Means (#20)

* New module

* First implementation of mean and harmonic_mean

* Return a Result instead of panicking

* Added documentation

* Improved test suite

* Implemented geometric mean

* Reorganized to only expose the extension trait, instead of the whole submodule tree

* Implement review comments

* Fixed documentation

* Use Rust 1.31

.travis.yml

@@ -7,7 +7,7 @@ addons:
       - libssl-dev
 cache: cargo
 rust:
-  - 1.30.0
+  - 1.31.0
   - stable
   - beta
   - nightly

Cargo.toml

@@ -24,3 +24,4 @@ itertools = { version = "0.7.0", default-features = false }
 [dev-dependencies]
 quickcheck = "0.7"
 ndarray-rand = "0.9"
+approx = "0.3"

src/lib.rs

@@ -37,15 +37,20 @@ extern crate ndarray_rand;
 #[cfg(test)]
 #[macro_use(quickcheck)]
 extern crate quickcheck;
+#[cfg(test)]
+#[macro_use(abs_diff_eq)]
+extern crate approx;
 
 pub use maybe_nan::{MaybeNan, MaybeNanExt};
 pub use quantile::{interpolate, QuantileExt, Quantile1dExt};
 pub use sort::Sort1dExt;
 pub use correlation::CorrelationExt;
 pub use histogram::HistogramExt;
+pub use summary_statistics::SummaryStatisticsExt;
 
 mod maybe_nan;
 mod quantile;
 mod sort;
 mod correlation;
-pub mod histogram;
+mod summary_statistics;
+pub mod histogram;

src/summary_statistics/means.rs

@@ -0,0 +1,97 @@
+use ndarray::{Data, Dimension, ArrayBase};
+use num_traits::{FromPrimitive, Float, Zero};
+use std::ops::{Add, Div};
+use super::SummaryStatisticsExt;
+
+
+impl<A, S, D> SummaryStatisticsExt<A, S, D> for ArrayBase<S, D>
+where
+    S: Data<Elem = A>,
+    D: Dimension,
+{
+    fn mean(&self) -> Option<A>
+    where
+        A: Clone + FromPrimitive + Add<Output=A> + Div<Output=A> + Zero
+    {
+        let n_elements = self.len();
+        if n_elements == 0 {
+            None
+        } else {
+            let n_elements = A::from_usize(n_elements)
+                .expect("Converting number of elements to `A` must not fail.");
+            Some(self.sum() / n_elements)
+        }
+    }
+
+    fn harmonic_mean(&self) -> Option<A>
+    where
+        A: Float + FromPrimitive,
+    {
+        self.map(|x| x.recip()).mean().map(|x| x.recip())
+    }
+
+    fn geometric_mean(&self) -> Option<A>
+        where
+            A: Float + FromPrimitive,
+    {
+        self.map(|x| x.ln()).mean().map(|x| x.exp())
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::SummaryStatisticsExt;
+    use std::f64;
+    use noisy_float::types::N64;
+    use ndarray::Array1;
+
+    #[test]
+    fn test_means_with_nan_values() {
+        let a = array![f64::NAN, 1.];
+        assert!(a.mean().unwrap().is_nan());
+        assert!(a.harmonic_mean().unwrap().is_nan());
+        assert!(a.geometric_mean().unwrap().is_nan());
+    }
+
+    #[test]
+    fn test_means_with_empty_array_of_floats() {
+        let a: Array1<f64> = array![];
+        assert!(a.mean().is_none());
+        assert!(a.harmonic_mean().is_none());
+        assert!(a.geometric_mean().is_none());
+    }
+
+    #[test]
+    fn test_means_with_empty_array_of_noisy_floats() {
+        let a: Array1<N64> = array![];
+        assert!(a.mean().is_none());
+        assert!(a.harmonic_mean().is_none());
+        assert!(a.geometric_mean().is_none());
+    }
+
+    #[test]
+    fn test_means_with_array_of_floats() {
+        let a: Array1<f64> = array![
+            0.99889651, 0.0150731 , 0.28492482, 0.83819218, 0.48413156,
+            0.80710412, 0.41762936, 0.22879429, 0.43997224, 0.23831807,
+            0.02416466, 0.6269962 , 0.47420614, 0.56275487, 0.78995021,
+            0.16060581, 0.64635041, 0.34876609, 0.78543249, 0.19938356,
+            0.34429457, 0.88072369, 0.17638164, 0.60819363, 0.250392  ,
+            0.69912532, 0.78855523, 0.79140914, 0.85084218, 0.31839879,
+            0.63381769, 0.22421048, 0.70760302, 0.99216018, 0.80199153,
+            0.19239188, 0.61356023, 0.31505352, 0.06120481, 0.66417377,
+            0.63608897, 0.84959691, 0.43599069, 0.77867775, 0.88267754,
+            0.83003623, 0.67016118, 0.67547638, 0.65220036, 0.68043427
+        ];
+        // Computed using NumPy
+        let expected_mean = 0.5475494059146699;
+        // Computed using SciPy
+        let expected_harmonic_mean = 0.21790094950226022;
+        // Computed using SciPy
+        let expected_geometric_mean = 0.4345897639796527;
+
+        abs_diff_eq!(a.mean().unwrap(), expected_mean, epsilon = f64::EPSILON);
+        abs_diff_eq!(a.harmonic_mean().unwrap(), expected_harmonic_mean, epsilon = f64::EPSILON);
+        abs_diff_eq!(a.geometric_mean().unwrap(), expected_geometric_mean, epsilon = f64::EPSILON);
+    }
+}

src/summary_statistics/mod.rs

@@ -0,0 +1,66 @@
+//! Summary statistics (e.g. mean, variance, etc.).
+use ndarray::{Data, Dimension};
+use num_traits::{FromPrimitive, Float, Zero};
+use std::ops::{Add, Div};
+
+/// Extension trait for `ArrayBase` providing methods
+/// to compute several summary statistics (e.g. mean, variance, etc.).
+pub trait SummaryStatisticsExt<A, S, D>
+    where
+        S: Data<Elem = A>,
+        D: Dimension,
+{
+    /// Returns the [`arithmetic mean`] x̅ of all elements in the array:
+    ///
+    /// ```text
+    ///     1   n
+    /// x̅ = ―   ∑ xᵢ
+    ///     n  i=1
+    /// ```
+    ///
+    /// If the array is empty, `None` is returned.
+    ///
+    /// **Panics** if `A::from_usize()` fails to convert the number of elements in the array.
+    ///
+    /// [`arithmetic mean`]: https://en.wikipedia.org/wiki/Arithmetic_mean
+    fn mean(&self) -> Option<A>
+        where
+            A: Clone + FromPrimitive + Add<Output=A> + Div<Output=A> + Zero;
+
+    /// Returns the [`harmonic mean`] `HM(X)` of all elements in the array:
+    ///
+    /// ```text
+    ///           ⎛ n     ⎞⁻¹
+    /// HM(X) = n ⎜ ∑ xᵢ⁻¹⎟
+    ///           ⎝i=1    ⎠
+    /// ```
+    ///
+    /// If the array is empty, `None` is returned.
+    ///
+    /// **Panics** if `A::from_usize()` fails to convert the number of elements in the array.
+    ///
+    /// [`harmonic mean`]: https://en.wikipedia.org/wiki/Harmonic_mean
+    fn harmonic_mean(&self) -> Option<A>
+        where
+            A: Float + FromPrimitive;
+
+    /// Returns the [`geometric mean`] `GM(X)` of all elements in the array:
+    ///
+    /// ```text
+    ///         ⎛ n   ⎞¹⁄ₙ
+    /// GM(X) = ⎜ ∏ xᵢ⎟
+    ///         ⎝i=1  ⎠
+    /// ```
+    ///
+    /// If the array is empty, `None` is returned.
+    ///
+    /// **Panics** if `A::from_usize()` fails to convert the number of elements in the array.
+    ///
+    /// [`geometric mean`]: https://en.wikipedia.org/wiki/Geometric_mean
+    fn geometric_mean(&self) -> Option<A>
+        where
+            A: Float + FromPrimitive;
+
+}
+
+mod means;