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/mod.rs

@@ -0,0 +1,68 @@
+//! # Collection of Distance Functions
+//!
+//! Many algorithms in machine learning require a measure of distance between data points. Distance metric (or metric) is a function that defines a distance between a pair of point elements of a set.
+//! Formally, the distance can be any metric measure that is defined as \\( d(x, y) \geq 0\\) and follows three conditions:
+//! 1. \\( d(x, y) = 0 \\) if and only \\( x = y \\), positive definiteness
+//! 1. \\( d(x, y) = d(y, x) \\), symmetry
+//! 1. \\( d(x, y) \leq d(x, z) + d(z, y) \\), subadditivity or triangle inequality
+//!
+//! for all \\(x, y, z \in Z \\)
+//!
+//! A good distance metric helps to improve the performance of classification, clustering and information retrieval algorithms significantly.
+//!
+//! <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>
+
+/// Euclidean Distance is the straight-line distance between two points in Euclidean spacere that presents the shortest distance between these points.
+pub mod euclidian;
+/// Hamming Distance between two strings is the number of positions at which the corresponding symbols are different.
+pub mod hamming;
+/// The Mahalanobis distance is the distance between two points in multivariate space.
+pub mod mahalanobis;
+/// Also known as rectilinear distance, city block distance, taxicab metric.
+pub mod manhattan;
+/// A generalization of both the Euclidean distance and the Manhattan distance.
+pub mod minkowski;
+
+use crate::linalg::basic::arrays::Array2;
+use crate::linalg::traits::lu::LUDecomposable;
+use crate::numbers::basenum::Number;
+
+/// Distance metric, a function that calculates distance between two points
+pub trait Distance<T>: Clone {
+    /// Calculates distance between _a_ and _b_
+    fn distance(&self, a: &T, b: &T) -> f64;
+}
+
+/// Multitude of distance metric functions
+pub struct Distances {}
+
+impl Distances {
+    /// Euclidian distance, see [`Euclidian`](euclidian/index.html)
+    pub fn euclidian<T: Number>() -> euclidian::Euclidian<T> {
+        euclidian::Euclidian::new()
+    }
+
+    /// Minkowski distance, see [`Minkowski`](minkowski/index.html)
+    /// * `p` - function order. Should be >= 1
+    pub fn minkowski<T: Number>(p: u16) -> minkowski::Minkowski<T> {
+        minkowski::Minkowski::new(p)
+    }
+
+    /// Manhattan distance, see [`Manhattan`](manhattan/index.html)
+    pub fn manhattan<T: Number>() -> manhattan::Manhattan<T> {
+        manhattan::Manhattan::new()
+    }
+
+    /// Hamming distance, see [`Hamming`](hamming/index.html)
+    pub fn hamming<T: Number>() -> hamming::Hamming<T> {
+        hamming::Hamming::new()
+    }
+
+    /// Mahalanobis distance, see [`Mahalanobis`](mahalanobis/index.html)
+    pub fn mahalanobis<T: Number, M: Array2<T>, C: Array2<f64> + LUDecomposable<f64>>(
+        data: &M,
+    ) -> mahalanobis::Mahalanobis<T, C> {
+        mahalanobis::Mahalanobis::new(data)
+    }
+}