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| </pre><pre class="rust"><code><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"><span class="kw">crate</span>::utils::ziggurat</span>; |
| <span class="kw">use</span> <span class="ident">num_traits::Float</span>; |
| <span class="kw">use</span> <span class="kw">crate</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">rand::Rng</span>; |
| <span class="kw">use</span> <span class="ident">core::fmt</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_distr::StandardNormal;</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// let val: f64 = thread_rng().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="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">StandardNormal</span>; |
| |
| <span class="kw">impl</span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">f32</span><span class="op">></span> <span class="kw">for</span> <span class="ident">StandardNormal</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">&mut</span> <span class="ident">R</span>) -> <span class="ident">f32</span> { |
| <span class="comment">// TODO: use optimal 32-bit implementation</span> |
| <span class="kw">let</span> <span class="ident">x</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">sample</span>(<span class="ident">rng</span>); |
| <span class="ident">x</span> <span class="kw">as</span> <span class="ident">f32</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">&mut</span> <span class="ident">R</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="ident">f64</span> { |
| (<span class="op">-</span><span class="ident">x</span> <span class="op">*</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">&mut</span> <span class="ident">R</span>, <span class="ident">u</span>: <span class="ident">f64</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::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::ZIG_NORM_R</span> |
| } <span class="kw">else</span> { |
| <span class="ident">ziggurat_tables::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::ZIG_NORM_X</span>, |
| <span class="kw-2">&</span><span class="ident">ziggurat_tables::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_distr::{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).unwrap();</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::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="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">Normal</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="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> |
| { |
| <span class="ident">mean</span>: <span class="ident">F</span>, |
| <span class="ident">std_dev</span>: <span class="ident">F</span>, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Normal::new` and `LogNormal::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">/// The mean value is too small (log-normal samples must be positive)</span> |
| <span class="ident">MeanTooSmall</span>, |
| <span class="doccomment">/// The standard deviation or other dispersion parameter is not finite.</span> |
| <span class="ident">BadVariance</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::MeanTooSmall</span> => <span class="string">"mean < 0 or NaN in log-normal distribution"</span>, |
| <span class="ident">Error::BadVariance</span> => <span class="string">"variation parameter is non-finite in (log)normal 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">Normal</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="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> |
| { |
| <span class="doccomment">/// Construct, from mean and standard deviation</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Parameters:</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// - mean (`μ`, unrestricted)</span> |
| <span class="doccomment">/// - standard deviation (`σ`, must be finite)</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">F</span>, <span class="ident">std_dev</span>: <span class="ident">F</span>) -> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Normal</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">std_dev</span>.<span class="ident">is_finite</span>() { |
| <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error::BadVariance</span>); |
| } |
| <span class="prelude-val">Ok</span>(<span class="ident">Normal</span> { <span class="ident">mean</span>, <span class="ident">std_dev</span> }) |
| } |
| |
| <span class="doccomment">/// Construct, from mean and coefficient of variation</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Parameters:</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// - mean (`μ`, unrestricted)</span> |
| <span class="doccomment">/// - coefficient of variation (`cv = abs(σ / μ)`)</span> |
| <span class="attribute">#[<span class="ident">inline</span>]</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_mean_cv</span>(<span class="ident">mean</span>: <span class="ident">F</span>, <span class="ident">cv</span>: <span class="ident">F</span>) -> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Normal</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">cv</span>.<span class="ident">is_finite</span>() <span class="op">|</span><span class="op">|</span> <span class="ident">cv</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::BadVariance</span>); |
| } |
| <span class="kw">let</span> <span class="ident">std_dev</span> <span class="op">=</span> <span class="ident">cv</span> <span class="op">*</span> <span class="ident">mean</span>; |
| <span class="prelude-val">Ok</span>(<span class="ident">Normal</span> { <span class="ident">mean</span>, <span class="ident">std_dev</span> }) |
| } |
| |
| <span class="doccomment">/// Sample from a z-score</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// This may be useful for generating correlated samples `x1` and `x2`</span> |
| <span class="doccomment">/// from two different distributions, as follows.</span> |
| <span class="doccomment">/// ```</span> |
| <span class="doccomment">/// # use rand::prelude::*;</span> |
| <span class="doccomment">/// # use rand_distr::{Normal, StandardNormal};</span> |
| <span class="doccomment">/// let mut rng = thread_rng();</span> |
| <span class="doccomment">/// let z = StandardNormal.sample(&mut rng);</span> |
| <span class="doccomment">/// let x1 = Normal::new(0.0, 1.0).unwrap().from_zscore(z);</span> |
| <span class="doccomment">/// let x2 = Normal::new(2.0, -3.0).unwrap().from_zscore(z);</span> |
| <span class="doccomment">/// ```</span> |
| <span class="attribute">#[<span class="ident">inline</span>]</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_zscore</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">zscore</span>: <span class="ident">F</span>) -> <span class="ident">F</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">zscore</span> |
| } |
| |
| <span class="doccomment">/// Returns the mean (`μ`) of the distribution.</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">mean</span>(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="ident">F</span> { |
| <span class="self">self</span>.<span class="ident">mean</span> |
| } |
| |
| <span class="doccomment">/// Returns the standard deviation (`σ`) of the distribution.</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">std_dev</span>(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="ident">F</span> { |
| <span class="self">self</span>.<span class="ident">std_dev</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">Normal</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="ident">StandardNormal</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="self">self</span>.<span class="ident">from_zscore</span>(<span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">StandardNormal</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_distr::{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).unwrap();</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="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">LogNormal</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="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> |
| { |
| <span class="ident">norm</span>: <span class="ident">Normal</span><span class="op"><</span><span class="ident">F</span><span class="op">></span>, |
| } |
| |
| <span class="kw">impl</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> <span class="ident">LogNormal</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="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op"><</span><span class="ident">F</span><span class="op">></span> |
| { |
| <span class="doccomment">/// Construct, from (log-space) mean and standard deviation</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Parameters are the "standard" log-space measures (these are the mean</span> |
| <span class="doccomment">/// and standard deviation of the logarithm of samples):</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// - `mu` (`μ`, unrestricted) is the mean of the underlying distribution</span> |
| <span class="doccomment">/// - `sigma` (`σ`, must be finite) is the standard deviation of the</span> |
| <span class="doccomment">/// underlying Normal distribution</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">mu</span>: <span class="ident">F</span>, <span class="ident">sigma</span>: <span class="ident">F</span>) -> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">LogNormal</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">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="ident">Normal::new</span>(<span class="ident">mu</span>, <span class="ident">sigma</span>)<span class="question-mark">?</span>; |
| <span class="prelude-val">Ok</span>(<span class="ident">LogNormal</span> { <span class="ident">norm</span> }) |
| } |
| |
| <span class="doccomment">/// Construct, from (linear-space) mean and coefficient of variation</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Parameters are linear-space measures:</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// - mean (`μ > 0`) is the (real) mean of the distribution</span> |
| <span class="doccomment">/// - coefficient of variation (`cv = σ / μ`, requiring `cv ≥ 0`) is a</span> |
| <span class="doccomment">/// standardized measure of dispersion</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// As a special exception, `μ = 0, cv = 0` is allowed (samples are `-inf`).</span> |
| <span class="attribute">#[<span class="ident">inline</span>]</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_mean_cv</span>(<span class="ident">mean</span>: <span class="ident">F</span>, <span class="ident">cv</span>: <span class="ident">F</span>) -> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">LogNormal</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="ident">cv</span> <span class="op">==</span> <span class="ident">F::zero</span>() { |
| <span class="kw">let</span> <span class="ident">mu</span> <span class="op">=</span> <span class="ident">mean</span>.<span class="ident">ln</span>(); |
| <span class="kw">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="ident">Normal::new</span>(<span class="ident">mu</span>, <span class="ident">F::zero</span>()).<span class="ident">unwrap</span>(); |
| <span class="kw">return</span> <span class="prelude-val">Ok</span>(<span class="ident">LogNormal</span> { <span class="ident">norm</span> }); |
| } |
| <span class="kw">if</span> <span class="op">!</span>(<span class="ident">mean</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::MeanTooSmall</span>); |
| } |
| <span class="kw">if</span> <span class="op">!</span>(<span class="ident">cv</span> <span class="op">></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::BadVariance</span>); |
| } |
| |
| <span class="comment">// Using X ~ lognormal(μ, σ), CV² = Var(X) / E(X)²</span> |
| <span class="comment">// E(X) = exp(μ + σ² / 2) = exp(μ) × exp(σ² / 2)</span> |
| <span class="comment">// Var(X) = exp(2μ + σ²)(exp(σ²) - 1) = E(X)² × (exp(σ²) - 1)</span> |
| <span class="comment">// but Var(X) = (CV × E(X))² so CV² = exp(σ²) - 1</span> |
| <span class="comment">// thus σ² = log(CV² + 1)</span> |
| <span class="comment">// and exp(μ) = E(X) / exp(σ² / 2) = E(X) / sqrt(CV² + 1)</span> |
| <span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">F::one</span>() <span class="op">+</span> <span class="ident">cv</span> <span class="op">*</span> <span class="ident">cv</span>; <span class="comment">// e</span> |
| <span class="kw">let</span> <span class="ident">mu</span> <span class="op">=</span> <span class="ident">F::from</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>() <span class="op">*</span> (<span class="ident">mean</span> <span class="op">*</span> <span class="ident">mean</span> <span class="op">/</span> <span class="ident">a</span>).<span class="ident">ln</span>(); |
| <span class="kw">let</span> <span class="ident">sigma</span> <span class="op">=</span> <span class="ident">a</span>.<span class="ident">ln</span>().<span class="ident">sqrt</span>(); |
| <span class="kw">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="ident">Normal::new</span>(<span class="ident">mu</span>, <span class="ident">sigma</span>)<span class="question-mark">?</span>; |
| <span class="prelude-val">Ok</span>(<span class="ident">LogNormal</span> { <span class="ident">norm</span> }) |
| } |
| |
| <span class="doccomment">/// Sample from a z-score</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// This may be useful for generating correlated samples `x1` and `x2`</span> |
| <span class="doccomment">/// from two different distributions, as follows.</span> |
| <span class="doccomment">/// ```</span> |
| <span class="doccomment">/// # use rand::prelude::*;</span> |
| <span class="doccomment">/// # use rand_distr::{LogNormal, StandardNormal};</span> |
| <span class="doccomment">/// let mut rng = thread_rng();</span> |
| <span class="doccomment">/// let z = StandardNormal.sample(&mut rng);</span> |
| <span class="doccomment">/// let x1 = LogNormal::from_mean_cv(3.0, 1.0).unwrap().from_zscore(z);</span> |
| <span class="doccomment">/// let x2 = LogNormal::from_mean_cv(2.0, 4.0).unwrap().from_zscore(z);</span> |
| <span class="doccomment">/// ```</span> |
| <span class="attribute">#[<span class="ident">inline</span>]</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_zscore</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">zscore</span>: <span class="ident">F</span>) -> <span class="ident">F</span> { |
| <span class="self">self</span>.<span class="ident">norm</span>.<span class="ident">from_zscore</span>(<span class="ident">zscore</span>).<span class="ident">exp</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">LogNormal</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="ident">StandardNormal</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">&mut</span> <span class="ident">R</span>) -> <span class="ident">F</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="kw">super</span>::<span class="kw-2">*</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::new</span>(<span class="number">10.0</span>, <span class="number">10.0</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">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">&mut</span> <span class="ident">rng</span>); |
| } |
| } |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">test_normal_cv</span>() { |
| <span class="kw">let</span> <span class="ident">norm</span> <span class="op">=</span> <span class="ident">Normal::from_mean_cv</span>(<span class="number">1024.0</span>, <span class="number">1.0</span> <span class="op">/</span> <span class="number">256.0</span>).<span class="ident">unwrap</span>(); |
| <span class="macro">assert_eq!</span>((<span class="ident">norm</span>.<span class="ident">mean</span>, <span class="ident">norm</span>.<span class="ident">std_dev</span>), (<span class="number">1024.0</span>, <span class="number">4.0</span>)); |
| } |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">test_normal_invalid_sd</span>() { |
| <span class="macro">assert!</span>(<span class="ident">Normal::from_mean_cv</span>(<span class="number">10.0</span>, <span class="op">-</span><span class="number">1.0</span>).<span class="ident">is_err</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::new</span>(<span class="number">10.0</span>, <span class="number">10.0</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">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">&mut</span> <span class="ident">rng</span>); |
| } |
| } |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">test_log_normal_cv</span>() { |
| <span class="kw">let</span> <span class="ident">lnorm</span> <span class="op">=</span> <span class="ident">LogNormal::from_mean_cv</span>(<span class="number">0.0</span>, <span class="number">0.0</span>).<span class="ident">unwrap</span>(); |
| <span class="macro">assert_eq!</span>((<span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">mean</span>, <span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">std_dev</span>), (<span class="op">-</span><span class="ident">core::f64::INFINITY</span>, <span class="number">0.0</span>)); |
| |
| <span class="kw">let</span> <span class="ident">lnorm</span> <span class="op">=</span> <span class="ident">LogNormal::from_mean_cv</span>(<span class="number">1.0</span>, <span class="number">0.0</span>).<span class="ident">unwrap</span>(); |
| <span class="macro">assert_eq!</span>((<span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">mean</span>, <span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">std_dev</span>), (<span class="number">0.0</span>, <span class="number">0.0</span>)); |
| |
| <span class="kw">let</span> <span class="ident">e</span> <span class="op">=</span> <span class="ident">core::f64::consts::E</span>; |
| <span class="kw">let</span> <span class="ident">lnorm</span> <span class="op">=</span> <span class="ident">LogNormal::from_mean_cv</span>(<span class="ident">e</span>.<span class="ident">sqrt</span>(), (<span class="ident">e</span> <span class="op">-</span> <span class="number">1.0</span>).<span class="ident">sqrt</span>()).<span class="ident">unwrap</span>(); |
| <span class="macro">assert_almost_eq!</span>(<span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">mean</span>, <span class="number">0.0</span>, <span class="number">2e-16</span>); |
| <span class="macro">assert_almost_eq!</span>(<span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">std_dev</span>, <span class="number">1.0</span>, <span class="number">2e-16</span>); |
| |
| <span class="kw">let</span> <span class="ident">lnorm</span> <span class="op">=</span> <span class="ident">LogNormal::from_mean_cv</span>(<span class="ident">e</span>.<span class="ident">powf</span>(<span class="number">1.5</span>), (<span class="ident">e</span> <span class="op">-</span> <span class="number">1.0</span>).<span class="ident">sqrt</span>()).<span class="ident">unwrap</span>(); |
| <span class="macro">assert_almost_eq!</span>(<span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">mean</span>, <span class="number">1.0</span>, <span class="number">1e-15</span>); |
| <span class="macro">assert_eq!</span>(<span class="ident">lnorm</span>.<span class="ident">norm</span>.<span class="ident">std_dev</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_invalid_sd</span>() { |
| <span class="macro">assert!</span>(<span class="ident">LogNormal::from_mean_cv</span>(<span class="op">-</span><span class="number">1.0</span>, <span class="number">1.0</span>).<span class="ident">is_err</span>()); |
| <span class="macro">assert!</span>(<span class="ident">LogNormal::from_mean_cv</span>(<span class="number">0.0</span>, <span class="number">1.0</span>).<span class="ident">is_err</span>()); |
| <span class="macro">assert!</span>(<span class="ident">LogNormal::from_mean_cv</span>(<span class="number">1.0</span>, <span class="op">-</span><span class="number">1.0</span>).<span class="ident">is_err</span>()); |
| } |
| } |
| </code></pre></div> |
| </section><section id="search" class="content hidden"></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="rand_distr" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.60.0-nightly (1bd4fdc94 2022-01-12)" ></div> |
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