Merge potential next release v0.4 (#187) Breaking Changes

* First draft of the new n-dimensional arrays + NB use case
* Improves default implementation of multiple Array methods
* Refactors tree methods
* Adds matrix decomposition routines
* Adds matrix decomposition methods to ndarray and nalgebra bindings
* Refactoring + linear regression now uses array2
* Ridge & Linear regression
* LBFGS optimizer & logistic regression
* LBFGS optimizer & logistic regression
* Changes linear methods, metrics and model selection methods to new n-dimensional arrays
* Switches KNN and clustering algorithms to new n-d array layer
* Refactors distance metrics
* Optimizes knn and clustering methods
* Refactors metrics module
* Switches decomposition methods to n-dimensional arrays
* Linalg refactoring - cleanup rng merge (#172)
* Remove legacy DenseMatrix and BaseMatrix implementation. Port the new Number, FloatNumber and Array implementation into module structure.
* Exclude AUC metrics. Needs reimplementation
* Improve developers walkthrough

New traits system in place at `src/numbers` and `src/linalg`
Co-authored-by: Lorenzo <tunedconsulting@gmail.com>

* Provide SupervisedEstimator with a constructor to avoid explicit dynamical box allocation in 'cross_validate' and 'cross_validate_predict' as required by the use of 'dyn' as per Rust 2021
* Implement getters to use as_ref() in src/neighbors
* Implement getters to use as_ref() in src/naive_bayes
* Implement getters to use as_ref() in src/linear
* Add Clone to src/naive_bayes
* Change signature for cross_validate and other model_selection functions to abide to use of dyn in Rust 2021
* Implement ndarray-bindings. Remove FloatNumber from implementations
* Drop nalgebra-bindings support (as decided in conf-call to go for ndarray)
* Remove benches. Benches will have their own repo at smartcore-benches
* Implement SVC
* Implement SVC serialization. Move search parameters in dedicated module
* Implement SVR. Definitely too slow
* Fix compilation issues for wasm (#202)

Co-authored-by: Luis Moreno <morenol@users.noreply.github.com>
* Fix tests (#203)

* Port linalg/traits/stats.rs
* Improve methods naming
* Improve Display for DenseMatrix

Co-authored-by: Montana Low <montanalow@users.noreply.github.com>
Co-authored-by: VolodymyrOrlov <volodymyr.orlov@gmail.com>

src/metrics/distance/minkowski.rs

@@ -0,0 +1,97 @@
+//! # Minkowski Distance
+//!
+//! The Minkowski distance  of order _p_ (where _p_ is an integer) is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance.
+//! The Manhattan distance between two points \\(x \in ℝ^n \\) and \\( y \in ℝ^n \\) in n-dimensional space is defined as:
+//!
+//! \\[ d(x, y) = \left(\sum_{i=0}^n \lvert x_i - y_i \rvert^p\right)^{1/p} \\]
+//!
+//! Example:
+//!
+//! ```
+//! use smartcore::metrics::distance::Distance;
+//! use smartcore::metrics::distance::minkowski::Minkowski;
+//!
+//! let x = vec![1., 1.];
+//! let y = vec![2., 2.];
+//!
+//! let l1: f64 = Minkowski::new(1).distance(&x, &y);
+//! let l2: f64 = Minkowski::new(2).distance(&x, &y);
+//!
+//! ```
+//! <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
+//! <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+
+#[cfg(feature = "serde")]
+use serde::{Deserialize, Serialize};
+use std::marker::PhantomData;
+
+use crate::linalg::basic::arrays::ArrayView1;
+use crate::numbers::basenum::Number;
+
+use super::Distance;
+
+/// Defines the Minkowski distance of order `p`
+#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+#[derive(Debug, Clone)]
+pub struct Minkowski<T: Number> {
+    /// order, integer
+    pub p: u16,
+    _t: PhantomData<T>,
+}
+
+impl<T: Number> Minkowski<T> {
+    /// instatiate the initial structure
+    pub fn new(p: u16) -> Minkowski<T> {
+        Minkowski { p, _t: PhantomData }
+    }
+}
+
+impl<T: Number, A: ArrayView1<T>> Distance<A> for Minkowski<T> {
+    fn distance(&self, x: &A, y: &A) -> f64 {
+        if x.shape() != y.shape() {
+            panic!("Input vector sizes are different");
+        }
+        if self.p < 1 {
+            panic!("p must be at least 1");
+        }
+
+        let p_t = self.p as f64;
+
+        let dist: f64 = x
+            .iterator(0)
+            .zip(y.iterator(0))
+            .map(|(&a, &b)| (a - b).to_f64().unwrap().abs().powf(p_t))
+            .sum();
+
+        dist.powf(1f64 / p_t)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[cfg_attr(target_arch = "wasm32", wasm_bindgen_test::wasm_bindgen_test)]
+    #[test]
+    fn minkowski_distance() {
+        let a = vec![1., 2., 3.];
+        let b = vec![4., 5., 6.];
+
+        let l1: f64 = Minkowski::new(1).distance(&a, &b);
+        let l2: f64 = Minkowski::new(2).distance(&a, &b);
+        let l3: f64 = Minkowski::new(3).distance(&a, &b);
+
+        assert!((l1 - 9.0).abs() < 1e-8);
+        assert!((l2 - 5.19615242).abs() < 1e-8);
+        assert!((l3 - 4.32674871).abs() < 1e-8);
+    }
+
+    #[test]
+    #[should_panic(expected = "p must be at least 1")]
+    fn minkowski_distance_negative_p() {
+        let a = vec![1., 2., 3.];
+        let b = vec![4., 5., 6.];
+
+        let _: f64 = Minkowski::new(0).distance(&a, &b);
+    }
+}