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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 <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 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'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(&mut rand::thread_rng());</span> |
| <span class="doccomment">/// println!("{} is from a Cauchy(2, 5) 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="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"serde1"</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"><</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">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 <= 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">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&mut</span> <span class="ident">fmt::Formatter</span><span class="op"><</span><span class="lifetime">'_</span><span class="op">></span>) -> <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> => <span class="string">"scale is not positive in Cauchy 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="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">"std"</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"><</span><span class="ident">F</span><span class="op">></span> <span class="ident">Cauchy</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 `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>) -> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Cauchy</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">scale</span> <span class="op">></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"><</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">Cauchy</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="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">&mut</span> <span class="ident">R</span>) -> <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">&mut</span> [<span class="ident">f64</span>]) -> <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">&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">&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">&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">&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">"std"</span>)]</span> |
| <span class="macro">std::println!</span>(<span class="string">"Cauchy median: {}"</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"><</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">"std"</span>)]</span> |
| <span class="macro">std::println!</span>(<span class="string">"Cauchy mean: {}"</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">></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"><</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">></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">&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"><</span><span class="ident">F</span><span class="op">></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">&</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">&mut</span> <span class="ident">buf</span>); |
| <span class="macro">assert_eq!</span>(<span class="kw-2">&</span><span class="ident">buf</span>, <span class="kw-2">&</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'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">&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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