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</pre><pre class="rust"><code><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 &lt;LICENSE-APACHE or</span>
<span class="comment">// https://www.apache.org/licenses/LICENSE-2.0&gt; or the MIT license</span>
<span class="comment">// &lt;LICENSE-MIT or https://opensource.org/licenses/MIT&gt;, 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 Cauchy 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">Distribution</span>, <span class="ident">Standard</span>};
<span class="kw">use</span> <span class="ident">rand::Rng</span>;
<span class="kw">use</span> <span class="ident">core::fmt</span>;
<span class="doccomment">/// The Cauchy distribution `Cauchy(median, scale)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This distribution has a density function:</span>
<span class="doccomment">/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Note that at least for `f32`, results are not fully portable due to minor</span>
<span class="doccomment">/// differences in the target system&#39;s *tan* implementation, `tanf`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use rand_distr::{Cauchy, Distribution};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let cau = Cauchy::new(2.0, 5.0).unwrap();</span>
<span class="doccomment">/// let v = cau.sample(&amp;mut rand::thread_rng());</span>
<span class="doccomment">/// println!(&quot;{} is from a Cauchy(2, 5) distribution&quot;, 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="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">serde::Serialize</span>, <span class="ident">serde::Deserialize</span>))]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Cauchy</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</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">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
{
<span class="ident">median</span>: <span class="ident">F</span>,
<span class="ident">scale</span>: <span class="ident">F</span>,
}
<span class="doccomment">/// Error type returned from `Cauchy::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">/// `scale &lt;= 0` or `nan`.</span>
<span class="ident">ScaleTooSmall</span>,
}
<span class="kw">impl</span> <span class="ident">fmt::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">&amp;</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&amp;mut</span> <span class="ident">fmt::Formatter</span><span class="op">&lt;</span><span class="lifetime">&#39;_</span><span class="op">&gt;</span>) -&gt; <span class="ident">fmt::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::ScaleTooSmall</span> =&gt; <span class="string">&quot;scale is not positive in Cauchy distribution&quot;</span>,
})
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
<span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)))]</span>
<span class="kw">impl</span> <span class="ident">std::error::Error</span> <span class="kw">for</span> <span class="ident">Error</span> {}
<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Cauchy</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</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">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
{
<span class="doccomment">/// Construct a new `Cauchy` with the given shape parameters</span>
<span class="doccomment">/// `median` the peak location and `scale` the scale factor.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">median</span>: <span class="ident">F</span>, <span class="ident">scale</span>: <span class="ident">F</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">Cauchy</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>, <span class="ident">Error</span><span class="op">&gt;</span> {
<span class="kw">if</span> <span class="op">!</span>(<span class="ident">scale</span> <span class="op">&gt;</span> <span class="ident">F::zero</span>()) {
<span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error::ScaleTooSmall</span>);
}
<span class="prelude-val">Ok</span>(<span class="ident">Cauchy</span> { <span class="ident">median</span>, <span class="ident">scale</span> })
}
}
<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Cauchy</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</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">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
{
<span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</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">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
<span class="comment">// sample from [0, 1)</span>
<span class="kw">let</span> <span class="ident">x</span> <span class="op">=</span> <span class="ident">Standard</span>.<span class="ident">sample</span>(<span class="ident">rng</span>);
<span class="comment">// get standard cauchy random number</span>
<span class="comment">// note that π/2 is not exactly representable, even if x=0.5 the result is finite</span>
<span class="kw">let</span> <span class="ident">comp_dev</span> <span class="op">=</span> (<span class="ident">F::PI</span>() <span class="op">*</span> <span class="ident">x</span>).<span class="ident">tan</span>();
<span class="comment">// shift and scale according to parameters</span>
<span class="self">self</span>.<span class="ident">median</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">scale</span> <span class="op">*</span> <span class="ident">comp_dev</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">median</span>(<span class="ident">numbers</span>: <span class="kw-2">&amp;mut</span> [<span class="ident">f64</span>]) -&gt; <span class="ident">f64</span> {
<span class="ident">sort</span>(<span class="ident">numbers</span>);
<span class="kw">let</span> <span class="ident">mid</span> <span class="op">=</span> <span class="ident">numbers</span>.<span class="ident">len</span>() <span class="op">/</span> <span class="number">2</span>;
<span class="ident">numbers</span>[<span class="ident">mid</span>]
}
<span class="kw">fn</span> <span class="ident">sort</span>(<span class="ident">numbers</span>: <span class="kw-2">&amp;mut</span> [<span class="ident">f64</span>]) {
<span class="ident">numbers</span>.<span class="ident">sort_by</span>(<span class="op">|</span><span class="ident">a</span>, <span class="ident">b</span><span class="op">|</span> <span class="ident">a</span>.<span class="ident">partial_cmp</span>(<span class="ident">b</span>).<span class="ident">unwrap</span>());
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_cauchy_averages</span>() {
<span class="comment">// NOTE: given that the variance and mean are undefined,</span>
<span class="comment">// this test does not have any rigorous statistical meaning.</span>
<span class="kw">let</span> <span class="ident">cauchy</span> <span class="op">=</span> <span class="ident">Cauchy::new</span>(<span class="number">10.0</span>, <span class="number">5.0</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="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">123</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">numbers</span>: [<span class="ident">f64</span>; <span class="number">1000</span>] <span class="op">=</span> [<span class="number">0.0</span>; <span class="number">1000</span>];
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sum</span> <span class="op">=</span> <span class="number">0.0</span>;
<span class="kw">for</span> <span class="ident">number</span> <span class="kw">in</span> <span class="kw-2">&amp;mut</span> <span class="ident">numbers</span>[..] {
<span class="kw-2">*</span><span class="ident">number</span> <span class="op">=</span> <span class="ident">cauchy</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>);
<span class="ident">sum</span> <span class="op">+</span><span class="op">=</span> <span class="kw-2">*</span><span class="ident">number</span>;
}
<span class="kw">let</span> <span class="ident">median</span> <span class="op">=</span> <span class="ident">median</span>(<span class="kw-2">&amp;mut</span> <span class="ident">numbers</span>);
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
<span class="macro">std::println!</span>(<span class="string">&quot;Cauchy median: {}&quot;</span>, <span class="ident">median</span>);
<span class="macro">assert!</span>((<span class="ident">median</span> <span class="op">-</span> <span class="number">10.0</span>).<span class="ident">abs</span>() <span class="op">&lt;</span> <span class="number">0.4</span>); <span class="comment">// not 100% certain, but probable enough</span>
<span class="kw">let</span> <span class="ident">mean</span> <span class="op">=</span> <span class="ident">sum</span> <span class="op">/</span> <span class="number">1000.0</span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
<span class="macro">std::println!</span>(<span class="string">&quot;Cauchy mean: {}&quot;</span>, <span class="ident">mean</span>);
<span class="comment">// for a Cauchy distribution the mean should not converge</span>
<span class="macro">assert!</span>((<span class="ident">mean</span> <span class="op">-</span> <span class="number">10.0</span>).<span class="ident">abs</span>() <span class="op">&gt;</span> <span class="number">0.4</span>); <span class="comment">// not 100% certain, but probable enough</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_cauchy_invalid_scale_zero</span>() {
<span class="ident">Cauchy::new</span>(<span class="number">0.0</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_cauchy_invalid_scale_neg</span>() {
<span class="ident">Cauchy::new</span>(<span class="number">0.0</span>, <span class="op">-</span><span class="number">10.0</span>).<span class="ident">unwrap</span>();
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">value_stability</span>() {
<span class="kw">fn</span> <span class="ident">gen_samples</span><span class="op">&lt;</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">core::fmt::Debug</span><span class="op">&gt;</span>(<span class="ident">m</span>: <span class="ident">F</span>, <span class="ident">s</span>: <span class="ident">F</span>, <span class="ident">buf</span>: <span class="kw-2">&amp;mut</span> [<span class="ident">F</span>])
<span class="kw">where</span> <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> {
<span class="kw">let</span> <span class="ident">distr</span> <span class="op">=</span> <span class="ident">Cauchy::new</span>(<span class="ident">m</span>, <span class="ident">s</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="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">353</span>);
<span class="kw">for</span> <span class="ident">x</span> <span class="kw">in</span> <span class="ident">buf</span> {
<span class="kw-2">*</span><span class="ident">x</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;</span><span class="ident">distr</span>);
}
}
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">buf</span> <span class="op">=</span> [<span class="number">0.0</span>; <span class="number">4</span>];
<span class="ident">gen_samples</span>(<span class="number">100f64</span>, <span class="number">10.0</span>, <span class="kw-2">&amp;mut</span> <span class="ident">buf</span>);
<span class="macro">assert_eq!</span>(<span class="kw-2">&amp;</span><span class="ident">buf</span>, <span class="kw-2">&amp;</span>[
<span class="number">77.93369152808678</span>,
<span class="number">90.1606912098641</span>,
<span class="number">125.31516221323625</span>,
<span class="number">86.10217834773925</span>
]);
<span class="comment">// Unfortunately this test is not fully portable due to reliance on the</span>
<span class="comment">// system&#39;s implementation of tanf (see doc on Cauchy struct).</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">buf</span> <span class="op">=</span> [<span class="number">0.0</span>; <span class="number">4</span>];
<span class="ident">gen_samples</span>(<span class="number">10f32</span>, <span class="number">7.0</span>, <span class="kw-2">&amp;mut</span> <span class="ident">buf</span>);
<span class="kw">let</span> <span class="ident">expected</span> <span class="op">=</span> [<span class="number">15.023088</span>, <span class="op">-</span><span class="number">5.446413</span>, <span class="number">3.7092876</span>, <span class="number">3.112482</span>];
<span class="kw">for</span> (<span class="ident">a</span>, <span class="ident">b</span>) <span class="kw">in</span> <span class="ident">buf</span>.<span class="ident">iter</span>().<span class="ident">zip</span>(<span class="ident">expected</span>.<span class="ident">iter</span>()) {
<span class="macro">assert_almost_eq!</span>(<span class="kw-2">*</span><span class="ident">a</span>, <span class="kw-2">*</span><span class="ident">b</span>, <span class="number">1e-5</span>);
}
}
}
</code></pre></div>
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