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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 2013 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 normal and derived distributions.</span>
<span class="kw">use</span> <span class="ident">Rng</span>;
<span class="kw">use</span> <span class="ident">distributions</span>::{<span class="ident">ziggurat_tables</span>, <span class="ident">Distribution</span>, <span class="ident">Open01</span>};
<span class="kw">use</span> <span class="ident">distributions</span>::<span class="ident">utils</span>::<span class="ident">ziggurat</span>;
<span class="doccomment">/// Samples floating-point numbers according to the normal distribution</span>
<span class="doccomment">/// `N(0, 1)` (a.k.a. a standard normal, or Gaussian). This is equivalent to</span>
<span class="doccomment">/// `Normal::new(0.0, 1.0)` but faster.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// See `Normal` for the general normal distribution.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Implemented via the ZIGNOR variant[^1] of the Ziggurat method.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// [^1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to</span>
<span class="doccomment">/// Generate Normal Random Samples*](</span>
<span class="doccomment">/// https://www.doornik.com/research/ziggurat.pdf).</span>
<span class="doccomment">/// Nuffield College, Oxford</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use rand::prelude::*;</span>
<span class="doccomment">/// use rand::distributions::StandardNormal;</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let val: f64 = SmallRng::from_entropy().sample(StandardNormal);</span>
<span class="doccomment">/// println!("{}", val);</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">StandardNormal</span>;
<span class="kw">impl</span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">StandardNormal</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">f64</span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">pdf</span>(<span class="ident">x</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
(<span class="op">-</span><span class="ident">x</span><span class="kw-2">*</span><span class="ident">x</span><span class="op">/</span><span class="number">2.0</span>).<span class="ident">exp</span>()
}
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">zero_case</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="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>, <span class="ident">u</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="comment">// compute a random number in the tail by hand</span>
<span class="comment">// strange initial conditions, because the loop is not</span>
<span class="comment">// do-while, so the condition should be true on the first</span>
<span class="comment">// run, they get overwritten anyway (0 < 1, so these are</span>
<span class="comment">// good).</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="number">1.0f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">y</span> <span class="op">=</span> <span class="number">0.0f64</span>;
<span class="kw">while</span> <span class="op">-</span><span class="number">2.0</span> <span class="op">*</span> <span class="ident">y</span> <span class="op"><</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> {
<span class="kw">let</span> <span class="ident">x_</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);
<span class="kw">let</span> <span class="ident">y_</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);
<span class="ident">x</span> <span class="op">=</span> <span class="ident">x_</span>.<span class="ident">ln</span>() <span class="op">/</span> <span class="ident">ziggurat_tables</span>::<span class="ident">ZIG_NORM_R</span>;
<span class="ident">y</span> <span class="op">=</span> <span class="ident">y_</span>.<span class="ident">ln</span>();
}
<span class="kw">if</span> <span class="ident">u</span> <span class="op"><</span> <span class="number">0.0</span> { <span class="ident">x</span> <span class="op">-</span> <span class="ident">ziggurat_tables</span>::<span class="ident">ZIG_NORM_R</span> } <span class="kw">else</span> { <span class="ident">ziggurat_tables</span>::<span class="ident">ZIG_NORM_R</span> <span class="op">-</span> <span class="ident">x</span> }
}
<span class="ident">ziggurat</span>(<span class="ident">rng</span>, <span class="bool-val">true</span>, <span class="comment">// this is symmetric</span>
<span class="kw-2">&</span><span class="ident">ziggurat_tables</span>::<span class="ident">ZIG_NORM_X</span>,
<span class="kw-2">&</span><span class="ident">ziggurat_tables</span>::<span class="ident">ZIG_NORM_F</span>,
<span class="ident">pdf</span>, <span class="ident">zero_case</span>)
}
}
<span class="doccomment">/// The normal distribution `N(mean, std_dev**2)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This uses the ZIGNOR variant of the Ziggurat method, see [`StandardNormal`]</span>
<span class="doccomment">/// for more details.</span>
<span class="doccomment">/// </span>
<span class="doccomment">/// Note that [`StandardNormal`] is an optimised implementation for mean 0, and</span>
<span class="doccomment">/// standard deviation 1.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use rand::distributions::{Normal, Distribution};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // mean 2, standard deviation 3</span>
<span class="doccomment">/// let normal = Normal::new(2.0, 3.0);</span>
<span class="doccomment">/// let v = normal.sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from a N(2, 9) distribution", v)</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">///</span>
<span class="doccomment">/// [`StandardNormal`]: crate::distributions::StandardNormal</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">Normal</span> {
<span class="ident">mean</span>: <span class="ident">f64</span>,
<span class="ident">std_dev</span>: <span class="ident">f64</span>,
}
<span class="kw">impl</span> <span class="ident">Normal</span> {
<span class="doccomment">/// Construct a new `Normal` distribution with the given mean and</span>
<span class="doccomment">/// standard deviation.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Panics</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Panics if `std_dev < 0`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">mean</span>: <span class="ident">f64</span>, <span class="ident">std_dev</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">Normal</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">std_dev</span> <span class="op">></span><span class="op">=</span> <span class="number">0.0</span>, <span class="string">"Normal::new called with `std_dev` < 0"</span>);
<span class="ident">Normal</span> {
<span class="ident">mean</span>,
<span class="ident">std_dev</span>
}
}
}
<span class="kw">impl</span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Normal</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">f64</span> {
<span class="kw">let</span> <span class="ident">n</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">StandardNormal</span>);
<span class="self">self</span>.<span class="ident">mean</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">std_dev</span> <span class="op">*</span> <span class="ident">n</span>
}
}
<span class="doccomment">/// The log-normal distribution `ln N(mean, std_dev**2)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// If `X` is log-normal distributed, then `ln(X)` is `N(mean, std_dev**2)`</span>
<span class="doccomment">/// distributed.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use rand::distributions::{LogNormal, Distribution};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// // mean 2, standard deviation 3</span>
<span class="doccomment">/// let log_normal = LogNormal::new(2.0, 3.0);</span>
<span class="doccomment">/// let v = log_normal.sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from an ln N(2, 9) 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">LogNormal</span> {
<span class="ident">norm</span>: <span class="ident">Normal</span>
}
<span class="kw">impl</span> <span class="ident">LogNormal</span> {
<span class="doccomment">/// Construct a new `LogNormal` distribution with the given mean</span>
<span class="doccomment">/// and standard deviation.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Panics</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Panics if `std_dev < 0`.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">mean</span>: <span class="ident">f64</span>, <span class="ident">std_dev</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">LogNormal</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">std_dev</span> <span class="op">></span><span class="op">=</span> <span class="number">0.0</span>, <span class="string">"LogNormal::new called with `std_dev` < 0"</span>);
<span class="ident">LogNormal</span> { <span class="ident">norm</span>: <span class="ident">Normal</span>::<span class="ident">new</span>(<span class="ident">mean</span>, <span class="ident">std_dev</span>) }
}
}
<span class="kw">impl</span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">f64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">LogNormal</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">f64</span> {
<span class="self">self</span>.<span class="ident">norm</span>.<span class="ident">sample</span>(<span class="ident">rng</span>).<span class="ident">exp</span>()
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="ident">tests</span> {
<span class="kw">use</span> <span class="ident">distributions</span>::<span class="ident">Distribution</span>;
<span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">Normal</span>, <span class="ident">LogNormal</span>};
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_normal</span>() {
<span class="kw">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="ident">Normal</span>::<span class="ident">new</span>(<span class="number">10.0</span>, <span class="number">10.0</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> ::<span class="ident">test</span>::<span class="ident">rng</span>(<span class="number">210</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">norm</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</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_normal_invalid_sd</span>() {
<span class="ident">Normal</span>::<span class="ident">new</span>(<span class="number">10.0</span>, <span class="op">-</span><span class="number">1.0</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_log_normal</span>() {
<span class="kw">let</span> <span class="ident">lnorm</span> <span class="op">=</span> <span class="ident">LogNormal</span>::<span class="ident">new</span>(<span class="number">10.0</span>, <span class="number">10.0</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> ::<span class="ident">test</span>::<span class="ident">rng</span>(<span class="number">211</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">lnorm</span>.<span class="ident">sample</span>(<span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</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_log_normal_invalid_sd</span>() {
<span class="ident">LogNormal</span>::<span class="ident">new</span>(<span class="number">10.0</span>, <span class="op">-</span><span class="number">1.0</span>);
}
}
</pre></div>
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