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//! Summary statistics (e.g. mean, variance, etc.). use crate::errors::{EmptyInput, MultiInputError}; use ndarray::{Array, ArrayBase, Axis, Data, Dimension, Ix1, RemoveAxis}; use num_traits::{Float, FromPrimitive, Zero}; use std::ops::{Add, Div, Mul}; /// 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, `Err(EmptyInput)` 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) -> Result<A, EmptyInput> where A: Clone + FromPrimitive + Add<Output = A> + Div<Output = A> + Zero; /// Returns the [`arithmetic weighted mean`] x̅ of all elements in the array. Use `weighted_sum` /// if the `weights` are normalized (they sum up to 1.0). /// /// ```text /// n /// ∑ wᵢxᵢ /// i=1 /// x̅ = ――――――――― /// n /// ∑ wᵢ /// i=1 /// ``` /// /// **Panics** if division by zero panics for type A. /// /// The following **errors** may be returned: /// /// * `MultiInputError::EmptyInput` if `self` is empty /// * `MultiInputError::ShapeMismatch` if `self` and `weights` don't have the same shape /// /// [`arithmetic weighted mean`] https://en.wikipedia.org/wiki/Weighted_arithmetic_mean fn weighted_mean(&self, weights: &Self) -> Result<A, MultiInputError> where A: Copy + Div<Output = A> + Mul<Output = A> + Zero; /// Returns the weighted sum of all elements in the array, that is, the dot product of the /// arrays `self` and `weights`. Equivalent to `weighted_mean` if the `weights` are normalized. /// /// ```text /// n /// x̅ = ∑ wᵢxᵢ /// i=1 /// ``` /// /// The following **errors** may be returned: /// /// * `MultiInputError::ShapeMismatch` if `self` and `weights` don't have the same shape fn weighted_sum(&self, weights: &Self) -> Result<A, MultiInputError> where A: Copy + Mul<Output = A> + Zero; /// Returns the [`arithmetic weighted mean`] x̅ along `axis`. Use `weighted_mean_axis ` if the /// `weights` are normalized. /// /// ```text /// n /// ∑ wᵢxᵢ /// i=1 /// x̅ = ――――――――― /// n /// ∑ wᵢ /// i=1 /// ``` /// /// **Panics** if `axis` is out of bounds. /// /// The following **errors** may be returned: /// /// * `MultiInputError::EmptyInput` if `self` is empty /// * `MultiInputError::ShapeMismatch` if `self` length along axis is not equal to `weights` length /// /// [`arithmetic weighted mean`] https://en.wikipedia.org/wiki/Weighted_arithmetic_mean fn weighted_mean_axis( &self, axis: Axis, weights: &ArrayBase<S, Ix1>, ) -> Result<Array<A, D::Smaller>, MultiInputError> where A: Copy + Div<Output = A> + Mul<Output = A> + Zero, D: RemoveAxis; /// Returns the weighted sum along `axis`, that is, the dot product of `weights` and each lane /// of `self` along `axis`. Equivalent to `weighted_mean_axis` if the `weights` are normalized. /// /// ```text /// n /// x̅ = ∑ wᵢxᵢ /// i=1 /// ``` /// /// **Panics** if `axis` is out of bounds. /// /// The following **errors** may be returned /// /// * `MultiInputError::ShapeMismatch` if `self` and `weights` don't have the same shape fn weighted_sum_axis( &self, axis: Axis, weights: &ArrayBase<S, Ix1>, ) -> Result<Array<A, D::Smaller>, MultiInputError> where A: Copy + Mul<Output = A> + Zero, D: RemoveAxis; /// 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, `Err(EmptyInput)` 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) -> Result<A, EmptyInput> 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, `Err(EmptyInput)` 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) -> Result<A, EmptyInput> where A: Float + FromPrimitive; /// Returns the [kurtosis] `Kurt[X]` of all elements in the array: /// /// ```text /// Kurt[X] = μ₄ / σ⁴ /// ``` /// /// where μ₄ is the fourth central moment and σ is the standard deviation of /// the elements in the array. /// /// This is sometimes referred to as _Pearson's kurtosis_. Fisher's kurtosis can be /// computed by subtracting 3 from Pearson's kurtosis. /// /// If the array is empty, `Err(EmptyInput)` is returned. /// /// **Panics** if `A::from_usize()` fails to convert the number of elements in the array. /// /// [kurtosis]: https://en.wikipedia.org/wiki/Kurtosis fn kurtosis(&self) -> Result<A, EmptyInput> where A: Float + FromPrimitive; /// Returns the [Pearson's moment coefficient of skewness] γ₁ of all elements in the array: /// /// ```text /// γ₁ = μ₃ / σ³ /// ``` /// /// where μ₃ is the third central moment and σ is the standard deviation of /// the elements in the array. /// /// If the array is empty, `Err(EmptyInput)` is returned. /// /// **Panics** if `A::from_usize()` fails to convert the number of elements in the array. /// /// [Pearson's moment coefficient of skewness]: https://en.wikipedia.org/wiki/Skewness fn skewness(&self) -> Result<A, EmptyInput> where A: Float + FromPrimitive; /// Returns the *p*-th [central moment] of all elements in the array, μₚ: /// /// ```text /// 1 n /// μₚ = ― ∑ (xᵢ-x̅)ᵖ /// n i=1 /// ``` /// /// If the array is empty, `Err(EmptyInput)` is returned. /// /// The *p*-th central moment is computed using a corrected two-pass algorithm (see Section 3.5 /// in [Pébay et al., 2016]). Complexity is *O(np)* when *n >> p*, *p > 1*. /// /// **Panics** if `A::from_usize()` fails to convert the number of elements /// in the array or if `order` overflows `i32`. /// /// [central moment]: https://en.wikipedia.org/wiki/Central_moment /// [Pébay et al., 2016]: https://www.osti.gov/pages/servlets/purl/1427275 fn central_moment(&self, order: u16) -> Result<A, EmptyInput> where A: Float + FromPrimitive; /// Returns the first *p* [central moments] of all elements in the array, see [central moment] /// for more details. /// /// If the array is empty, `Err(EmptyInput)` is returned. /// /// This method reuses the intermediate steps for the *k*-th moment to compute the *(k+1)*-th, /// being thus more efficient than repeated calls to [central moment] if the computation /// of central moments of multiple orders is required. /// /// **Panics** if `A::from_usize()` fails to convert the number of elements /// in the array or if `order` overflows `i32`. /// /// [central moments]: https://en.wikipedia.org/wiki/Central_moment /// [central moment]: #tymethod.central_moment fn central_moments(&self, order: u16) -> Result<Vec<A>, EmptyInput> where A: Float + FromPrimitive; private_decl! {} } mod means;