src/mapping.rs

Sat, 10 Dec 2022 16:23:58 +0200

author
Tuomo Valkonen <tuomov@iki.fi>
date
Sat, 10 Dec 2022 16:23:58 +0200
changeset 21
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parent 13
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1 /*!
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2 Traits for mathematical functions.
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3 */
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4
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5 use std::marker::PhantomData;
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6 use crate::types::{Float};
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7 use serde::Serialize;
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8 use crate::loc::Loc;
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9
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10 /// Trait for application of `Self` as a mathematical function or operator on `X`.
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11 pub trait Apply<X> {
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12 type Output;
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13
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14 /// Compute the value of `self` at `x`.
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15 fn apply(&self, x : X) -> Self::Output;
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16 }
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18 /// This blanket implementation is a workaround helper to Rust trait system limitations.
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19 ///
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20 /// It is introduced because the trait system does not allow blanket implementations of both
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21 /// [`Apply<X>`] and [`Apply<&'a X>`]. With this, the latter is implemented automatically for
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22 /// the reference, which can be sufficient to apply the operation in another blanket implementation.
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23 impl<'a, T, X> Apply<X> for &'a T where T : Apply<X> {
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24 type Output = <T as Apply<X>>::Output;
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25
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26 #[inline]
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27 fn apply(&self, x : X) -> Self::Output {
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28 (*self).apply(x)
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29 }
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30 }
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31
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32 /// A mapping from `Domain` to `Codomain`.
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33 ///
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34 /// This is automatically implemented when the relevant [`Apply`] are implemented.
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35 pub trait Mapping<Domain> : Apply<Domain, Output=Self::Codomain>
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36 + for<'a> Apply<&'a Domain, Output=Self::Codomain> {
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37 type Codomain;
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38 }
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40 impl<Domain, Codomain, T> Mapping<Domain> for T
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41 where T : Apply<Domain, Output=Codomain> + for<'a> Apply<&'a Domain, Output=Codomain> {
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42 type Codomain = Codomain;
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43 }
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44
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45
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46 /// A helper trait alias for referring to [`Mapping`]s from [`Loc<F, N>`] to `F` a [`Float`].
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47 pub trait RealMapping<F : Float, const N : usize> : Mapping<Loc<F, N>, Codomain = F> {}
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48
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49 impl<F : Float, T, const N : usize> RealMapping<F, N> for T
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50 where T : Mapping<Loc<F, N>, Codomain = F> {}
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51
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52
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53 /// Trait for calculation the differential of `Self` as a mathematical function on `X`.
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54 pub trait Differentiate<X> {
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55 type Output;
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56
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57 /// Compute the differential of `self` at `x`.
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58 fn differential(&self, x : X) -> Self::Output;
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59 }
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61
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62 /// A differentiable mapping from `Domain` to [`Mapping::Codomain`], with differentials
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63 /// `Differential`.
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64 ///
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65 /// This is automatically implemented when the relevant [`Differentiate`] are implemented.
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66 pub trait DifferentiableMapping<Domain>
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67 : Mapping<Domain>
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68 + Differentiate<Domain, Output=Self::Differential>
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69 + for<'a> Differentiate<&'a Domain, Output=Self::Differential>{
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70 type Differential;
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71 }
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74 impl<Domain, Differential, T> DifferentiableMapping<Domain> for T
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75 where T : Mapping<Domain>
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76 + Differentiate<Domain, Output=Differential>
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77 + for<'a> Differentiate<&'a Domain, Output=Differential> {
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78 type Differential = Differential;
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79 }
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80
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81 /// A sum of [`Mapping`]s.
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82 #[derive(Serialize, Debug, Clone)]
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83 pub struct Sum<Domain, M : Mapping<Domain>> {
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84 components : Vec<M>,
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85 _domain : PhantomData<Domain>,
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86 }
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87
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88 impl<Domain, M : Mapping<Domain>> Sum<Domain, M> {
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89 /// Construct from an iterator.
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90 pub fn new<I : Iterator<Item = M>>(iter : I) -> Self {
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91 Sum { components : iter.collect(), _domain : PhantomData }
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92 }
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93 }
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94
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95
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96 impl<Domain : Copy, M> Apply<Domain> for Sum<Domain, M>
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97 where M : Mapping<Domain>,
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98 M::Codomain : std::iter::Sum {
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99 type Output = M::Codomain;
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100
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101 fn apply(&self, x : Domain) -> Self::Output {
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102 self.components.iter().map(|c| c.apply(x)).sum()
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103 }
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104 }
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105
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106 impl<Domain, M> Differentiate<Domain> for Sum<Domain, M>
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107 where M : DifferentiableMapping<Domain>,
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108 M :: Codomain : std::iter::Sum,
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109 M :: Differential : std::iter::Sum,
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110 Domain : Copy {
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111
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112 type Output = M::Differential;
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113
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114 fn differential(&self, x : Domain) -> Self::Output {
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115 self.components.iter().map(|c| c.differential(x)).sum()
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116 }
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117 }

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