diff -r 6105b5cd8d89 -r f0e8704d3f0e src/regularisation.rs
--- a/src/regularisation.rs	Tue Aug 01 10:25:09 2023 +0300
+++ b/src/regularisation.rs	Mon Feb 17 13:54:53 2025 -0500
@@ -2,25 +2,41 @@
 Regularisation terms
 */
 
-use serde::{Serialize, Deserialize};
-use alg_tools::norms::Norm;
-use alg_tools::linops::Apply;
-use alg_tools::loc::Loc;
+#[allow(unused_imports)] // Used by documentation.
+use crate::fb::pointsource_fb_reg;
+use crate::fb::FBGenericConfig;
+use crate::measures::{DeltaMeasure, Radon, RNDM};
+#[allow(unused_imports)] // Used by documentation.
+use crate::sliding_fb::pointsource_sliding_fb_reg;
 use crate::types::*;
-use crate::measures::{
-    DiscreteMeasure,
-    Radon
+use alg_tools::instance::Instance;
+use alg_tools::linops::Mapping;
+use alg_tools::loc::Loc;
+use alg_tools::norms::Norm;
+use numeric_literals::replace_float_literals;
+use serde::{Deserialize, Serialize};
+
+use crate::subproblem::{
+    l1squared_nonneg::l1squared_nonneg, l1squared_unconstrained::l1squared_unconstrained,
+    nonneg::quadratic_nonneg, unconstrained::quadratic_unconstrained,
 };
-#[allow(unused_imports)] // Used by documentation.
-use crate::fb::generic_pointsource_fb_reg;
+use alg_tools::bisection_tree::{
+    BTSearch, Bounded, Bounds, LocalAnalysis, P2Minimise, SupportGenerator, BTFN,
+};
+use alg_tools::iterate::AlgIteratorFactory;
+use alg_tools::nalgebra_support::ToNalgebraRealField;
+use nalgebra::{DMatrix, DVector};
 
-/// The regularisation term $α\\|μ\\|\_{ℳ(Ω)} + δ_{≥ 0}(μ)$ for [`generic_pointsource_fb_reg`].
+use std::cmp::Ordering::{Equal, Greater, Less};
+
+/// The regularisation term $α\\|μ\\|\_{ℳ(Ω)} + δ_{≥ 0}(μ)$ for [`pointsource_fb_reg`] and other
+/// algorithms.
 ///
 /// The only member of the struct is the regularisation parameter α.
 #[derive(Copy, Clone, Debug, Serialize, Deserialize)]
-pub struct NonnegRadonRegTerm<F : Float>(pub F /* α */);
+pub struct NonnegRadonRegTerm<F: Float>(pub F /* α */);
 
-impl<'a, F : Float> NonnegRadonRegTerm<F> {
+impl<'a, F: Float> NonnegRadonRegTerm<F> {
     /// Returns the regularisation parameter
     pub fn α(&self) -> F {
         let &NonnegRadonRegTerm(α) = self;
@@ -28,24 +44,24 @@
     }
 }
 
-impl<'a, F : Float, const N : usize> Apply<&'a DiscreteMeasure<Loc<F, N>, F>>
-for NonnegRadonRegTerm<F> {
-    type Output = F;
-    
-    fn apply(&self, μ : &'a DiscreteMeasure<Loc<F, N>, F>) -> F {
-        self.α() * μ.norm(Radon)
+impl<'a, F: Float, const N: usize> Mapping<RNDM<F, N>> for NonnegRadonRegTerm<F> {
+    type Codomain = F;
+
+    fn apply<I>(&self, μ: I) -> F
+    where
+        I: Instance<RNDM<F, N>>,
+    {
+        self.α() * μ.eval(|x| x.norm(Radon))
     }
 }
 
-
-/// The regularisation term $α\|μ\|_{ℳ(Ω)}$ for [`generic_pointsource_fb_reg`].
+/// The regularisation term $α\|μ\|_{ℳ(Ω)}$ for [`pointsource_fb_reg`].
 ///
 /// The only member of the struct is the regularisation parameter α.
 #[derive(Copy, Clone, Debug, Serialize, Deserialize)]
-pub struct RadonRegTerm<F : Float>(pub F /* α */);
+pub struct RadonRegTerm<F: Float>(pub F /* α */);
 
-
-impl<'a, F : Float> RadonRegTerm<F> {
+impl<'a, F: Float> RadonRegTerm<F> {
     /// Returns the regularisation parameter
     pub fn α(&self) -> F {
         let &RadonRegTerm(α) = self;
@@ -53,32 +69,615 @@
     }
 }
 
-impl<'a, F : Float, const N : usize> Apply<&'a DiscreteMeasure<Loc<F, N>, F>>
-for RadonRegTerm<F> {
-    type Output = F;
-    
-    fn apply(&self, μ : &'a DiscreteMeasure<Loc<F, N>, F>) -> F {
-        self.α() * μ.norm(Radon)
+impl<'a, F: Float, const N: usize> Mapping<RNDM<F, N>> for RadonRegTerm<F> {
+    type Codomain = F;
+
+    fn apply<I>(&self, μ: I) -> F
+    where
+        I: Instance<RNDM<F, N>>,
+    {
+        self.α() * μ.eval(|x| x.norm(Radon))
     }
 }
 
 /// Regularisation term configuration
 #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
-pub enum Regularisation<F : Float> {
+pub enum Regularisation<F: Float> {
     /// $α \\|μ\\|\_{ℳ(Ω)}$
     Radon(F),
     /// $α\\|μ\\|\_{ℳ(Ω)} + δ_{≥ 0}(μ)$
     NonnegRadon(F),
 }
 
-impl<'a, F : Float, const N : usize> Apply<&'a DiscreteMeasure<Loc<F, N>, F>>
-for Regularisation<F> {
-    type Output = F;
-    
-    fn apply(&self, μ : &'a DiscreteMeasure<Loc<F, N>, F>) -> F {
+impl<'a, F: Float, const N: usize> Mapping<RNDM<F, N>> for Regularisation<F> {
+    type Codomain = F;
+
+    fn apply<I>(&self, μ: I) -> F
+    where
+        I: Instance<RNDM<F, N>>,
+    {
         match *self {
             Self::Radon(α) => RadonRegTerm(α).apply(μ),
             Self::NonnegRadon(α) => NonnegRadonRegTerm(α).apply(μ),
         }
     }
 }
+
+/// Abstraction of regularisation terms.
+pub trait RegTerm<F: Float + ToNalgebraRealField, const N: usize>:
+    Mapping<RNDM<F, N>, Codomain = F>
+{
+    /// Approximately solve the problem
+    /// <div>$$
+    ///     \min_{x ∈ ℝ^n} \frac{1}{2} x^⊤Ax - g^⊤ x + τ G(x)
+    /// $$</div>
+    /// for $G$ depending on the trait implementation.
+    ///
+    /// The parameter `mA` is $A$. An estimate for its opeator norm should be provided in
+    /// `mA_normest`. The initial iterate and output is `x`. The current main tolerance is `ε`.
+    ///
+    /// Returns the number of iterations taken.
+    fn solve_findim(
+        &self,
+        mA: &DMatrix<F::MixedType>,
+        g: &DVector<F::MixedType>,
+        τ: F,
+        x: &mut DVector<F::MixedType>,
+        mA_normest: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> usize;
+
+    /// Approximately solve the problem
+    /// <div>$$
+    ///     \min_{x ∈ ℝ^n} \frac{1}{2} |x-y|_1^2 - g^⊤ x + τ G(x)
+    /// $$</div>
+    /// for $G$ depending on the trait implementation.
+    ///
+    /// Returns the number of iterations taken.
+    fn solve_findim_l1squared(
+        &self,
+        y: &DVector<F::MixedType>,
+        g: &DVector<F::MixedType>,
+        τ: F,
+        x: &mut DVector<F::MixedType>,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> usize;
+
+    /// Find a point where `d` may violate the tolerance `ε`.
+    ///
+    /// If `skip_by_rough_check` is set, do not find the point if a rough check indicates that we
+    /// are in bounds. `ε` is the current main tolerance and `τ` a scaling factor for the
+    /// regulariser.
+    ///
+    /// Returns `None` if `d` is in bounds either based on the rough check, or a more precise check
+    /// terminating early. Otherwise returns a possibly violating point, the value of `d` there,
+    /// and a boolean indicating whether the found point is in bounds.
+    fn find_tolerance_violation<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        τ: F,
+        ε: F,
+        skip_by_rough_check: bool,
+        config: &FBGenericConfig<F>,
+    ) -> Option<(Loc<F, N>, F, bool)>
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        self.find_tolerance_violation_slack(d, τ, ε, skip_by_rough_check, config, F::ZERO)
+    }
+
+    /// Find a point where `d` may violate the tolerance `ε`.
+    ///
+    /// This version includes a `slack` parameter to expand the tolerances.
+    /// It is used for Radon-norm squared proximal term in [`crate::prox_penalty::radon_squared`].
+    ///
+    /// If `skip_by_rough_check` is set, do not find the point if a rough check indicates that we
+    /// are in bounds. `ε` is the current main tolerance and `τ` a scaling factor for the
+    /// regulariser.
+    ///
+    /// Returns `None` if `d` is in bounds either based on the rough check, or a more precise check
+    /// terminating early. Otherwise returns a possibly violating point, the value of `d` there,
+    /// and a boolean indicating whether the found point is in bounds.
+    fn find_tolerance_violation_slack<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        τ: F,
+        ε: F,
+        skip_by_rough_check: bool,
+        config: &FBGenericConfig<F>,
+        slack: F,
+    ) -> Option<(Loc<F, N>, F, bool)>
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>;
+
+    /// Verify that `d` is in bounds `ε` for a merge candidate `μ`
+    ///
+    /// `ε` is the current main tolerance and `τ` a scaling factor for the regulariser.
+    fn verify_merge_candidate<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        μ: &RNDM<F, N>,
+        τ: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> bool
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>;
+
+    /// Verify that `d` is in bounds `ε` for a merge candidate `μ`
+    ///
+    /// This version is s used for Radon-norm squared proximal term in
+    /// [`crate::prox_penalty::radon_squared`].
+    /// The [measures][crate::measures::DiscreteMeasure] `μ` and `radon_μ` are supposed to have
+    /// same coordinates at same agreeing indices.
+    ///
+    /// `ε` is the current main tolerance and `τ` a scaling factor for the regulariser.
+    fn verify_merge_candidate_radonsq<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        μ: &RNDM<F, N>,
+        τ: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+        radon_μ: &RNDM<F, N>,
+    ) -> bool
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>;
+
+    /// TODO: document this
+    fn target_bounds(&self, τ: F, ε: F) -> Option<Bounds<F>>;
+
+    /// Returns a scaling factor for the tolerance sequence.
+    ///
+    /// Typically this is the regularisation parameter.
+    fn tolerance_scaling(&self) -> F;
+}
+
+/// Abstraction of regularisation terms for [`pointsource_sliding_fb_reg`].
+pub trait SlidingRegTerm<F: Float + ToNalgebraRealField, const N: usize>: RegTerm<F, N> {
+    /// Calculate $τ[w(z) - w(y)]$ for some w in the subdifferential of the regularisation
+    /// term, such that $-ε ≤ τw - d ≤ ε$.
+    fn goodness<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        μ: &RNDM<F, N>,
+        y: &Loc<F, N>,
+        z: &Loc<F, N>,
+        τ: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> F
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>;
+
+    /// Convert bound on the regulariser to a bond on the Radon norm
+    fn radon_norm_bound(&self, b: F) -> F;
+}
+
+#[replace_float_literals(F::cast_from(literal))]
+impl<F: Float + ToNalgebraRealField, const N: usize> RegTerm<F, N> for NonnegRadonRegTerm<F>
+where
+    Cube<F, N>: P2Minimise<Loc<F, N>, F>,
+{
+    fn solve_findim(
+        &self,
+        mA: &DMatrix<F::MixedType>,
+        g: &DVector<F::MixedType>,
+        τ: F,
+        x: &mut DVector<F::MixedType>,
+        mA_normest: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> usize {
+        let inner_tolerance = ε * config.inner.tolerance_mult;
+        let inner_it = config.inner.iterator_options.stop_target(inner_tolerance);
+        quadratic_nonneg(mA, g, τ * self.α(), x, mA_normest, &config.inner, inner_it)
+    }
+
+    fn solve_findim_l1squared(
+        &self,
+        y: &DVector<F::MixedType>,
+        g: &DVector<F::MixedType>,
+        τ: F,
+        x: &mut DVector<F::MixedType>,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> usize {
+        let inner_tolerance = ε * config.inner.tolerance_mult;
+        let inner_it = config.inner.iterator_options.stop_target(inner_tolerance);
+        l1squared_nonneg(y, g, τ * self.α(), 1.0, x, &config.inner, inner_it)
+    }
+
+    #[inline]
+    fn find_tolerance_violation_slack<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        τ: F,
+        ε: F,
+        skip_by_rough_check: bool,
+        config: &FBGenericConfig<F>,
+        slack: F,
+    ) -> Option<(Loc<F, N>, F, bool)>
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let τα = τ * self.α();
+        let keep_above = -τα - slack - ε;
+        let minimise_below = -τα - slack - ε * config.insertion_cutoff_factor;
+        let refinement_tolerance = ε * config.refinement.tolerance_mult;
+
+        // If preliminary check indicates that we are in bounds, and if it otherwise matches
+        // the insertion strategy, skip insertion.
+        if skip_by_rough_check && d.bounds().lower() >= keep_above {
+            None
+        } else {
+            // If the rough check didn't indicate no insertion needed, find minimising point.
+            d.minimise_below(
+                minimise_below,
+                refinement_tolerance,
+                config.refinement.max_steps,
+            )
+            .map(|(ξ, v_ξ)| (ξ, v_ξ, v_ξ >= keep_above))
+        }
+    }
+
+    fn verify_merge_candidate<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        μ: &RNDM<F, N>,
+        τ: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> bool
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let τα = τ * self.α();
+        let refinement_tolerance = ε * config.refinement.tolerance_mult;
+        let merge_tolerance = config.merge_tolerance_mult * ε;
+        let keep_above = -τα - merge_tolerance;
+        let keep_supp_below = -τα + merge_tolerance;
+        let bnd = d.bounds();
+
+        return (bnd.upper() <= keep_supp_below
+            || μ
+                .iter_spikes()
+                .all(|&DeltaMeasure { α, ref x }| (α == 0.0) || d.apply(x) <= keep_supp_below))
+            && (bnd.lower() >= keep_above
+                || d.has_lower_bound(
+                    keep_above,
+                    refinement_tolerance,
+                    config.refinement.max_steps,
+                ));
+    }
+
+    fn verify_merge_candidate_radonsq<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        μ: &RNDM<F, N>,
+        τ: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+        radon_μ: &RNDM<F, N>,
+    ) -> bool
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let τα = τ * self.α();
+        let refinement_tolerance = ε * config.refinement.tolerance_mult;
+        let merge_tolerance = config.merge_tolerance_mult * ε;
+        let slack = radon_μ.norm(Radon);
+        let bnd = d.bounds();
+
+        return {
+            μ.both_matching(radon_μ).all(|(α, rα, x)| {
+                let v = -d.apply(x); // TODO: observe ad hoc negation here, after minus_τv
+                                     // switch to τv.
+                let (l1, u1) = match α.partial_cmp(&0.0).unwrap_or(Equal) {
+                    Greater => (τα, τα),
+                    _ => (F::NEG_INFINITY, τα),
+                    // Less should not happen; treated as Equal
+                };
+                let (l2, u2) = match rα.partial_cmp(&0.0).unwrap_or(Equal) {
+                    Greater => (slack, slack),
+                    Equal => (-slack, slack),
+                    Less => (-slack, -slack),
+                };
+                // TODO: both fail.
+                (l1 + l2 - merge_tolerance <= v) && (v <= u1 + u2 + merge_tolerance)
+            })
+        } && {
+            let keep_above = -τα - slack - merge_tolerance;
+            bnd.lower() <= keep_above
+                || d.has_lower_bound(
+                    keep_above,
+                    refinement_tolerance,
+                    config.refinement.max_steps,
+                )
+        };
+    }
+
+    fn target_bounds(&self, τ: F, ε: F) -> Option<Bounds<F>> {
+        let τα = τ * self.α();
+        Some(Bounds(τα - ε, τα + ε))
+    }
+
+    fn tolerance_scaling(&self) -> F {
+        self.α()
+    }
+}
+
+#[replace_float_literals(F::cast_from(literal))]
+impl<F: Float + ToNalgebraRealField, const N: usize> SlidingRegTerm<F, N> for NonnegRadonRegTerm<F>
+where
+    Cube<F, N>: P2Minimise<Loc<F, N>, F>,
+{
+    fn goodness<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        _μ: &RNDM<F, N>,
+        y: &Loc<F, N>,
+        z: &Loc<F, N>,
+        τ: F,
+        ε: F,
+        _config: &FBGenericConfig<F>,
+    ) -> F
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let w = |x| 1.0.min((ε + d.apply(x)) / (τ * self.α()));
+        w(z) - w(y)
+    }
+
+    fn radon_norm_bound(&self, b: F) -> F {
+        b / self.α()
+    }
+}
+
+#[replace_float_literals(F::cast_from(literal))]
+impl<F: Float + ToNalgebraRealField, const N: usize> RegTerm<F, N> for RadonRegTerm<F>
+where
+    Cube<F, N>: P2Minimise<Loc<F, N>, F>,
+{
+    fn solve_findim(
+        &self,
+        mA: &DMatrix<F::MixedType>,
+        g: &DVector<F::MixedType>,
+        τ: F,
+        x: &mut DVector<F::MixedType>,
+        mA_normest: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> usize {
+        let inner_tolerance = ε * config.inner.tolerance_mult;
+        let inner_it = config.inner.iterator_options.stop_target(inner_tolerance);
+        quadratic_unconstrained(mA, g, τ * self.α(), x, mA_normest, &config.inner, inner_it)
+    }
+
+    fn solve_findim_l1squared(
+        &self,
+        y: &DVector<F::MixedType>,
+        g: &DVector<F::MixedType>,
+        τ: F,
+        x: &mut DVector<F::MixedType>,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> usize {
+        let inner_tolerance = ε * config.inner.tolerance_mult;
+        let inner_it = config.inner.iterator_options.stop_target(inner_tolerance);
+        l1squared_unconstrained(y, g, τ * self.α(), 1.0, x, &config.inner, inner_it)
+    }
+
+    fn find_tolerance_violation_slack<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        τ: F,
+        ε: F,
+        skip_by_rough_check: bool,
+        config: &FBGenericConfig<F>,
+        slack: F,
+    ) -> Option<(Loc<F, N>, F, bool)>
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let τα = τ * self.α();
+        let keep_below = τα + slack + ε;
+        let keep_above = -(τα + slack) - ε;
+        let maximise_above = τα + slack + ε * config.insertion_cutoff_factor;
+        let minimise_below = -(τα + slack) - ε * config.insertion_cutoff_factor;
+        let refinement_tolerance = ε * config.refinement.tolerance_mult;
+
+        // If preliminary check indicates that we are in bonds, and if it otherwise matches
+        // the insertion strategy, skip insertion.
+        if skip_by_rough_check && Bounds(keep_above, keep_below).superset(&d.bounds()) {
+            None
+        } else {
+            // If the rough check didn't indicate no insertion needed, find maximising point.
+            let mx = d.maximise_above(
+                maximise_above,
+                refinement_tolerance,
+                config.refinement.max_steps,
+            );
+            let mi = d.minimise_below(
+                minimise_below,
+                refinement_tolerance,
+                config.refinement.max_steps,
+            );
+
+            match (mx, mi) {
+                (None, None) => None,
+                (Some((ξ, v_ξ)), None) => Some((ξ, v_ξ, keep_below >= v_ξ)),
+                (None, Some((ζ, v_ζ))) => Some((ζ, v_ζ, keep_above <= v_ζ)),
+                (Some((ξ, v_ξ)), Some((ζ, v_ζ))) => {
+                    if v_ξ - τα > τα - v_ζ {
+                        Some((ξ, v_ξ, keep_below >= v_ξ))
+                    } else {
+                        Some((ζ, v_ζ, keep_above <= v_ζ))
+                    }
+                }
+            }
+        }
+    }
+
+    fn verify_merge_candidate<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        μ: &RNDM<F, N>,
+        τ: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+    ) -> bool
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let τα = τ * self.α();
+        let refinement_tolerance = ε * config.refinement.tolerance_mult;
+        let merge_tolerance = config.merge_tolerance_mult * ε;
+        let keep_below = τα + merge_tolerance;
+        let keep_above = -τα - merge_tolerance;
+        let keep_supp_pos_above = τα - merge_tolerance;
+        let keep_supp_neg_below = -τα + merge_tolerance;
+        let bnd = d.bounds();
+
+        return ((bnd.lower() >= keep_supp_pos_above && bnd.upper() <= keep_supp_neg_below)
+            || μ
+                .iter_spikes()
+                .all(|&DeltaMeasure { α: β, ref x }| match β.partial_cmp(&0.0) {
+                    Some(Greater) => d.apply(x) >= keep_supp_pos_above,
+                    Some(Less) => d.apply(x) <= keep_supp_neg_below,
+                    _ => true,
+                }))
+            && (bnd.upper() <= keep_below
+                || d.has_upper_bound(
+                    keep_below,
+                    refinement_tolerance,
+                    config.refinement.max_steps,
+                ))
+            && (bnd.lower() >= keep_above
+                || d.has_lower_bound(
+                    keep_above,
+                    refinement_tolerance,
+                    config.refinement.max_steps,
+                ));
+    }
+
+    fn verify_merge_candidate_radonsq<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        μ: &RNDM<F, N>,
+        τ: F,
+        ε: F,
+        config: &FBGenericConfig<F>,
+        radon_μ: &RNDM<F, N>,
+    ) -> bool
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let τα = τ * self.α();
+        let refinement_tolerance = ε * config.refinement.tolerance_mult;
+        let merge_tolerance = config.merge_tolerance_mult * ε;
+        let slack = radon_μ.norm(Radon);
+        let bnd = d.bounds();
+
+        return {
+            μ.both_matching(radon_μ).all(|(α, rα, x)| {
+                let v = d.apply(x);
+                let (l1, u1) = match α.partial_cmp(&0.0).unwrap_or(Equal) {
+                    Greater => (τα, τα),
+                    Equal => (-τα, τα),
+                    Less => (-τα, -τα),
+                };
+                let (l2, u2) = match rα.partial_cmp(&0.0).unwrap_or(Equal) {
+                    Greater => (slack, slack),
+                    Equal => (-slack, slack),
+                    Less => (-slack, -slack),
+                };
+                (l1 + l2 - merge_tolerance <= v) && (v <= u1 + u2 + merge_tolerance)
+            })
+        } && {
+            let keep_below = τα + slack + merge_tolerance;
+            bnd.upper() <= keep_below
+                || d.has_upper_bound(
+                    keep_below,
+                    refinement_tolerance,
+                    config.refinement.max_steps,
+                )
+        } && {
+            let keep_above = -τα - slack - merge_tolerance;
+            bnd.lower() >= keep_above
+                || d.has_lower_bound(
+                    keep_above,
+                    refinement_tolerance,
+                    config.refinement.max_steps,
+                )
+        };
+    }
+
+    fn target_bounds(&self, τ: F, ε: F) -> Option<Bounds<F>> {
+        let τα = τ * self.α();
+        Some(Bounds(-τα - ε, τα + ε))
+    }
+
+    fn tolerance_scaling(&self) -> F {
+        self.α()
+    }
+}
+
+#[replace_float_literals(F::cast_from(literal))]
+impl<F: Float + ToNalgebraRealField, const N: usize> SlidingRegTerm<F, N> for RadonRegTerm<F>
+where
+    Cube<F, N>: P2Minimise<Loc<F, N>, F>,
+{
+    fn goodness<G, BT>(
+        &self,
+        d: &mut BTFN<F, G, BT, N>,
+        _μ: &RNDM<F, N>,
+        y: &Loc<F, N>,
+        z: &Loc<F, N>,
+        τ: F,
+        ε: F,
+        _config: &FBGenericConfig<F>,
+    ) -> F
+    where
+        BT: BTSearch<F, N, Agg = Bounds<F>>,
+        G: SupportGenerator<F, N, Id = BT::Data>,
+        G::SupportType: Mapping<Loc<F, N>, Codomain = F> + LocalAnalysis<F, Bounds<F>, N>,
+    {
+        let α = self.α();
+        let w = |x| {
+            let dx = d.apply(x);
+            ((-ε + dx) / (τ * α)).max(1.0.min(ε + dx) / (τ * α))
+        };
+        w(z) - w(y)
+    }
+
+    fn radon_norm_bound(&self, b: F) -> F {
+        b / self.α()
+    }
+}