Mercurial > repos > pointsource_algs / file comparison
comparison: src/kernels/hat.rs
src/kernels/hat.rs
- changeset 0
- eb3c7813b67a
- child 35
- b087e3eab191
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| -1:000000000000 | 0:eb3c7813b67a |
|---|---|
| 1 //! Implementation of the hat function | |
| 2 | |
| 3 use numeric_literals::replace_float_literals; | |
| 4 use serde::Serialize; | |
| 5 use alg_tools::types::*; | |
| 6 use alg_tools::norms::*; | |
| 7 use alg_tools::loc::Loc; | |
| 8 use alg_tools::sets::Cube; | |
| 9 use alg_tools::bisection_tree::{ | |
| 10 Support, | |
| 11 Constant, | |
| 12 Bounds, | |
| 13 LocalAnalysis, | |
| 14 GlobalAnalysis, | |
| 15 Bounded, | |
| 16 }; | |
| 17 use alg_tools::mapping::Apply; | |
| 18 use alg_tools::maputil::{array_init}; | |
| 19 | |
| 20 /// Representation of the hat function $f(x)=1-\\|x\\|\_1/ε$ of `width` $ε$ on $ℝ^N$. | |
| 21 #[derive(Copy,Clone,Serialize,Debug,Eq,PartialEq)] | |
| 22 pub struct Hat<C : Constant, const N : usize> { | |
| 23 /// The parameter $ε>0$. | |
| 24 pub width : C, | |
| 25 } | |
| 26 | |
| 27 #[replace_float_literals(C::Type::cast_from(literal))] | |
| 28 impl<'a, C : Constant, const N : usize> Apply<&'a Loc<C::Type, N>> for Hat<C, N> { | |
| 29 type Output = C::Type; | |
| 30 #[inline] | |
| 31 fn apply(&self, x : &'a Loc<C::Type, N>) -> Self::Output { | |
| 32 let ε = self.width.value(); | |
| 33 0.0.max(1.0-x.norm(L1)/ε) | |
| 34 } | |
| 35 } | |
| 36 | |
| 37 #[replace_float_literals(C::Type::cast_from(literal))] | |
| 38 impl<C : Constant, const N : usize> Apply<Loc<C::Type, N>> for Hat<C, N> { | |
| 39 type Output = C::Type; | |
| 40 #[inline] | |
| 41 fn apply(&self, x : Loc<C::Type, N>) -> Self::Output { | |
| 42 self.apply(&x) | |
| 43 } | |
| 44 } | |
| 45 | |
| 46 | |
| 47 #[replace_float_literals(C::Type::cast_from(literal))] | |
| 48 impl<'a, C : Constant, const N : usize> Support<C::Type, N> for Hat<C, N> { | |
| 49 #[inline] | |
| 50 fn support_hint(&self) -> Cube<C::Type,N> { | |
| 51 let ε = self.width.value(); | |
| 52 array_init(|| [-ε, ε]).into() | |
| 53 } | |
| 54 | |
| 55 #[inline] | |
| 56 fn in_support(&self, x : &Loc<C::Type,N>) -> bool { | |
| 57 x.norm(L1) < self.width.value() | |
| 58 } | |
| 59 | |
| 60 /*fn fully_in_support(&self, _cube : &Cube<C::Type,N>) -> bool { | |
| 61 todo!("Not implemented, but not used at the moment") | |
| 62 }*/ | |
| 63 | |
| 64 #[inline] | |
| 65 fn bisection_hint(&self, cube : &Cube<C::Type,N>) -> [Option<C::Type>; N] { | |
| 66 let ε = self.width.value(); | |
| 67 cube.map(|a, b| { | |
| 68 if a < 1.0 { | |
| 69 if 1.0 < b { | |
| 70 Some(1.0) | |
| 71 } else { | |
| 72 if a < -ε { | |
| 73 if b > -ε { Some(-ε) } else { None } | |
| 74 } else { | |
| 75 None | |
| 76 } | |
| 77 } | |
| 78 } else { | |
| 79 if b > ε { Some(ε) } else { None } | |
| 80 } | |
| 81 }); | |
| 82 todo!("also diagonals") | |
| 83 } | |
| 84 } | |
| 85 | |
| 86 | |
| 87 #[replace_float_literals(C::Type::cast_from(literal))] | |
| 88 impl<'a, C : Constant, const N : usize> | |
| 89 GlobalAnalysis<C::Type, Bounds<C::Type>> | |
| 90 for Hat<C, N> { | |
| 91 #[inline] | |
| 92 fn global_analysis(&self) -> Bounds<C::Type> { | |
| 93 Bounds(0.0, 1.0) | |
| 94 } | |
| 95 } | |
| 96 | |
| 97 impl<'a, C : Constant, const N : usize> | |
| 98 LocalAnalysis<C::Type, Bounds<C::Type>, N> | |
| 99 for Hat<C, N> { | |
| 100 #[inline] | |
| 101 fn local_analysis(&self, cube : &Cube<C::Type, N>) -> Bounds<C::Type> { | |
| 102 // The function is maximised/minimised where the 1-norm is minimised/maximised. | |
| 103 let lower = self.apply(cube.maxnorm_point()); | |
| 104 let upper = self.apply(cube.minnorm_point()); | |
| 105 Bounds(lower, upper) | |
| 106 } | |
| 107 } | |
| 108 | |
| 109 #[replace_float_literals(C::Type::cast_from(literal))] | |
| 110 impl<'a, C : Constant, const N : usize> | |
| 111 Norm<C::Type, Linfinity> | |
| 112 for Hat<C, N> { | |
| 113 #[inline] | |
| 114 fn norm(&self, _ : Linfinity) -> C::Type { | |
| 115 self.bounds().upper() | |
| 116 } | |
| 117 } | |
| 118 |
