comparison: src/euclidean.rs
src/euclidean.rs
- branch
- dev
- changeset 63
- f7b87d84864d
- parent 62
- d8305c9b6fdf
- child 64
- 4f6ca107ccb1
equal
deleted
inserted
replaced
| 62:d8305c9b6fdf | 63:f7b87d84864d |
|---|---|
| 2 Euclidean spaces. | 2 Euclidean spaces. |
| 3 */ | 3 */ |
| 4 | 4 |
| 5 use std::ops::{Mul, MulAssign, Div, DivAssign, Add, Sub, AddAssign, SubAssign, Neg}; | 5 use std::ops::{Mul, MulAssign, Div, DivAssign, Add, Sub, AddAssign, SubAssign, Neg}; |
| 6 use crate::types::*; | 6 use crate::types::*; |
| 7 use crate::mapping::Space; | 7 use crate::instance::Instance; |
| 8 | 8 use crate::norms::{HasDual, Reflexive}; |
| 9 /// Space (type) with a defined dot product. | |
| 10 /// | |
| 11 /// `U` is the space of the multiplier, and `F` the space of scalars. | |
| 12 /// Since `U` ≠ `Self`, this trait can also implement dual products. | |
| 13 pub trait Dot<U, F> { | |
| 14 fn dot(&self, other : &U) -> F; | |
| 15 } | |
| 16 | 9 |
| 17 /// Space (type) with Euclidean and vector space structure | 10 /// Space (type) with Euclidean and vector space structure |
| 18 /// | 11 /// |
| 19 /// The type should implement vector space operations (addition, subtraction, scalar | 12 /// The type should implement vector space operations (addition, subtraction, scalar |
| 20 /// multiplication and scalar division) along with their assignment versions, as well | 13 /// multiplication and scalar division) along with their assignment versions, as well |
| 21 /// as the [`Dot`] product with respect to `Self`. | 14 /// as an inner product. |
| 22 pub trait Euclidean<F : Float> : Space + Dot<Self,F> | 15 pub trait Euclidean<F : Float> : HasDual<F, DualSpace=Self> + Reflexive<F> |
| 23 + Mul<F, Output=<Self as Euclidean<F>>::Output> + MulAssign<F> | 16 + Mul<F, Output=<Self as Euclidean<F>>::Output> + MulAssign<F> |
| 24 + Div<F, Output=<Self as Euclidean<F>>::Output> + DivAssign<F> | 17 + Div<F, Output=<Self as Euclidean<F>>::Output> + DivAssign<F> |
| 25 + Add<Self, Output=<Self as Euclidean<F>>::Output> | 18 + Add<Self, Output=<Self as Euclidean<F>>::Output> |
| 26 + Sub<Self, Output=<Self as Euclidean<F>>::Output> | 19 + Sub<Self, Output=<Self as Euclidean<F>>::Output> |
| 27 + for<'b> Add<&'b Self, Output=<Self as Euclidean<F>>::Output> | 20 + for<'b> Add<&'b Self, Output=<Self as Euclidean<F>>::Output> |
| 28 + for<'b> Sub<&'b Self, Output=<Self as Euclidean<F>>::Output> | 21 + for<'b> Sub<&'b Self, Output=<Self as Euclidean<F>>::Output> |
| 29 + AddAssign<Self> + for<'b> AddAssign<&'b Self> | 22 + AddAssign<Self> + for<'b> AddAssign<&'b Self> |
| 30 + SubAssign<Self> + for<'b> SubAssign<&'b Self> | 23 + SubAssign<Self> + for<'b> SubAssign<&'b Self> |
| 31 + Neg<Output=<Self as Euclidean<F>>::Output> { | 24 + Neg<Output=<Self as Euclidean<F>>::Output> |
| 25 { | |
| 32 type Output : Euclidean<F>; | 26 type Output : Euclidean<F>; |
| 33 | 27 |
| 28 // Inner product | |
| 29 fn dot<I : Instance<Self>>(&self, other : I) -> F; | |
| 30 | |
| 34 /// Calculate the square of the 2-norm, $\frac{1}{2}\\|x\\|_2^2$, where `self` is $x$. | 31 /// Calculate the square of the 2-norm, $\frac{1}{2}\\|x\\|_2^2$, where `self` is $x$. |
| 35 #[inline] | 32 /// |
| 36 fn norm2_squared(&self) -> F { | 33 /// This is not automatically implemented to avoid imposing |
| 37 self.dot(self) | 34 /// `for <'a> &'a Self : Instance<Self>` trait bound bloat. |
| 38 } | 35 fn norm2_squared(&self) -> F; |
| 39 | 36 |
| 40 /// Calculate the square of the 2-norm divided by 2, $\frac{1}{2}\\|x\\|_2^2$, | 37 /// Calculate the square of the 2-norm divided by 2, $\frac{1}{2}\\|x\\|_2^2$, |
| 41 /// where `self` is $x$. | 38 /// where `self` is $x$. |
| 42 #[inline] | 39 #[inline] |
| 43 fn norm2_squared_div2(&self) -> F { | 40 fn norm2_squared_div2(&self) -> F { |
