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//! Quantile-quantile plot points for Student's t and F distributions, ports of
//! limma's `qqt` and `qqf`. Only the numeric core is ported — the plotting
//! arguments (`plot.it`, `main`, `xlab`, ...) are out of scope — so each
//! function returns `(x, y)`, where `x` are the theoretical quantiles ordered to
//! match the ranks of `y` and `y` is the input with `NaN`s removed.
use crate::special::{f_qf, t_ppf};
use anyhow::{bail, Result};
use statrs::distribution::{ContinuousCDF, Normal};
/// Plotting positions `(i - a) / (n + 1 - 2a)` with `a = 3/8` for `n <= 10` and
/// `a = 1/2` otherwise — R's `ppoints(n)`.
fn ppoints(n: usize) -> Vec<f64> {
let a = if n <= 10 { 3.0 / 8.0 } else { 0.5 };
(1..=n)
.map(|i| (i as f64 - a) / (n as f64 + 1.0 - 2.0 * a))
.collect()
}
/// Zero-based ranks of `y` (R's `order(order(y))` minus 1), stable on ties so
/// that equal values keep their input order.
fn ranks(y: &[f64]) -> Vec<usize> {
let mut idx: Vec<usize> = (0..y.len()).collect();
idx.sort_by(|&a, &b| y[a].partial_cmp(&y[b]).unwrap().then(a.cmp(&b)));
let mut r = vec![0usize; y.len()];
for (k, &orig) in idx.iter().enumerate() {
r[orig] = k;
}
r
}
/// Shared core: strip `NaN`s from `y`, evaluate the theoretical quantile at each
/// `ppoints` position, then scatter those (ascending) quantiles onto the ranks
/// of `y`.
fn qq(y: &[f64], theo_at: impl Fn(f64) -> f64) -> Result<(Vec<f64>, Vec<f64>)> {
let yc: Vec<f64> = y.iter().copied().filter(|v| !v.is_nan()).collect();
if yc.is_empty() {
bail!("y is empty");
}
let theo: Vec<f64> = ppoints(yc.len()).iter().map(|&p| theo_at(p)).collect();
let x: Vec<f64> = ranks(&yc).iter().map(|&rk| theo[rk]).collect();
Ok((x, yc))
}
/// Student's t Q-Q plot points. `df = f64::INFINITY` gives the normal-quantile
/// (Gaussian) reference, matching `qt(p, df = Inf)`.
pub fn qqt(y: &[f64], df: f64) -> Result<(Vec<f64>, Vec<f64>)> {
if df.is_infinite() {
let z = Normal::new(0.0, 1.0).unwrap();
qq(y, |p| z.inverse_cdf(p))
} else {
qq(y, |p| t_ppf(p, df))
}
}
/// F-distribution Q-Q plot points (port of `qqf`).
pub fn qqf(y: &[f64], df1: f64, df2: f64) -> Result<(Vec<f64>, Vec<f64>)> {
qq(y, |p| f_qf(p, df1, df2))
}
#[cfg(test)]
mod tests {
use super::*;
const Y: [f64; 12] = [
0.3,
-1.7,
1.2,
2.5,
-0.4,
1.2,
f64::NAN,
0.9,
-2.1,
3.3,
0.1,
-0.8,
];
// Y with the NaN removed, in input order.
const YC: [f64; 11] = [0.3, -1.7, 1.2, 2.5, -0.4, 1.2, 0.9, -2.1, 3.3, 0.1, -0.8];
fn assert_close(got: &[f64], want: &[f64]) {
assert_eq!(got.len(), want.len());
for (g, w) in got.iter().zip(want.iter()) {
assert!((g - w).abs() < 1e-9, "got {g}, want {w}");
}
}
#[test]
fn qqt_matches_r() {
// df = 5 (finite t).
let (x, y) = qqt(&Y, 5.0).unwrap();
assert_close(
&x,
&[
0.0,
-1.23198711032414,
0.502953281687005,
1.23198711032414,
-0.502953281687005,
0.810383997809011,
0.242287404471427,
-2.08992002958375,
2.08992002958375,
-0.242287404471427,
-0.810383997809011,
],
);
assert_close(&y, &YC);
// df = 20.
let (x, _) = qqt(&Y, 20.0).unwrap();
assert_close(
&x,
&[
0.0,
-1.12786228696882,
0.480102454500496,
1.12786228696882,
-0.480102454500497,
0.762698567276393,
0.232931568020726,
-1.7762457881447,
1.7762457881447,
-0.232931568020726,
-0.762698567276393,
],
);
// df = Inf -> normal quantiles.
let (x, _) = qqt(&Y, f64::INFINITY).unwrap();
assert_close(
&x,
&[
0.0,
-1.09680356209351,
0.472789120992267,
1.09680356209351,
-0.472789120992267,
0.747858594763302,
0.229884117579232,
-1.6906216295849,
1.6906216295849,
-0.229884117579232,
-0.747858594763302,
],
);
}
#[test]
fn qqf_matches_r() {
let (x, y) = qqf(&Y, 3.0, 10.0).unwrap();
assert_close(
&x,
&[
0.845080576591714,
0.244118830691621,
1.33260260140614,
2.32729903285299,
0.513954579920213,
1.71221115610176,
1.05924859191604,
0.106213291153813,
3.85329085611296,
0.667597469205698,
0.375423754916837,
],
);
assert_close(&y, &YC);
let (x, _) = qqf(&Y, 4.0, 8.0).unwrap();
assert_close(
&x,
&[
0.914645355977072,
0.309870602043059,
1.39570462056132,
2.3949374906501,
0.586390018113275,
1.77344818558774,
1.12570692785527,
0.156549563940445,
3.99319919728592,
0.739322903995197,
0.446405502584276,
],
);
let (x, _) = qqf(&Y, 1.0, 50.0).unwrap();
assert_close(
&x,
&[
0.461622679398699,
0.0298023566924766,
1.01659865168114,
2.29169880496666,
0.170063583948288,
1.49435871823477,
0.693040444198623,
0.00328172082098011,
4.20947435594102,
0.292682224702878,
0.084319979645453,
],
);
}
#[test]
fn empty_after_nan_strip_errors() {
assert!(qqt(&[f64::NAN, f64::NAN], 5.0).is_err());
}
}