146 lines
3.0 KiB
Rust
146 lines
3.0 KiB
Rust
use statrs::distribution::{Continuous, Normal, Univariate};
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const S2PI: f64 = 2.50662827463100050242_e0;
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const P0: [f64; 5] = [
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-5.99633501014107895267_e1,
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9.80010754185999661536_e1,
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-5.66762857469070293439_e1,
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1.39312609387279679503_e1,
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-1.23916583867381258016_e0,
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];
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const Q0: [f64; 8] = [
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1.95448858338141759834_e0,
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4.67627912898881538453_e0,
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8.63602421390890590575_e1,
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-2.25462687854119370527_e2,
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2.00260212380060660359_e2,
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-8.20372256168333339912_e1,
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1.59056225126211695515_e1,
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-1.18331621121330003142_e0,
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];
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const P1: [f64; 9] = [
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4.05544892305962419923_e0,
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3.15251094599893866154_e1,
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5.71628192246421288162_e1,
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4.40805073893200834700_e1,
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1.46849561928858024014_e1,
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2.18663306850790267539_e0,
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-1.40256079171354495875_e-1,
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-3.50424626827848203418_e-2,
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-8.57456785154685413611_e-4,
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];
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const Q1: [f64; 8] = [
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1.57799883256466749731_e1,
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4.53907635128879210584_e1,
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4.13172038254672030440_e1,
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1.50425385692907503408_e1,
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2.50464946208309415979_e0,
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-1.42182922854787788574_e-1,
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-3.80806407691578277194_e-2,
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-9.33259480895457427372_e-4,
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];
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const P2: [f64; 9] = [
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3.23774891776946035970_e0,
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6.91522889068984211695_e0,
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3.93881025292474443415_e0,
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1.33303460815807542389_e0,
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2.01485389549179081538_e-1,
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1.23716634817820021358_e-2,
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3.01581553508235416007_e-4,
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2.65806974686737550832_e-6,
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6.23974539184983293730_e-9,
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];
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const Q2: [f64; 8] = [
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6.02427039364742014255_e0,
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3.67983563856160859403_e0,
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1.37702099489081330271_e0,
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2.16236993594496635890_e-1,
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1.34204006088543189037_e-2,
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3.28014464682127739104_e-4,
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2.89247864745380683936_e-6,
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6.79019408009981274425_e-9,
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];
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fn polevl(x: f64, coef: &[f64], n: usize) -> f64 {
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let mut ans = coef[0];
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for i in 1..n + 1 {
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ans = ans * x + coef[i];
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}
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ans
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}
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fn p1evl(x: f64, coef: &[f64], n: usize) -> f64 {
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let mut ans = x + coef[0];
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for i in 1..n {
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ans = ans * x + coef[i];
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}
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ans
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}
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fn ndtri(y0: f64) -> f64 {
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let mut y = y0;
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let code = if y > (1.0 - 0.13533528323661269189) {
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y = 1.0 - y;
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false
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} else {
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true
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};
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if y > 0.13533528323661269189 {
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y = y - 0.5;
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let y2 = y * y;
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return (y + y * (y2 * polevl(y2, &P0, 4) / p1evl(y2, &Q0, 8))) * S2PI;
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}
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let x = (-2.0 * y.ln()).sqrt();
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let z = 1.0 / x;
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let x0 = x - x.ln() / x;
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let x1 = if x < 8.0 {
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z * polevl(z, &P1, 8) / p1evl(z, &Q1, 8)
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} else {
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z * polevl(z, &P2, 8) / p1evl(z, &Q2, 8)
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};
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if code {
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x1 - x0
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} else {
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x0 - x1
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}
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}
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pub fn cdf(x: f64) -> f64 {
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Normal::new(0.0, 1.0).unwrap().cdf(x)
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}
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pub fn pdf(x: f64) -> f64 {
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Normal::new(0.0, 1.0).unwrap().pdf(x)
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}
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pub fn icdf(x: f64) -> f64 {
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ndtri(x)
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_cdf() {
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assert_eq!(cdf(0.5), 0.6914624612740131);
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}
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}
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