pointsource_algs: comparison src/sliding

-:6105b5cd8d89
+:f0e8704d3f0e
+/*!
+Solver for the point source localisation problem using a sliding
+forward-backward splitting method.
+*/
+use numeric_literals::replace_float_literals;
+use serde::{Deserialize, Serialize};
+//use colored::Colorize;
+//use nalgebra::{DVector, DMatrix};
+use itertools::izip;
+use std::iter::Iterator;
+use alg_tools::euclidean::Euclidean;
+use alg_tools::iterate::AlgIteratorFactory;
+use alg_tools::mapping::{DifferentiableRealMapping, Instance, Mapping};
+use alg_tools::nalgebra_support::ToNalgebraRealField;
+use alg_tools::norms::Norm;
+use crate::forward_model::{AdjointProductBoundedBy, BoundedCurvature, ForwardModel};
+use crate::measures::merging::SpikeMerging;
+use crate::measures::{DiscreteMeasure, Radon, RNDM};
+use crate::types::*;
+//use crate::tolerance::Tolerance;
+use crate::dataterm::{calculate_residual, calculate_residual2, DataTerm, L2Squared};
+use crate::fb::*;
+use crate::plot::{PlotLookup, Plotting, SeqPlotter};
+use crate::regularisation::SlidingRegTerm;
+//use crate::transport::TransportLipschitz;
+/// Transport settings for [`pointsource_sliding_fb_reg`].
+#[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
+#[serde(default)]
+pub struct TransportConfig<F: Float> {
+/// Transport step length $θ$ normalised to $(0, 1)$.
+pub θ0: F,
+/// Factor in $(0, 1)$ for decreasing transport to adapt to tolerance.
+pub adaptation: F,
+/// A posteriori transport tolerance multiplier (C_pos)
+pub tolerance_mult_con: F,
+}
+#[replace_float_literals(F::cast_from(literal))]
+impl<F: Float> TransportConfig<F> {
+/// Check that the parameters are ok. Panics if not.
+pub fn check(&self) {
+assert!(self.θ0 > 0.0);
+assert!(0.0 < self.adaptation && self.adaptation < 1.0);
+assert!(self.tolerance_mult_con > 0.0);
+}
+}
+#[replace_float_literals(F::cast_from(literal))]
+impl<F: Float> Default for TransportConfig<F> {
+fn default() -> Self {
+TransportConfig {
+θ0: 0.9,
+adaptation: 0.9,
+tolerance_mult_con: 100.0,
+}
+}
+}
+/// Settings for [`pointsource_sliding_fb_reg`].
+#[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
+#[serde(default)]
+pub struct SlidingFBConfig<F: Float> {
+/// Step length scaling
+pub τ0: 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 SlidingFBConfig<F> {
+fn default() -> Self {
+SlidingFBConfig {
+τ0: 0.99,
+transport: Default::default(),
+insertion: Default::default(),
+}
+}
+}
+/// Internal type of adaptive transport step length calculation
+pub(crate) enum TransportStepLength<F: Float, G: Fn(F, F) -> F> {
+/// Fixed, known step length
+#[allow(dead_code)]
+Fixed(F),
+/// Adaptive step length, only wrt. maximum transport.
+/// Content of `l` depends on use case, while `g` calculates the step length from `l`.
+AdaptiveMax { l: F, max_transport: F, g: G },
+/// Adaptive step length.
+/// Content of `l` depends on use case, while `g` calculates the step length from `l`.
+FullyAdaptive { l: F, max_transport: F, g: G },
+}
+/// Constrution of initial transport `γ1` from initial measure `μ` and `v=F'(μ)`
+/// with step lengh τ and transport step length `θ_or_adaptive`.
+#[replace_float_literals(F::cast_from(literal))]
+pub(crate) fn initial_transport<F, G, D, const N: usize>(
+γ1: &mut RNDM<F, N>,
+μ: &mut RNDM<F, N>,
+τ: F,
+θ_or_adaptive: &mut TransportStepLength<F, G>,
+v: D,
+) -> (Vec<F>, RNDM<F, N>)
+where
+F: Float + ToNalgebraRealField,
+G: Fn(F, F) -> F,
+D: DifferentiableRealMapping<F, N>,
+{
+use TransportStepLength::*;
+// Save current base point and shift μ to new positions. Idea is that
+//  μ_base(_masses) = μ^k (vector of masses)
+//  μ_base_minus_γ0 = μ^k - π_♯^0γ^{k+1}
+//  γ1 = π_♯^1γ^{k+1}
+//  μ = μ^{k+1}
+let μ_base_masses: Vec<F> = μ.iter_masses().collect();
+let mut μ_base_minus_γ0 = μ.clone(); // Weights will be set in the loop below.
+// Construct μ^{k+1} and π_♯^1γ^{k+1} initial candidates
+//let mut sum_norm_dv = 0.0;
+let γ_prev_len = γ1.len();
+assert!(μ.len() >= γ_prev_len);
+γ1.extend(μ[γ_prev_len..].iter().cloned());
+// Calculate initial transport and step length.
+// First calculate initial transported weights
+for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) {
+// If old transport has opposing sign, the new transport will be none.
+ρ.α = if (ρ.α > 0.0 && δ.α < 0.0) || (ρ.α < 0.0 && δ.α > 0.0) {
+0.0
+} else {
+δ.α
+};
+}
+// Calculate transport rays.
+match *θ_or_adaptive {
+Fixed(θ) => {
+let θτ = τ * θ;
+for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) {
+ρ.x = δ.x - v.differential(&δ.x) * (ρ.α.signum() * θτ);
+}
+}
+AdaptiveMax {
+l: ℓ_F,
+ref mut max_transport,
+g: ref calculate_θ,
+} => {
+*max_transport = max_transport.max(γ1.norm(Radon));
+let θτ = τ * calculate_θ(ℓ_F, *max_transport);
+for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) {
+ρ.x = δ.x - v.differential(&δ.x) * (ρ.α.signum() * θτ);
+}
+}
+FullyAdaptive {
+l: ref mut adaptive_ℓ_F,
+ref mut max_transport,
+g: ref calculate_θ,
+} => {
+*max_transport = max_transport.max(γ1.norm(Radon));
+let mut θ = calculate_θ(*adaptive_ℓ_F, *max_transport);
+// Do two runs through the spikes to update θ, breaking if first run did not cause
+// a change.
+for _i in 0..=1 {
+let mut changes = false;
+for (δ, ρ) in izip!(μ.iter_spikes(), γ1.iter_spikes_mut()) {
+let dv_x = v.differential(&δ.x);
+let g = &dv_x * (ρ.α.signum() * θ * τ);
+ρ.x = δ.x - g;
+let n = g.norm2();
+if n >= F::EPSILON {
+// Estimate Lipschitz factor of ∇v
+let this_ℓ_F = (dv_x - v.differential(&ρ.x)).norm2() / n;
+*adaptive_ℓ_F = adaptive_ℓ_F.max(this_ℓ_F);
+θ = calculate_θ(*adaptive_ℓ_F, *max_transport);
+changes = true
+}
+}
+if !changes {
+break;
+}
+}
+}
+}
+// Set initial guess for μ=μ^{k+1}.
+for (δ, ρ, &β) in izip!(μ.iter_spikes_mut(), γ1.iter_spikes(), μ_base_masses.iter()) {
+if ρ.α.abs() > F::EPSILON {
+δ.x = ρ.x;
+//δ.α = ρ.α; // already set above
+} else {
+δ.α = β;
+}
+}
+// Calculate μ^k-π_♯^0γ^{k+1} and v̆ = A_*(A[μ_transported + μ_transported_base]-b)
+μ_base_minus_γ0.set_masses(
+μ_base_masses
+.iter()
+.zip(γ1.iter_masses())
+.map(|(&a, b)| a - b),
+);
+(μ_base_masses, μ_base_minus_γ0)
+}
+/// A posteriori transport adaptation.
+#[replace_float_literals(F::cast_from(literal))]
+pub(crate) fn aposteriori_transport<F, const N: usize>(
+γ1: &mut RNDM<F, N>,
+μ: &mut RNDM<F, N>,
+μ_base_minus_γ0: &mut RNDM<F, N>,
+μ_base_masses: &Vec<F>,
+extra: Option<F>,
+ε: F,
+tconfig: &TransportConfig<F>,
+) -> bool
+where
+F: Float + ToNalgebraRealField,
+{
+// 1. If π_♯^1γ^{k+1} = γ1 has non-zero mass at some point y, but μ = μ^{k+1} does not,
+// then the ansatz ∇w̃_x(y) = w^{k+1}(y) may not be satisfied. So set the mass of γ1
+// at that point to zero, and retry.
+let mut all_ok = true;
+for (α_μ, α_γ1) in izip!(μ.iter_masses(), γ1.iter_masses_mut()) {
+if α_μ == 0.0 && *α_γ1 != 0.0 {
+all_ok = false;
+*α_γ1 = 0.0;
+}
+}
+// 2. Through bounding ∫ B_ω(y, z) dλ(x, y, z).
+//    through the estimate ≤ C ‖Δ‖‖γ^{k+1}‖ for Δ := μ^{k+1}-μ^k-(π_♯^1-π_♯^0)γ^{k+1},
+//    which holds for some some C if the convolution kernel in 𝒟 has Lipschitz gradient.
+let nγ = γ1.norm(Radon);
+let nΔ = μ_base_minus_γ0.norm(Radon) + μ.dist_matching(&γ1) + extra.unwrap_or(0.0);
+let t = ε * tconfig.tolerance_mult_con;
+if nγ * nΔ > t {
+// Since t/(nγ*nΔ)<1, and the constant tconfig.adaptation < 1,
+// this will guarantee that eventually ‖γ‖ decreases sufficiently that we
+// will not enter here.
+*γ1 *= tconfig.adaptation * t / (nγ * nΔ);
+all_ok = false
+}
+if !all_ok {
+// Update weights for μ_base_minus_γ0 = μ^k - π_♯^0γ^{k+1}
+μ_base_minus_γ0.set_masses(
+μ_base_masses
+.iter()
+.zip(γ1.iter_masses())
+.map(|(&a, b)| a - b),
+);
+}
+all_ok
+}
+/// Iteratively solve the pointsource localisation problem using sliding forward-backward
+/// splitting
+///
+/// The parametrisation is as for [`pointsource_fb_reg`].
+/// Inertia is currently not supported.
+#[replace_float_literals(F::cast_from(literal))]
+pub fn pointsource_sliding_fb_reg<F, I, A, Reg, P, const N: usize>(
+opA: &A,
+b: &A::Observable,
+reg: Reg,
+prox_penalty: &P,
+config: &SlidingFBConfig<F>,
+iterator: I,
+mut plotter: SeqPlotter<F, N>,
+) -> RNDM<F, N>
+where
+F: Float + ToNalgebraRealField,
+I: AlgIteratorFactory<IterInfo<F, N>>,
+A: ForwardModel<RNDM<F, N>, F>
++ AdjointProductBoundedBy<RNDM<F, N>, P, FloatType = F>
++ BoundedCurvature<FloatType = F>,
+for<'b> &'b A::Observable: std::ops::Neg<Output = A::Observable> + Instance<A::Observable>,
+A::PreadjointCodomain: DifferentiableRealMapping<F, N>,
+RNDM<F, N>: SpikeMerging<F>,
+Reg: SlidingRegTerm<F, N>,
+P: ProxPenalty<F, A::PreadjointCodomain, Reg, N>,
+PlotLookup: Plotting<N>,
+{
+// Check parameters
+assert!(config.τ0 > 0.0, "Invalid step length parameter");
+config.transport.check();
+// Initialise iterates
+let mut μ = DiscreteMeasure::new();
+let mut γ1 = DiscreteMeasure::new();
+let mut residual = -b; // Has to equal $Aμ-b$.
+// Set up parameters
+// let opAnorm = opA.opnorm_bound(Radon, L2);
+//let max_transport = config.max_transport.scale
+//                    * reg.radon_norm_bound(b.norm2_squared() / 2.0);
+//let ℓ = opA.transport.lipschitz_factor(L2Squared) * max_transport;
+let ℓ = 0.0;
+let τ = config.τ0 / opA.adjoint_product_bound(prox_penalty).unwrap();
+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))
+};
+let mut θ_or_adaptive = match maybe_ℓ_F0 {
+//Some(ℓ_F0) => TransportStepLength::Fixed(calculate_θ(ℓ_F0 * b.norm2(), 0.0)),
+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: 10.0 * F::EPSILON, // Start with something very small to estimate differentials
+max_transport: 0.0,
+g: calculate_θ,
+},
+};
+// 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();
+// Statistics
+let full_stats = |residual: &A::Observable, μ: &RNDM<F, N>, ε, stats| IterInfo {
+value: residual.norm2_squared_div2() + reg.apply(μ),
+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, ε, stats.clone())) {
+// Calculate initial transport
+let v = opA.preadjoint().apply(residual);
+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) = 'adapt_transport: loop {
+// Calculate τv̆ = τA_*(A[μ_transported + μ_transported_base]-b)
+let residual_μ̆ = calculate_residual2(&γ1, &μ_base_minus_γ0, opA, b);
+let mut τv̆ = opA.preadjoint().apply(residual_μ̆ * τ);
+// 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,
+);
+// A posteriori transport adaptation.
+if aposteriori_transport(
+&mut γ1,
+&mut μ,
+&mut μ_base_minus_γ0,
+&μ_base_masses,
+None,
+ε,
+&config.transport,
+) {
+break 'adapt_transport (maybe_d, within_tolerances, τv̆);
+}
+};
+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(
+&mut μ,
+&mut τv̆,
+&γ1,
+Some(&μ_base_minus_γ0),
+τ,
+ε,
+ins,
+&reg,
+Some(|μ̃: &RNDM<F, N>| L2Squared.calculate_fit_op(μ̃, opA, b)),
+);
+}
+// 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;
+}
+// Update residual
+residual = calculate_residual(&μ, opA, b);
+let iter = state.iteration();
+stats.this_iters += 1;
+// Give statistics if requested
+state.if_verbose(|| {
+plotter.plot_spikes(iter, maybe_d.as_ref(), Some(&τv̆), &μ);
+full_stats(
+&residual,
+&μ,
+ε,
+std::mem::replace(&mut stats, IterInfo::new()),
+)
+});
+// Update main tolerance for next iteration
+ε = tolerance.update(ε, iter);
+}
+postprocess(μ, &config.insertion, L2Squared, opA, b)
+}

comparison: src/sliding_fb.rs

src/sliding_fb.rs

Mercurial > repos > pointsource_algs / file comparison

comparison: src/sliding_fb.rs

src/sliding_fb.rs