src/bisection_tree/support.rs

Wed, 26 Oct 2022 22:16:57 +0300

author
Tuomo Valkonen <tuomov@iki.fi>
date
Wed, 26 Oct 2022 22:16:57 +0300
changeset 7
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Added tag unthreaded for changeset d80b87b8acd0

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2 /*!
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3 Traits for representing the support of a [`Mapping`], and analysing the mapping on a [`Cube`].
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4 */
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5 use serde::Serialize;
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6 use std::ops::{MulAssign,DivAssign,Neg};
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7 use crate::types::{Float, Num};
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8 use crate::maputil::map2;
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9 use crate::mapping::Mapping;
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10 use crate::sets::Cube;
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11 use crate::loc::Loc;
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12 use super::aggregator::Bounds;
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13 use crate::norms::{Norm, L1, L2, Linfinity};
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14
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15 /// A trait for encoding constant [`Float`] values
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16 pub trait Constant : Copy + 'static + std::fmt::Debug + Into<Self::Type> {
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17 /// The type of the value
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18 type Type : Float;
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19 /// Returns the value of the constant
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20 fn value(&self) -> Self::Type;
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21 }
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22
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23 impl<F : Float> Constant for F {
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24 type Type = F;
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25 #[inline]
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26 fn value(&self) -> F { *self }
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27 }
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29
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30 /// A trait for working with the supports of [`Mapping`]s.
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31 ///
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32 /// Mapping is not a super-trait to allow more general use.
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33 pub trait Support<F : Num, const N : usize> : Sized {
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34 /// Return a cube containing the support of the function represented by `self`.
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35 ///
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36 /// The hint may be larger than the actual support, but must contain it.
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37 fn support_hint(&self) -> Cube<F,N>;
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38
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39 /// Indicate whether `x` is in the support of the function represented by `self`.
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40 fn in_support(&self, x : &Loc<F,N>) -> bool;
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41
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42 // Indicate whether `cube` is fully in the support of the function represented by `self`.
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43 //fn fully_in_support(&self, cube : &Cube<F,N>) -> bool;
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44
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45 /// Return an optional hint for bisecting the support.
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46 ///
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47 /// The output along each axis a possible coordinate at which to bisect `cube`.
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48 ///
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49 /// This is useful for nonsmooth functions to make finite element models as used by
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50 /// [`BTFN`][super::btfn::BTFN] minimisation/maximisation compatible with points of
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51 /// non-differentiability.
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52 ///
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53 /// The default implementation returns `[None; N]`.
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54 #[inline]
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55 #[allow(unused_variables)]
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56 fn bisection_hint(&self, cube : &Cube<F, N>) -> [Option<F>; N] {
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57 [None; N]
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58 }
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59
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60 /// Translate `self` by `x`.
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61 #[inline]
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62 fn shift(self, x : Loc<F, N>) -> Shift<Self, F, N> {
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63 Shift { shift : x, base_fn : self }
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64 }
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65
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66 /// Multiply `self` by the scalar `a`.
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67 #[inline]
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68 fn weigh<C : Constant<Type=F>>(self, a : C) -> Weighted<Self, C> {
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69 Weighted { weight : a, base_fn : self }
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70 }
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71 }
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72
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73 /// Trait for globally analysing a property `A` of a [`Mapping`].
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74 ///
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75 /// Typically `A` is an [`Aggregator`][super::aggregator::Aggregator] such as
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76 /// [`Bounds`][super::aggregator::Bounds].
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77 pub trait GlobalAnalysis<F : Num, A> {
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78 /// Perform global analysis of the property `A` of `Self`.
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79 ///
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80 /// As an example, in the case of `A` being [`Bounds`][super::aggregator::Bounds],
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81 /// this function will return global upper and lower bounds for the mapping
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82 /// represented by `self`.
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83 fn global_analysis(&self) -> A;
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84 }
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85
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86 // default impl<F, A, N, L> GlobalAnalysis<F, A, N> for L
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87 // where L : LocalAnalysis<F, A, N> {
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88 // #[inline]
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89 // fn global_analysis(&self) -> Bounds<F> {
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90 // self.local_analysis(&self.support_hint())
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91 // }
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92 // }
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93
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94 /// Trait for locally analysing a property `A` of a [`Mapping`] (implementing [`Support`])
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95 /// within a [`Cube`].
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96 ///
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97 /// Typically `A` is an [`Aggregator`][super::aggregator::Aggregator] such as
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98 /// [`Bounds`][super::aggregator::Bounds].
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99 pub trait LocalAnalysis<F : Num, A, const N : usize> : GlobalAnalysis<F, A> + Support<F, N> {
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100 /// Perform local analysis of the property `A` of `Self`.
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101 ///
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102 /// As an example, in the case of `A` being [`Bounds`][super::aggregator::Bounds],
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103 /// this function will return upper and lower bounds within `cube` for the mapping
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104 /// represented by `self`.
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105 fn local_analysis(&self, cube : &Cube<F, N>) -> A;
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106 }
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107
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108 /// Trait for determining the upper and lower bounds of an float-valued [`Mapping`].
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109 ///
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110 /// This is a blanket-implemented alias for [`GlobalAnalysis`]`<F, Bounds<F>>`
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111 /// [`Mapping`] is not a supertrait to allow flexibility in the implementation of either
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112 /// reference or non-reference arguments.
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113 pub trait Bounded<F : Float> : GlobalAnalysis<F, Bounds<F>> {
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114 /// Return lower and upper bounds for the values of of `self`.
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115 #[inline]
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116 fn bounds(&self) -> Bounds<F> {
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117 self.global_analysis()
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118 }
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119 }
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120
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121 impl<F : Float, T : GlobalAnalysis<F, Bounds<F>>> Bounded<F> for T { }
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122
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123 /// Shift of [`Support`] and [`Mapping`]; output of [`Support::shift`].
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124 #[derive(Copy,Clone,Debug,Serialize)] // Serialize! but not implemented by Loc.
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125 pub struct Shift<T, F, const N : usize> {
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126 shift : Loc<F, N>,
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127 base_fn : T,
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128 }
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129
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130 impl<'a, T, V, F : Float, const N : usize> Mapping<&'a Loc<F, N>> for Shift<T,F,N>
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131 where T : for<'b> Mapping<&'b Loc<F,N>,Codomain=V> {
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132 type Codomain = V;
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133 #[inline]
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134 fn value(&self, x : &'a Loc<F, N>) -> Self::Codomain {
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135 self.base_fn.value(&(x - &self.shift))
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136 }
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137 }
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138
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139 impl<'a, T, V, F : Float, const N : usize> Mapping<Loc<F, N>> for Shift<T,F,N>
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140 where T : for<'b> Mapping<Loc<F,N>,Codomain=V> {
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141 type Codomain = V;
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142 #[inline]
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143 fn value(&self, x : Loc<F, N>) -> Self::Codomain {
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144 self.base_fn.value(x - &self.shift)
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145 }
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146 }
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147
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148 impl<'a, T, F : Float, const N : usize> Support<F,N> for Shift<T,F,N>
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149 where T : Support<F, N> {
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150 #[inline]
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151 fn support_hint(&self) -> Cube<F,N> {
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152 self.base_fn.support_hint().shift(&self.shift)
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153 }
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154
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155 #[inline]
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156 fn in_support(&self, x : &Loc<F,N>) -> bool {
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157 self.base_fn.in_support(&(x - &self.shift))
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158 }
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159
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160 // fn fully_in_support(&self, _cube : &Cube<F,N>) -> bool {
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161 // //self.base_fn.fully_in_support(cube.shift(&vectorneg(self.shift)))
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162 // todo!("Not implemented, but not used at the moment")
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163 // }
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164
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165 #[inline]
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166 fn bisection_hint(&self, cube : &Cube<F,N>) -> [Option<F>; N] {
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167 let base_hint = self.base_fn.bisection_hint(cube);
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168 map2(base_hint, &self.shift, |h, s| h.map(|z| z + *s))
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169 }
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170
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171 }
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172
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173 impl<'a, T, F : Float, const N : usize> GlobalAnalysis<F, Bounds<F>> for Shift<T,F,N>
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174 where T : LocalAnalysis<F, Bounds<F>, N> {
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175 #[inline]
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176 fn global_analysis(&self) -> Bounds<F> {
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177 self.base_fn.global_analysis()
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178 }
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179 }
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180
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181 impl<'a, T, F : Float, const N : usize> LocalAnalysis<F, Bounds<F>, N> for Shift<T,F,N>
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182 where T : LocalAnalysis<F, Bounds<F>, N> {
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183 #[inline]
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184 fn local_analysis(&self, cube : &Cube<F, N>) -> Bounds<F> {
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185 self.base_fn.local_analysis(&cube.shift(&(-self.shift)))
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186 }
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187 }
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188
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189 macro_rules! impl_shift_norm {
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190 ($($norm:ident)*) => { $(
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191 impl<'a, T, F : Float, const N : usize> Norm<F, $norm> for Shift<T,F,N>
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192 where T : Norm<F, $norm> {
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193 #[inline]
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194 fn norm(&self, n : $norm) -> F {
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195 self.base_fn.norm(n)
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196 }
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197 }
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198 )* }
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199 }
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200
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201 impl_shift_norm!(L1 L2 Linfinity);
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202
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203 /// Weighting of a [`Support`] and [`Mapping`] by scalar multiplication;
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204 /// output of [`Support::weigh`].
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205 #[derive(Copy,Clone,Debug,Serialize)]
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206 pub struct Weighted<T, C : Constant> {
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207 /// The weight
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208 pub weight : C,
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209 /// The base [`Support`] or [`Mapping`] being weighted.
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210 pub base_fn : T,
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211 }
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212
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213 impl<'a, T, V, F : Float, C, const N : usize> Mapping<&'a Loc<F, N>> for Weighted<T, C>
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214 where T : for<'b> Mapping<&'b Loc<F,N>,Codomain=V>,
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215 V : std::ops::Mul<F,Output=V>,
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216 C : Constant<Type=F> {
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217 type Codomain = V;
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218 #[inline]
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219 fn value(&self, x : &'a Loc<F, N>) -> Self::Codomain {
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220 self.base_fn.value(x) * self.weight.value()
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221 }
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222 }
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223
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224 impl<'a, T, V, F : Float, C, const N : usize> Mapping<Loc<F, N>> for Weighted<T, C>
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225 where T : for<'b> Mapping<Loc<F,N>,Codomain=V>,
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226 V : std::ops::Mul<F,Output=V>,
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227 C : Constant<Type=F> {
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228 type Codomain = V;
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229 #[inline]
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230 fn value(&self, x : Loc<F, N>) -> Self::Codomain {
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231 self.base_fn.value(x) * self.weight.value()
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232 }
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233 }
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234
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235 impl<'a, T, F : Float, C, const N : usize> Support<F,N> for Weighted<T, C>
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236 where T : Support<F, N>,
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237 C : Constant<Type=F> {
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238
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239 #[inline]
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240 fn support_hint(&self) -> Cube<F,N> {
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241 self.base_fn.support_hint()
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242 }
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243
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244 #[inline]
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245 fn in_support(&self, x : &Loc<F,N>) -> bool {
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246 self.base_fn.in_support(x)
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247 }
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248
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249 // fn fully_in_support(&self, cube : &Cube<F,N>) -> bool {
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250 // self.base_fn.fully_in_support(cube)
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251 // }
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252
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253 #[inline]
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254 fn bisection_hint(&self, cube : &Cube<F,N>) -> [Option<F>; N] {
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255 self.base_fn.bisection_hint(cube)
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256 }
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257 }
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258
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259 impl<'a, T, F : Float, C> GlobalAnalysis<F, Bounds<F>> for Weighted<T, C>
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260 where T : GlobalAnalysis<F, Bounds<F>>,
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261 C : Constant<Type=F> {
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262 #[inline]
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263 fn global_analysis(&self) -> Bounds<F> {
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264 let Bounds(lower, upper) = self.base_fn.global_analysis();
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265 match self.weight.value() {
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266 w if w < F::ZERO => Bounds(w * upper, w * lower),
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267 w => Bounds(w * lower, w * upper),
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268 }
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269 }
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270 }
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271
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272 impl<'a, T, F : Float, C, const N : usize> LocalAnalysis<F, Bounds<F>, N> for Weighted<T, C>
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273 where T : LocalAnalysis<F, Bounds<F>, N>,
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274 C : Constant<Type=F> {
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275 #[inline]
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276 fn local_analysis(&self, cube : &Cube<F, N>) -> Bounds<F> {
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277 let Bounds(lower, upper) = self.base_fn.local_analysis(cube);
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278 match self.weight.value() {
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279 w if w < F::ZERO => Bounds(w * upper, w * lower),
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280 w => Bounds(w * lower, w * upper),
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281 }
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282 }
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283 }
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284
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285 macro_rules! make_weighted_scalarop_rhs {
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286 ($trait:ident, $fn:ident, $trait_assign:ident, $fn_assign:ident) => {
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287 impl<F : Float, T> std::ops::$trait_assign<F> for Weighted<T, F> {
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288 #[inline]
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289 fn $fn_assign(&mut self, t : F) {
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290 self.weight.$fn_assign(t);
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291 }
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292 }
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293
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294 impl<'a, F : Float, T> std::ops::$trait<F> for Weighted<T, F> {
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295 type Output = Self;
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296 #[inline]
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297 fn $fn(mut self, t : F) -> Self {
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298 self.weight.$fn_assign(t);
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299 self
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300 }
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301 }
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302
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303 impl<'a, F : Float, T> std::ops::$trait<F> for &'a Weighted<T, F>
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304 where T : Clone {
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305 type Output = Weighted<T, F>;
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306 #[inline]
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307 fn $fn(self, t : F) -> Self::Output {
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308 Weighted { weight : self.weight.$fn(t), base_fn : self.base_fn.clone() }
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309 }
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310 }
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311 }
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312 }
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313
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314 make_weighted_scalarop_rhs!(Mul, mul, MulAssign, mul_assign);
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315 make_weighted_scalarop_rhs!(Div, div, DivAssign, div_assign);
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316
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317 macro_rules! impl_weighted_norm {
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318 ($($norm:ident)*) => { $(
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319 impl<'a, T, F : Float> Norm<F, $norm> for Weighted<T,F>
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320 where T : Norm<F, $norm> {
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321 #[inline]
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322 fn norm(&self, n : $norm) -> F {
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323 self.base_fn.norm(n) * self.weight.abs()
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324 }
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325 }
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326 )* }
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327 }
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328
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329 impl_weighted_norm!(L1 L2 Linfinity);
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330
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331
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332 /// Normalisation of [`Support`] and [`Mapping`] to L¹ norm 1.
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333 ///
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334 /// Currently only scalar-valued functions are supported.
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335 #[derive(Copy, Clone, Debug, Serialize, PartialEq)]
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336 pub struct Normalised<T>(
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337 /// The base [`Support`] or [`Mapping`].
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338 pub T
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339 );
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340
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341 impl<'a, T, F : Float, const N : usize> Mapping<&'a Loc<F, N>> for Normalised<T>
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342 where T : Norm<F, L1> + for<'b> Mapping<&'b Loc<F,N>, Codomain=F> {
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343 type Codomain = F;
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344 #[inline]
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345 fn value(&self, x : &'a Loc<F, N>) -> Self::Codomain {
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346 let w = self.0.norm(L1);
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347 if w == F::ZERO { F::ZERO } else { self.0.value(x) / w }
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348 }
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349 }
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350
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351 impl<'a, T, F : Float, const N : usize> Mapping<Loc<F, N>> for Normalised<T>
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352 where T : Norm<F, L1> + for<'b> Mapping<Loc<F,N>, Codomain=F> {
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353 type Codomain = F;
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354 #[inline]
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355 fn value(&self, x : Loc<F, N>) -> Self::Codomain {
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356 let w = self.0.norm(L1);
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357 if w == F::ZERO { F::ZERO } else { self.0.value(x) / w }
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358 }
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359 }
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360
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361 impl<'a, T, F : Float, const N : usize> Support<F,N> for Normalised<T>
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362 where T : Norm<F, L1> + Support<F, N> {
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363
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364 #[inline]
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365 fn support_hint(&self) -> Cube<F,N> {
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366 self.0.support_hint()
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367 }
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368
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369 #[inline]
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370 fn in_support(&self, x : &Loc<F,N>) -> bool {
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371 self.0.in_support(x)
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372 }
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373
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374 // fn fully_in_support(&self, cube : &Cube<F,N>) -> bool {
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375 // self.0.fully_in_support(cube)
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376 // }
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377
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378 #[inline]
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379 fn bisection_hint(&self, cube : &Cube<F,N>) -> [Option<F>; N] {
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380 self.0.bisection_hint(cube)
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381 }
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382 }
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383
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384 impl<'a, T, F : Float> GlobalAnalysis<F, Bounds<F>> for Normalised<T>
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385 where T : Norm<F, L1> + GlobalAnalysis<F, Bounds<F>> {
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386 #[inline]
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387 fn global_analysis(&self) -> Bounds<F> {
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388 let Bounds(lower, upper) = self.0.global_analysis();
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389 let w = self.0.norm(L1);
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390 debug_assert!(w >= F::ZERO);
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391 Bounds(w * lower, w * upper)
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392 }
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393 }
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394
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395 impl<'a, T, F : Float, const N : usize> LocalAnalysis<F, Bounds<F>, N> for Normalised<T>
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396 where T : Norm<F, L1> + LocalAnalysis<F, Bounds<F>, N> {
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397 #[inline]
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398 fn local_analysis(&self, cube : &Cube<F, N>) -> Bounds<F> {
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399 let Bounds(lower, upper) = self.0.local_analysis(cube);
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400 let w = self.0.norm(L1);
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401 debug_assert!(w >= F::ZERO);
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402 Bounds(w * lower, w * upper)
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403 }
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404 }
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405
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406 impl<'a, T, F : Float> Norm<F, L1> for Normalised<T>
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407 where T : Norm<F, L1> {
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408 #[inline]
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409 fn norm(&self, _ : L1) -> F {
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410 let w = self.0.norm(L1);
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411 if w == F::ZERO { F::ZERO } else { F::ONE }
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412 }
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413 }
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414
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415 macro_rules! impl_normalised_norm {
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416 ($($norm:ident)*) => { $(
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417 impl<'a, T, F : Float> Norm<F, $norm> for Normalised<T>
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418 where T : Norm<F, $norm> + Norm<F, L1> {
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419 #[inline]
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420 fn norm(&self, n : $norm) -> F {
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421 let w = self.0.norm(L1);
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422 if w == F::ZERO { F::ZERO } else { self.0.norm(n) / w }
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423 }
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424 }
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425 )* }
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426 }
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427
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428 impl_normalised_norm!(L2 Linfinity);
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429
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430 /*
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431 impl<F : Num, S : Support<F, N>, const N : usize> LocalAnalysis<F, NullAggregator, N> for S {
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432 fn local_analysis(&self, _cube : &Cube<F, N>) -> NullAggregator { NullAggregator }
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433 }
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434
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435 impl<F : Float, S : Bounded<F>, const N : usize> LocalAnalysis<F, Bounds<F>, N> for S {
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436 #[inline]
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437 fn local_analysis(&self, cube : &Cube<F, N>) -> Bounds<F> {
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438 self.bounds(cube)
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439 }
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440 }*/
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441
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442 /// Generator of [`Support`]-implementing component functions based on low storage requirement
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443 /// [ids][`Self::Id`].
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444 pub trait SupportGenerator<F : Float, const N : usize>
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445 : MulAssign<F> + DivAssign<F> + Neg<Output=Self> {
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446 /// The identification type
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447 type Id : 'static + Copy;
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448 /// The type of the [`Support`] (often also a [`Mapping`]).
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449 type SupportType : 'static + Support<F, N>;
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450 /// An iterator over all the [`Support`]s of the generator.
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451 type AllDataIter<'a> : Iterator<Item=(Self::Id, Self::SupportType)> where Self : 'a;
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452
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453 /// Returns the component identified by `id`.
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454 ///
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455 /// Panics if `id` is an invalid identifier.
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456 fn support_for(&self, id : Self::Id) -> Self::SupportType;
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457
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458 /// Returns the number of different components in this generator.
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459 fn support_count(&self) -> usize;
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460
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461 /// Returns an iterator over all pairs of `(id, support)`.
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462 fn all_data(&self) -> Self::AllDataIter<'_>;
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463 }
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464

mercurial