--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/prox_penalty/radon_squared.rs Thu Jan 23 23:35:28 2025 +0100
@@ -0,0 +1,170 @@
+/*!
+Solver for the point source localisation problem using a simplified forward-backward splitting method.
+
+Instead of the $𝒟$-norm of `fb.rs`, this uses a standard Radon norm for the proximal map.
+*/
+
+use numeric_literals::replace_float_literals;
+use serde::{Serialize, Deserialize};
+use nalgebra::DVector;
+
+use alg_tools::iterate::{
+ AlgIteratorIteration,
+ AlgIterator
+};
+use alg_tools::norms::L2;
+use alg_tools::linops::Mapping;
+use alg_tools::bisection_tree::{
+ BTFN,
+ Bounds,
+ BTSearch,
+ SupportGenerator,
+ LocalAnalysis,
+};
+use alg_tools::mapping::RealMapping;
+use alg_tools::nalgebra_support::ToNalgebraRealField;
+
+use crate::types::*;
+use crate::measures::{
+ RNDM,
+ DeltaMeasure,
+ Radon,
+};
+use crate::measures::merging::SpikeMerging;
+use crate::regularisation::RegTerm;
+use crate::forward_model::{
+ ForwardModel,
+ AdjointProductBoundedBy
+};
+use super::{
+ FBGenericConfig,
+ ProxPenalty,
+};
+
+/// Radon-norm squared proximal penalty
+
+#[derive(Copy,Clone,Serialize,Deserialize)]
+pub struct RadonSquared;
+
+#[replace_float_literals(F::cast_from(literal))]
+impl<F, GA, BTA, S, Reg, const N : usize>
+ProxPenalty<F, BTFN<F, GA, BTA, N>, Reg, N> for RadonSquared
+where
+ F : Float + ToNalgebraRealField,
+ GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone,
+ BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>,
+ S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>,
+ Reg : RegTerm<F, N>,
+ RNDM<F, N> : SpikeMerging<F>,
+{
+ type ReturnMapping = BTFN<F, GA, BTA, N>;
+
+ fn insert_and_reweigh<I>(
+ &self,
+ μ : &mut RNDM<F, N>,
+ τv : &mut BTFN<F, GA, BTA, N>,
+ μ_base : &RNDM<F, N>,
+ ν_delta: Option<&RNDM<F, N>>,
+ τ : F,
+ ε : F,
+ config : &FBGenericConfig<F>,
+ reg : &Reg,
+ _state : &AlgIteratorIteration<I>,
+ stats : &mut IterInfo<F, N>,
+ ) -> (Option<Self::ReturnMapping>, bool)
+ where
+ I : AlgIterator
+ {
+ assert!(ν_delta.is_none(), "Transport not implemented for Radon-squared prox term");
+
+ let mut y = μ_base.masses_vec();
+
+ 'i_and_w: for i in 0..=1 {
+ // Optimise weights
+ if μ.len() > 0 {
+ // Form finite-dimensional subproblem. The subproblem references to the original μ^k
+ // from the beginning of the iteration are all contained in the immutable c and g.
+ // TODO: observe negation of -τv after switch from minus_τv: finite-dimensional
+ // problems have not yet been updated to sign change.
+ let g̃ = DVector::from_iterator(μ.len(),
+ μ.iter_locations()
+ .map(|ζ| - F::to_nalgebra_mixed(τv.apply(ζ))));
+ let mut x = μ.masses_dvector();
+ // Ugly hack because DVector::push doesn't push but copies.
+ let yvec = DVector::from_column_slice(y.as_slice());
+ // Solve finite-dimensional subproblem.
+ stats.inner_iters += reg.solve_findim_l1squared(&yvec, &g̃, τ, &mut x, ε, config);
+
+ // Update masses of μ based on solution of finite-dimensional subproblem.
+ μ.set_masses_dvector(&x);
+ }
+
+ if i>0 {
+ // Simple debugging test to see if more inserts would be needed. Doesn't seem so.
+ //let n = μ.dist_matching(μ_base);
+ //println!("{:?}", reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n));
+ break 'i_and_w
+ }
+
+ // Calculate ‖μ - μ_base‖_ℳ
+ let n = μ.dist_matching(μ_base);
+
+ // Find a spike to insert, if needed.
+ // This only check the overall tolerances, not tolerances on support of μ-μ_base or μ,
+ // which are supposed to have been guaranteed by the finite-dimensional weight optimisation.
+ match reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n) {
+ None => { break 'i_and_w },
+ Some((ξ, _v_ξ, _in_bounds)) => {
+ // Weight is found out by running the finite-dimensional optimisation algorithm
+ // above
+ *μ += DeltaMeasure { x : ξ, α : 0.0 };
+ //*μ_base += DeltaMeasure { x : ξ, α : 0.0 };
+ y.push(0.0.to_nalgebra_mixed());
+ stats.inserted += 1;
+ }
+ };
+ }
+
+ (None, true)
+ }
+
+ fn merge_spikes(
+ &self,
+ μ : &mut RNDM<F, N>,
+ τv : &mut BTFN<F, GA, BTA, N>,
+ μ_base : &RNDM<F, N>,
+ τ : F,
+ ε : F,
+ config : &FBGenericConfig<F>,
+ reg : &Reg,
+ ) -> usize
+ {
+ μ.merge_spikes(config.merging, |μ_candidate| {
+ // Important: μ_candidate's new points are afterwards,
+ // and do not conflict with μ_base.
+ // TODO: could simplify to requiring μ_base instead of μ_radon.
+ // but may complicate with sliding base's exgtra points that need to be
+ // after μ_candidate's extra points.
+ // TODO: doesn't seem to work, maybe need to merge μ_base as well?
+ // Although that doesn't seem to make sense.
+ let μ_radon = μ_candidate.sub_matching(μ_base);
+ reg.verify_merge_candidate_radonsq(τv, μ_candidate, τ, ε, &config, &μ_radon)
+ //let n = μ_candidate.dist_matching(μ_base);
+ //reg.find_tolerance_violation_slack(τv, τ, ε, false, config, n).is_none()
+ })
+ }
+}
+
+
+impl<F, A, const N : usize> AdjointProductBoundedBy<RNDM<F, N>, RadonSquared>
+for A
+where
+ F : Float,
+ A : ForwardModel<RNDM<F, N>, F>
+{
+ type FloatType = F;
+
+ fn adjoint_product_bound(&self, _ : &RadonSquared) -> Option<Self::FloatType> {
+ self.opnorm_bound(Radon, L2).powi(2).into()
+ }
+}