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| </pre><pre class="rust"><code><span class="doccomment">//! The hypergeometric distribution. |
| |
| </span><span class="kw">use </span><span class="kw">crate</span>::Distribution; |
| <span class="kw">use </span>rand::Rng; |
| <span class="kw">use </span>rand::distributions::uniform::Uniform; |
| <span class="kw">use </span>core::fmt; |
| <span class="attribute">#[allow(unused_imports)] |
| </span><span class="kw">use </span>num_traits::Float; |
| |
| <span class="attribute">#[derive(Clone, Copy, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(serde::Serialize, serde::Deserialize))] |
| </span><span class="kw">enum </span>SamplingMethod { |
| InverseTransform{ initial_p: f64, initial_x: i64 }, |
| RejectionAcceptance{ |
| m: f64, |
| a: f64, |
| lambda_l: f64, |
| lambda_r: f64, |
| x_l: f64, |
| x_r: f64, |
| p1: f64, |
| p2: f64, |
| p3: f64 |
| }, |
| } |
| |
| <span class="doccomment">/// The hypergeometric distribution `Hypergeometric(N, K, n)`. |
| /// |
| /// This is the distribution of successes in samples of size `n` drawn without |
| /// replacement from a population of size `N` containing `K` success states. |
| /// It has the density function: |
| /// `f(k) = binomial(K, k) * binomial(N-K, n-k) / binomial(N, n)`, |
| /// where `binomial(a, b) = a! / (b! * (a - b)!)`. |
| /// |
| /// The [binomial distribution](crate::Binomial) is the analogous distribution |
| /// for sampling with replacement. It is a good approximation when the population |
| /// size is much larger than the sample size. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand_distr::{Distribution, Hypergeometric}; |
| /// |
| /// let hypergeo = Hypergeometric::new(60, 24, 7).unwrap(); |
| /// let v = hypergeo.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a hypergeometric distribution", v); |
| /// ``` |
| </span><span class="attribute">#[derive(Copy, Clone, Debug)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(serde::Serialize, serde::Deserialize))] |
| </span><span class="kw">pub struct </span>Hypergeometric { |
| n1: u64, |
| n2: u64, |
| k: u64, |
| offset_x: i64, |
| sign_x: i64, |
| sampling_method: SamplingMethod, |
| } |
| |
| <span class="doccomment">/// Error type returned from `Hypergeometric::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>Error { |
| <span class="doccomment">/// `total_population_size` is too large, causing floating point underflow. |
| </span>PopulationTooLarge, |
| <span class="doccomment">/// `population_with_feature > total_population_size`. |
| </span>ProbabilityTooLarge, |
| <span class="doccomment">/// `sample_size > total_population_size`. |
| </span>SampleSizeTooLarge, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>Error { |
| <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>{ |
| Error::PopulationTooLarge => <span class="string">"total_population_size is too large causing underflow in geometric distribution"</span>, |
| Error::ProbabilityTooLarge => <span class="string">"population_with_feature > total_population_size in geometric distribution"</span>, |
| Error::SampleSizeTooLarge => <span class="string">"sample_size > total_population_size in geometric 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>Error {} |
| |
| <span class="comment">// evaluate fact(numerator.0)*fact(numerator.1) / fact(denominator.0)*fact(denominator.1) |
| </span><span class="kw">fn </span>fraction_of_products_of_factorials(numerator: (u64, u64), denominator: (u64, u64)) -> f64 { |
| <span class="kw">let </span>min_top = u64::min(numerator.<span class="number">0</span>, numerator.<span class="number">1</span>); |
| <span class="kw">let </span>min_bottom = u64::min(denominator.<span class="number">0</span>, denominator.<span class="number">1</span>); |
| <span class="comment">// the factorial of this will cancel out: |
| </span><span class="kw">let </span>min_all = u64::min(min_top, min_bottom); |
| |
| <span class="kw">let </span>max_top = u64::max(numerator.<span class="number">0</span>, numerator.<span class="number">1</span>); |
| <span class="kw">let </span>max_bottom = u64::max(denominator.<span class="number">0</span>, denominator.<span class="number">1</span>); |
| <span class="kw">let </span>max_all = u64::max(max_top, max_bottom); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>result = <span class="number">1.0</span>; |
| <span class="kw">for </span>i <span class="kw">in </span>(min_all + <span class="number">1</span>)..=max_all { |
| <span class="kw">if </span>i <= min_top { |
| result <span class="kw-2">*</span>= i <span class="kw">as </span>f64; |
| } |
| |
| <span class="kw">if </span>i <= min_bottom { |
| result /= i <span class="kw">as </span>f64; |
| } |
| |
| <span class="kw">if </span>i <= max_top { |
| result <span class="kw-2">*</span>= i <span class="kw">as </span>f64; |
| } |
| |
| <span class="kw">if </span>i <= max_bottom { |
| result /= i <span class="kw">as </span>f64; |
| } |
| } |
| |
| result |
| } |
| |
| <span class="kw">fn </span>ln_of_factorial(v: f64) -> f64 { |
| <span class="comment">// the paper calls for ln(v!), but also wants to pass in fractions, |
| // so we need to use Stirling's approximation to fill in the gaps: |
| </span>v * v.ln() - v |
| } |
| |
| <span class="kw">impl </span>Hypergeometric { |
| <span class="doccomment">/// Constructs a new `Hypergeometric` with the shape parameters |
| /// `N = total_population_size`, |
| /// `K = population_with_feature`, |
| /// `n = sample_size`. |
| </span><span class="attribute">#[allow(clippy::many_single_char_names)] </span><span class="comment">// Same names as in the reference. |
| </span><span class="kw">pub fn </span>new(total_population_size: u64, population_with_feature: u64, sample_size: u64) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, Error> { |
| <span class="kw">if </span>population_with_feature > total_population_size { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::ProbabilityTooLarge); |
| } |
| |
| <span class="kw">if </span>sample_size > total_population_size { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::SampleSizeTooLarge); |
| } |
| |
| <span class="comment">// set-up constants as function of original parameters |
| </span><span class="kw">let </span>n = total_population_size; |
| <span class="kw">let </span>(<span class="kw-2">mut </span>sign_x, <span class="kw-2">mut </span>offset_x) = (<span class="number">1</span>, <span class="number">0</span>); |
| <span class="kw">let </span>(n1, n2) = { |
| <span class="comment">// switch around success and failure states if necessary to ensure n1 <= n2 |
| </span><span class="kw">let </span>population_without_feature = n - population_with_feature; |
| <span class="kw">if </span>population_with_feature > population_without_feature { |
| sign_x = -<span class="number">1</span>; |
| offset_x = sample_size <span class="kw">as </span>i64; |
| (population_without_feature, population_with_feature) |
| } <span class="kw">else </span>{ |
| (population_with_feature, population_without_feature) |
| } |
| }; |
| <span class="comment">// when sampling more than half the total population, take the smaller |
| // group as sampled instead (we can then return n1-x instead). |
| // |
| // Note: the boundary condition given in the paper is `sample_size < n / 2`; |
| // we're deviating here, because when n is even, it doesn't matter whether |
| // we switch here or not, but when n is odd `n/2 < n - n/2`, so switching |
| // when `k == n/2`, we'd actually be taking the _larger_ group as sampled. |
| </span><span class="kw">let </span>k = <span class="kw">if </span>sample_size <= n / <span class="number">2 </span>{ |
| sample_size |
| } <span class="kw">else </span>{ |
| offset_x += n1 <span class="kw">as </span>i64 * sign_x; |
| sign_x <span class="kw-2">*</span>= -<span class="number">1</span>; |
| n - sample_size |
| }; |
| |
| <span class="comment">// Algorithm H2PE has bounded runtime only if `M - max(0, k-n2) >= 10`, |
| // where `M` is the mode of the distribution. |
| // Use algorithm HIN for the remaining parameter space. |
| // |
| // Voratas Kachitvichyanukul and Bruce W. Schmeiser. 1985. Computer |
| // generation of hypergeometric random variates. |
| // J. Statist. Comput. Simul. Vol.22 (August 1985), 127-145 |
| // https://www.researchgate.net/publication/233212638 |
| </span><span class="kw">const </span>HIN_THRESHOLD: f64 = <span class="number">10.0</span>; |
| <span class="kw">let </span>m = ((k + <span class="number">1</span>) <span class="kw">as </span>f64 * (n1 + <span class="number">1</span>) <span class="kw">as </span>f64 / (n + <span class="number">2</span>) <span class="kw">as </span>f64).floor(); |
| <span class="kw">let </span>sampling_method = <span class="kw">if </span>m - f64::max(<span class="number">0.0</span>, k <span class="kw">as </span>f64 - n2 <span class="kw">as </span>f64) < HIN_THRESHOLD { |
| <span class="kw">let </span>(initial_p, initial_x) = <span class="kw">if </span>k < n2 { |
| (fraction_of_products_of_factorials((n2, n - k), (n, n2 - k)), <span class="number">0</span>) |
| } <span class="kw">else </span>{ |
| (fraction_of_products_of_factorials((n1, k), (n, k - n2)), (k - n2) <span class="kw">as </span>i64) |
| }; |
| |
| <span class="kw">if </span>initial_p <= <span class="number">0.0 </span>|| !initial_p.is_finite() { |
| <span class="kw">return </span><span class="prelude-val">Err</span>(Error::PopulationTooLarge); |
| } |
| |
| SamplingMethod::InverseTransform { initial_p, initial_x } |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>a = ln_of_factorial(m) + |
| ln_of_factorial(n1 <span class="kw">as </span>f64 - m) + |
| ln_of_factorial(k <span class="kw">as </span>f64 - m) + |
| ln_of_factorial((n2 - k) <span class="kw">as </span>f64 + m); |
| |
| <span class="kw">let </span>numerator = (n - k) <span class="kw">as </span>f64 * k <span class="kw">as </span>f64 * n1 <span class="kw">as </span>f64 * n2 <span class="kw">as </span>f64; |
| <span class="kw">let </span>denominator = (n - <span class="number">1</span>) <span class="kw">as </span>f64 * n <span class="kw">as </span>f64 * n <span class="kw">as </span>f64; |
| <span class="kw">let </span>d = <span class="number">1.5 </span>* (numerator / denominator).sqrt() + <span class="number">0.5</span>; |
| |
| <span class="kw">let </span>x_l = m - d + <span class="number">0.5</span>; |
| <span class="kw">let </span>x_r = m + d + <span class="number">0.5</span>; |
| |
| <span class="kw">let </span>k_l = f64::exp(a - |
| ln_of_factorial(x_l) - |
| ln_of_factorial(n1 <span class="kw">as </span>f64 - x_l) - |
| ln_of_factorial(k <span class="kw">as </span>f64 - x_l) - |
| ln_of_factorial((n2 - k) <span class="kw">as </span>f64 + x_l)); |
| <span class="kw">let </span>k_r = f64::exp(a - |
| ln_of_factorial(x_r - <span class="number">1.0</span>) - |
| ln_of_factorial(n1 <span class="kw">as </span>f64 - x_r + <span class="number">1.0</span>) - |
| ln_of_factorial(k <span class="kw">as </span>f64 - x_r + <span class="number">1.0</span>) - |
| ln_of_factorial((n2 - k) <span class="kw">as </span>f64 + x_r - <span class="number">1.0</span>)); |
| |
| <span class="kw">let </span>numerator = x_l * ((n2 - k) <span class="kw">as </span>f64 + x_l); |
| <span class="kw">let </span>denominator = (n1 <span class="kw">as </span>f64 - x_l + <span class="number">1.0</span>) * (k <span class="kw">as </span>f64 - x_l + <span class="number">1.0</span>); |
| <span class="kw">let </span>lambda_l = -((numerator / denominator).ln()); |
| |
| <span class="kw">let </span>numerator = (n1 <span class="kw">as </span>f64 - x_r + <span class="number">1.0</span>) * (k <span class="kw">as </span>f64 - x_r + <span class="number">1.0</span>); |
| <span class="kw">let </span>denominator = x_r * ((n2 - k) <span class="kw">as </span>f64 + x_r); |
| <span class="kw">let </span>lambda_r = -((numerator / denominator).ln()); |
| |
| <span class="comment">// the paper literally gives `p2 + kL/lambdaL` where it (probably) |
| // should have been `p2 <- p1 + kL/lambdaL`; another print error?! |
| </span><span class="kw">let </span>p1 = <span class="number">2.0 </span>* d; |
| <span class="kw">let </span>p2 = p1 + k_l / lambda_l; |
| <span class="kw">let </span>p3 = p2 + k_r / lambda_r; |
| |
| SamplingMethod::RejectionAcceptance { |
| m, a, lambda_l, lambda_r, x_l, x_r, p1, p2, p3 |
| } |
| }; |
| |
| <span class="prelude-val">Ok</span>(Hypergeometric { n1, n2, k, offset_x, sign_x, sampling_method }) |
| } |
| } |
| |
| <span class="kw">impl </span>Distribution<u64> <span class="kw">for </span>Hypergeometric { |
| <span class="attribute">#[allow(clippy::many_single_char_names)] </span><span class="comment">// Same names as in the reference. |
| </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) -> u64 { |
| <span class="kw">use </span>SamplingMethod::<span class="kw-2">*</span>; |
| |
| <span class="kw">let </span>Hypergeometric { n1, n2, k, sign_x, offset_x, sampling_method } = <span class="kw-2">*</span><span class="self">self</span>; |
| <span class="kw">let </span>x = <span class="kw">match </span>sampling_method { |
| InverseTransform { initial_p: <span class="kw-2">mut </span>p, initial_x: <span class="kw-2">mut </span>x } => { |
| <span class="kw">let </span><span class="kw-2">mut </span>u = rng.gen::<f64>(); |
| <span class="kw">while </span>u > p && x < k <span class="kw">as </span>i64 { <span class="comment">// the paper erroneously uses `until n < p`, which doesn't make any sense |
| </span>u -= p; |
| p <span class="kw-2">*</span>= ((n1 <span class="kw">as </span>i64 - x <span class="kw">as </span>i64) * (k <span class="kw">as </span>i64 - x <span class="kw">as </span>i64)) <span class="kw">as </span>f64; |
| p /= ((x <span class="kw">as </span>i64 + <span class="number">1</span>) * (n2 <span class="kw">as </span>i64 - k <span class="kw">as </span>i64 + <span class="number">1 </span>+ x <span class="kw">as </span>i64)) <span class="kw">as </span>f64; |
| x += <span class="number">1</span>; |
| } |
| x |
| }, |
| RejectionAcceptance { m, a, lambda_l, lambda_r, x_l, x_r, p1, p2, p3 } => { |
| <span class="kw">let </span>distr_region_select = Uniform::new(<span class="number">0.0</span>, p3); |
| <span class="kw">loop </span>{ |
| <span class="kw">let </span>(y, v) = <span class="kw">loop </span>{ |
| <span class="kw">let </span>u = distr_region_select.sample(rng); |
| <span class="kw">let </span>v = rng.gen::<f64>(); <span class="comment">// for the accept/reject decision |
| |
| </span><span class="kw">if </span>u <= p1 { |
| <span class="comment">// Region 1, central bell |
| </span><span class="kw">let </span>y = (x_l + u).floor(); |
| <span class="kw">break </span>(y, v); |
| } <span class="kw">else if </span>u <= p2 { |
| <span class="comment">// Region 2, left exponential tail |
| </span><span class="kw">let </span>y = (x_l + v.ln() / lambda_l).floor(); |
| <span class="kw">if </span>y <span class="kw">as </span>i64 >= i64::max(<span class="number">0</span>, k <span class="kw">as </span>i64 - n2 <span class="kw">as </span>i64) { |
| <span class="kw">let </span>v = v * (u - p1) * lambda_l; |
| <span class="kw">break </span>(y, v); |
| } |
| } <span class="kw">else </span>{ |
| <span class="comment">// Region 3, right exponential tail |
| </span><span class="kw">let </span>y = (x_r - v.ln() / lambda_r).floor(); |
| <span class="kw">if </span>y <span class="kw">as </span>u64 <= u64::min(n1, k) { |
| <span class="kw">let </span>v = v * (u - p2) * lambda_r; |
| <span class="kw">break </span>(y, v); |
| } |
| } |
| }; |
| |
| <span class="comment">// Step 4: Acceptance/Rejection Comparison |
| </span><span class="kw">if </span>m < <span class="number">100.0 </span>|| y <= <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>f = <span class="number">1.0</span>; |
| <span class="kw">if </span>m < y { |
| <span class="kw">for </span>i <span class="kw">in </span>(m <span class="kw">as </span>u64 + <span class="number">1</span>)..=(y <span class="kw">as </span>u64) { |
| f <span class="kw-2">*</span>= (n1 - i + <span class="number">1</span>) <span class="kw">as </span>f64 * (k - i + <span class="number">1</span>) <span class="kw">as </span>f64; |
| f /= i <span class="kw">as </span>f64 * (n2 - k + i) <span class="kw">as </span>f64; |
| } |
| } <span class="kw">else </span>{ |
| <span class="kw">for </span>i <span class="kw">in </span>(y <span class="kw">as </span>u64 + <span class="number">1</span>)..=(m <span class="kw">as </span>u64) { |
| f <span class="kw-2">*</span>= i <span class="kw">as </span>f64 * (n2 - k + i) <span class="kw">as </span>f64; |
| f /= (n1 - i) <span class="kw">as </span>f64 * (k - i) <span class="kw">as </span>f64; |
| } |
| } |
| |
| <span class="kw">if </span>v <= f { <span class="kw">break </span>y <span class="kw">as </span>i64; } |
| } <span class="kw">else </span>{ |
| <span class="comment">// Step 4.2: Squeezing |
| </span><span class="kw">let </span>y1 = y + <span class="number">1.0</span>; |
| <span class="kw">let </span>ym = y - m; |
| <span class="kw">let </span>yn = n1 <span class="kw">as </span>f64 - y + <span class="number">1.0</span>; |
| <span class="kw">let </span>yk = k <span class="kw">as </span>f64 - y + <span class="number">1.0</span>; |
| <span class="kw">let </span>nk = n2 <span class="kw">as </span>f64 - k <span class="kw">as </span>f64 + y1; |
| <span class="kw">let </span>r = -ym / y1; |
| <span class="kw">let </span>s = ym / yn; |
| <span class="kw">let </span>t = ym / yk; |
| <span class="kw">let </span>e = -ym / nk; |
| <span class="kw">let </span>g = yn * yk / (y1 * nk) - <span class="number">1.0</span>; |
| <span class="kw">let </span>dg = <span class="kw">if </span>g < <span class="number">0.0 </span>{ |
| <span class="number">1.0 </span>+ g |
| } <span class="kw">else </span>{ |
| <span class="number">1.0 |
| </span>}; |
| <span class="kw">let </span>gu = g * (<span class="number">1.0 </span>+ g * (-<span class="number">0.5 </span>+ g / <span class="number">3.0</span>)); |
| <span class="kw">let </span>gl = gu - g.powi(<span class="number">4</span>) / (<span class="number">4.0 </span>* dg); |
| <span class="kw">let </span>xm = m + <span class="number">0.5</span>; |
| <span class="kw">let </span>xn = n1 <span class="kw">as </span>f64 - m + <span class="number">0.5</span>; |
| <span class="kw">let </span>xk = k <span class="kw">as </span>f64 - m + <span class="number">0.5</span>; |
| <span class="kw">let </span>nm = n2 <span class="kw">as </span>f64 - k <span class="kw">as </span>f64 + xm; |
| <span class="kw">let </span>ub = xm * r * (<span class="number">1.0 </span>+ r * (-<span class="number">0.5 </span>+ r / <span class="number">3.0</span>)) + |
| xn * s * (<span class="number">1.0 </span>+ s * (-<span class="number">0.5 </span>+ s / <span class="number">3.0</span>)) + |
| xk * t * (<span class="number">1.0 </span>+ t * (-<span class="number">0.5 </span>+ t / <span class="number">3.0</span>)) + |
| nm * e * (<span class="number">1.0 </span>+ e * (-<span class="number">0.5 </span>+ e / <span class="number">3.0</span>)) + |
| y * gu - m * gl + <span class="number">0.0034</span>; |
| <span class="kw">let </span>av = v.ln(); |
| <span class="kw">if </span>av > ub { <span class="kw">continue</span>; } |
| <span class="kw">let </span>dr = <span class="kw">if </span>r < <span class="number">0.0 </span>{ |
| xm * r.powi(<span class="number">4</span>) / (<span class="number">1.0 </span>+ r) |
| } <span class="kw">else </span>{ |
| xm * r.powi(<span class="number">4</span>) |
| }; |
| <span class="kw">let </span>ds = <span class="kw">if </span>s < <span class="number">0.0 </span>{ |
| xn * s.powi(<span class="number">4</span>) / (<span class="number">1.0 </span>+ s) |
| } <span class="kw">else </span>{ |
| xn * s.powi(<span class="number">4</span>) |
| }; |
| <span class="kw">let </span>dt = <span class="kw">if </span>t < <span class="number">0.0 </span>{ |
| xk * t.powi(<span class="number">4</span>) / (<span class="number">1.0 </span>+ t) |
| } <span class="kw">else </span>{ |
| xk * t.powi(<span class="number">4</span>) |
| }; |
| <span class="kw">let </span>de = <span class="kw">if </span>e < <span class="number">0.0 </span>{ |
| nm * e.powi(<span class="number">4</span>) / (<span class="number">1.0 </span>+ e) |
| } <span class="kw">else </span>{ |
| nm * e.powi(<span class="number">4</span>) |
| }; |
| |
| <span class="kw">if </span>av < ub - <span class="number">0.25</span><span class="kw-2">*</span>(dr + ds + dt + de) + (y + m)<span class="kw-2">*</span>(gl - gu) - <span class="number">0.0078 </span>{ |
| <span class="kw">break </span>y <span class="kw">as </span>i64; |
| } |
| |
| <span class="comment">// Step 4.3: Final Acceptance/Rejection Test |
| </span><span class="kw">let </span>av_critical = a - |
| ln_of_factorial(y) - |
| ln_of_factorial(n1 <span class="kw">as </span>f64 - y) - |
| ln_of_factorial(k <span class="kw">as </span>f64 - y) - |
| ln_of_factorial((n2 - k) <span class="kw">as </span>f64 + y); |
| <span class="kw">if </span>v.ln() <= av_critical { |
| <span class="kw">break </span>y <span class="kw">as </span>i64; |
| } |
| } |
| } |
| } |
| }; |
| |
| (offset_x + sign_x * x) <span class="kw">as </span>u64 |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>test { |
| <span class="kw">use super</span>::<span class="kw-2">*</span>; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_hypergeometric_invalid_params() { |
| <span class="macro">assert!</span>(Hypergeometric::new(<span class="number">100</span>, <span class="number">101</span>, <span class="number">5</span>).is_err()); |
| <span class="macro">assert!</span>(Hypergeometric::new(<span class="number">100</span>, <span class="number">10</span>, <span class="number">101</span>).is_err()); |
| <span class="macro">assert!</span>(Hypergeometric::new(<span class="number">100</span>, <span class="number">101</span>, <span class="number">101</span>).is_err()); |
| <span class="macro">assert!</span>(Hypergeometric::new(<span class="number">100</span>, <span class="number">10</span>, <span class="number">5</span>).is_ok()); |
| } |
| |
| <span class="kw">fn </span>test_hypergeometric_mean_and_variance<R: Rng>(n: u64, k: u64, s: u64, rng: <span class="kw-2">&mut </span>R) |
| { |
| <span class="kw">let </span>distr = Hypergeometric::new(n, k, s).unwrap(); |
| |
| <span class="kw">let </span>expected_mean = s <span class="kw">as </span>f64 * k <span class="kw">as </span>f64 / n <span class="kw">as </span>f64; |
| <span class="kw">let </span>expected_variance = { |
| <span class="kw">let </span>numerator = (s * k * (n - k) * (n - s)) <span class="kw">as </span>f64; |
| <span class="kw">let </span>denominator = (n * n * (n - <span class="number">1</span>)) <span class="kw">as </span>f64; |
| numerator / denominator |
| }; |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>results = [<span class="number">0.0</span>; <span class="number">1000</span>]; |
| <span class="kw">for </span>i <span class="kw">in </span>results.iter_mut() { |
| <span class="kw-2">*</span>i = distr.sample(rng) <span class="kw">as </span>f64; |
| } |
| |
| <span class="kw">let </span>mean = results.iter().sum::<f64>() / results.len() <span class="kw">as </span>f64; |
| <span class="macro">assert!</span>((mean <span class="kw">as </span>f64 - expected_mean).abs() < expected_mean / <span class="number">50.0</span>); |
| |
| <span class="kw">let </span>variance = |
| results.iter().map(|x| (x - mean) * (x - mean)).sum::<f64>() / results.len() <span class="kw">as </span>f64; |
| <span class="macro">assert!</span>((variance - expected_variance).abs() < expected_variance / <span class="number">10.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_hypergeometric() { |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">737</span>); |
| |
| <span class="comment">// exercise algorithm HIN: |
| </span>test_hypergeometric_mean_and_variance(<span class="number">500</span>, <span class="number">400</span>, <span class="number">30</span>, <span class="kw-2">&mut </span>rng); |
| test_hypergeometric_mean_and_variance(<span class="number">250</span>, <span class="number">200</span>, <span class="number">230</span>, <span class="kw-2">&mut </span>rng); |
| test_hypergeometric_mean_and_variance(<span class="number">100</span>, <span class="number">20</span>, <span class="number">6</span>, <span class="kw-2">&mut </span>rng); |
| test_hypergeometric_mean_and_variance(<span class="number">50</span>, <span class="number">10</span>, <span class="number">47</span>, <span class="kw-2">&mut </span>rng); |
| |
| <span class="comment">// exercise algorithm H2PE |
| </span>test_hypergeometric_mean_and_variance(<span class="number">5000</span>, <span class="number">2500</span>, <span class="number">500</span>, <span class="kw-2">&mut </span>rng); |
| test_hypergeometric_mean_and_variance(<span class="number">10100</span>, <span class="number">10000</span>, <span class="number">1000</span>, <span class="kw-2">&mut </span>rng); |
| test_hypergeometric_mean_and_variance(<span class="number">100100</span>, <span class="number">100</span>, <span class="number">10000</span>, <span class="kw-2">&mut </span>rng); |
| } |
| } |
| </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> |
