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Support quartiles #15

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2 changes: 1 addition & 1 deletion src/lib.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@ use num_traits::ToPrimitive;
pub use frequency::Frequencies;
pub use minmax::MinMax;
pub use online::{OnlineStats, stddev, variance, mean};
pub use unsorted::{Unsorted, median, mode, modes};
pub use unsorted::{Unsorted, median, quartiles, mode, modes};

/// Partial wraps a type that satisfies `PartialOrd` and implements `Ord`.
///
Expand Down
114 changes: 113 additions & 1 deletion src/unsorted.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,14 @@ pub fn median<I>(it: I) -> Option<f64>
it.collect::<Unsorted<_>>().median()
}

/// Compute the exact 1-, 2-, and 3-quartiles (Q1, Q2 a.k.a. median, and Q3) on a stream of data.
///
/// (This has time complexity `O(nlogn)` and space complexity `O(n)`.)
pub fn quartiles<I>(it: I) -> Option<(f64, f64, f64)>
where I: Iterator, <I as Iterator>::Item: PartialOrd + ToPrimitive {
it.collect::<Unsorted<_>>().quartiles()
}

/// Compute the exact mode on a stream of data.
///
/// (This has time complexity `O(nlogn)` and space complexity `O(n)`.)
Expand Down Expand Up @@ -60,6 +68,80 @@ fn median_on_sorted<T>(data: &[T]) -> Option<f64>
})
}

fn quartiles_on_sorted<T>(data: &[T]) -> Option<(f64, f64, f64)>
where T: PartialOrd + ToPrimitive {
Some(match data.len() {
0..=2 => return None,
3 => (data[0].to_f64().unwrap(),
data[1].to_f64().unwrap(),
data[2].to_f64().unwrap()),
len => {
let r = len % 4;
let k = (len - r) / 4;
match r {
// Let data = {x_i}_{i=0..4k} where k is positive integer.
// Median q2 = (x_{2k-1} + x_{2k}) / 2.
// If we divide data into two parts {x_i < q2} as L and
// {x_i > q2} as R, #L == #R == 2k holds true. Thus,
// q1 = (x_{k-1} + x_{k}) / 2 and q3 = (x_{3k-1} + x_{3k}) / 2.
0 => {
let (q1_l, q1_r, q2_l, q2_r, q3_l, q3_r) = (
data[k - 1].to_f64().unwrap(),
data[k].to_f64().unwrap(),
data[2 * k - 1].to_f64().unwrap(),
data[2 * k].to_f64().unwrap(),
data[3 * k - 1].to_f64().unwrap(),
data[3 * k].to_f64().unwrap()
);
((q1_l + q1_r) / 2., (q2_l + q2_r) / 2., (q3_l + q3_r) / 2.)
},
// Let data = {x_i}_{i=0..4k+1} where k is positive integer.
// Median q2 = x_{2k}.
// If we divide data other than q2 into two parts {x_i < q2}
// as L and {x_i > q2} as R, #L == #R == 2k holds true. Thus,
// q1 = (x_{k-1} + x_{k}) / 2 and q3 = (x_{3k} + x_{3k+1}) / 2.
1 => {
let (q1_l, q1_r, q2, q3_l, q3_r) = (
data[k - 1].to_f64().unwrap(),
data[k].to_f64().unwrap(),
data[2 * k].to_f64().unwrap(),
data[3 * k].to_f64().unwrap(),
data[3 * k + 1].to_f64().unwrap()
);
((q1_l + q1_r) / 2., q2, (q3_l + q3_r) / 2.)
},
// Let data = {x_i}_{i=0..4k+2} where k is positive integer.
// Median q2 = (x_{(2k+1)-1} + x_{2k+1}) / 2.
// If we divide data into two parts {x_i < q2} as L and
// {x_i > q2} as R, it's true that #L == #R == 2k+1.
// Thus, q1 = x_{k} and q3 = x_{3k+1}.
2 => {
let (q1, q2_l, q2_r, q3) = (
data[k].to_f64().unwrap(),
data[2 * k].to_f64().unwrap(),
data[2 * k + 1].to_f64().unwrap(),
data[3 * k + 1].to_f64().unwrap()
);
(q1, (q2_l + q2_r) / 2., q3)
},
// Let data = {x_i}_{i=0..4k+3} where k is positive integer.
// Median q2 = x_{2k+1}.
// If we divide data other than q2 into two parts {x_i < q2}
// as L and {x_i > q2} as R, #L == #R == 2k+1 holds true.
// Thus, q1 = x_{k} and q3 = x_{3k+2}.
_ => {
let (q1, q2, q3) = (
data[k].to_f64().unwrap(),
data[2 * k + 1].to_f64().unwrap(),
data[3 * k + 2].to_f64().unwrap()
);
(q1, q2, q3)
},
}
},
})
}

fn mode_on_sorted<T, I>(it: I) -> Option<T>
where T: PartialOrd, I: Iterator<Item=T> {
// This approach to computing the mode works very nicely when the
Expand Down Expand Up @@ -199,6 +281,14 @@ impl<T: PartialOrd + ToPrimitive> Unsorted<T> {
}
}

impl<T: PartialOrd + ToPrimitive> Unsorted<T> {
/// Returns the quartiles of the data.
pub fn quartiles(&mut self) -> Option<(f64, f64, f64)> {
self.sort();
quartiles_on_sorted(&*self.data)
}
}

impl<T: PartialOrd> Commute for Unsorted<T> {
fn merge(&mut self, v: Unsorted<T>) {
self.dirtied();
Expand Down Expand Up @@ -232,7 +322,7 @@ impl<T: PartialOrd> Extend<T> for Unsorted<T> {

#[cfg(test)]
mod test {
use super::{median, mode, modes};
use super::{median, quartiles, mode, modes};

#[test]
fn median_stream() {
Expand Down Expand Up @@ -283,4 +373,26 @@ mod test {
assert_eq!(modes(vec![3_f64, 3.0, 4.0, 4.0].into_iter()), vec![3.0, 4.0]);
assert_eq!(modes(vec![1_f64, 1.0, 2.0, 3.0, 3.0].into_iter()), vec![1.0, 3.0]);
}

#[test]
fn quartiles_stream() {
assert_eq!(quartiles(vec![3usize, 5, 7].into_iter()), Some((3., 5., 7.)));
assert_eq!(quartiles(vec![3usize, 5, 7, 9].into_iter()), Some((4., 6., 8.)));
assert_eq!(quartiles(vec![1usize, 2, 7, 11].into_iter()), Some((1.5, 4.5, 9.)));
assert_eq!(quartiles(vec![3usize, 5, 7, 9, 12].into_iter()), Some((4., 7., 10.5)));
assert_eq!(quartiles(vec![2usize, 2, 3, 8, 10].into_iter()), Some((2., 3., 9.)));
assert_eq!(quartiles(vec![3usize, 5, 7, 9, 12, 20].into_iter()), Some((5., 8., 12.)));
assert_eq!(quartiles(vec![0usize, 2, 4, 8, 10, 11].into_iter()), Some((2., 6., 10.)));
assert_eq!(quartiles(vec![3usize, 5, 7, 9, 12, 20, 21].into_iter()), Some((5., 9., 20.)));
assert_eq!(quartiles(vec![1usize, 5, 6, 6, 7, 10, 19].into_iter()), Some((5., 6., 10.)));
}

#[test]
fn quartiles_floats() {
assert_eq!(quartiles(vec![3_f64, 5., 7.].into_iter()), Some((3., 5., 7.)));
assert_eq!(quartiles(vec![3_f64, 5., 7., 9.].into_iter()), Some((4., 6., 8.)));
assert_eq!(quartiles(vec![3_f64, 5., 7., 9., 12.].into_iter()), Some((4., 7., 10.5)));
assert_eq!(quartiles(vec![3_f64, 5., 7., 9., 12., 20.].into_iter()), Some((5., 8., 12.)));
assert_eq!(quartiles(vec![3_f64, 5., 7., 9., 12., 20., 21.].into_iter()), Some((5., 9., 20.)));
}
}