Tue, 06 Dec 2022 08:58:49 +0200
README improvements
/*! Euclidean spaces. */ use crate::types::*; use std::ops::{Mul, MulAssign, Div, DivAssign, Add, Sub, AddAssign, SubAssign, Neg}; /// Space (type) with a defined dot product. /// /// `U` is the space of the multiplier, and `F` the space of scalars. /// Since `U` ≠ `Self`, this trait can also implement dual products. pub trait Dot<U, F> { fn dot(&self, other : &U) -> F; } /// Space (type) with Euclidean and vector space structure /// /// The type should implement vector space operations (addition, subtraction, scalar /// multiplication and scalar division) along with their assignment versions, as well /// as the [`Dot`] product with respect to `Self`. pub trait Euclidean<F : Float> : Sized + Dot<Self,F> + Mul<F, Output=<Self as Euclidean<F>>::Output> + MulAssign<F> + Div<F, Output=<Self as Euclidean<F>>::Output> + DivAssign<F> + Add<Self, Output=<Self as Euclidean<F>>::Output> + Sub<Self, Output=<Self as Euclidean<F>>::Output> + for<'b> Add<&'b Self, Output=<Self as Euclidean<F>>::Output> + for<'b> Sub<&'b Self, Output=<Self as Euclidean<F>>::Output> + AddAssign<Self> + for<'b> AddAssign<&'b Self> + SubAssign<Self> + for<'b> SubAssign<&'b Self> + Neg<Output=<Self as Euclidean<F>>::Output> { type Output : Euclidean<F>; /// Returns origin of same dimensions as `self`. fn similar_origin(&self) -> <Self as Euclidean<F>>::Output; /// Calculate the square of the 2-norm, $\frac{1}{2}\\|x\\|_2^2$, where `self` is $x$. #[inline] fn norm2_squared(&self) -> F { self.dot(self) } /// Calculate the square of the 2-norm divided by 2, $\frac{1}{2}\\|x\\|_2^2$, /// where `self` is $x$. #[inline] fn norm2_squared_div2(&self) -> F { self.norm2_squared()/F::TWO } /// Calculate the 2-norm $‖x‖_2$, where `self` is $x$. #[inline] fn norm2(&self) -> F { self.norm2_squared().sqrt() } /// Calculate the 2-distance squared $\\|x-y\\|_2^2$, where `self` is $x$. fn dist2_squared(&self, y : &Self) -> F; /// Calculate the 2-distance $\\|x-y\\|_2$, where `self` is $x$. #[inline] fn dist2(&self, y : &Self) -> F { self.dist2_squared(y).sqrt() } /// Projection to the 2-ball. #[inline] fn proj_ball2(mut self, ρ : F) -> Self { self.proj_ball2_mut(ρ); self } /// In-place projection to the 2-ball. #[inline] fn proj_ball2_mut(&mut self, ρ : F) { let r = self.norm2(); if r>ρ { *self *= ρ/r } } } /// Trait for [`Euclidean`] spaces with dimensions known at compile time. pub trait StaticEuclidean<F : Float> : Euclidean<F> { /// Returns the origin fn origin() -> <Self as Euclidean<F>>::Output; }