Merge pull request #1 from LukeMathWalker/interpolation-strategy

Interpolation strategy

Author: LukeMathWalker

src/impl_1d.rs

@@ -27,13 +27,18 @@ impl<A, S> ArrayBase<S, Ix1>
         }
     }
 
-    /// Return the element that would occupy the `i`-th position if the array
-    /// were sorted in increasing order.
+    /// Return the element that would occupy the `i`-th position if
+    /// the array were sorted in increasing order.
     ///
     /// The array is shuffled **in place** to retrieve the desired element:
     /// no copy of the array is allocated.
-    /// No assumptions should be made on the ordering of elements
-    /// after this computation.
+    /// After the shuffling, all elements with an index smaller than `i`
+    /// are smaller than the desired element, while all elements with
+    /// an index greater or equal than `i` are greater than or equal
+    /// to the desired element.
+    ///
+    /// No other assumptions should be made on the ordering of the
+    /// elements after this computation.
     ///
     /// Complexity ([quickselect](https://en.wikipedia.org/wiki/Quickselect)):
     /// - average case: O(`n`);

src/numeric/impl_numeric.rs

@@ -19,13 +19,69 @@ use {
     Zip,
 };
 
-/// Used to choose the interpolation strategy in [`percentile_axis_mut`].
+/// Used to provide an interpolation strategy to [`percentile_axis_mut`].
 ///
 /// [`percentile_axis_mut`]: struct.ArrayBase.html#method.percentile_axis_mut
-pub enum InterpolationStrategy {
-    Lower,
-    Nearest,
-    Higher,
+pub trait Interpolate<T> {
+    fn float_percentile_index(q: f64, len: usize) -> f64 {
+        ((len - 1) as f64) * q
+    }
+
+    fn lower_index(q: f64, len: usize) -> usize {
+        Self::float_percentile_index(q, len).floor() as usize
+    }
+
+    fn upper_index(q: f64, len: usize) -> usize {
+        Self::float_percentile_index(q, len).ceil() as usize
+    }
+    fn needs_lower(q: f64, len: usize) -> bool;
+    fn needs_upper(q: f64, len: usize) -> bool;
+    fn interpolate(lower: Option<T>, upper: Option<T>, q: f64, len: usize) -> T;
+}
+
+pub struct Upper;
+pub struct Lower;
+pub struct Nearest;
+
+impl<T> Interpolate<T> for Upper {
+    fn needs_lower(_q: f64, _len: usize) -> bool {
+        false
+    }
+    fn needs_upper(_q: f64, _len: usize) -> bool {
+        true
+    }
+    fn interpolate(_lower: Option<T>, upper: Option<T>, _q: f64, _len: usize) -> T {
+       upper.unwrap()
+    }
+}
+
+impl<T> Interpolate<T> for Lower {
+    fn needs_lower(_q: f64, _len: usize) -> bool {
+        true
+    }
+    fn needs_upper(_q: f64, _len: usize) -> bool {
+        false
+    }
+    fn interpolate(lower: Option<T>, _upper: Option<T>, _q: f64, _len: usize) -> T {
+        lower.unwrap()
+    }
+}
+
+impl<T> Interpolate<T> for Nearest {
+    fn needs_lower(q: f64, len: usize) -> bool {
+        let lower = <Self as Interpolate<T>>::lower_index(q, len);
+        ((lower as f64) - <Self as Interpolate<T>>::float_percentile_index(q, len)) <= 0.
+    }
+    fn needs_upper(q: f64, len: usize) -> bool {
+        !<Self as Interpolate<T>>::needs_lower(q, len)
+    }
+    fn interpolate(lower: Option<T>, upper: Option<T>, q: f64, len: usize) -> T {
+        if <Self as Interpolate<T>>::needs_lower(q, len) {
+            lower.unwrap()
+        } else {
+            upper.unwrap()
+        }
+    }
 }
 
 /// Numerical methods for arrays.
@@ -154,19 +210,33 @@ impl<A, S, D> ArrayBase<S, D>
     ///
     /// **Panics** if `axis` is out of bounds or if `q` is not between
     /// `0.` and `1.` (inclusive).
-    pub fn percentile_axis_mut(&mut self, axis: Axis, q: f64, interpolation_strategy: InterpolationStrategy) -> Array<A, D::Smaller>
+    pub fn percentile_axis_mut<I>(&mut self, axis: Axis, q: f64) -> Array<A, D::Smaller>
         where D: RemoveAxis,
               A: Ord + Clone + Zero,
               S: DataMut,
+              I: Interpolate<Array<A, D::Smaller>>,
     {
         assert!((0. <= q) && (q <= 1.));
-        let float_percentile_index = ((self.len_of(axis) - 1) as f64) * q;
-        let percentile_index = match interpolation_strategy {
-            InterpolationStrategy::Lower => float_percentile_index.floor() as usize,
-            InterpolationStrategy::Nearest => float_percentile_index.round() as usize,
-            InterpolationStrategy::Higher => float_percentile_index.ceil() as usize,
+        let mut lower = None;
+        let mut upper = None;
+        let axis_len = self.len_of(axis);
+        if I::needs_lower(q, axis_len) {
+            lower = Some(
+                self.map_axis_mut(
+                    axis,
+                    |mut x| x.sorted_get_mut(I::lower_index(q, axis_len))
+                )
+            );
+        };
+        if I::needs_upper(q, axis_len) {
+            upper = Some(
+                self.map_axis_mut(
+                    axis,
+                    |mut x| x.sorted_get_mut(I::upper_index(q, axis_len))
+                )
+            );
         };
-        self.map_axis_mut(axis, |mut x| x.sorted_get_mut(percentile_index))
+        I::interpolate(lower, upper, q, axis_len)
     }
 
     /// Return variance along `axis`.

src/numeric/mod.rs

@@ -1,3 +1,3 @@
+pub use self::impl_numeric::*;
 
-pub mod impl_numeric;
-pub use self::impl_numeric::InterpolationStrategy;
+mod impl_numeric;

tests/array.rs

@@ -8,7 +8,7 @@ extern crate itertools;
 
 use ndarray::{Slice, SliceInfo, SliceOrIndex};
 use ndarray::prelude::*;
-use ndarray::numeric::InterpolationStrategy;
+use ndarray::numeric::{Lower};
 use ndarray::{
     rcarr2,
     arr3,
@@ -1759,7 +1759,7 @@ fn test_percentile_axis_mut_with_odd_axis_length() {
         [3, 5, 6, 12]
         ]
     );
-    let p = a.percentile_axis_mut(Axis(0), 0.5, InterpolationStrategy::Lower);
+    let p = a.percentile_axis_mut::<Lower>(Axis(0), 0.5);
     assert!(p == a.subview(Axis(0), 1));
 }
 
@@ -1773,20 +1773,20 @@ fn test_percentile_axis_mut_with_even_axis_length() {
         [4, 6, 7, 13]
         ]
     );
-    let q = b.percentile_axis_mut(Axis(0), 0.5, InterpolationStrategy::Lower);
+    let q = b.percentile_axis_mut::<Lower>(Axis(0), 0.5);
     assert!(q == b.subview(Axis(0), 1));
 }
 
 #[test]
 fn test_percentile_axis_mut_to_get_minimum() {
     let mut b = arr2(&[[1, 3, 22, 10]]);
-    let q = b.percentile_axis_mut(Axis(1), 0., InterpolationStrategy::Lower);
+    let q = b.percentile_axis_mut::<Lower>(Axis(1), 0.);
     assert!(q == arr1(&[1]));
 }
 
 #[test]
 fn test_percentile_axis_mut_to_get_maximum() {
     let mut b = arr1(&[1, 3, 22, 10]);
-    let q = b.percentile_axis_mut(Axis(0), 1., InterpolationStrategy::Lower);
+    let q = b.percentile_axis_mut::<Lower>(Axis(0), 1.);
     assert!(q == arr0(22));
 }