#![allow(missing_docs)]
#![allow(deprecated)] // Float
use std::cmp::Ordering::{self, Equal, Greater, Less};
use std::mem;
#[cfg(test)]
mod tests;
fn local_cmp(x: f64, y: f64) -> Ordering {
// arbitrarily decide that NaNs are larger than everything.
if y.is_nan() {
Less
} else if x.is_nan() {
Greater
} else if x < y {
Less
} else if x == y {
Equal
} else {
Greater
}
}
fn local_sort(v: &mut [f64]) {
v.sort_by(|x: &f64, y: &f64| local_cmp(*x, *y));
}
/// Trait that provides simple descriptive statistics on a univariate set of numeric samples.
pub trait Stats {
/// Sum of the samples.
///
/// Note: this method sacrifices performance at the altar of accuracy
/// Depends on IEEE-754 arithmetic guarantees. See proof of correctness at:
/// ["Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric
/// Predicates"][paper]
///
/// [paper]: http://www.cs.cmu.edu/~quake-papers/robust-arithmetic.ps
fn sum(&self) -> f64;
/// Minimum value of the samples.
fn min(&self) -> f64;
/// Maximum value of the samples.
fn max(&self) -> f64;
/// Arithmetic mean (average) of the samples: sum divided by sample-count.
///
/// See: <https://en.wikipedia.org/wiki/Arithmetic_mean>
fn mean(&self) -> f64;
/// Median of the samples: value separating the lower half of the samples from the higher half.
/// Equal to `self.percentile(50.0)`.
///
/// See: <https://en.wikipedia.org/wiki/Median>
fn median(&self) -> f64;
/// Variance of the samples: bias-corrected mean of the squares of the differences of each
/// sample from the sample mean. Note that this calculates the _sample variance_ rather than the
/// population variance, which is assumed to be unknown. It therefore corrects the `(n-1)/n`
/// bias that would appear if we calculated a population variance, by dividing by `(n-1)` rather
/// than `n`.
///
/// See: <https://en.wikipedia.org/wiki/Variance>
fn var(&self) -> f64;
/// Standard deviation: the square root of the sample variance.
///
/// Note: this is not a robust statistic for non-normal distributions. Prefer the
/// `median_abs_dev` for unknown distributions.
///
/// See: <https://en.wikipedia.org/wiki/Standard_deviation>
fn std_dev(&self) -> f64;
/// Standard deviation as a percent of the mean value. See `std_dev` and `mean`.
///
/// Note: this is not a robust statistic for non-normal distributions. Prefer the
/// `median_abs_dev_pct` for unknown distributions.
fn std_dev_pct(&self) -> f64;
/// Scaled median of the absolute deviations of each sample from the sample median. This is a
/// robust (distribution-agnostic) estimator of sample variability. Use this in preference to
/// `std_dev` if you cannot assume your sample is normally distributed. Note that this is scaled
/// by the constant `1.4826` to allow its use as a consistent estimator for the standard
/// deviation.
///
/// See: <https://en.wikipedia.org/wiki/Median_absolute_deviation>
fn median_abs_dev(&self) -> f64;
/// Median absolute deviation as a percent of the median. See `median_abs_dev` and `median`.
fn median_abs_dev_pct(&self) -> f64;
/// Percentile: the value below which `pct` percent of the values in `self` fall. For example,
/// percentile(95.0) will return the value `v` such that 95% of the samples `s` in `self`
/// satisfy `s <= v`.
///
/// Calculated by linear interpolation between closest ranks.
///
/// See: <https://en.wikipedia.org/wiki/Percentile>
fn percentile(&self, pct: f64) -> f64;
/// Quartiles of the sample: three values that divide the sample into four equal groups, each
/// with 1/4 of the data. The middle value is the median. See `median` and `percentile`. This
/// function may calculate the 3 quartiles more efficiently than 3 calls to `percentile`, but
/// is otherwise equivalent.
///
/// See also: <https://en.wikipedia.org/wiki/Quartile>
fn quartiles(&self) -> (f64, f64, f64);
/// Inter-quartile range: the difference between the 25th percentile (1st quartile) and the 75th
/// percentile (3rd quartile). See `quartiles`.
///
/// See also: <https://en.wikipedia.org/wiki/Interquartile_range>
fn iqr(&self) -> f64;
}
/// Extracted collection of all the summary statistics of a sample set.
#[derive(Debug, Clone, PartialEq, Copy)]
#[allow(missing_docs)]
pub struct Summary {
pub sum: f64,
pub min: f64,
pub max: f64,
pub mean: f64,
pub median: f64,
pub var: f64,
pub std_dev: f64,
pub std_dev_pct: f64,
pub median_abs_dev: f64,
pub median_abs_dev_pct: f64,
pub quartiles: (f64, f64, f64),
pub iqr: f64,
}
impl Summary {
/// Construct a new summary of a sample set.
pub fn new(samples: &[f64]) -> Summary {
Summary {
sum: samples.sum(),
min: samples.min(),
max: samples.max(),
mean: samples.mean(),
median: samples.median(),
var: samples.var(),
std_dev: samples.std_dev(),
std_dev_pct: samples.std_dev_pct(),
median_abs_dev: samples.median_abs_dev(),
median_abs_dev_pct: samples.median_abs_dev_pct(),
quartiles: samples.quartiles(),
iqr: samples.iqr(),
}
}
}
impl Stats for [f64] {
// FIXME #11059 handle NaN, inf and overflow
fn sum(&self) -> f64 {
let mut partials = vec![];
for &x in self {
let mut x = x;
let mut j = 0;
// This inner loop applies `hi`/`lo` summation to each
// partial so that the list of partial sums remains exact.
for i in 0..partials.len() {
let mut y: f64 = partials[i];
if x.abs() < y.abs() {
mem::swap(&mut x, &mut y);
}
// Rounded `x+y` is stored in `hi` with round-off stored in
// `lo`. Together `hi+lo` are exactly equal to `x+y`.
let hi = x + y;
let lo = y - (hi - x);
if lo != 0.0 {
partials[j] = lo;
j += 1;
}
x = hi;
}
if j >= partials.len() {
partials.push(x);
} else {
partials[j] = x;
partials.truncate(j + 1);
}
}
let zero: f64 = 0.0;
partials.iter().fold(zero, |p, q| p + *q)
}
fn min(&self) -> f64 {
assert!(!self.is_empty());
self.iter().fold(self[0], |p, q| p.min(*q))
}
fn max(&self) -> f64 {
assert!(!self.is_empty());
self.iter().fold(self[0], |p, q| p.max(*q))
}
fn mean(&self) -> f64 {
assert!(!self.is_empty());
self.sum() / (self.len() as f64)
}
fn median(&self) -> f64 {
self.percentile(50_f64)
}
fn var(&self) -> f64 {
if self.len() < 2 {
0.0
} else {
let mean = self.mean();
let mut v: f64 = 0.0;
for s in self {
let x = *s - mean;
v += x * x;
}
// N.B., this is _supposed to be_ len-1, not len. If you
// change it back to len, you will be calculating a
// population variance, not a sample variance.
let denom = (self.len() - 1) as f64;
v / denom
}
}
fn std_dev(&self) -> f64 {
self.var().sqrt()
}
fn std_dev_pct(&self) -> f64 {
let hundred = 100_f64;
(self.std_dev() / self.mean()) * hundred
}
fn median_abs_dev(&self) -> f64 {
let med = self.median();
let abs_devs: Vec<f64> = self.iter().map(|&v| (med - v).abs()).collect();
// This constant is derived by smarter statistics brains than me, but it is
// consistent with how R and other packages treat the MAD.
let number = 1.4826;
abs_devs.median() * number
}
fn median_abs_dev_pct(&self) -> f64 {
let hundred = 100_f64;
(self.median_abs_dev() / self.median()) * hundred
}
fn percentile(&self, pct: f64) -> f64 {
let mut tmp = self.to_vec();
local_sort(&mut tmp);
percentile_of_sorted(&tmp, pct)
}
fn quartiles(&self) -> (f64, f64, f64) {
let mut tmp = self.to_vec();
local_sort(&mut tmp);
let first = 25_f64;
let a = percentile_of_sorted(&tmp, first);
let second = 50_f64;
let b = percentile_of_sorted(&tmp, second);
let third = 75_f64;
let c = percentile_of_sorted(&tmp, third);
(a, b, c)
}
fn iqr(&self) -> f64 {
let (a, _, c) = self.quartiles();
c - a
}
}
// Helper function: extract a value representing the `pct` percentile of a sorted sample-set, using
// linear interpolation. If samples are not sorted, return nonsensical value.
fn percentile_of_sorted(sorted_samples: &[f64], pct: f64) -> f64 {
assert!(!sorted_samples.is_empty());
if sorted_samples.len() == 1 {
return sorted_samples[0];
}
let zero: f64 = 0.0;
assert!(zero <= pct);
let hundred = 100_f64;
assert!(pct <= hundred);
if pct == hundred {
return sorted_samples[sorted_samples.len() - 1];
}
let length = (sorted_samples.len() - 1) as f64;
let rank = (pct / hundred) * length;
let lrank = rank.floor();
let d = rank - lrank;
let n = lrank as usize;
let lo = sorted_samples[n];
let hi = sorted_samples[n + 1];
lo + (hi - lo) * d
}
/// Winsorize a set of samples, replacing values above the `100-pct` percentile
/// and below the `pct` percentile with those percentiles themselves. This is a
/// way of minimizing the effect of outliers, at the cost of biasing the sample.
/// It differs from trimming in that it does not change the number of samples,
/// just changes the values of those that are outliers.
///
/// See: <https://en.wikipedia.org/wiki/Winsorising>
pub fn winsorize(samples: &mut [f64], pct: f64) {
let mut tmp = samples.to_vec();
local_sort(&mut tmp);
let lo = percentile_of_sorted(&tmp, pct);
let hundred = 100_f64;
let hi = percentile_of_sorted(&tmp, hundred - pct);
for samp in samples {
if *samp > hi {
*samp = hi
} else if *samp < lo {
*samp = lo
}
}
}