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| </pre><pre class="rust"><code><span class="doccomment">//! The hypergeometric distribution.</span> |
| |
| <span class="kw">use</span> <span class="ident"><span class="kw">crate</span>::Distribution</span>; |
| <span class="kw">use</span> <span class="ident">rand::Rng</span>; |
| <span class="kw">use</span> <span class="ident">rand::distributions::uniform::Uniform</span>; |
| <span class="kw">use</span> <span class="ident">core::fmt</span>; |
| <span class="attribute">#[<span class="ident">allow</span>(<span class="ident">unused_imports</span>)]</span> |
| <span class="kw">use</span> <span class="ident">num_traits::Float</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">enum</span> <span class="ident">SamplingMethod</span> { |
| <span class="ident">InverseTransform</span>{ <span class="ident">initial_p</span>: <span class="ident">f64</span>, <span class="ident">initial_x</span>: <span class="ident">i64</span> }, |
| <span class="ident">RejectionAcceptance</span>{ |
| <span class="ident">m</span>: <span class="ident">f64</span>, |
| <span class="ident">a</span>: <span class="ident">f64</span>, |
| <span class="ident">lambda_l</span>: <span class="ident">f64</span>, |
| <span class="ident">lambda_r</span>: <span class="ident">f64</span>, |
| <span class="ident">x_l</span>: <span class="ident">f64</span>, |
| <span class="ident">x_r</span>: <span class="ident">f64</span>, |
| <span class="ident">p1</span>: <span class="ident">f64</span>, |
| <span class="ident">p2</span>: <span class="ident">f64</span>, |
| <span class="ident">p3</span>: <span class="ident">f64</span> |
| }, |
| } |
| |
| <span class="doccomment">/// The hypergeometric distribution `Hypergeometric(N, K, n)`.</span> |
| <span class="doccomment">/// </span> |
| <span class="doccomment">/// This is the distribution of successes in samples of size `n` drawn without</span> |
| <span class="doccomment">/// replacement from a population of size `N` containing `K` success states.</span> |
| <span class="doccomment">/// It has the density function:</span> |
| <span class="doccomment">/// `f(k) = binomial(K, k) * binomial(N-K, n-k) / binomial(N, n)`,</span> |
| <span class="doccomment">/// where `binomial(a, b) = a! / (b! * (a - b)!)`.</span> |
| <span class="doccomment">/// </span> |
| <span class="doccomment">/// The [binomial distribution](crate::Binomial) is the analogous distribution</span> |
| <span class="doccomment">/// for sampling with replacement. It is a good approximation when the population</span> |
| <span class="doccomment">/// size is much larger than the sample size.</span> |
| <span class="doccomment">/// </span> |
| <span class="doccomment">/// # Example</span> |
| <span class="doccomment">/// </span> |
| <span class="doccomment">/// ```</span> |
| <span class="doccomment">/// use rand_distr::{Distribution, Hypergeometric};</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// let hypergeo = Hypergeometric::new(60, 24, 7).unwrap();</span> |
| <span class="doccomment">/// let v = hypergeo.sample(&mut rand::thread_rng());</span> |
| <span class="doccomment">/// println!("{} is from a hypergeometric distribution", v);</span> |
| <span class="doccomment">/// ```</span> |
| <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Copy</span>, <span class="ident">Clone</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">Hypergeometric</span> { |
| <span class="ident">n1</span>: <span class="ident">u64</span>, |
| <span class="ident">n2</span>: <span class="ident">u64</span>, |
| <span class="ident">k</span>: <span class="ident">u64</span>, |
| <span class="ident">offset_x</span>: <span class="ident">i64</span>, |
| <span class="ident">sign_x</span>: <span class="ident">i64</span>, |
| <span class="ident">sampling_method</span>: <span class="ident">SamplingMethod</span>, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Hypergeometric::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">/// `total_population_size` is too large, causing floating point underflow.</span> |
| <span class="ident">PopulationTooLarge</span>, |
| <span class="doccomment">/// `population_with_feature > total_population_size`.</span> |
| <span class="ident">ProbabilityTooLarge</span>, |
| <span class="doccomment">/// `sample_size > total_population_size`.</span> |
| <span class="ident">SampleSizeTooLarge</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::PopulationTooLarge</span> => <span class="string">"total_population_size is too large causing underflow in geometric distribution"</span>, |
| <span class="ident">Error::ProbabilityTooLarge</span> => <span class="string">"population_with_feature > total_population_size in geometric distribution"</span>, |
| <span class="ident">Error::SampleSizeTooLarge</span> => <span class="string">"sample_size > total_population_size in geometric 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="comment">// evaluate fact(numerator.0)*fact(numerator.1) / fact(denominator.0)*fact(denominator.1)</span> |
| <span class="kw">fn</span> <span class="ident">fraction_of_products_of_factorials</span>(<span class="ident">numerator</span>: (<span class="ident">u64</span>, <span class="ident">u64</span>), <span class="ident">denominator</span>: (<span class="ident">u64</span>, <span class="ident">u64</span>)) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">min_top</span> <span class="op">=</span> <span class="ident">u64::min</span>(<span class="ident">numerator</span>.<span class="number">0</span>, <span class="ident">numerator</span>.<span class="number">1</span>); |
| <span class="kw">let</span> <span class="ident">min_bottom</span> <span class="op">=</span> <span class="ident">u64::min</span>(<span class="ident">denominator</span>.<span class="number">0</span>, <span class="ident">denominator</span>.<span class="number">1</span>); |
| <span class="comment">// the factorial of this will cancel out:</span> |
| <span class="kw">let</span> <span class="ident">min_all</span> <span class="op">=</span> <span class="ident">u64::min</span>(<span class="ident">min_top</span>, <span class="ident">min_bottom</span>); |
| |
| <span class="kw">let</span> <span class="ident">max_top</span> <span class="op">=</span> <span class="ident">u64::max</span>(<span class="ident">numerator</span>.<span class="number">0</span>, <span class="ident">numerator</span>.<span class="number">1</span>); |
| <span class="kw">let</span> <span class="ident">max_bottom</span> <span class="op">=</span> <span class="ident">u64::max</span>(<span class="ident">denominator</span>.<span class="number">0</span>, <span class="ident">denominator</span>.<span class="number">1</span>); |
| <span class="kw">let</span> <span class="ident">max_all</span> <span class="op">=</span> <span class="ident">u64::max</span>(<span class="ident">max_top</span>, <span class="ident">max_bottom</span>); |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">result</span> <span class="op">=</span> <span class="number">1.0</span>; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="ident">min_all</span> <span class="op">+</span> <span class="number">1</span>)..<span class="op">=</span><span class="ident">max_all</span> { |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op"><</span><span class="op">=</span> <span class="ident">min_top</span> { |
| <span class="ident">result</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op"><</span><span class="op">=</span> <span class="ident">min_bottom</span> { |
| <span class="ident">result</span> <span class="op">/</span><span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op"><</span><span class="op">=</span> <span class="ident">max_top</span> { |
| <span class="ident">result</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">i</span> <span class="op"><</span><span class="op">=</span> <span class="ident">max_bottom</span> { |
| <span class="ident">result</span> <span class="op">/</span><span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| } |
| } |
| |
| <span class="ident">result</span> |
| } |
| |
| <span class="kw">fn</span> <span class="ident">ln_of_factorial</span>(<span class="ident">v</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="comment">// the paper calls for ln(v!), but also wants to pass in fractions,</span> |
| <span class="comment">// so we need to use Stirling's approximation to fill in the gaps:</span> |
| <span class="ident">v</span> <span class="op">*</span> <span class="ident">v</span>.<span class="ident">ln</span>() <span class="op">-</span> <span class="ident">v</span> |
| } |
| |
| <span class="kw">impl</span> <span class="ident">Hypergeometric</span> { |
| <span class="doccomment">/// Constructs a new `Hypergeometric` with the shape parameters</span> |
| <span class="doccomment">/// `N = total_population_size`,</span> |
| <span class="doccomment">/// `K = population_with_feature`,</span> |
| <span class="doccomment">/// `n = sample_size`.</span> |
| <span class="attribute">#[<span class="ident">allow</span>(<span class="ident">clippy::many_single_char_names</span>)]</span> <span class="comment">// Same names as in the reference.</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">total_population_size</span>: <span class="ident">u64</span>, <span class="ident">population_with_feature</span>: <span class="ident">u64</span>, <span class="ident">sample_size</span>: <span class="ident">u64</span>) -> <span class="prelude-ty">Result</span><span class="op"><</span><span class="self">Self</span>, <span class="ident">Error</span><span class="op">></span> { |
| <span class="kw">if</span> <span class="ident">population_with_feature</span> <span class="op">></span> <span class="ident">total_population_size</span> { |
| <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error::ProbabilityTooLarge</span>); |
| } |
| |
| <span class="kw">if</span> <span class="ident">sample_size</span> <span class="op">></span> <span class="ident">total_population_size</span> { |
| <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error::SampleSizeTooLarge</span>); |
| } |
| |
| <span class="comment">// set-up constants as function of original parameters</span> |
| <span class="kw">let</span> <span class="ident">n</span> <span class="op">=</span> <span class="ident">total_population_size</span>; |
| <span class="kw">let</span> (<span class="kw-2">mut</span> <span class="ident">sign_x</span>, <span class="kw-2">mut</span> <span class="ident">offset_x</span>) <span class="op">=</span> (<span class="number">1</span>, <span class="number">0</span>); |
| <span class="kw">let</span> (<span class="ident">n1</span>, <span class="ident">n2</span>) <span class="op">=</span> { |
| <span class="comment">// switch around success and failure states if necessary to ensure n1 <= n2</span> |
| <span class="kw">let</span> <span class="ident">population_without_feature</span> <span class="op">=</span> <span class="ident">n</span> <span class="op">-</span> <span class="ident">population_with_feature</span>; |
| <span class="kw">if</span> <span class="ident">population_with_feature</span> <span class="op">></span> <span class="ident">population_without_feature</span> { |
| <span class="ident">sign_x</span> <span class="op">=</span> <span class="op">-</span><span class="number">1</span>; |
| <span class="ident">offset_x</span> <span class="op">=</span> <span class="ident">sample_size</span> <span class="kw">as</span> <span class="ident">i64</span>; |
| (<span class="ident">population_without_feature</span>, <span class="ident">population_with_feature</span>) |
| } <span class="kw">else</span> { |
| (<span class="ident">population_with_feature</span>, <span class="ident">population_without_feature</span>) |
| } |
| }; |
| <span class="comment">// when sampling more than half the total population, take the smaller</span> |
| <span class="comment">// group as sampled instead (we can then return n1-x instead).</span> |
| <span class="comment">// </span> |
| <span class="comment">// Note: the boundary condition given in the paper is `sample_size < n / 2`;</span> |
| <span class="comment">// we're deviating here, because when n is even, it doesn't matter whether</span> |
| <span class="comment">// we switch here or not, but when n is odd `n/2 < n - n/2`, so switching</span> |
| <span class="comment">// when `k == n/2`, we'd actually be taking the _larger_ group as sampled.</span> |
| <span class="kw">let</span> <span class="ident">k</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">sample_size</span> <span class="op"><</span><span class="op">=</span> <span class="ident">n</span> <span class="op">/</span> <span class="number">2</span> { |
| <span class="ident">sample_size</span> |
| } <span class="kw">else</span> { |
| <span class="ident">offset_x</span> <span class="op">+</span><span class="op">=</span> <span class="ident">n1</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">*</span> <span class="ident">sign_x</span>; |
| <span class="ident">sign_x</span> <span class="kw-2">*</span><span class="op">=</span> <span class="op">-</span><span class="number">1</span>; |
| <span class="ident">n</span> <span class="op">-</span> <span class="ident">sample_size</span> |
| }; |
| |
| <span class="comment">// Algorithm H2PE has bounded runtime only if `M - max(0, k-n2) >= 10`,</span> |
| <span class="comment">// where `M` is the mode of the distribution.</span> |
| <span class="comment">// Use algorithm HIN for the remaining parameter space.</span> |
| <span class="comment">// </span> |
| <span class="comment">// Voratas Kachitvichyanukul and Bruce W. Schmeiser. 1985. Computer</span> |
| <span class="comment">// generation of hypergeometric random variates.</span> |
| <span class="comment">// J. Statist. Comput. Simul. Vol.22 (August 1985), 127-145</span> |
| <span class="comment">// https://www.researchgate.net/publication/233212638</span> |
| <span class="kw">const</span> <span class="ident">HIN_THRESHOLD</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">10.0</span>; |
| <span class="kw">let</span> <span class="ident">m</span> <span class="op">=</span> ((<span class="ident">k</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> (<span class="ident">n1</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">/</span> (<span class="ident">n</span> <span class="op">+</span> <span class="number">2</span>) <span class="kw">as</span> <span class="ident">f64</span>).<span class="ident">floor</span>(); |
| <span class="kw">let</span> <span class="ident">sampling_method</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">m</span> <span class="op">-</span> <span class="ident">f64::max</span>(<span class="number">0.0</span>, <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">n2</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op"><</span> <span class="ident">HIN_THRESHOLD</span> { |
| <span class="kw">let</span> (<span class="ident">initial_p</span>, <span class="ident">initial_x</span>) <span class="op">=</span> <span class="kw">if</span> <span class="ident">k</span> <span class="op"><</span> <span class="ident">n2</span> { |
| (<span class="ident">fraction_of_products_of_factorials</span>((<span class="ident">n2</span>, <span class="ident">n</span> <span class="op">-</span> <span class="ident">k</span>), (<span class="ident">n</span>, <span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span>)), <span class="number">0</span>) |
| } <span class="kw">else</span> { |
| (<span class="ident">fraction_of_products_of_factorials</span>((<span class="ident">n1</span>, <span class="ident">k</span>), (<span class="ident">n</span>, <span class="ident">k</span> <span class="op">-</span> <span class="ident">n2</span>)), (<span class="ident">k</span> <span class="op">-</span> <span class="ident">n2</span>) <span class="kw">as</span> <span class="ident">i64</span>) |
| }; |
| |
| <span class="kw">if</span> <span class="ident">initial_p</span> <span class="op"><</span><span class="op">=</span> <span class="number">0.0</span> <span class="op">|</span><span class="op">|</span> <span class="op">!</span><span class="ident">initial_p</span>.<span class="ident">is_finite</span>() { |
| <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error::PopulationTooLarge</span>); |
| } |
| |
| <span class="ident">SamplingMethod::InverseTransform</span> { <span class="ident">initial_p</span>, <span class="ident">initial_x</span> } |
| } <span class="kw">else</span> { |
| <span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">ln_of_factorial</span>(<span class="ident">m</span>) <span class="op">+</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">m</span>) <span class="op">+</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">m</span>) <span class="op">+</span> |
| <span class="ident">ln_of_factorial</span>((<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">m</span>); |
| |
| <span class="kw">let</span> <span class="ident">numerator</span> <span class="op">=</span> (<span class="ident">n</span> <span class="op">-</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">n2</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">denominator</span> <span class="op">=</span> (<span class="ident">n</span> <span class="op">-</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">d</span> <span class="op">=</span> <span class="number">1.5</span> <span class="op">*</span> (<span class="ident">numerator</span> <span class="op">/</span> <span class="ident">denominator</span>).<span class="ident">sqrt</span>() <span class="op">+</span> <span class="number">0.5</span>; |
| |
| <span class="kw">let</span> <span class="ident">x_l</span> <span class="op">=</span> <span class="ident">m</span> <span class="op">-</span> <span class="ident">d</span> <span class="op">+</span> <span class="number">0.5</span>; |
| <span class="kw">let</span> <span class="ident">x_r</span> <span class="op">=</span> <span class="ident">m</span> <span class="op">+</span> <span class="ident">d</span> <span class="op">+</span> <span class="number">0.5</span>; |
| |
| <span class="kw">let</span> <span class="ident">k_l</span> <span class="op">=</span> <span class="ident">f64::exp</span>(<span class="ident">a</span> <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">x_l</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_l</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_l</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>((<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">x_l</span>)); |
| <span class="kw">let</span> <span class="ident">k_r</span> <span class="op">=</span> <span class="ident">f64::exp</span>(<span class="ident">a</span> <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">x_r</span> <span class="op">-</span> <span class="number">1.0</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_r</span> <span class="op">+</span> <span class="number">1.0</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_r</span> <span class="op">+</span> <span class="number">1.0</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>((<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">x_r</span> <span class="op">-</span> <span class="number">1.0</span>)); |
| |
| <span class="kw">let</span> <span class="ident">numerator</span> <span class="op">=</span> <span class="ident">x_l</span> <span class="op">*</span> ((<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">x_l</span>); |
| <span class="kw">let</span> <span class="ident">denominator</span> <span class="op">=</span> (<span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_l</span> <span class="op">+</span> <span class="number">1.0</span>) <span class="op">*</span> (<span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_l</span> <span class="op">+</span> <span class="number">1.0</span>); |
| <span class="kw">let</span> <span class="ident">lambda_l</span> <span class="op">=</span> <span class="op">-</span>((<span class="ident">numerator</span> <span class="op">/</span> <span class="ident">denominator</span>).<span class="ident">ln</span>()); |
| |
| <span class="kw">let</span> <span class="ident">numerator</span> <span class="op">=</span> (<span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_r</span> <span class="op">+</span> <span class="number">1.0</span>) <span class="op">*</span> (<span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">x_r</span> <span class="op">+</span> <span class="number">1.0</span>); |
| <span class="kw">let</span> <span class="ident">denominator</span> <span class="op">=</span> <span class="ident">x_r</span> <span class="op">*</span> ((<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">x_r</span>); |
| <span class="kw">let</span> <span class="ident">lambda_r</span> <span class="op">=</span> <span class="op">-</span>((<span class="ident">numerator</span> <span class="op">/</span> <span class="ident">denominator</span>).<span class="ident">ln</span>()); |
| |
| <span class="comment">// the paper literally gives `p2 + kL/lambdaL` where it (probably)</span> |
| <span class="comment">// should have been `p2 <- p1 + kL/lambdaL`; another print error?!</span> |
| <span class="kw">let</span> <span class="ident">p1</span> <span class="op">=</span> <span class="number">2.0</span> <span class="op">*</span> <span class="ident">d</span>; |
| <span class="kw">let</span> <span class="ident">p2</span> <span class="op">=</span> <span class="ident">p1</span> <span class="op">+</span> <span class="ident">k_l</span> <span class="op">/</span> <span class="ident">lambda_l</span>; |
| <span class="kw">let</span> <span class="ident">p3</span> <span class="op">=</span> <span class="ident">p2</span> <span class="op">+</span> <span class="ident">k_r</span> <span class="op">/</span> <span class="ident">lambda_r</span>; |
| |
| <span class="ident">SamplingMethod::RejectionAcceptance</span> { |
| <span class="ident">m</span>, <span class="ident">a</span>, <span class="ident">lambda_l</span>, <span class="ident">lambda_r</span>, <span class="ident">x_l</span>, <span class="ident">x_r</span>, <span class="ident">p1</span>, <span class="ident">p2</span>, <span class="ident">p3</span> |
| } |
| }; |
| |
| <span class="prelude-val">Ok</span>(<span class="ident">Hypergeometric</span> { <span class="ident">n1</span>, <span class="ident">n2</span>, <span class="ident">k</span>, <span class="ident">offset_x</span>, <span class="ident">sign_x</span>, <span class="ident">sampling_method</span> }) |
| } |
| } |
| |
| <span class="kw">impl</span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">u64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Hypergeometric</span> { |
| <span class="attribute">#[<span class="ident">allow</span>(<span class="ident">clippy::many_single_char_names</span>)]</span> <span class="comment">// Same names as in the reference.</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">u64</span> { |
| <span class="kw">use</span> <span class="ident">SamplingMethod</span>::<span class="kw-2">*</span>; |
| |
| <span class="kw">let</span> <span class="ident">Hypergeometric</span> { <span class="ident">n1</span>, <span class="ident">n2</span>, <span class="ident">k</span>, <span class="ident">sign_x</span>, <span class="ident">offset_x</span>, <span class="ident">sampling_method</span> } <span class="op">=</span> <span class="kw-2">*</span><span class="self">self</span>; |
| <span class="kw">let</span> <span class="ident">x</span> <span class="op">=</span> <span class="kw">match</span> <span class="ident">sampling_method</span> { |
| <span class="ident">InverseTransform</span> { <span class="ident">initial_p</span>: <span class="kw-2">mut</span> <span class="ident">p</span>, <span class="ident">initial_x</span>: <span class="kw-2">mut</span> <span class="ident">x</span> } => { |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">u</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>(); |
| <span class="kw">while</span> <span class="ident">u</span> <span class="op">></span> <span class="ident">p</span> <span class="op">&&</span> <span class="ident">x</span> <span class="op"><</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">i64</span> { <span class="comment">// the paper erroneously uses `until n < p`, which doesn't make any sense</span> |
| <span class="ident">u</span> <span class="op">-</span><span class="op">=</span> <span class="ident">p</span>; |
| <span class="ident">p</span> <span class="kw-2">*</span><span class="op">=</span> ((<span class="ident">n1</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">-</span> <span class="ident">x</span> <span class="kw">as</span> <span class="ident">i64</span>) <span class="op">*</span> (<span class="ident">k</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">-</span> <span class="ident">x</span> <span class="kw">as</span> <span class="ident">i64</span>)) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">p</span> <span class="op">/</span><span class="op">=</span> ((<span class="ident">x</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">+</span> <span class="number">1</span>) <span class="op">*</span> (<span class="ident">n2</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">-</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">+</span> <span class="number">1</span> <span class="op">+</span> <span class="ident">x</span> <span class="kw">as</span> <span class="ident">i64</span>)) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">x</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| } |
| <span class="ident">x</span> |
| }, |
| <span class="ident">RejectionAcceptance</span> { <span class="ident">m</span>, <span class="ident">a</span>, <span class="ident">lambda_l</span>, <span class="ident">lambda_r</span>, <span class="ident">x_l</span>, <span class="ident">x_r</span>, <span class="ident">p1</span>, <span class="ident">p2</span>, <span class="ident">p3</span> } => { |
| <span class="kw">let</span> <span class="ident">distr_region_select</span> <span class="op">=</span> <span class="ident">Uniform::new</span>(<span class="number">0.0</span>, <span class="ident">p3</span>); |
| <span class="kw">loop</span> { |
| <span class="kw">let</span> (<span class="ident">y</span>, <span class="ident">v</span>) <span class="op">=</span> <span class="kw">loop</span> { |
| <span class="kw">let</span> <span class="ident">u</span> <span class="op">=</span> <span class="ident">distr_region_select</span>.<span class="ident">sample</span>(<span class="ident">rng</span>); |
| <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>(); <span class="comment">// for the accept/reject decision</span> |
| |
| <span class="kw">if</span> <span class="ident">u</span> <span class="op"><</span><span class="op">=</span> <span class="ident">p1</span> { |
| <span class="comment">// Region 1, central bell</span> |
| <span class="kw">let</span> <span class="ident">y</span> <span class="op">=</span> (<span class="ident">x_l</span> <span class="op">+</span> <span class="ident">u</span>).<span class="ident">floor</span>(); |
| <span class="kw">break</span> (<span class="ident">y</span>, <span class="ident">v</span>); |
| } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">u</span> <span class="op"><</span><span class="op">=</span> <span class="ident">p2</span> { |
| <span class="comment">// Region 2, left exponential tail</span> |
| <span class="kw">let</span> <span class="ident">y</span> <span class="op">=</span> (<span class="ident">x_l</span> <span class="op">+</span> <span class="ident">v</span>.<span class="ident">ln</span>() <span class="op">/</span> <span class="ident">lambda_l</span>).<span class="ident">floor</span>(); |
| <span class="kw">if</span> <span class="ident">y</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">></span><span class="op">=</span> <span class="ident">i64::max</span>(<span class="number">0</span>, <span class="ident">k</span> <span class="kw">as</span> <span class="ident">i64</span> <span class="op">-</span> <span class="ident">n2</span> <span class="kw">as</span> <span class="ident">i64</span>) { |
| <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">v</span> <span class="op">*</span> (<span class="ident">u</span> <span class="op">-</span> <span class="ident">p1</span>) <span class="op">*</span> <span class="ident">lambda_l</span>; |
| <span class="kw">break</span> (<span class="ident">y</span>, <span class="ident">v</span>); |
| } |
| } <span class="kw">else</span> { |
| <span class="comment">// Region 3, right exponential tail</span> |
| <span class="kw">let</span> <span class="ident">y</span> <span class="op">=</span> (<span class="ident">x_r</span> <span class="op">-</span> <span class="ident">v</span>.<span class="ident">ln</span>() <span class="op">/</span> <span class="ident">lambda_r</span>).<span class="ident">floor</span>(); |
| <span class="kw">if</span> <span class="ident">y</span> <span class="kw">as</span> <span class="ident">u64</span> <span class="op"><</span><span class="op">=</span> <span class="ident">u64::min</span>(<span class="ident">n1</span>, <span class="ident">k</span>) { |
| <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">v</span> <span class="op">*</span> (<span class="ident">u</span> <span class="op">-</span> <span class="ident">p2</span>) <span class="op">*</span> <span class="ident">lambda_r</span>; |
| <span class="kw">break</span> (<span class="ident">y</span>, <span class="ident">v</span>); |
| } |
| } |
| }; |
| |
| <span class="comment">// Step 4: Acceptance/Rejection Comparison</span> |
| <span class="kw">if</span> <span class="ident">m</span> <span class="op"><</span> <span class="number">100.0</span> <span class="op">|</span><span class="op">|</span> <span class="ident">y</span> <span class="op"><</span><span class="op">=</span> <span class="number">50.0</span> { |
| <span class="comment">// Step 4.1: evaluate f(y) via recursive relationship</span> |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">f</span> <span class="op">=</span> <span class="number">1.0</span>; |
| <span class="kw">if</span> <span class="ident">m</span> <span class="op"><</span> <span class="ident">y</span> { |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="ident">m</span> <span class="kw">as</span> <span class="ident">u64</span> <span class="op">+</span> <span class="number">1</span>)..<span class="op">=</span>(<span class="ident">y</span> <span class="kw">as</span> <span class="ident">u64</span>) { |
| <span class="ident">f</span> <span class="kw-2">*</span><span class="op">=</span> (<span class="ident">n1</span> <span class="op">-</span> <span class="ident">i</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> (<span class="ident">k</span> <span class="op">-</span> <span class="ident">i</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">f</span> <span class="op">/</span><span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> (<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span> <span class="op">+</span> <span class="ident">i</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| } |
| } <span class="kw">else</span> { |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> (<span class="ident">y</span> <span class="kw">as</span> <span class="ident">u64</span> <span class="op">+</span> <span class="number">1</span>)..<span class="op">=</span>(<span class="ident">m</span> <span class="kw">as</span> <span class="ident">u64</span>) { |
| <span class="ident">f</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> (<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span> <span class="op">+</span> <span class="ident">i</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">f</span> <span class="op">/</span><span class="op">=</span> (<span class="ident">n1</span> <span class="op">-</span> <span class="ident">i</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> (<span class="ident">k</span> <span class="op">-</span> <span class="ident">i</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| } |
| } |
| |
| <span class="kw">if</span> <span class="ident">v</span> <span class="op"><</span><span class="op">=</span> <span class="ident">f</span> { <span class="kw">break</span> <span class="ident">y</span> <span class="kw">as</span> <span class="ident">i64</span>; } |
| } <span class="kw">else</span> { |
| <span class="comment">// Step 4.2: Squeezing</span> |
| <span class="kw">let</span> <span class="ident">y1</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">1.0</span>; |
| <span class="kw">let</span> <span class="ident">ym</span> <span class="op">=</span> <span class="ident">y</span> <span class="op">-</span> <span class="ident">m</span>; |
| <span class="kw">let</span> <span class="ident">yn</span> <span class="op">=</span> <span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">1.0</span>; |
| <span class="kw">let</span> <span class="ident">yk</span> <span class="op">=</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">1.0</span>; |
| <span class="kw">let</span> <span class="ident">nk</span> <span class="op">=</span> <span class="ident">n2</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">y1</span>; |
| <span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="op">-</span><span class="ident">ym</span> <span class="op">/</span> <span class="ident">y1</span>; |
| <span class="kw">let</span> <span class="ident">s</span> <span class="op">=</span> <span class="ident">ym</span> <span class="op">/</span> <span class="ident">yn</span>; |
| <span class="kw">let</span> <span class="ident">t</span> <span class="op">=</span> <span class="ident">ym</span> <span class="op">/</span> <span class="ident">yk</span>; |
| <span class="kw">let</span> <span class="ident">e</span> <span class="op">=</span> <span class="op">-</span><span class="ident">ym</span> <span class="op">/</span> <span class="ident">nk</span>; |
| <span class="kw">let</span> <span class="ident">g</span> <span class="op">=</span> <span class="ident">yn</span> <span class="op">*</span> <span class="ident">yk</span> <span class="op">/</span> (<span class="ident">y1</span> <span class="op">*</span> <span class="ident">nk</span>) <span class="op">-</span> <span class="number">1.0</span>; |
| <span class="kw">let</span> <span class="ident">dg</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">g</span> <span class="op"><</span> <span class="number">0.0</span> { |
| <span class="number">1.0</span> <span class="op">+</span> <span class="ident">g</span> |
| } <span class="kw">else</span> { |
| <span class="number">1.0</span> |
| }; |
| <span class="kw">let</span> <span class="ident">gu</span> <span class="op">=</span> <span class="ident">g</span> <span class="op">*</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">g</span> <span class="op">*</span> (<span class="op">-</span><span class="number">0.5</span> <span class="op">+</span> <span class="ident">g</span> <span class="op">/</span> <span class="number">3.0</span>)); |
| <span class="kw">let</span> <span class="ident">gl</span> <span class="op">=</span> <span class="ident">gu</span> <span class="op">-</span> <span class="ident">g</span>.<span class="ident">powi</span>(<span class="number">4</span>) <span class="op">/</span> (<span class="number">4.0</span> <span class="op">*</span> <span class="ident">dg</span>); |
| <span class="kw">let</span> <span class="ident">xm</span> <span class="op">=</span> <span class="ident">m</span> <span class="op">+</span> <span class="number">0.5</span>; |
| <span class="kw">let</span> <span class="ident">xn</span> <span class="op">=</span> <span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">m</span> <span class="op">+</span> <span class="number">0.5</span>; |
| <span class="kw">let</span> <span class="ident">xk</span> <span class="op">=</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">m</span> <span class="op">+</span> <span class="number">0.5</span>; |
| <span class="kw">let</span> <span class="ident">nm</span> <span class="op">=</span> <span class="ident">n2</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">xm</span>; |
| <span class="kw">let</span> <span class="ident">ub</span> <span class="op">=</span> <span class="ident">xm</span> <span class="op">*</span> <span class="ident">r</span> <span class="op">*</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">*</span> (<span class="op">-</span><span class="number">0.5</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">/</span> <span class="number">3.0</span>)) <span class="op">+</span> |
| <span class="ident">xn</span> <span class="op">*</span> <span class="ident">s</span> <span class="op">*</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="op">-</span><span class="number">0.5</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">/</span> <span class="number">3.0</span>)) <span class="op">+</span> |
| <span class="ident">xk</span> <span class="op">*</span> <span class="ident">t</span> <span class="op">*</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">*</span> (<span class="op">-</span><span class="number">0.5</span> <span class="op">+</span> <span class="ident">t</span> <span class="op">/</span> <span class="number">3.0</span>)) <span class="op">+</span> |
| <span class="ident">nm</span> <span class="op">*</span> <span class="ident">e</span> <span class="op">*</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">e</span> <span class="op">*</span> (<span class="op">-</span><span class="number">0.5</span> <span class="op">+</span> <span class="ident">e</span> <span class="op">/</span> <span class="number">3.0</span>)) <span class="op">+</span> |
| <span class="ident">y</span> <span class="op">*</span> <span class="ident">gu</span> <span class="op">-</span> <span class="ident">m</span> <span class="op">*</span> <span class="ident">gl</span> <span class="op">+</span> <span class="number">0.0034</span>; |
| <span class="kw">let</span> <span class="ident">av</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">ln</span>(); |
| <span class="kw">if</span> <span class="ident">av</span> <span class="op">></span> <span class="ident">ub</span> { <span class="kw">continue</span>; } |
| <span class="kw">let</span> <span class="ident">dr</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">r</span> <span class="op"><</span> <span class="number">0.0</span> { |
| <span class="ident">xm</span> <span class="op">*</span> <span class="ident">r</span>.<span class="ident">powi</span>(<span class="number">4</span>) <span class="op">/</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">r</span>) |
| } <span class="kw">else</span> { |
| <span class="ident">xm</span> <span class="op">*</span> <span class="ident">r</span>.<span class="ident">powi</span>(<span class="number">4</span>) |
| }; |
| <span class="kw">let</span> <span class="ident">ds</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">s</span> <span class="op"><</span> <span class="number">0.0</span> { |
| <span class="ident">xn</span> <span class="op">*</span> <span class="ident">s</span>.<span class="ident">powi</span>(<span class="number">4</span>) <span class="op">/</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">s</span>) |
| } <span class="kw">else</span> { |
| <span class="ident">xn</span> <span class="op">*</span> <span class="ident">s</span>.<span class="ident">powi</span>(<span class="number">4</span>) |
| }; |
| <span class="kw">let</span> <span class="ident">dt</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">t</span> <span class="op"><</span> <span class="number">0.0</span> { |
| <span class="ident">xk</span> <span class="op">*</span> <span class="ident">t</span>.<span class="ident">powi</span>(<span class="number">4</span>) <span class="op">/</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">t</span>) |
| } <span class="kw">else</span> { |
| <span class="ident">xk</span> <span class="op">*</span> <span class="ident">t</span>.<span class="ident">powi</span>(<span class="number">4</span>) |
| }; |
| <span class="kw">let</span> <span class="ident">de</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">e</span> <span class="op"><</span> <span class="number">0.0</span> { |
| <span class="ident">nm</span> <span class="op">*</span> <span class="ident">e</span>.<span class="ident">powi</span>(<span class="number">4</span>) <span class="op">/</span> (<span class="number">1.0</span> <span class="op">+</span> <span class="ident">e</span>) |
| } <span class="kw">else</span> { |
| <span class="ident">nm</span> <span class="op">*</span> <span class="ident">e</span>.<span class="ident">powi</span>(<span class="number">4</span>) |
| }; |
| |
| <span class="kw">if</span> <span class="ident">av</span> <span class="op"><</span> <span class="ident">ub</span> <span class="op">-</span> <span class="number">0.25</span><span class="kw-2">*</span>(<span class="ident">dr</span> <span class="op">+</span> <span class="ident">ds</span> <span class="op">+</span> <span class="ident">dt</span> <span class="op">+</span> <span class="ident">de</span>) <span class="op">+</span> (<span class="ident">y</span> <span class="op">+</span> <span class="ident">m</span>)<span class="kw-2">*</span>(<span class="ident">gl</span> <span class="op">-</span> <span class="ident">gu</span>) <span class="op">-</span> <span class="number">0.0078</span> { |
| <span class="kw">break</span> <span class="ident">y</span> <span class="kw">as</span> <span class="ident">i64</span>; |
| } |
| |
| <span class="comment">// Step 4.3: Final Acceptance/Rejection Test</span> |
| <span class="kw">let</span> <span class="ident">av_critical</span> <span class="op">=</span> <span class="ident">a</span> <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">y</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">n1</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">y</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>(<span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">y</span>) <span class="op">-</span> |
| <span class="ident">ln_of_factorial</span>((<span class="ident">n2</span> <span class="op">-</span> <span class="ident">k</span>) <span class="kw">as</span> <span class="ident">f64</span> <span class="op">+</span> <span class="ident">y</span>); |
| <span class="kw">if</span> <span class="ident">v</span>.<span class="ident">ln</span>() <span class="op"><</span><span class="op">=</span> <span class="ident">av_critical</span> { |
| <span class="kw">break</span> <span class="ident">y</span> <span class="kw">as</span> <span class="ident">i64</span>; |
| } |
| } |
| } |
| } |
| }; |
| |
| (<span class="ident">offset_x</span> <span class="op">+</span> <span class="ident">sign_x</span> <span class="op">*</span> <span class="ident">x</span>) <span class="kw">as</span> <span class="ident">u64</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="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">test_hypergeometric_invalid_params</span>() { |
| <span class="macro">assert!</span>(<span class="ident">Hypergeometric::new</span>(<span class="number">100</span>, <span class="number">101</span>, <span class="number">5</span>).<span class="ident">is_err</span>()); |
| <span class="macro">assert!</span>(<span class="ident">Hypergeometric::new</span>(<span class="number">100</span>, <span class="number">10</span>, <span class="number">101</span>).<span class="ident">is_err</span>()); |
| <span class="macro">assert!</span>(<span class="ident">Hypergeometric::new</span>(<span class="number">100</span>, <span class="number">101</span>, <span class="number">101</span>).<span class="ident">is_err</span>()); |
| <span class="macro">assert!</span>(<span class="ident">Hypergeometric::new</span>(<span class="number">100</span>, <span class="number">10</span>, <span class="number">5</span>).<span class="ident">is_ok</span>()); |
| } |
| |
| <span class="kw">fn</span> <span class="ident">test_hypergeometric_mean_and_variance</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="ident">n</span>: <span class="ident">u64</span>, <span class="ident">k</span>: <span class="ident">u64</span>, <span class="ident">s</span>: <span class="ident">u64</span>, <span class="ident">rng</span>: <span class="kw-2">&mut</span> <span class="ident">R</span>) |
| { |
| <span class="kw">let</span> <span class="ident">distr</span> <span class="op">=</span> <span class="ident">Hypergeometric::new</span>(<span class="ident">n</span>, <span class="ident">k</span>, <span class="ident">s</span>).<span class="ident">unwrap</span>(); |
| |
| <span class="kw">let</span> <span class="ident">expected_mean</span> <span class="op">=</span> <span class="ident">s</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">/</span> <span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">expected_variance</span> <span class="op">=</span> { |
| <span class="kw">let</span> <span class="ident">numerator</span> <span class="op">=</span> (<span class="ident">s</span> <span class="op">*</span> <span class="ident">k</span> <span class="op">*</span> (<span class="ident">n</span> <span class="op">-</span> <span class="ident">k</span>) <span class="op">*</span> (<span class="ident">n</span> <span class="op">-</span> <span class="ident">s</span>)) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">denominator</span> <span class="op">=</span> (<span class="ident">n</span> <span class="op">*</span> <span class="ident">n</span> <span class="op">*</span> (<span class="ident">n</span> <span class="op">-</span> <span class="number">1</span>)) <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">numerator</span> <span class="op">/</span> <span class="ident">denominator</span> |
| }; |
| |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">results</span> <span class="op">=</span> [<span class="number">0.0</span>; <span class="number">1000</span>]; |
| <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="ident">results</span>.<span class="ident">iter_mut</span>() { |
| <span class="kw-2">*</span><span class="ident">i</span> <span class="op">=</span> <span class="ident">distr</span>.<span class="ident">sample</span>(<span class="ident">rng</span>) <span class="kw">as</span> <span class="ident">f64</span>; |
| } |
| |
| <span class="kw">let</span> <span class="ident">mean</span> <span class="op">=</span> <span class="ident">results</span>.<span class="ident">iter</span>().<span class="ident">sum</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>() <span class="op">/</span> <span class="ident">results</span>.<span class="ident">len</span>() <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="macro">assert!</span>((<span class="ident">mean</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">expected_mean</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="ident">expected_mean</span> <span class="op">/</span> <span class="number">50.0</span>); |
| |
| <span class="kw">let</span> <span class="ident">variance</span> <span class="op">=</span> |
| <span class="ident">results</span>.<span class="ident">iter</span>().<span class="ident">map</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="ident">mean</span>) <span class="op">*</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">mean</span>)).<span class="ident">sum</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>() <span class="op">/</span> <span class="ident">results</span>.<span class="ident">len</span>() <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="macro">assert!</span>((<span class="ident">variance</span> <span class="op">-</span> <span class="ident">expected_variance</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="ident">expected_variance</span> <span class="op">/</span> <span class="number">10.0</span>); |
| } |
| |
| <span class="attribute">#[<span class="ident">test</span>]</span> |
| <span class="kw">fn</span> <span class="ident">test_hypergeometric</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">737</span>); |
| |
| <span class="comment">// exercise algorithm HIN:</span> |
| <span class="ident">test_hypergeometric_mean_and_variance</span>(<span class="number">500</span>, <span class="number">400</span>, <span class="number">30</span>, <span class="kw-2">&mut</span> <span class="ident">rng</span>); |
| <span class="ident">test_hypergeometric_mean_and_variance</span>(<span class="number">250</span>, <span class="number">200</span>, <span class="number">230</span>, <span class="kw-2">&mut</span> <span class="ident">rng</span>); |
| <span class="ident">test_hypergeometric_mean_and_variance</span>(<span class="number">100</span>, <span class="number">20</span>, <span class="number">6</span>, <span class="kw-2">&mut</span> <span class="ident">rng</span>); |
| <span class="ident">test_hypergeometric_mean_and_variance</span>(<span class="number">50</span>, <span class="number">10</span>, <span class="number">47</span>, <span class="kw-2">&mut</span> <span class="ident">rng</span>); |
| |
| <span class="comment">// exercise algorithm H2PE</span> |
| <span class="ident">test_hypergeometric_mean_and_variance</span>(<span class="number">5000</span>, <span class="number">2500</span>, <span class="number">500</span>, <span class="kw-2">&mut</span> <span class="ident">rng</span>); |
| <span class="ident">test_hypergeometric_mean_and_variance</span>(<span class="number">10100</span>, <span class="number">10000</span>, <span class="number">1000</span>, <span class="kw-2">&mut</span> <span class="ident">rng</span>); |
| <span class="ident">test_hypergeometric_mean_and_variance</span>(<span class="number">100100</span>, <span class="number">100</span>, <span class="number">10000</span>, <span class="kw-2">&mut</span> <span class="ident">rng</span>); |
| } |
| } |
| </code></pre></div> |
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