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| </pre><pre class="rust"><code><span class="comment">// Copyright 2021 Developers of the Rand project. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your |
| // option. This file may not be copied, modified, or distributed |
| // except according to those terms. |
| |
| </span><span class="doccomment">//! The Zeta and related distributions. |
| |
| </span><span class="kw">use </span>num_traits::Float; |
| <span class="kw">use crate</span>::{Distribution, Standard}; |
| <span class="kw">use </span>rand::{Rng, distributions::OpenClosed01}; |
| <span class="kw">use </span>core::fmt; |
| |
| <span class="doccomment">/// Samples integers according to the [zeta distribution]. |
| /// |
| /// The zeta distribution is a limit of the [`Zipf`] distribution. Sometimes it |
| /// is called one of the following: discrete Pareto, Riemann-Zeta, Zipf, or |
| /// Zipf–Estoup distribution. |
| /// |
| /// It has the density function `f(k) = k^(-a) / C(a)` for `k >= 1`, where `a` |
| /// is the parameter and `C(a)` is the Riemann zeta function. |
| /// |
| /// # Example |
| /// ``` |
| /// use rand::prelude::*; |
| /// use rand_distr::Zeta; |
| /// |
| /// let val: f64 = thread_rng().sample(Zeta::new(1.5).unwrap()); |
| /// println!("{}", val); |
| /// ``` |
| /// |
| /// # Remarks |
| /// |
| /// The zeta distribution has no upper limit. Sampled values may be infinite. |
| /// In particular, a value of infinity might be returned for the following |
| /// reasons: |
| /// 1. it is the best representation in the type `F` of the actual sample. |
| /// 2. to prevent infinite loops for very small `a`. |
| /// |
| /// # Implementation details |
| /// |
| /// We are using the algorithm from [Non-Uniform Random Variate Generation], |
| /// Section 6.1, page 551. |
| /// |
| /// [zeta distribution]: https://en.wikipedia.org/wiki/Zeta_distribution |
| /// [Non-Uniform Random Variate Generation]: https://doi.org/10.1007/978-1-4613-8643-8 |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">pub struct </span>Zeta<F> |
| <span class="kw">where </span>F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F> |
| { |
| a_minus_1: F, |
| b: F, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Zeta::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>ZetaError { |
| <span class="doccomment">/// `a <= 1` or `nan`. |
| </span>ATooSmall, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>ZetaError { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| ZetaError::ATooSmall => <span class="string">"a <= 1 or is NaN in Zeta distribution"</span>, |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">"std"</span>)))] |
| </span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>ZetaError {} |
| |
| <span class="kw">impl</span><F> Zeta<F> |
| <span class="kw">where </span>F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F> |
| { |
| <span class="doccomment">/// Construct a new `Zeta` distribution with given `a` parameter. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>new(a: F) -> <span class="prelude-ty">Result</span><Zeta<F>, ZetaError> { |
| <span class="kw">if </span>!(a > F::one()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(ZetaError::ATooSmall); |
| } |
| <span class="kw">let </span>a_minus_1 = a - F::one(); |
| <span class="kw">let </span>two = F::one() + F::one(); |
| <span class="prelude-val">Ok</span>(Zeta { |
| a_minus_1, |
| b: two.powf(a_minus_1), |
| }) |
| } |
| } |
| |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>Zeta<F> |
| <span class="kw">where </span>F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F> |
| { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">loop </span>{ |
| <span class="kw">let </span>u = rng.sample(OpenClosed01); |
| <span class="kw">let </span>x = u.powf(-F::one() / <span class="self">self</span>.a_minus_1).floor(); |
| <span class="macro">debug_assert!</span>(x >= F::one()); |
| <span class="kw">if </span>x.is_infinite() { |
| <span class="comment">// For sufficiently small `a`, `x` will always be infinite, |
| // which is rejected, resulting in an infinite loop. We avoid |
| // this by always returning infinity instead. |
| </span><span class="kw">return </span>x; |
| } |
| |
| <span class="kw">let </span>t = (F::one() + F::one() / x).powf(<span class="self">self</span>.a_minus_1); |
| |
| <span class="kw">let </span>v = rng.sample(Standard); |
| <span class="kw">if </span>v * x * (t - F::one()) * <span class="self">self</span>.b <= t * (<span class="self">self</span>.b - F::one()) { |
| <span class="kw">return </span>x; |
| } |
| } |
| } |
| } |
| |
| <span class="doccomment">/// Samples integers according to the Zipf distribution. |
| /// |
| /// The samples follow Zipf's law: The frequency of each sample from a finite |
| /// set of size `n` is inversely proportional to a power of its frequency rank |
| /// (with exponent `s`). |
| /// |
| /// For large `n`, this converges to the [`Zeta`] distribution. |
| /// |
| /// For `s = 0`, this becomes a uniform distribution. |
| /// |
| /// # Example |
| /// ``` |
| /// use rand::prelude::*; |
| /// use rand_distr::Zipf; |
| /// |
| /// let val: f64 = thread_rng().sample(Zipf::new(10, 1.5).unwrap()); |
| /// println!("{}", val); |
| /// ``` |
| /// |
| /// # Implementation details |
| /// |
| /// Implemented via [rejection sampling](https://en.wikipedia.org/wiki/Rejection_sampling), |
| /// due to Jason Crease[1]. |
| /// |
| /// [1]: https://jasoncrease.medium.com/rejection-sampling-the-zipf-distribution-6b359792cffa |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">pub struct </span>Zipf<F> |
| <span class="kw">where </span>F: Float, Standard: Distribution<F> { |
| n: F, |
| s: F, |
| t: F, |
| q: F, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Zipf::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>ZipfError { |
| <span class="doccomment">/// `s < 0` or `nan`. |
| </span>STooSmall, |
| <span class="doccomment">/// `n < 1`. |
| </span>NTooSmall, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>ZipfError { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| ZipfError::STooSmall => <span class="string">"s < 0 or is NaN in Zipf distribution"</span>, |
| ZipfError::NTooSmall => <span class="string">"n < 1 in Zipf distribution"</span>, |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">"std"</span>)))] |
| </span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>ZipfError {} |
| |
| <span class="kw">impl</span><F> Zipf<F> |
| <span class="kw">where </span>F: Float, Standard: Distribution<F> { |
| <span class="doccomment">/// Construct a new `Zipf` distribution for a set with `n` elements and a |
| /// frequency rank exponent `s`. |
| /// |
| /// For large `n`, rounding may occur to fit the number into the float type. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>new(n: u64, s: F) -> <span class="prelude-ty">Result</span><Zipf<F>, ZipfError> { |
| <span class="kw">if </span>!(s >= F::zero()) { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(ZipfError::STooSmall); |
| } |
| <span class="kw">if </span>n < <span class="number">1 </span>{ |
| <span class="kw">return </span><span class="prelude-val">Err</span>(ZipfError::NTooSmall); |
| } |
| <span class="kw">let </span>n = F::from(n).unwrap(); <span class="comment">// This does not fail. |
| </span><span class="kw">let </span>q = <span class="kw">if </span>s != F::one() { |
| <span class="comment">// Make sure to calculate the division only once. |
| </span>F::one() / (F::one() - s) |
| } <span class="kw">else </span>{ |
| <span class="comment">// This value is never used. |
| </span>F::zero() |
| }; |
| <span class="kw">let </span>t = <span class="kw">if </span>s != F::one() { |
| (n.powf(F::one() - s) - s) * q |
| } <span class="kw">else </span>{ |
| F::one() + n.ln() |
| }; |
| <span class="macro">debug_assert!</span>(t > F::zero()); |
| <span class="prelude-val">Ok</span>(Zipf { |
| n, s, t, q |
| }) |
| } |
| |
| <span class="doccomment">/// Inverse cumulative density function |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">fn </span>inv_cdf(<span class="kw-2">&</span><span class="self">self</span>, p: F) -> F { |
| <span class="kw">let </span>one = F::one(); |
| <span class="kw">let </span>pt = p * <span class="self">self</span>.t; |
| <span class="kw">if </span>pt <= one { |
| pt |
| } <span class="kw">else if </span><span class="self">self</span>.s != one { |
| (pt * (one - <span class="self">self</span>.s) + <span class="self">self</span>.s).powf(<span class="self">self</span>.q) |
| } <span class="kw">else </span>{ |
| (pt - one).exp() |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><F> Distribution<F> <span class="kw">for </span>Zipf<F> |
| <span class="kw">where </span>F: Float, Standard: Distribution<F> |
| { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> F { |
| <span class="kw">let </span>one = F::one(); |
| <span class="kw">loop </span>{ |
| <span class="kw">let </span>inv_b = <span class="self">self</span>.inv_cdf(rng.sample(Standard)); |
| <span class="kw">let </span>x = (inv_b + one).floor(); |
| <span class="kw">let </span><span class="kw-2">mut </span>ratio = x.powf(-<span class="self">self</span>.s); |
| <span class="kw">if </span>x > one { |
| ratio = ratio * inv_b.powf(<span class="self">self</span>.s) |
| }; |
| |
| <span class="kw">let </span>y = rng.sample(Standard); |
| <span class="kw">if </span>y < ratio { |
| <span class="kw">return </span>x; |
| } |
| } |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use super</span>::<span class="kw-2">*</span>; |
| |
| <span class="kw">fn </span>test_samples<F: Float + core::fmt::Debug, D: Distribution<F>>( |
| distr: D, zero: F, expected: <span class="kw-2">&</span>[F], |
| ) { |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">213</span>); |
| <span class="kw">let </span><span class="kw-2">mut </span>buf = [zero; <span class="number">4</span>]; |
| <span class="kw">for </span>x <span class="kw">in </span><span class="kw-2">&mut </span>buf { |
| <span class="kw-2">*</span>x = rng.sample(<span class="kw-2">&</span>distr); |
| } |
| <span class="macro">assert_eq!</span>(buf, expected); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>zeta_invalid() { |
| Zeta::new(<span class="number">1.</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>zeta_nan() { |
| Zeta::new(core::f64::NAN).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zeta_sample() { |
| <span class="kw">let </span>a = <span class="number">2.0</span>; |
| <span class="kw">let </span>d = Zeta::new(a).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">1</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| <span class="kw">let </span>r = d.sample(<span class="kw-2">&mut </span>rng); |
| <span class="macro">assert!</span>(r >= <span class="number">1.</span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zeta_small_a() { |
| <span class="kw">let </span>a = <span class="number">1. </span>+ <span class="number">1e-15</span>; |
| <span class="kw">let </span>d = Zeta::new(a).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">2</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| <span class="kw">let </span>r = d.sample(<span class="kw-2">&mut </span>rng); |
| <span class="macro">assert!</span>(r >= <span class="number">1.</span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zeta_value_stability() { |
| test_samples(Zeta::new(<span class="number">1.5</span>).unwrap(), <span class="number">0f32</span>, <span class="kw-2">&</span>[ |
| <span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>, |
| ]); |
| test_samples(Zeta::new(<span class="number">2.0</span>).unwrap(), <span class="number">0f64</span>, <span class="kw-2">&</span>[ |
| <span class="number">2.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>, <span class="number">1.0</span>, |
| ]); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>zipf_s_too_small() { |
| Zipf::new(<span class="number">10</span>, -<span class="number">1.</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>zipf_n_too_small() { |
| Zipf::new(<span class="number">0</span>, <span class="number">1.</span>).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| #[should_panic] |
| </span><span class="kw">fn </span>zipf_nan() { |
| Zipf::new(<span class="number">10</span>, core::f64::NAN).unwrap(); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zipf_sample() { |
| <span class="kw">let </span>d = Zipf::new(<span class="number">10</span>, <span class="number">0.5</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">2</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| <span class="kw">let </span>r = d.sample(<span class="kw-2">&mut </span>rng); |
| <span class="macro">assert!</span>(r >= <span class="number">1.</span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zipf_sample_s_1() { |
| <span class="kw">let </span>d = Zipf::new(<span class="number">10</span>, <span class="number">1.</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">2</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| <span class="kw">let </span>r = d.sample(<span class="kw-2">&mut </span>rng); |
| <span class="macro">assert!</span>(r >= <span class="number">1.</span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zipf_sample_s_0() { |
| <span class="kw">let </span>d = Zipf::new(<span class="number">10</span>, <span class="number">0.</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">2</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| <span class="kw">let </span>r = d.sample(<span class="kw-2">&mut </span>rng); |
| <span class="macro">assert!</span>(r >= <span class="number">1.</span>); |
| } |
| <span class="comment">// TODO: verify that this is a uniform distribution |
| </span>} |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zipf_sample_large_n() { |
| <span class="kw">let </span>d = Zipf::new(core::u64::MAX, <span class="number">1.5</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">2</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">1000 </span>{ |
| <span class="kw">let </span>r = d.sample(<span class="kw-2">&mut </span>rng); |
| <span class="macro">assert!</span>(r >= <span class="number">1.</span>); |
| } |
| <span class="comment">// TODO: verify that this is a zeta distribution |
| </span>} |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zipf_value_stability() { |
| test_samples(Zipf::new(<span class="number">10</span>, <span class="number">0.5</span>).unwrap(), <span class="number">0f32</span>, <span class="kw-2">&</span>[ |
| <span class="number">10.0</span>, <span class="number">2.0</span>, <span class="number">6.0</span>, <span class="number">7.0 |
| </span>]); |
| test_samples(Zipf::new(<span class="number">10</span>, <span class="number">2.0</span>).unwrap(), <span class="number">0f64</span>, <span class="kw-2">&</span>[ |
| <span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">3.0</span>, <span class="number">2.0 |
| </span>]); |
| } |
| } |
| </code></pre></div> |
| </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="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |