diff -r 6105b5cd8d89 -r f0e8704d3f0e src/sliding_pdps.rs
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/sliding_pdps.rs	Mon Feb 17 13:54:53 2025 -0500
@@ -0,0 +1,373 @@
+/*!
+Solver for the point source localisation problem using a sliding
+primal-dual proximal splitting method.
+*/
+
+use numeric_literals::replace_float_literals;
+use serde::{Deserialize, Serialize};
+//use colored::Colorize;
+//use nalgebra::{DVector, DMatrix};
+use std::iter::Iterator;
+
+use alg_tools::convex::{Conjugable, Prox};
+use alg_tools::direct_product::Pair;
+use alg_tools::euclidean::Euclidean;
+use alg_tools::iterate::AlgIteratorFactory;
+use alg_tools::linops::{Adjointable, BoundedLinear, IdOp, AXPY, GEMV};
+use alg_tools::mapping::{DifferentiableRealMapping, Instance, Mapping};
+use alg_tools::nalgebra_support::ToNalgebraRealField;
+use alg_tools::norms::{Dist, Norm};
+use alg_tools::norms::{PairNorm, L2};
+
+use crate::forward_model::{AdjointProductPairBoundedBy, BoundedCurvature, ForwardModel};
+use crate::measures::merging::SpikeMerging;
+use crate::measures::{DiscreteMeasure, Radon, RNDM};
+use crate::types::*;
+// use crate::transport::TransportLipschitz;
+//use crate::tolerance::Tolerance;
+use crate::fb::*;
+use crate::plot::{PlotLookup, Plotting, SeqPlotter};
+use crate::regularisation::SlidingRegTerm;
+// use crate::dataterm::L2Squared;
+use crate::dataterm::{calculate_residual, calculate_residual2};
+use crate::sliding_fb::{
+    aposteriori_transport, initial_transport, TransportConfig, TransportStepLength,
+};
+
+/// Settings for [`pointsource_sliding_pdps_pair`].
+#[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
+#[serde(default)]
+pub struct SlidingPDPSConfig<F: Float> {
+    /// Primal step length scaling.
+    pub τ0: F,
+    /// Primal step length scaling.
+    pub σp0: F,
+    /// Dual step length scaling.
+    pub σd0: F,
+    /// Transport parameters
+    pub transport: TransportConfig<F>,
+    /// Generic parameters
+    pub insertion: FBGenericConfig<F>,
+}
+
+#[replace_float_literals(F::cast_from(literal))]
+impl<F: Float> Default for SlidingPDPSConfig<F> {
+    fn default() -> Self {
+        SlidingPDPSConfig {
+            τ0: 0.99,
+            σd0: 0.05,
+            σp0: 0.99,
+            transport: TransportConfig {
+                θ0: 0.9,
+                ..Default::default()
+            },
+            insertion: Default::default(),
+        }
+    }
+}
+
+type MeasureZ<F, Z, const N: usize> = Pair<RNDM<F, N>, Z>;
+
+/// Iteratively solve the pointsource localisation with an additional variable
+/// using sliding primal-dual proximal splitting
+///
+/// The parametrisation is as for [`crate::forward_pdps::pointsource_forward_pdps_pair`].
+#[replace_float_literals(F::cast_from(literal))]
+pub fn pointsource_sliding_pdps_pair<
+    F,
+    I,
+    A,
+    S,
+    Reg,
+    P,
+    Z,
+    R,
+    Y,
+    /*KOpM, */ KOpZ,
+    H,
+    const N: usize,
+>(
+    opA: &A,
+    b: &A::Observable,
+    reg: Reg,
+    prox_penalty: &P,
+    config: &SlidingPDPSConfig<F>,
+    iterator: I,
+    mut plotter: SeqPlotter<F, N>,
+    //opKμ : KOpM,
+    opKz: &KOpZ,
+    fnR: &R,
+    fnH: &H,
+    mut z: Z,
+    mut y: Y,
+) -> MeasureZ<F, Z, N>
+where
+    F: Float + ToNalgebraRealField,
+    I: AlgIteratorFactory<IterInfo<F, N>>,
+    A: ForwardModel<MeasureZ<F, Z, N>, F, PairNorm<Radon, L2, L2>, PreadjointCodomain = Pair<S, Z>>
+        + AdjointProductPairBoundedBy<MeasureZ<F, Z, N>, P, IdOp<Z>, FloatType = F>
+        + BoundedCurvature<FloatType = F>,
+    S: DifferentiableRealMapping<F, N>,
+    for<'b> &'b A::Observable: std::ops::Neg<Output = A::Observable> + Instance<A::Observable>,
+    PlotLookup: Plotting<N>,
+    RNDM<F, N>: SpikeMerging<F>,
+    Reg: SlidingRegTerm<F, N>,
+    P: ProxPenalty<F, S, Reg, N>,
+    // KOpM : Linear<RNDM<F, N>, Codomain=Y>
+    //     + GEMV<F, RNDM<F, N>>
+    //     + Preadjointable<
+    //         RNDM<F, N>, Y,
+    //         PreadjointCodomain = S,
+    //     >
+    //     + TransportLipschitz<L2Squared, FloatType=F>
+    //     + AdjointProductBoundedBy<RNDM<F, N>, 𝒟, FloatType=F>,
+    // for<'b> KOpM::Preadjoint<'b> : GEMV<F, Y>,
+    // Since Z is Hilbert, we may just as well use adjoints for K_z.
+    KOpZ: BoundedLinear<Z, L2, L2, F, Codomain = Y>
+        + GEMV<F, Z>
+        + Adjointable<Z, Y, AdjointCodomain = Z>,
+    for<'b> KOpZ::Adjoint<'b>: GEMV<F, Y>,
+    Y: AXPY<F> + Euclidean<F, Output = Y> + Clone + ClosedAdd,
+    for<'b> &'b Y: Instance<Y>,
+    Z: AXPY<F, Owned = Z> + Euclidean<F, Output = Z> + Clone + Norm<F, L2> + Dist<F, L2>,
+    for<'b> &'b Z: Instance<Z>,
+    R: Prox<Z, Codomain = F>,
+    H: Conjugable<Y, F, Codomain = F>,
+    for<'b> H::Conjugate<'b>: Prox<Y>,
+{
+    // Check parameters
+    assert!(
+        config.τ0 > 0.0
+            && config.τ0 < 1.0
+            && config.σp0 > 0.0
+            && config.σp0 < 1.0
+            && config.σd0 > 0.0
+            && config.σp0 * config.σd0 <= 1.0,
+        "Invalid step length parameters"
+    );
+    config.transport.check();
+
+    // Initialise iterates
+    let mut μ = DiscreteMeasure::new();
+    let mut γ1 = DiscreteMeasure::new();
+    let mut residual = calculate_residual(Pair(&μ, &z), opA, b);
+    let zero_z = z.similar_origin();
+
+    // Set up parameters
+    // TODO: maybe this PairNorm doesn't make sense here?
+    // let opAnorm = opA.opnorm_bound(PairNorm(Radon, L2, L2), L2);
+    let bigθ = 0.0; //opKμ.transport_lipschitz_factor(L2Squared);
+    let bigM = 0.0; //opKμ.adjoint_product_bound(&op𝒟).unwrap().sqrt();
+    let nKz = opKz.opnorm_bound(L2, L2);
+    let ℓ = 0.0;
+    let opIdZ = IdOp::new();
+    let (l, l_z) = opA
+        .adjoint_product_pair_bound(prox_penalty, &opIdZ)
+        .unwrap();
+    // We need to satisfy
+    //
+    //     τσ_dM(1-σ_p L_z)/(1 - τ L) + [σ_p L_z + σ_pσ_d‖K_z‖^2] < 1
+    //                                  ^^^^^^^^^^^^^^^^^^^^^^^^^
+    // with 1 > σ_p L_z and 1 > τ L.
+    //
+    // To do so, we first solve σ_p and σ_d from standard PDPS step length condition
+    // ^^^^^ < 1. then we solve τ from  the rest.
+    let σ_d = config.σd0 / nKz;
+    let σ_p = config.σp0 / (l_z + config.σd0 * nKz);
+    // Observe that = 1 - ^^^^^^^^^^^^^^^^^^^^^ = 1 - σ_{p,0}
+    // We get the condition τσ_d M (1-σ_p L_z) < (1-σ_{p,0})*(1-τ L)
+    // ⟺ τ [ σ_d M (1-σ_p L_z) + (1-σ_{p,0}) L ] < (1-σ_{p,0})
+    let φ = 1.0 - config.σp0;
+    let a = 1.0 - σ_p * l_z;
+    let τ = config.τ0 * φ / (σ_d * bigM * a + φ * l);
+    let ψ = 1.0 - τ * l;
+    let β = σ_p * config.σd0 * nKz / a; // σ_p * σ_d * (nKz * nK_z) / a;
+    assert!(β < 1.0);
+    // Now we need κ‖K_μ(π_♯^1 - π_♯^0)γ‖^2 ≤ (1/θ - τ[ℓ_F + ℓ]) ∫ c_2 dγ for κ defined as:
+    let κ = τ * σ_d * ψ / ((1.0 - β) * ψ - τ * σ_d * bigM);
+    //  The factor two in the manuscript disappears due to the definition of 𝚹 being
+    // for ‖x-y‖₂² instead of c_2(x, y)=‖x-y‖₂²/2.
+    let (maybe_ℓ_F0, maybe_transport_lip) = opA.curvature_bound_components();
+    let transport_lip = maybe_transport_lip.unwrap();
+    let calculate_θ = |ℓ_F, max_transport| {
+        let ℓ_r = transport_lip * max_transport;
+        config.transport.θ0 / (τ * (ℓ + ℓ_F + ℓ_r) + κ * bigθ * max_transport)
+    };
+    let mut θ_or_adaptive = match maybe_ℓ_F0 {
+        // We assume that the residual is decreasing.
+        Some(ℓ_F0) => TransportStepLength::AdaptiveMax {
+            l: ℓ_F0 * b.norm2(), // TODO: could estimate computing the real reesidual
+            max_transport: 0.0,
+            g: calculate_θ,
+        },
+        None => TransportStepLength::FullyAdaptive {
+            l: F::EPSILON,
+            max_transport: 0.0,
+            g: calculate_θ,
+        },
+    };
+    // Acceleration is not currently supported
+    // let γ = dataterm.factor_of_strong_convexity();
+    let ω = 1.0;
+
+    // We multiply tolerance by τ for FB since our subproblems depending on tolerances are scaled
+    // by τ compared to the conditional gradient approach.
+    let tolerance = config.insertion.tolerance * τ * reg.tolerance_scaling();
+    let mut ε = tolerance.initial();
+
+    let starH = fnH.conjugate();
+
+    // Statistics
+    let full_stats = |residual: &A::Observable, μ: &RNDM<F, N>, z: &Z, ε, stats| IterInfo {
+        value: residual.norm2_squared_div2()
+            + fnR.apply(z)
+            + reg.apply(μ)
+            + fnH.apply(/* opKμ.apply(μ) + */ opKz.apply(z)),
+        n_spikes: μ.len(),
+        ε,
+        // postprocessing: config.insertion.postprocessing.then(|| μ.clone()),
+        ..stats
+    };
+    let mut stats = IterInfo::new();
+
+    // Run the algorithm
+    for state in iterator.iter_init(|| full_stats(&residual, &μ, &z, ε, stats.clone())) {
+        // Calculate initial transport
+        let Pair(v, _) = opA.preadjoint().apply(&residual);
+        //opKμ.preadjoint().apply_add(&mut v, y);
+        // We want to proceed as in Example 4.12 but with v and v̆ as in §5.
+        // With A(ν, z) = A_μ ν + A_z z, following Example 5.1, we have
+        // P_ℳ[F'(ν, z) + Ξ(ν, z, y)]= A_ν^*[A_ν ν + A_z z] + K_μ ν = A_ν^*A(ν, z) + K_μ ν,
+        // where A_ν^* becomes a multiplier.
+        // This is much easier with K_μ = 0, which is the only reason why are enforcing it.
+        // TODO: Write a version of initial_transport that can deal with K_μ ≠ 0.
+
+        let (μ_base_masses, mut μ_base_minus_γ0) =
+            initial_transport(&mut γ1, &mut μ, τ, &mut θ_or_adaptive, v);
+
+        // Solve finite-dimensional subproblem several times until the dual variable for the
+        // regularisation term conforms to the assumptions made for the transport above.
+        let (maybe_d, _within_tolerances, mut τv̆, z_new) = 'adapt_transport: loop {
+            // Calculate τv̆ = τA_*(A[μ_transported + μ_transported_base]-b)
+            let residual_μ̆ =
+                calculate_residual2(Pair(&γ1, &z), Pair(&μ_base_minus_γ0, &zero_z), opA, b);
+            let Pair(mut τv̆, τz̆) = opA.preadjoint().apply(residual_μ̆ * τ);
+            // opKμ.preadjoint().gemv(&mut τv̆, τ, y, 1.0);
+
+            // Construct μ^{k+1} by solving finite-dimensional subproblems and insert new spikes.
+            let (maybe_d, within_tolerances) = prox_penalty.insert_and_reweigh(
+                &mut μ,
+                &mut τv̆,
+                &γ1,
+                Some(&μ_base_minus_γ0),
+                τ,
+                ε,
+                &config.insertion,
+                &reg,
+                &state,
+                &mut stats,
+            );
+
+            // Do z variable primal update here to able to estimate B_{v̆^k-v^{k+1}}
+            let mut z_new = τz̆;
+            opKz.adjoint().gemv(&mut z_new, -σ_p, &y, -σ_p / τ);
+            z_new = fnR.prox(σ_p, z_new + &z);
+
+            // A posteriori transport adaptation.
+            if aposteriori_transport(
+                &mut γ1,
+                &mut μ,
+                &mut μ_base_minus_γ0,
+                &μ_base_masses,
+                Some(z_new.dist(&z, L2)),
+                ε,
+                &config.transport,
+            ) {
+                break 'adapt_transport (maybe_d, within_tolerances, τv̆, z_new);
+            }
+        };
+
+        stats.untransported_fraction = Some({
+            assert_eq!(μ_base_masses.len(), γ1.len());
+            let (a, b) = stats.untransported_fraction.unwrap_or((0.0, 0.0));
+            let source = μ_base_masses.iter().map(|v| v.abs()).sum();
+            (a + μ_base_minus_γ0.norm(Radon), b + source)
+        });
+        stats.transport_error = Some({
+            assert_eq!(μ_base_masses.len(), γ1.len());
+            let (a, b) = stats.transport_error.unwrap_or((0.0, 0.0));
+            (a + μ.dist_matching(&γ1), b + γ1.norm(Radon))
+        });
+
+        // Merge spikes.
+        // This crucially expects the merge routine to be stable with respect to spike locations,
+        // and not to performing any pruning. That is be to done below simultaneously for γ.
+        let ins = &config.insertion;
+        if ins.merge_now(&state) {
+            stats.merged += prox_penalty.merge_spikes_no_fitness(
+                &mut μ,
+                &mut τv̆,
+                &γ1,
+                Some(&μ_base_minus_γ0),
+                τ,
+                ε,
+                ins,
+                &reg,
+                //Some(|μ̃ : &RNDM<F, N>| calculate_residual(Pair(μ̃, &z), opA, b).norm2_squared_div2()),
+            );
+        }
+
+        // Prune spikes with zero weight. To maintain correct ordering between μ and γ1, also the
+        // latter needs to be pruned when μ is.
+        // TODO: This could do with a two-vector Vec::retain to avoid copies.
+        let μ_new = DiscreteMeasure::from_iter(μ.iter_spikes().filter(|δ| δ.α != F::ZERO).cloned());
+        if μ_new.len() != μ.len() {
+            let mut μ_iter = μ.iter_spikes();
+            γ1.prune_by(|_| μ_iter.next().unwrap().α != F::ZERO);
+            stats.pruned += μ.len() - μ_new.len();
+            μ = μ_new;
+        }
+
+        // Do dual update
+        // opKμ.gemv(&mut y, σ_d*(1.0 + ω), &μ, 1.0);    // y = y + σ_d K[(1+ω)(μ,z)^{k+1}]
+        opKz.gemv(&mut y, σ_d * (1.0 + ω), &z_new, 1.0);
+        // opKμ.gemv(&mut y, -σ_d*ω, μ_base, 1.0);// y = y + σ_d K[(1+ω)(μ,z)^{k+1} - ω (μ,z)^k]-b
+        opKz.gemv(&mut y, -σ_d * ω, z, 1.0); // y = y + σ_d K[(1+ω)(μ,z)^{k+1} - ω (μ,z)^k]-b
+        y = starH.prox(σ_d, y);
+        z = z_new;
+
+        // Update residual
+        residual = calculate_residual(Pair(&μ, &z), opA, b);
+
+        // Update step length parameters
+        // let ω = pdpsconfig.acceleration.accelerate(&mut τ, &mut σ, γ);
+
+        // Give statistics if requested
+        let iter = state.iteration();
+        stats.this_iters += 1;
+
+        state.if_verbose(|| {
+            plotter.plot_spikes(iter, maybe_d.as_ref(), Some(&τv̆), &μ);
+            full_stats(
+                &residual,
+                &μ,
+                &z,
+                ε,
+                std::mem::replace(&mut stats, IterInfo::new()),
+            )
+        });
+
+        // Update main tolerance for next iteration
+        ε = tolerance.update(ε, iter);
+    }
+
+    let fit = |μ̃: &RNDM<F, N>| {
+        (opA.apply(Pair(μ̃, &z))-b).norm2_squared_div2()
+        //+ fnR.apply(z) + reg.apply(μ)
+        + fnH.apply(/* opKμ.apply(&μ̃) + */ opKz.apply(&z))
+    };
+
+    μ.merge_spikes_fitness(config.insertion.final_merging_method(), fit, |&v| v);
+    μ.prune();
+    Pair(μ, z)
+}