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pub struct Ecdf<T: Ord> {
samples: Vec<T>,
length: usize,
}
impl<T: Ord + Clone> Ecdf<T> {
pub fn new(samples: &[T]) -> Ecdf<T> {
let length = samples.len();
assert!(length > 0);
let mut sorted = samples.to_vec();
sorted.sort();
Ecdf {
samples: sorted,
length: length,
}
}
pub fn value(&self, t: T) -> f64 {
let num_samples_leq_t = match self.samples.binary_search(&t) {
Ok(mut index) => {
while index + 1 < self.length && self.samples[index + 1] == t {
index += 1;
}
index + 1
}
Err(index) => {
index
}
};
num_samples_leq_t as f64 / self.length as f64
}
}
#[cfg(test)]
mod tests {
extern crate quickcheck;
extern crate rand;
use self::quickcheck::{Arbitrary, Gen, QuickCheck, Testable, TestResult, StdGen};
use std::cmp;
use std::usize;
use super::Ecdf;
fn check<A: Testable>(f: A) {
let g = StdGen::new(rand::thread_rng(), usize::MAX);
QuickCheck::new().gen(g).quickcheck(f);
}
#[derive(Debug, Clone)]
struct Samples {
vec: Vec<u64>,
}
impl Arbitrary for Samples {
fn arbitrary<G: Gen>(g: &mut G) -> Samples {
let max = cmp::min(g.size(), 1024);
let size = g.gen_range(1, max);
let vec = (0..size).map(|_| u64::arbitrary(g)).collect();
Samples { vec: vec }
}
fn shrink(&self) -> Box<Iterator<Item = Samples>> {
let vec: Vec<u64> = self.vec.clone();
let shrunk: Box<Iterator<Item = Vec<u64>>> = vec.shrink();
Box::new(shrunk.filter(|v| v.len() > 0).map(|v| Samples { vec: v }))
}
}
#[test]
#[should_panic(expected="assertion failed: length > 0")]
fn ecdf_panics_on_empty_samples_set() {
let xs: Vec<u64> = vec![];
Ecdf::new(&xs);
}
#[test]
fn ecdf_between_zero_and_one() {
fn prop(xs: Samples, val: u64) -> bool {
let ecdf = Ecdf::new(&xs.vec);
let actual = ecdf.value(val);
0.0 <= actual && actual <= 1.0
}
check(prop as fn(Samples, u64) -> bool);
}
#[test]
fn ecdf_is_an_increasing_function() {
fn prop(xs: Samples, val: u64) -> bool {
let ecdf = Ecdf::new(&xs.vec);
let actual = ecdf.value(val);
ecdf.value(val - 1) <= actual && actual <= ecdf.value(val + 1)
}
check(prop as fn(Samples, u64) -> bool);
}
#[test]
fn ecdf_sample_min_minus_one_is_zero() {
fn prop(xs: Samples) -> bool {
let &min = xs.vec.iter().min().unwrap();
let ecdf = Ecdf::new(&xs.vec);
ecdf.value(min - 1) == 0.0
}
check(prop as fn(Samples) -> bool);
}
#[test]
fn ecdf_sample_max_is_one() {
fn prop(xs: Samples) -> bool {
let &max = xs.vec.iter().max().unwrap();
let ecdf = Ecdf::new(&xs.vec);
ecdf.value(max) == 1.0
}
check(prop as fn(Samples) -> bool);
}
#[test]
fn ecdf_sample_val_is_num_samples_leq_val_div_length() {
fn prop(xs: Samples) -> bool {
let &val = xs.vec.first().unwrap();
let num_samples = xs.vec
.iter()
.filter(|&&x| x <= val)
.count();
let expected = num_samples as f64 / xs.vec.len() as f64;
let ecdf = Ecdf::new(&xs.vec);
ecdf.value(val) == expected
}
check(prop as fn(Samples) -> bool);
}
#[test]
fn ecdf_non_sample_val_is_num_samples_leq_val_div_length() {
fn prop(xs: Samples, val: u64) -> TestResult {
let length = xs.vec.len();
if xs.vec.iter().any(|&x| x == val) {
return TestResult::discard();
}
let num_samples = xs.vec
.iter()
.filter(|&&x| x <= val)
.count();
let expected = num_samples as f64 / length as f64;
let ecdf = Ecdf::new(&xs.vec);
TestResult::from_bool(ecdf.value(val) == expected)
}
check(prop as fn(Samples, u64) -> TestResult);
}
}