pointsource_algs: comparison src/prox

-:fb911f72e698
+:c5d8bd1a7728
+/*!
+Basic proximal penalty based on convolution operators $𝒟$.
+*/
+use numeric_literals::replace_float_literals;
+use nalgebra::DVector;
+use colored::Colorize;
+use alg_tools::types::*;
+use alg_tools::loc::Loc;
+use alg_tools::mapping::{Mapping, RealMapping};
+use alg_tools::nalgebra_support::ToNalgebraRealField;
+use alg_tools::norms::Linfinity;
+use alg_tools::iterate::{
+AlgIteratorIteration,
+AlgIterator,
+};
+use alg_tools::bisection_tree::{
+BTFN,
+PreBTFN,
+Bounds,
+BTSearch,
+SupportGenerator,
+LocalAnalysis,
+BothGenerators,
+};
+use crate::measures::{
+RNDM,
+DeltaMeasure,
+Radon,
+};
+use crate::measures::merging::{
+SpikeMerging,
+};
+use crate::seminorms::DiscreteMeasureOp;
+use crate::types::{
+IterInfo,
+};
+use crate::measures::merging::SpikeMergingMethod;
+use crate::regularisation::RegTerm;
+use super::{ProxPenalty, FBGenericConfig};
+#[replace_float_literals(F::cast_from(literal))]
+impl<F, GA, BTA, S, Reg, 𝒟, G𝒟, K, const N : usize>
+ProxPenalty<F, BTFN<F, GA, BTA, N>, Reg, N> for 𝒟
+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>,
+G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone,
+𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>>,
+𝒟::Codomain : RealMapping<F, N>,
+K : RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>,
+Reg : RegTerm<F, N>,
+RNDM<F, N> : SpikeMerging<F>,
+{
+type ReturnMapping = BTFN<F, BothGenerators<GA, G𝒟>, 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<BTFN<F, BothGenerators<GA, G𝒟>, BTA, N>>, bool)
+where
+I : AlgIterator
+{
+// TODO: is this inefficient to do in every iteration?
+let op𝒟norm = self.opnorm_bound(Radon, Linfinity);
+// Maximum insertion count and measure difference calculation depend on insertion style.
+let (max_insertions, warn_insertions) = match (state.iteration(), config.bootstrap_insertions) {
+(i, Some((l, k))) if i <= l => (k, false),
+_ => (config.max_insertions, !state.is_quiet()),
+};
+let ω0 = match ν_delta {
+None => self.apply(μ_base),
+Some(ν) => self.apply(μ_base + ν),
+};
+// Add points to support until within error tolerance or maximum insertion count reached.
+let mut count = 0;
+let (within_tolerances, d) = 'insertion: loop {
+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 Ã = self.findim_matrix(μ.iter_locations());
+let g̃ = DVector::from_iterator(μ.len(),
+μ.iter_locations()
+.map(|ζ| ω0.apply(ζ) - τv.apply(ζ))
+.map(F::to_nalgebra_mixed));
+let mut x = μ.masses_dvector();
+// The gradient of the forward component of the inner objective is C^*𝒟Cx - g̃.
+// We have |C^*𝒟Cx|_2 = sup_{|z|_2 ≤ 1} ⟨z, C^*𝒟Cx⟩ = sup_{|z|_2 ≤ 1} ⟨Cz|𝒟Cx⟩
+// ≤ sup_{|z|_2 ≤ 1} |Cz|_ℳ |𝒟Cx|_∞ ≤  sup_{|z|_2 ≤ 1} |Cz|_ℳ |𝒟| |Cx|_ℳ
+// ≤ sup_{|z|_2 ≤ 1} |z|_1 |𝒟| |x|_1 ≤ sup_{|z|_2 ≤ 1} n |z|_2 |𝒟| |x|_2
+// = n |𝒟| |x|_2, where n is the number of points. Therefore
+let Ã_normest = op𝒟norm * F::cast_from(μ.len());
+// Solve finite-dimensional subproblem.
+stats.inner_iters += reg.solve_findim(&Ã, &g̃, τ, &mut x, Ã_normest, ε, config);
+// Update masses of μ based on solution of finite-dimensional subproblem.
+μ.set_masses_dvector(&x);
+}
+// Form d = τv + 𝒟μ - ω0 = τv + 𝒟(μ - μ^k) for checking the proximate optimality
+// conditions in the predual space, and finding new points for insertion, if necessary.
+let mut d = &*τv + match ν_delta {
+None => self.preapply(μ.sub_matching(μ_base)),
+Some(ν) => self.preapply(μ.sub_matching(μ_base) - ν)
+};
+// If no merging heuristic is used, let's be more conservative about spike insertion,
+// and skip it after first round. If merging is done, being more greedy about spike
+// insertion also seems to improve performance.
+let skip_by_rough_check = if let SpikeMergingMethod::None = config.merging {
+false
+} else {
+count > 0
+};
+// Find a spike to insert, if needed
+let (ξ, _v_ξ, in_bounds) =  match reg.find_tolerance_violation(
+&mut d, τ, ε, skip_by_rough_check, config
+) {
+None => break 'insertion (true, d),
+Some(res) => res,
+};
+// Break if maximum insertion count reached
+if count >= max_insertions {
+break 'insertion (in_bounds, d)
+}
+// No point in optimising the weight here; the finite-dimensional algorithm is fast.
+*μ += DeltaMeasure { x : ξ, α : 0.0 };
+count += 1;
+stats.inserted += 1;
+};
+if !within_tolerances && warn_insertions {
+// Complain (but continue) if we failed to get within tolerances
+// by inserting more points.
+let err = format!("Maximum insertions reached without achieving \
+subproblem solution tolerance");
+println!("{}", err.red());
+}
+(Some(d), within_tolerances)
+}
+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| {
+let mut d = &*τv + self.preapply(μ_candidate.sub_matching(μ_base));
+reg.verify_merge_candidate(&mut d, μ_candidate, τ, ε, config)
+})
+}
+}

comparison: src/prox_penalty/wave.rs

src/prox_penalty/wave.rs

Mercurial > repos > pointsource_algs / file comparison

comparison: src/prox_penalty/wave.rs

src/prox_penalty/wave.rs