criterion/stats/univariate/sample.rs
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use std::{mem, ops};
use cast;
use rayon::prelude::*;
use stats::float::Float;
use stats::tuple::{Tuple, TupledDistributionsBuilder};
use stats::univariate::Percentiles;
use stats::univariate::Resamples;
/// A collection of data points drawn from a population
///
/// Invariants:
///
/// - The sample contains at least 2 data points
/// - The sample contains no `NaN`s
pub struct Sample<A>([A]);
// TODO(rust-lang/rfcs#735) move this `impl` into a private percentiles module
impl<A> Sample<A>
where
A: Float,
{
/// Creates a new sample from an existing slice
///
/// # Panics
///
/// Panics if `slice` contains any `NaN` or if `slice` has less than two elements
#[cfg_attr(feature = "cargo-clippy", allow(clippy::new_ret_no_self))]
pub fn new(slice: &[A]) -> &Sample<A> {
assert!(slice.len() > 1 && slice.iter().all(|x| !x.is_nan()));
unsafe { mem::transmute(slice) }
}
/// Returns the biggest element in the sample
///
/// - Time: `O(length)`
pub fn max(&self) -> A {
let mut elems = self.iter();
match elems.next() {
Some(&head) => elems.fold(head, |a, &b| a.max(b)),
// NB `unreachable!` because `Sample` is guaranteed to have at least one data point
None => unreachable!(),
}
}
/// Returns the arithmetic average of the sample
///
/// - Time: `O(length)`
pub fn mean(&self) -> A {
let n = self.len();
self.sum() / A::cast(n)
}
/// Returns the median absolute deviation
///
/// The `median` can be optionally passed along to speed up (2X) the computation
///
/// - Time: `O(length)`
/// - Memory: `O(length)`
pub fn median_abs_dev(&self, median: Option<A>) -> A
where
usize: cast::From<A, Output = Result<usize, cast::Error>>,
{
let median = median.unwrap_or_else(|| self.percentiles().median());
// NB Although this operation can be SIMD accelerated, the gain is negligible because the
// bottle neck is the sorting operation which is part of the computation of the median
let abs_devs = self.iter().map(|&x| (x - median).abs()).collect::<Vec<_>>();
let abs_devs: &Self = Self::new(&abs_devs);
abs_devs.percentiles().median() * A::cast(1.4826)
}
/// Returns the median absolute deviation as a percentage of the median
///
/// - Time: `O(length)`
/// - Memory: `O(length)`
pub fn median_abs_dev_pct(&self) -> A
where
usize: cast::From<A, Output = Result<usize, cast::Error>>,
{
let _100 = A::cast(100);
let median = self.percentiles().median();
let mad = self.median_abs_dev(Some(median));
(mad / median) * _100
}
/// Returns the smallest element in the sample
///
/// - Time: `O(length)`
pub fn min(&self) -> A {
let mut elems = self.iter();
match elems.next() {
Some(&elem) => elems.fold(elem, |a, &b| a.min(b)),
// NB `unreachable!` because `Sample` is guaranteed to have at least one data point
None => unreachable!(),
}
}
/// Returns a "view" into the percentiles of the sample
///
/// This "view" makes consecutive computations of percentiles much faster (`O(1)`)
///
/// - Time: `O(N log N) where N = length`
/// - Memory: `O(length)`
pub fn percentiles(&self) -> Percentiles<A>
where
usize: cast::From<A, Output = Result<usize, cast::Error>>,
{
use std::cmp::Ordering;
// NB This function assumes that there are no `NaN`s in the sample
fn cmp<T>(a: &T, b: &T) -> Ordering
where
T: PartialOrd,
{
if a < b {
Ordering::Less
} else if a == b {
Ordering::Equal
} else {
Ordering::Greater
}
}
let mut v = self.to_vec().into_boxed_slice();
v.par_sort_unstable_by(cmp);
// NB :-1: to intra-crate privacy rules
unsafe { mem::transmute(v) }
}
/// Returns the standard deviation of the sample
///
/// The `mean` can be optionally passed along to speed up (2X) the computation
///
/// - Time: `O(length)`
pub fn std_dev(&self, mean: Option<A>) -> A {
self.var(mean).sqrt()
}
/// Returns the standard deviation as a percentage of the mean
///
/// - Time: `O(length)`
pub fn std_dev_pct(&self) -> A {
let _100 = A::cast(100);
let mean = self.mean();
let std_dev = self.std_dev(Some(mean));
(std_dev / mean) * _100
}
/// Returns the sum of all the elements of the sample
///
/// - Time: `O(length)`
pub fn sum(&self) -> A {
::stats::sum(self)
}
/// Returns the t score between these two samples
///
/// - Time: `O(length)`
pub fn t(&self, other: &Sample<A>) -> A {
let (x_bar, y_bar) = (self.mean(), other.mean());
let (s2_x, s2_y) = (self.var(Some(x_bar)), other.var(Some(y_bar)));
let n_x = A::cast(self.len());
let n_y = A::cast(other.len());
let num = x_bar - y_bar;
let den = (s2_x / n_x + s2_y / n_y).sqrt();
num / den
}
/// Returns the variance of the sample
///
/// The `mean` can be optionally passed along to speed up (2X) the computation
///
/// - Time: `O(length)`
pub fn var(&self, mean: Option<A>) -> A {
use std::ops::Add;
let mean = mean.unwrap_or_else(|| self.mean());
let slice = self;
let sum = slice
.iter()
.map(|&x| (x - mean).powi(2))
.fold(A::cast(0), Add::add);
sum / A::cast(slice.len() - 1)
}
// TODO Remove the `T` parameter in favor of `S::Output`
/// Returns the bootstrap distributions of the parameters estimated by the 1-sample statistic
///
/// - Multi-threaded
/// - Time: `O(nresamples)`
/// - Memory: `O(nresamples)`
pub fn bootstrap<T, S>(&self, nresamples: usize, statistic: S) -> T::Distributions
where
S: Fn(&Sample<A>) -> T,
S: Sync,
T: Tuple,
T: Send,
T::Distributions: Send,
T::Builder: Send,
{
(0..nresamples)
.into_par_iter()
.map_init(
|| Resamples::new(self),
|resamples, _| statistic(resamples.next()),
)
.fold(
|| T::Builder::new(0),
|mut sub_distributions, sample| {
sub_distributions.push(sample);
sub_distributions
},
)
.reduce(
|| T::Builder::new(0),
|mut a, mut b| {
a.extend(&mut b);
a
},
)
.complete()
}
#[cfg(test)]
pub fn iqr(&self) -> A
where
usize: cast::From<A, Output = Result<usize, cast::Error>>,
{
self.percentiles().iqr()
}
#[cfg(test)]
pub fn median(&self) -> A
where
usize: cast::From<A, Output = Result<usize, cast::Error>>,
{
self.percentiles().median()
}
}
impl<A> ops::Deref for Sample<A> {
type Target = [A];
fn deref(&self) -> &[A] {
&self.0
}
}