kw">if </span>scale &lt;= F::zero() || scale.is_infinite() || scale.is_nan() {
<span class="kw">return </span><span class="prelude-val">Err</span>(Error::ScaleNotPositive);
}
<span class="kw">if </span>location.is_infinite() || location.is_nan() {
<span class="kw">return </span><span class="prelude-val">Err</span>(Error::LocationNotFinite);
}
<span class="prelude-val">Ok</span>(Gumbel { location, scale })
}
}
<span class="kw">impl</span>&lt;F&gt; Distribution&lt;F&gt; <span class="kw">for </span>Gumbel&lt;F&gt;
<span class="kw">where
</span>F: Float,
OpenClosed01: Distribution&lt;F&gt;,
{
<span class="kw">fn </span>sample&lt;R: Rng + <span class="question-mark">?</span>Sized&gt;(<span class="kw-2">&amp;</span><span class="self">self</span>, rng: <span class="kw-2">&amp;mut </span>R) -&gt; F {
<span class="kw">let </span>x: F = rng.sample(OpenClosed01);
<span class="self">self</span>.location - <span class="self">self</span>.scale * (-x.ln()).ln()
}
}
<span class="attribute">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">use super</span>::<span class="kw-2">*</span>;
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_zero_scale() {
Gumbel::new(<span class="number">0.0</span>, <span class="number">0.0</span>).unwrap();
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_infinite_scale() {
Gumbel::new(<span class="number">0.0</span>, core::f64::INFINITY).unwrap();
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_nan_scale() {
Gumbel::new(<span class="number">0.0</span>, core::f64::NAN).unwrap();
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_infinite_location() {
Gumbel::new(core::f64::INFINITY, <span class="number">1.0</span>).unwrap();
}
<span class="attribute">#[test]
#[should_panic]
</span><span class="kw">fn </span>test_nan_location() {
Gumbel::new(core::f64::NAN, <span class="number">1.0</span>).unwrap();
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_sample_against_cdf() {
<span class="kw">fn </span>neg_log_log(x: f64) -&gt; f64 {
-(-x.ln()).ln()
}
<span class="kw">let </span>location = <span class="number">0.0</span>;
<span class="kw">let </span>scale = <span class="number">1.0</span>;
<span class="kw">let </span>iterations = <span class="number">100_000</span>;
<span class="kw">let </span>increment = <span class="number">1.0 </span>/ iterations <span class="kw">as </span>f64;
<span class="kw">let </span>probabilities = [<span class="number">0.1</span>, <span class="number">0.2</span>, <span class="number">0.3</span>, <span class="number">0.4</span>, <span class="number">0.5</span>, <span class="number">0.6</span>, <span class="number">0.7</span>, <span class="number">0.8</span>, <span class="number">0.9</span>];
<span class="kw">let </span><span class="kw-2">mut </span>quantiles = [<span class="number">0.0</span>; <span class="number">9</span>];
<span class="kw">for </span>(i, p) <span class="kw">in </span>probabilities.iter().enumerate() {
quantiles[i] = neg_log_log(<span class="kw-2">*</span>p);
}
<span class="kw">let </span><span class="kw-2">mut </span>proportions = [<span class="number">0.0</span>; <span class="number">9</span>];
<span class="kw">let </span>d = Gumbel::new(location, scale).unwrap();
<span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">1</span>);
<span class="kw">for _ in </span><span class="number">0</span>..iterations {
<span class="kw">let </span>replicate = d.sample(<span class="kw-2">&amp;mut </span>rng);
<span class="kw">for </span>(i, q) <span class="kw">in </span>quantiles.iter().enumerate() {
<span class="kw">if </span>replicate &lt; <span class="kw-2">*</span>q {
proportions[i] += increment;
}
}
}
<span class="macro">assert!</span>(proportions
.iter()
.zip(<span class="kw-2">&amp;</span>probabilities)
.all(|(p_hat, p)| (p_hat - p).abs() &lt; <span class="number">0.003</span>))
}
}
</code></pre></div>
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