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comparison: src/prox_penalty/radon_squared.rs

src/prox_penalty/radon_squared.rs

changeset 52
f0e8704d3f0e
parent 39
6316d68b58af
equal deleted inserted replaced
31:6105b5cd8d89 52:f0e8704d3f0e
1 /*!
2 Solver for the point source localisation problem using a simplified forward-backward splitting method.
3
4 Instead of the $𝒟$-norm of `fb.rs`, this uses a standard Radon norm for the proximal map.
5 */
6
7 use numeric_literals::replace_float_literals;
8 use serde::{Serialize, Deserialize};
9 use nalgebra::DVector;
10
11 use alg_tools::iterate::{
12 AlgIteratorIteration,
13 AlgIterator
14 };
15 use alg_tools::norms::{L2, Norm};
16 use alg_tools::linops::Mapping;
17 use alg_tools::bisection_tree::{
18 BTFN,
19 Bounds,
20 BTSearch,
21 SupportGenerator,
22 LocalAnalysis,
23 };
24 use alg_tools::mapping::RealMapping;
25 use alg_tools::nalgebra_support::ToNalgebraRealField;
26
27 use crate::types::*;
28 use crate::measures::{
29 RNDM,
30 DeltaMeasure,
31 Radon,
32 };
33 use crate::measures::merging::SpikeMerging;
34 use crate::regularisation::RegTerm;
35 use crate::forward_model::{
36 ForwardModel,
37 AdjointProductBoundedBy
38 };
39 use super::{
40 FBGenericConfig,
41 ProxPenalty,
42 };
43
44 /// Radon-norm squared proximal penalty
45
46 #[derive(Copy,Clone,Serialize,Deserialize)]
47 pub struct RadonSquared;
48
49 #[replace_float_literals(F::cast_from(literal))]
50 impl<F, GA, BTA, S, Reg, const N : usize>
51 ProxPenalty<F, BTFN<F, GA, BTA, N>, Reg, N> for RadonSquared
52 where
53 F : Float + ToNalgebraRealField,
54 GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone,
55 BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>,
56 S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>,
57 Reg : RegTerm<F, N>,
58 RNDM<F, N> : SpikeMerging<F>,
59 {
60 type ReturnMapping = BTFN<F, GA, BTA, N>;
61
62 fn insert_and_reweigh<I>(
63 &self,
64 μ : &mut RNDM<F, N>,
65 τv : &mut BTFN<F, GA, BTA, N>,
66 μ_base : &RNDM<F, N>,
67 ν_delta: Option<&RNDM<F, N>>,
68 τ : F,
69 ε : F,
70 config : &FBGenericConfig<F>,
71 reg : &Reg,
72 _state : &AlgIteratorIteration<I>,
73 stats : &mut IterInfo<F, N>,
74 ) -> (Option<Self::ReturnMapping>, bool)
75 where
76 I : AlgIterator
77 {
78 let mut y = μ_base.masses_dvector();
79
80 assert!(μ_base.len() <= μ.len());
81
82 'i_and_w: for i in 0..=1 {
83 // Optimise weights
84 if μ.len() > 0 {
85 // Form finite-dimensional subproblem. The subproblem references to the original μ^k
86 // from the beginning of the iteration are all contained in the immutable c and g.
87 // TODO: observe negation of -τv after switch from minus_τv: finite-dimensional
88 // problems have not yet been updated to sign change.
89 let g̃ = DVector::from_iterator(μ.len(),
90 μ.iter_locations()
91 .map(|ζ| - F::to_nalgebra_mixed(τv.apply(ζ))));
92 let mut x = μ.masses_dvector();
93 y.extend(std::iter::repeat(0.0.to_nalgebra_mixed()).take(0.max(x.len()-y.len())));
94 assert_eq!(y.len(), x.len());
95 // Solve finite-dimensional subproblem.
96 // TODO: This assumes that ν_delta has no common locations with μ-μ_base, to
97 // ignore it.
98 stats.inner_iters += reg.solve_findim_l1squared(&y, &g̃, τ, &mut x, ε, config);
99
100 // Update masses of μ based on solution of finite-dimensional subproblem.
101 μ.set_masses_dvector(&x);
102 }
103
104 if i>0 {
105 // Simple debugging test to see if more inserts would be needed. Doesn't seem so.
106 //let n = μ.dist_matching(μ_base);
107 //println!("{:?}", reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n));
108 break 'i_and_w
109 }
110
111 // Calculate ‖μ - μ_base‖_ℳ
112 // TODO: This assumes that ν_delta has no common locations with μ-μ_base.
113 let n = μ.dist_matching(μ_base) + ν_delta.map_or(0.0, |ν| ν.norm(Radon));
114
115 // Find a spike to insert, if needed.
116 // This only check the overall tolerances, not tolerances on support of μ-μ_base or μ,
117 // which are supposed to have been guaranteed by the finite-dimensional weight optimisation.
118 match reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n) {
119 None => { break 'i_and_w },
120 Some((ξ, _v_ξ, _in_bounds)) => {
121 // Weight is found out by running the finite-dimensional optimisation algorithm
122 // above
123 *μ += DeltaMeasure { x : ξ, α : 0.0 };
124 stats.inserted += 1;
125 }
126 };
127 }
128
129 (None, true)
130 }
131
132 fn merge_spikes(
133 &self,
134 μ : &mut RNDM<F, N>,
135 τv : &mut BTFN<F, GA, BTA, N>,
136 μ_base : &RNDM<F, N>,
137 ν_delta: Option<&RNDM<F, N>>,
138 τ : F,
139 ε : F,
140 config : &FBGenericConfig<F>,
141 reg : &Reg,
142 fitness : Option<impl Fn(&RNDM<F, N>) -> F>,
143 ) -> usize
144 {
145 if config.fitness_merging {
146 if let Some(f) = fitness {
147 return μ.merge_spikes_fitness(config.merging, f, |&v| v)
148 .1
149 }
150 }
151 μ.merge_spikes(config.merging, |μ_candidate| {
152 // Important: μ_candidate's new points are afterwards,
153 // and do not conflict with μ_base.
154 // TODO: could simplify to requiring μ_base instead of μ_radon.
155 // but may complicate with sliding base's exgtra points that need to be
156 // after μ_candidate's extra points.
157 // TODO: doesn't seem to work, maybe need to merge μ_base as well?
158 // Although that doesn't seem to make sense.
159 let μ_radon = match ν_delta {
160 None => μ_candidate.sub_matching(μ_base),
161 Some(ν) => μ_candidate.sub_matching(μ_base) - ν,
162 };
163 reg.verify_merge_candidate_radonsq(τv, μ_candidate, τ, ε, &config, &μ_radon)
164 //let n = μ_candidate.dist_matching(μ_base);
165 //reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n).is_none()
166 })
167 }
168 }
169
170
171 impl<F, A, const N : usize> AdjointProductBoundedBy<RNDM<F, N>, RadonSquared>
172 for A
173 where
174 F : Float,
175 A : ForwardModel<RNDM<F, N>, F>
176 {
177 type FloatType = F;
178
179 fn adjoint_product_bound(&self, _ : &RadonSquared) -> Option<Self::FloatType> {
180 self.opnorm_bound(Radon, L2).powi(2).into()
181 }
182 }

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