src/bisection_tree/aggregator.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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1 /*!
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2 Aggregation / summarisation of information in branches of bisection trees.
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3 */
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4
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5 use crate::types::*;
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6 use crate::sets::Set;
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7
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8 /// Trait for aggregating information about a branch of a [bisection tree][super::BT].
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9 ///
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10 /// Currently [`Bounds`] is the only provided aggregator.
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11 /// It keeps track of upper and lower bounds of a function representeed by the `BT` by
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12 /// summing [`Bounds`] produced by [`LocalAnalysis`][super::support::LocalAnalysis] of the
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13 /// [`Support`][super::support::Support]s of the data stored in the tree.
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14 /// For the `Bounds` aggregator:
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15 /// * [`Self::aggregate`] sums input bounds to the current bound. This provides a conservative
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16 /// estimate of the upper and lower bounds of a sum of functions.
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17 /// * [`Self::summarise`] takes the maximum of the input bounds. This calculates the bounds
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18 /// of a function on a greater domain from bounds on subdomains
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19 /// (in practise [`Cube`][crate::sets::Cube]s).
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20 ///
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21 pub trait Aggregator : Clone + std::fmt::Debug {
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22 /// Aggregate a new data to current state.
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23 fn aggregate<I>(&mut self, aggregates : I)
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24 where I : Iterator<Item=Self>;
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25
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26 /// Summarise several other aggregators, resetting current state.
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27 fn summarise<'a, I>(&'a mut self, aggregates : I)
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28 where I : Iterator<Item=&'a Self>;
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29
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30 /// Create a new “empty” aggregate data.
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31 fn new() -> Self;
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32 }
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33
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34 /// An [`Aggregator`] that doesn't aggregate anything.
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35 #[derive(Clone,Debug)]
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36 pub struct NullAggregator;
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37
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38 impl Aggregator for NullAggregator {
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39 // TODO: these should probabably also take a Cube as argument to
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40 // allow integrating etc.
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41 fn aggregate<I>(&mut self, _aggregates : I)
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42 where I : Iterator<Item=Self> {}
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43
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44 fn summarise<'a, I>(&'a mut self, _aggregates : I)
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45 where I : Iterator<Item=&'a Self> {}
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46
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47 fn new() -> Self { NullAggregator }
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48 }
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49
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50 /// Upper and lower bounds on an `F`-valued function.
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51 #[derive(Copy,Clone,Debug)]
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52 pub struct Bounds<F>(
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53 /// Lower bound
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54 pub F,
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55 /// Upper bound
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56 pub F
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57 );
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58
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59 impl<F : Copy> Bounds<F> {
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60 /// Returns the lower bound
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61 #[inline]
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62 pub fn lower(&self) -> F { self.0 }
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63
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64 /// Returns the upper bound
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65 #[inline]
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66 pub fn upper(&self) -> F { self.1 }
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67 }
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68
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69 impl<F : Float> Bounds<F> {
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70 /// Returns a uniform bound.
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71 ///
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72 /// This is maximum over the absolute values of the upper and lower bound.
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73 #[inline]
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74 pub fn uniform(&self) -> F {
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75 let &Bounds(lower, upper) = self;
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76 lower.abs().max(upper.abs())
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77 }
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78 }
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79
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80 impl<'a, F : Float> std::ops::Add<Self> for Bounds<F> {
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81 type Output = Self;
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82 #[inline]
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83 fn add(self, Bounds(l2, u2) : Self) -> Self::Output {
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84 let Bounds(l1, u1) = self;
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85 debug_assert!(l1 <= u1 && l2 <= u2);
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86 Bounds(l1 + l2, u1 + u2)
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87 }
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88 }
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89
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90 impl<'a, F : Float> std::ops::Mul<Self> for Bounds<F> {
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91 type Output = Self;
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92 #[inline]
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93 fn mul(self, Bounds(l2, u2) : Self) -> Self::Output {
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94 let Bounds(l1, u1) = self;
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95 debug_assert!(l1 <= u1 && l2 <= u2);
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96 let a = l1 * l2;
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97 let b = u1 * u2;
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98 // The order may flip when negative numbers are involved, so need min/max
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99 Bounds(a.min(b), a.max(b))
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100 }
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101 }
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102
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103 impl<F : Float> std::iter::Product for Bounds<F> {
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104 #[inline]
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105 fn product<I>(mut iter: I) -> Self
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106 where I: Iterator<Item = Self> {
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107 match iter.next() {
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108 None => Bounds(F::ZERO, F::ZERO),
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109 Some(init) => iter.fold(init, |a, b| a*b)
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110 }
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111 }
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112 }
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113
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114 impl<F : Float> Set<F> for Bounds<F> {
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115 fn contains(&self, item : &F) -> bool {
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116 let &Bounds(l, u) = self;
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117 debug_assert!(l <= u);
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118 l <= *item && *item <= u
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119 }
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120 }
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121
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122 impl<F : Float> Bounds<F> {
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123 /// Calculate a common bound (glb, lub) for two bounds.
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124 #[inline]
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125 pub fn common(&self, &Bounds(l2, u2) : &Self) -> Self {
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126 let &Bounds(l1, u1) = self;
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127 debug_assert!(l1 <= u1 && l2 <= u2);
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128 Bounds(l1.min(l2), u1.max(u2))
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129 }
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130
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131 /// Indicates whether `Self` is a superset of the argument bound.
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132 #[inline]
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133 pub fn superset(&self, &Bounds(l2, u2) : &Self) -> bool {
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134 let &Bounds(l1, u1) = self;
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135 debug_assert!(l1 <= u1 && l2 <= u2);
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136 l1 <= l2 && u2 <= u1
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137 }
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138
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139 /// Returns the greatest bound contained by both argument bounds, if one exists.
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140 #[inline]
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141 pub fn glb(&self, &Bounds(l2, u2) : &Self) -> Option<Self> {
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142 let &Bounds(l1, u1) = self;
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143 debug_assert!(l1 <= u1 && l2 <= u2);
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144 let l = l1.max(l2);
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145 let u = u1.min(u2);
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146 if l < u {
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147 Some(Bounds(l, u))
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148 } else {
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149 None
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150 }
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151 }
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152 }
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153
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154 impl<F : Float> Aggregator for Bounds<F> {
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155 #[inline]
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156 fn aggregate<I>(&mut self, aggregates : I)
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157 where I : Iterator<Item=Self> {
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158 *self = aggregates.fold(*self, |a, b| a + b);
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159 }
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160
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161 #[inline]
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162 fn summarise<'a, I>(&'a mut self, mut aggregates : I)
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163 where I : Iterator<Item=&'a Self> {
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164 *self = match aggregates.next() {
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165 None => Bounds(F::ZERO, F::ZERO), // No parts in this cube; the function is zero
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166 Some(&bounds) => {
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167 aggregates.fold(bounds, |a, b| a.common(b))
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168 }
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169 }
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170 }
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171
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172 #[inline]
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173 fn new() -> Self {
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174 Bounds(F::ZERO, F::ZERO)
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175 }
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176 }

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