--- a/src/regularisation.rs Fri Apr 28 13:15:19 2023 +0300
+++ b/src/regularisation.rs Tue Dec 31 09:34:24 2024 -0500
@@ -2,6 +2,7 @@
Regularisation terms
*/
+use numeric_literals::replace_float_literals;
use serde::{Serialize, Deserialize};
use alg_tools::norms::Norm;
use alg_tools::linops::Apply;
@@ -9,12 +10,35 @@
use crate::types::*;
use crate::measures::{
DiscreteMeasure,
+ DeltaMeasure,
Radon
};
+use crate::fb::FBGenericConfig;
#[allow(unused_imports)] // Used by documentation.
-use crate::fb::generic_pointsource_fb_reg;
+use crate::fb::pointsource_fb_reg;
+#[allow(unused_imports)] // Used by documentation.
+use crate::sliding_fb::pointsource_sliding_fb_reg;
-/// The regularisation term $α\\|μ\\|\_{ℳ(Ω)} + δ_{≥ 0}(μ)$ for [`generic_pointsource_fb_reg`].
+use nalgebra::{DVector, DMatrix};
+use alg_tools::nalgebra_support::ToNalgebraRealField;
+use alg_tools::mapping::Mapping;
+use alg_tools::bisection_tree::{
+ BTFN,
+ Bounds,
+ BTSearch,
+ P2Minimise,
+ SupportGenerator,
+ LocalAnalysis,
+ Bounded,
+};
+use crate::subproblem::{
+ nonneg::quadratic_nonneg,
+ unconstrained::quadratic_unconstrained,
+};
+use alg_tools::iterate::AlgIteratorFactory;
+
+/// 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)]
@@ -38,7 +62,7 @@
}
-/// 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)]
@@ -82,3 +106,365 @@
}
}
}
+
+/// Abstraction of regularisation terms for [`generic_pointsource_fb_reg`].
+pub trait RegTerm<F : Float + ToNalgebraRealField, const N : usize>
+: for<'a> Apply<&'a DiscreteMeasure<Loc<F, N>, F>, Output = 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;
+
+ /// 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>;
+
+ /// 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 : &DiscreteMeasure<Loc<F, N>, F>,
+ 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>;
+
+ /// 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 : &DiscreteMeasure<Loc<F, N>, F>,
+ 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>;
+}
+
+#[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);
+ let inner_τ = config.inner.τ0 / mA_normest;
+ quadratic_nonneg(config.inner.method, mA, g, τ * self.α(), x,
+ inner_τ, inner_it)
+ }
+
+ #[inline]
+ 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> {
+ let τα = τ * self.α();
+ let keep_below = τα + ε;
+ let maximise_above = τα + 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 && d.bounds().upper() <= keep_below {
+ None
+ } else {
+ // If the rough check didn't indicate no insertion needed, find maximising point.
+ d.maximise_above(maximise_above, refinement_tolerance, config.refinement.max_steps)
+ .map(|(ξ, v_ξ)| (ξ, v_ξ, v_ξ <= keep_below))
+ }
+ }
+
+ fn verify_merge_candidate<G, BT>(
+ &self,
+ d : &mut BTFN<F, G, BT, N>,
+ μ : &DiscreteMeasure<Loc<F, N>, F>,
+ 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_supp_above = τα - merge_tolerance;
+ let bnd = d.bounds();
+
+ return (
+ bnd.lower() >= keep_supp_above
+ ||
+ μ.iter_spikes().map(|&DeltaMeasure{ α : β, ref x }| {
+ (β == 0.0) || d.apply(x) >= keep_supp_above
+ }).all(std::convert::identity)
+ ) && (
+ bnd.upper() <= keep_below
+ ||
+ d.has_upper_bound(keep_below, 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 : &DiscreteMeasure<Loc<F, N>, F>,
+ 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()));
+ let τw = |x| τ.min((ε + d.apply(x))/self.α());
+ τw(z) - τw(y)
+ }
+}
+
+#[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);
+ let inner_τ = config.inner.τ0 / mA_normest;
+ quadratic_unconstrained(config.inner.method, mA, g, τ * self.α(), x,
+ inner_τ, inner_it)
+ }
+
+ 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> {
+ let τα = τ * self.α();
+ let keep_below = τα + ε;
+ let keep_above = -τα - ε;
+ let maximise_above = τα + ε * config.insertion_cutoff_factor;
+ let minimise_below = -τα - 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 : &DiscreteMeasure<Loc<F, N>, F>,
+ 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().map(|&DeltaMeasure{ α : β, ref x }| {
+ use std::cmp::Ordering::*;
+ 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,
+ }
+ }).all(std::convert::identity)
+ ) && (
+ 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 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 : &DiscreteMeasure<Loc<F, N>, F>,
+ 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))
+ // };
+ let τw = |x| {
+ let dx = d.apply(x);
+ ((-ε + dx)/α).max(τ.min(ε + dx)/α)
+ };
+ τw(z) - τw(y)
+ }
+}
\ No newline at end of file