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comparison: src/norms.rs

src/norms.rs

changeset 6
d80b87b8acd0
parent 5
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equal deleted inserted replaced
5:59dc4c5883f4 6:d80b87b8acd0
8 8
9 // 9 //
10 // Abstract norms 10 // Abstract norms
11 // 11 //
12 12
13 /// An exponent for norms.
14 ///
15 // Just a collection of desirabl attributes for a marker type
16 pub trait NormExponent : Copy + Send + Sync + 'static {}
17
18
13 /// Exponent type for the 1-[`Norm`]. 19 /// Exponent type for the 1-[`Norm`].
14 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)] 20 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)]
15 pub struct L1; 21 pub struct L1;
22 impl NormExponent for L1 {}
16 23
17 /// Exponent type for the 2-[`Norm`]. 24 /// Exponent type for the 2-[`Norm`].
18 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)] 25 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)]
19 pub struct L2; 26 pub struct L2;
27 impl NormExponent for L2 {}
20 28
21 /// Exponent type for the ∞-[`Norm`]. 29 /// Exponent type for the ∞-[`Norm`].
22 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)] 30 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)]
23 pub struct Linfinity; 31 pub struct Linfinity;
32 impl NormExponent for Linfinity {}
24 33
25 /// Exponent type for 2,1-[`Norm`]. 34 /// Exponent type for 2,1-[`Norm`].
26 /// (1-norm over a domain Ω, 2-norm of a vector at each point of the domain.) 35 /// (1-norm over a domain Ω, 2-norm of a vector at each point of the domain.)
27 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)] 36 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)]
28 pub struct L21; 37 pub struct L21;
38 impl NormExponent for L21 {}
29 39
30 /// A Huber/Moreau–Yosida smoothed [`L1`] norm. (Not a norm itself.) 40 /// A Huber/Moreau–Yosida smoothed [`L1`] norm. (Not a norm itself.)
31 /// 41 ///
32 /// The parameter γ of this type is the smoothing factor. Zero means no smoothing, and higher 42 /// The parameter γ of this type is the smoothing factor. Zero means no smoothing, and higher
33 /// values more smoothing. Behaviour with γ < 0 is undefined. 43 /// values more smoothing. Behaviour with γ < 0 is undefined.
34 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)] 44 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)]
35 pub struct HuberL1<F : Float>(pub F); 45 pub struct HuberL1<F : Float>(pub F);
46 impl<F : Float> NormExponent for HuberL1<F> {}
36 47
37 /// A Huber/Moreau–Yosida smoothed [`L21`] norm. (Not a norm itself.) 48 /// A Huber/Moreau–Yosida smoothed [`L21`] norm. (Not a norm itself.)
38 /// 49 ///
39 /// The parameter γ of this type is the smoothing factor. Zero means no smoothing, and higher 50 /// The parameter γ of this type is the smoothing factor. Zero means no smoothing, and higher
40 /// values more smoothing. Behaviour with γ < 0 is undefined. 51 /// values more smoothing. Behaviour with γ < 0 is undefined.
41 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)] 52 #[derive(Copy,Debug,Clone,Serialize,Eq,PartialEq)]
42 pub struct HuberL21<F : Float>(pub F); 53 pub struct HuberL21<F : Float>(pub F);
54 impl<F : Float> NormExponent for HuberL21<F> {}
55
43 56
44 /// A normed space (type) with exponent or other type `Exponent` for the norm. 57 /// A normed space (type) with exponent or other type `Exponent` for the norm.
45 /// 58 ///
46 /// Use as 59 /// Use as
47 /// ``` 60 /// ```
49 /// # use alg_tools::loc::Loc; 62 /// # use alg_tools::loc::Loc;
50 /// let x = Loc([1.0, 2.0, 3.0]); 63 /// let x = Loc([1.0, 2.0, 3.0]);
51 /// 64 ///
52 /// println!("{}, {} {}", x.norm(L1), x.norm(L2), x.norm(Linfinity)) 65 /// println!("{}, {} {}", x.norm(L1), x.norm(L2), x.norm(Linfinity))
53 /// ``` 66 /// ```
54 pub trait Norm<F, Exponent> { 67 pub trait Norm<F : Num, Exponent : NormExponent> {
55 /// Calculate the norm. 68 /// Calculate the norm.
56 fn norm(&self, _p : Exponent) -> F; 69 fn norm(&self, _p : Exponent) -> F;
57 } 70 }
58 71
59 /// Indicates that the `Self`-[`Norm`] is dominated by the `Exponent`-`Norm` on the space 72 /// Indicates that the `Self`-[`Norm`] is dominated by the `Exponent`-`Norm` on the space
60 /// `Elem` with the corresponding field `F`. 73 /// `Elem` with the corresponding field `F`.
61 pub trait Dominated<F : Num, Exponent, Elem> { 74 pub trait Dominated<F : Num, Exponent : NormExponent, Elem> {
62 /// Indicates the factor $c$ for the inequality $‖x‖ ≤ C ‖x‖_p$. 75 /// Indicates the factor $c$ for the inequality $‖x‖ ≤ C ‖x‖_p$.
63 fn norm_factor(&self, p : Exponent) -> F; 76 fn norm_factor(&self, p : Exponent) -> F;
64 /// Given a norm-value $‖x‖_p$, calculates $C‖x‖_p$ such that $‖x‖ ≤ C‖x‖_p$ 77 /// Given a norm-value $‖x‖_p$, calculates $C‖x‖_p$ such that $‖x‖ ≤ C‖x‖_p$
65 #[inline] 78 #[inline]
66 fn from_norm(&self, p_norm : F, p : Exponent) -> F { 79 fn from_norm(&self, p_norm : F, p : Exponent) -> F {
67 p_norm * self.norm_factor(p) 80 p_norm * self.norm_factor(p)
68 } 81 }
69 } 82 }
70 83
71 /// Trait for distances with respect to a norm. 84 /// Trait for distances with respect to a norm.
72 pub trait Dist<F,Exponent> : Norm<F, Exponent> { 85 pub trait Dist<F : Num, Exponent : NormExponent> : Norm<F, Exponent> {
73 /// Calculate the distance 86 /// Calculate the distance
74 fn dist(&self, other : &Self, _p : Exponent) -> F; 87 fn dist(&self, other : &Self, _p : Exponent) -> F;
75 } 88 }
76 89
77 /// Trait for Euclidean projections to the `Exponent`-[`Norm`]-ball. 90 /// Trait for Euclidean projections to the `Exponent`-[`Norm`]-ball.
82 /// # use alg_tools::loc::Loc; 95 /// # use alg_tools::loc::Loc;
83 /// let x = Loc([1.0, 2.0, 3.0]); 96 /// let x = Loc([1.0, 2.0, 3.0]);
84 /// 97 ///
85 /// println!("{:?}, {:?}", x.proj_ball(1.0, L2), x.proj_ball(0.5, Linfinity)); 98 /// println!("{:?}, {:?}", x.proj_ball(1.0, L2), x.proj_ball(0.5, Linfinity));
86 /// ``` 99 /// ```
87 pub trait Projection<F, Exponent> : Norm<F, Exponent> + Euclidean<F> where F : Float { 100 pub trait Projection<F : Num, Exponent : NormExponent> : Norm<F, Exponent> + Euclidean<F>
101 where F : Float {
88 /// Projection of `self` to the `q`-norm-ball of radius ρ. 102 /// Projection of `self` to the `q`-norm-ball of radius ρ.
89 fn proj_ball(mut self, ρ : F, q : Exponent) -> Self { 103 fn proj_ball(mut self, ρ : F, q : Exponent) -> Self {
90 self.proj_ball_mut(ρ, q); 104 self.proj_ball_mut(ρ, q);
91 self 105 self
92 } 106 }

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