src/fb.rs

Thu, 08 Dec 2022 14:10:07 +0200

author
Tuomo Valkonen <tuomov@iki.fi>
date
Thu, 08 Dec 2022 14:10:07 +0200
changeset 21
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parent 13
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child 24
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permissions
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Save more CSV files when iteration-wise plotting is enabled.

This helps to generate TikZ illustrations for presentations.

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1 /*!
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2 Solver for the point source localisation problem using a forward-backward splitting method.
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3
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4 This corresponds to the manuscript
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5
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6 * Valkonen T. - _Proximal methods for point source localisation_,
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7 [arXiv:2212.02991](https://arxiv.org/abs/2212.02991).
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8
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9 The main routine is [`pointsource_fb`]. It is based on [`generic_pointsource_fb`], which is also
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10 used by our [primal-dual proximal splitting][crate::pdps] implementation.
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11
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12 FISTA-type inertia can also be enabled through [`FBConfig::meta`].
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13
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14 ## Problem
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15
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16 <p>
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17 Our objective is to solve
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18 $$
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19 \min_{μ ∈ ℳ(Ω)}~ F_0(Aμ-b) + α \|μ\|_{ℳ(Ω)} + δ_{≥ 0}(μ),
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20 $$
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21 where $F_0(y)=\frac{1}{2}\|y\|_2^2$ and the forward operator $A \in 𝕃(ℳ(Ω); ℝ^n)$.
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22 </p>
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23
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24 ## Approach
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25
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26 <p>
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27 As documented in more detail in the paper, on each step we approximately solve
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28 $$
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29 \min_{μ ∈ ℳ(Ω)}~ F(x) + α \|μ\|_{ℳ(Ω)} + δ_{≥ 0}(x) + \frac{1}{2}\|μ-μ^k|_𝒟^2,
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30 $$
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31 where $𝒟: 𝕃(ℳ(Ω); C_c(Ω))$ is typically a convolution operator.
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32 </p>
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33
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34 ## Finite-dimensional subproblems.
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35
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36 With $C$ a projection from [`DiscreteMeasure`] to the weights, and $x^k$ such that $x^k=Cμ^k$, we
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37 form the discretised linearised inner problem
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38 <p>
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39 $$
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40 \min_{x ∈ ℝ^n}~ τ\bigl(F(Cx^k) + [C^*∇F(Cx^k)]^⊤(x-x^k) + α {\vec 1}^⊤ x\bigr)
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41 + δ_{≥ 0}(x) + \frac{1}{2}\|x-x^k\|_{C^*𝒟C}^2,
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42 $$
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43 equivalently
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44 $$
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45 \begin{aligned}
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46 \min_x~ & τF(Cx^k) - τ[C^*∇F(Cx^k)]^⊤x^k + \frac{1}{2} (x^k)^⊤ C^*𝒟C x^k
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47 \\
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48 &
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49 - [C^*𝒟C x^k - τC^*∇F(Cx^k)]^⊤ x
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50 \\
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51 &
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52 + \frac{1}{2} x^⊤ C^*𝒟C x
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53 + τα {\vec 1}^⊤ x + δ_{≥ 0}(x),
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54 \end{aligned}
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55 $$
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56 In other words, we obtain the quadratic non-negativity constrained problem
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57 $$
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58 \min_{x ∈ ℝ^n}~ \frac{1}{2} x^⊤ Ã x - b̃^⊤ x + c + τα {\vec 1}^⊤ x + δ_{≥ 0}(x).
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59 $$
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60 where
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61 $$
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62 \begin{aligned}
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63 Ã & = C^*𝒟C,
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64 \\
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65 g̃ & = C^*𝒟C x^k - τ C^*∇F(Cx^k)
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66 = C^* 𝒟 μ^k - τ C^*A^*(Aμ^k - b)
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67 \\
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68 c & = τ F(Cx^k) - τ[C^*∇F(Cx^k)]^⊤x^k + \frac{1}{2} (x^k)^⊤ C^*𝒟C x^k
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69 \\
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70 &
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71 = \frac{τ}{2} \|Aμ^k-b\|^2 - τ[Aμ^k-b]^⊤Aμ^k + \frac{1}{2} \|μ_k\|_{𝒟}^2
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72 \\
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73 &
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74 = -\frac{τ}{2} \|Aμ^k-b\|^2 + τ[Aμ^k-b]^⊤ b + \frac{1}{2} \|μ_k\|_{𝒟}^2.
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75 \end{aligned}
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76 $$
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77 </p>
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78
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79 We solve this with either SSN or FB via [`quadratic_nonneg`] as determined by
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80 [`InnerSettings`] in [`FBGenericConfig::inner`].
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81 */
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82
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83 use numeric_literals::replace_float_literals;
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84 use serde::{Serialize, Deserialize};
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85 use colored::Colorize;
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86 use nalgebra::DVector;
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87
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88 use alg_tools::iterate::{
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89 AlgIteratorFactory,
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90 AlgIteratorState,
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91 };
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92 use alg_tools::euclidean::Euclidean;
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93 use alg_tools::norms::Norm;
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94 use alg_tools::linops::Apply;
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95 use alg_tools::sets::Cube;
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96 use alg_tools::loc::Loc;
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97 use alg_tools::bisection_tree::{
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98 BTFN,
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99 PreBTFN,
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100 Bounds,
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101 BTNodeLookup,
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102 BTNode,
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103 BTSearch,
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104 P2Minimise,
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105 SupportGenerator,
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106 LocalAnalysis,
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107 Bounded,
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108 };
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109 use alg_tools::mapping::RealMapping;
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110 use alg_tools::nalgebra_support::ToNalgebraRealField;
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111
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112 use crate::types::*;
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113 use crate::measures::{
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114 DiscreteMeasure,
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115 DeltaMeasure,
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116 Radon
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117 };
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118 use crate::measures::merging::{
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119 SpikeMergingMethod,
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120 SpikeMerging,
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121 };
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122 use crate::forward_model::ForwardModel;
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123 use crate::seminorms::{
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124 DiscreteMeasureOp, Lipschitz
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125 };
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126 use crate::subproblem::{
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127 quadratic_nonneg,
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128 InnerSettings,
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129 InnerMethod,
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130 };
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131 use crate::tolerance::Tolerance;
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132 use crate::plot::{
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133 SeqPlotter,
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134 Plotting,
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135 PlotLookup
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136 };
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137
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138 /// Method for constructing $μ$ on each iteration
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139 #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
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140 #[allow(dead_code)]
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141 pub enum InsertionStyle {
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142 /// Resuse previous $μ$ from previous iteration, optimising weights
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143 /// before inserting new spikes.
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144 Reuse,
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145 /// Start each iteration with $μ=0$.
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146 Zero,
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147 }
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148
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149 /// Meta-algorithm type
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150 #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
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151 #[allow(dead_code)]
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152 pub enum FBMetaAlgorithm {
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153 /// No meta-algorithm
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154 None,
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155 /// FISTA-style inertia
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156 InertiaFISTA,
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157 }
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158
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159 /// Settings for [`pointsource_fb`].
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160 #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
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161 #[serde(default)]
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162 pub struct FBConfig<F : Float> {
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163 /// Step length scaling
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164 pub τ0 : F,
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165 /// Meta-algorithm to apply
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166 pub meta : FBMetaAlgorithm,
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167 /// Generic parameters
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168 pub insertion : FBGenericConfig<F>,
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169 }
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170
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171 /// Settings for the solution of the stepwise optimality condition in algorithms based on
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172 /// [`generic_pointsource_fb`].
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173 #[derive(Clone, Copy, Eq, PartialEq, Serialize, Deserialize, Debug)]
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174 #[serde(default)]
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175 pub struct FBGenericConfig<F : Float> {
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176 /// Method for constructing $μ$ on each iteration; see [`InsertionStyle`].
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177 pub insertion_style : InsertionStyle,
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178 /// Tolerance for point insertion.
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179 pub tolerance : Tolerance<F>,
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180 /// Stop looking for predual maximum (where to isert a new point) below
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181 /// `tolerance` multiplied by this factor.
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182 pub insertion_cutoff_factor : F,
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183 /// Settings for branch and bound refinement when looking for predual maxima
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184 pub refinement : RefinementSettings<F>,
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185 /// Maximum insertions within each outer iteration
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186 pub max_insertions : usize,
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187 /// Pair `(n, m)` for maximum insertions `m` on first `n` iterations.
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188 pub bootstrap_insertions : Option<(usize, usize)>,
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189 /// Inner method settings
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190 pub inner : InnerSettings<F>,
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191 /// Spike merging method
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192 pub merging : SpikeMergingMethod<F>,
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193 /// Tolerance multiplier for merges
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194 pub merge_tolerance_mult : F,
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195 /// Spike merging method after the last step
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196 pub final_merging : SpikeMergingMethod<F>,
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197 /// Iterations between merging heuristic tries
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198 pub merge_every : usize,
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199 /// Save $μ$ for postprocessing optimisation
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200 pub postprocessing : bool
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201 }
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202
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203 #[replace_float_literals(F::cast_from(literal))]
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204 impl<F : Float> Default for FBConfig<F> {
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205 fn default() -> Self {
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206 FBConfig {
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207 τ0 : 0.99,
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208 meta : FBMetaAlgorithm::None,
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209 insertion : Default::default()
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210 }
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211 }
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212 }
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213
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214 #[replace_float_literals(F::cast_from(literal))]
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215 impl<F : Float> Default for FBGenericConfig<F> {
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216 fn default() -> Self {
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217 FBGenericConfig {
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218 insertion_style : InsertionStyle::Reuse,
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219 tolerance : Default::default(),
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220 insertion_cutoff_factor : 1.0,
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221 refinement : Default::default(),
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222 max_insertions : 100,
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223 //bootstrap_insertions : None,
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224 bootstrap_insertions : Some((10, 1)),
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225 inner : InnerSettings {
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226 method : InnerMethod::SSN,
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227 .. Default::default()
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228 },
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229 merging : SpikeMergingMethod::None,
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230 //merging : Default::default(),
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231 final_merging : Default::default(),
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232 merge_every : 10,
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233 merge_tolerance_mult : 2.0,
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234 postprocessing : false,
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235 }
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236 }
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237 }
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238
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239 /// Trait for specialisation of [`generic_pointsource_fb`] to basic FB, FISTA.
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240 ///
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241 /// The idea is that the residual $Aμ - b$ in the forward step can be replaced by an arbitrary
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242 /// value. For example, to implement [primal-dual proximal splitting][crate::pdps] we replace it
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243 /// with the dual variable $y$. We can then also implement alternative data terms, as the
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244 /// (pre)differential of $F(μ)=F\_0(Aμ-b)$ is $F\'(μ) = A\_*F\_0\'(Aμ-b)$. In the case of the
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245 /// quadratic fidelity $F_0(y)=\frac{1}{2}\\|y\\|_2^2$ in a Hilbert space, of course,
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246 /// $F\_0\'(Aμ-b)=Aμ-b$ is the residual.
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247 pub trait FBSpecialisation<F : Float, Observable : Euclidean<F>, const N : usize> : Sized {
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248 /// Updates the residual and does any necessary pruning of `μ`.
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249 ///
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250 /// Returns the new residual and possibly a new step length.
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251 ///
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252 /// The measure `μ` may also be modified to apply, e.g., inertia to it.
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253 /// The updated residual should correspond to the residual at `μ`.
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254 /// See the [trait documentation][FBSpecialisation] for the use and meaning of the residual.
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255 ///
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256 /// The parameter `μ_base` is the base point of the iteration, typically the previous iterate,
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257 /// but for, e.g., FISTA has inertia applied to it.
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258 fn update(
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259 &mut self,
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260 μ : &mut DiscreteMeasure<Loc<F, N>, F>,
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261 μ_base : &DiscreteMeasure<Loc<F, N>, F>,
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262 ) -> (Observable, Option<F>);
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263
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264 /// Calculates the data term value corresponding to iterate `μ` and available residual.
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265 ///
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266 /// Inertia and other modifications, as deemed, necessary, should be applied to `μ`.
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267 ///
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268 /// The blanket implementation correspondsn to the 2-norm-squared data fidelity
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269 /// $\\|\text{residual}\\|\_2^2/2$.
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270 fn calculate_fit(
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271 &self,
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272 _μ : &DiscreteMeasure<Loc<F, N>, F>,
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273 residual : &Observable
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274 ) -> F {
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275 residual.norm2_squared_div2()
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276 }
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277
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278 /// Calculates the data term value at $μ$.
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279 ///
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280 /// Unlike [`Self::calculate_fit`], no inertia, etc., should be applied to `μ`.
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281 fn calculate_fit_simple(
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282 &self,
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283 μ : &DiscreteMeasure<Loc<F, N>, F>,
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284 ) -> F;
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285
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286 /// Returns the final iterate after any necessary postprocess pruning, merging, etc.
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287 fn postprocess(self, mut μ : DiscreteMeasure<Loc<F, N>, F>, merging : SpikeMergingMethod<F>)
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288 -> DiscreteMeasure<Loc<F, N>, F>
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289 where DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F> {
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290 μ.merge_spikes_fitness(merging,
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291 |μ̃| self.calculate_fit_simple(μ̃),
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292 |&v| v);
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293 μ.prune();
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294 μ
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295 }
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296
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297 /// Returns measure to be used for value calculations, which may differ from μ.
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298 fn value_μ<'c, 'b : 'c>(&'b self, μ : &'c DiscreteMeasure<Loc<F, N>, F>)
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299 -> &'c DiscreteMeasure<Loc<F, N>, F> {
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300 μ
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301 }
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302 }
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303
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304 /// Specialisation of [`generic_pointsource_fb`] to basic μFB.
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305 struct BasicFB<
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306 'a,
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307 F : Float + ToNalgebraRealField,
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308 A : ForwardModel<Loc<F, N>, F>,
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309 const N : usize
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310 > {
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311 /// The data
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312 b : &'a A::Observable,
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313 /// The forward operator
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314 opA : &'a A,
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315 }
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316
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317 /// Implementation of [`FBSpecialisation`] for basic μFB forward-backward splitting.
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318 #[replace_float_literals(F::cast_from(literal))]
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319 impl<'a, F : Float + ToNalgebraRealField , A : ForwardModel<Loc<F, N>, F>, const N : usize>
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320 FBSpecialisation<F, A::Observable, N> for BasicFB<'a, F, A, N> {
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321 fn update(
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322 &mut self,
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323 μ : &mut DiscreteMeasure<Loc<F, N>, F>,
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324 _μ_base : &DiscreteMeasure<Loc<F, N>, F>
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325 ) -> (A::Observable, Option<F>) {
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326 μ.prune();
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327 //*residual = self.opA.apply(μ) - self.b;
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328 let mut residual = self.b.clone();
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329 self.opA.gemv(&mut residual, 1.0, μ, -1.0);
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330 (residual, None)
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331 }
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diff changeset
332
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diff changeset
333 fn calculate_fit_simple(
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334 &self,
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diff changeset
335 μ : &DiscreteMeasure<Loc<F, N>, F>,
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
336 ) -> F {
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Tuomo Valkonen <tuomov@iki.fi>
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337 let mut residual = self.b.clone();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
338 self.opA.gemv(&mut residual, 1.0, μ, -1.0);
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
339 residual.norm2_squared_div2()
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diff changeset
340 }
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diff changeset
341 }
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diff changeset
342
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diff changeset
343 /// Specialisation of [`generic_pointsource_fb`] to FISTA.
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Tuomo Valkonen <tuomov@iki.fi>
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344 struct FISTA<
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Tuomo Valkonen <tuomov@iki.fi>
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345 'a,
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Tuomo Valkonen <tuomov@iki.fi>
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346 F : Float + ToNalgebraRealField,
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Tuomo Valkonen <tuomov@iki.fi>
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347 A : ForwardModel<Loc<F, N>, F>,
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Tuomo Valkonen <tuomov@iki.fi>
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348 const N : usize
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Tuomo Valkonen <tuomov@iki.fi>
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349 > {
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350 /// The data
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351 b : &'a A::Observable,
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Tuomo Valkonen <tuomov@iki.fi>
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352 /// The forward operator
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Tuomo Valkonen <tuomov@iki.fi>
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353 opA : &'a A,
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Tuomo Valkonen <tuomov@iki.fi>
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diff changeset
354 /// Current inertial parameter
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Tuomo Valkonen <tuomov@iki.fi>
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355 λ : F,
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356 /// Previous iterate without inertia applied.
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357 /// We need to store this here because `μ_base` passed to [`FBSpecialisation::update`] will
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358 /// have inertia applied to it, so is not useful to use.
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359 μ_prev : DiscreteMeasure<Loc<F, N>, F>,
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Tuomo Valkonen <tuomov@iki.fi>
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360 }
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361
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362 /// Implementation of [`FBSpecialisation`] for μFISTA inertial forward-backward splitting.
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363 #[replace_float_literals(F::cast_from(literal))]
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364 impl<'a, F : Float + ToNalgebraRealField, A : ForwardModel<Loc<F, N>, F>, const N : usize>
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Tuomo Valkonen <tuomov@iki.fi>
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365 FBSpecialisation<F, A::Observable, N> for FISTA<'a, F, A, N> {
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366 fn update(
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367 &mut self,
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Tuomo Valkonen <tuomov@iki.fi>
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368 μ : &mut DiscreteMeasure<Loc<F, N>, F>,
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Tuomo Valkonen <tuomov@iki.fi>
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369 _μ_base : &DiscreteMeasure<Loc<F, N>, F>
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Tuomo Valkonen <tuomov@iki.fi>
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370 ) -> (A::Observable, Option<F>) {
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parents:
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371 // Update inertial parameters
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Tuomo Valkonen <tuomov@iki.fi>
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372 let λ_prev = self.λ;
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373 self.λ = 2.0 * λ_prev / ( λ_prev + (4.0 + λ_prev * λ_prev).sqrt() );
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374 let θ = self.λ / λ_prev - self.λ;
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375 // Perform inertial update on μ.
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
376 // This computes μ ← (1 + θ) * μ - θ * μ_prev, pruning spikes where both μ
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377 // and μ_prev have zero weight. Since both have weights from the finite-dimensional
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378 // subproblem with a proximal projection step, this is likely to happen when the
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Tuomo Valkonen <tuomov@iki.fi>
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379 // spike is not needed. A copy of the pruned μ without artithmetic performed is
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
380 // stored in μ_prev.
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
381 μ.pruning_sub(1.0 + θ, θ, &mut self.μ_prev);
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diff changeset
382
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Tuomo Valkonen <tuomov@iki.fi>
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diff changeset
383 //*residual = self.opA.apply(μ) - self.b;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
384 let mut residual = self.b.clone();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
385 self.opA.gemv(&mut residual, 1.0, μ, -1.0);
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parents:
diff changeset
386 (residual, None)
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
387 }
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
388
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
389 fn calculate_fit_simple(
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parents:
diff changeset
390 &self,
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
391 μ : &DiscreteMeasure<Loc<F, N>, F>,
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
392 ) -> F {
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
393 let mut residual = self.b.clone();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
394 self.opA.gemv(&mut residual, 1.0, μ, -1.0);
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
395 residual.norm2_squared_div2()
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
396 }
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
397
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
398 fn calculate_fit(
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
399 &self,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
400 _μ : &DiscreteMeasure<Loc<F, N>, F>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
401 _residual : &A::Observable
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
402 ) -> F {
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
403 self.calculate_fit_simple(&self.μ_prev)
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
404 }
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
405
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
406 // For FISTA we need to do a final pruning as well, due to the limited
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
407 // pruning that can be done on each step.
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
408 fn postprocess(mut self, μ_base : DiscreteMeasure<Loc<F, N>, F>, merging : SpikeMergingMethod<F>)
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
409 -> DiscreteMeasure<Loc<F, N>, F>
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
410 where DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F> {
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
411 let mut μ = self.μ_prev;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
412 self.μ_prev = μ_base;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
413 μ.merge_spikes_fitness(merging,
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
414 |μ̃| self.calculate_fit_simple(μ̃),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
415 |&v| v);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
416 μ.prune();
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
417 μ
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
418 }
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
419
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
420 fn value_μ<'c, 'b : 'c>(&'c self, _μ : &'c DiscreteMeasure<Loc<F, N>, F>)
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
421 -> &'c DiscreteMeasure<Loc<F, N>, F> {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
422 &self.μ_prev
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
423 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
424 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
425
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
426 /// Iteratively solve the pointsource localisation problem using forward-backward splitting
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
427 ///
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
428 /// The settings in `config` have their [respective documentation](FBConfig). `opA` is the
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
429 /// forward operator $A$, $b$ the observable, and $\lambda$ the regularisation weight.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
430 /// The operator `op𝒟` is used for forming the proximal term. Typically it is a convolution
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
431 /// operator. Finally, the `iterator` is an outer loop verbosity and iteration count control
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
432 /// as documented in [`alg_tools::iterate`].
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
433 ///
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
434 /// For details on the mathematical formulation, see the [module level](self) documentation.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
435 ///
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
436 /// Returns the final iterate.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
437 #[replace_float_literals(F::cast_from(literal))]
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
438 pub fn pointsource_fb<'a, F, I, A, GA, 𝒟, BTA, G𝒟, S, K, const N : usize>(
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
439 opA : &'a A,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
440 b : &A::Observable,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
441 α : F,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
442 op𝒟 : &'a 𝒟,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
443 config : &FBConfig<F>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
444 iterator : I,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
445 plotter : SeqPlotter<F, N>
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
446 ) -> DiscreteMeasure<Loc<F, N>, F>
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
447 where F : Float + ToNalgebraRealField,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
448 I : AlgIteratorFactory<IterInfo<F, N>>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
449 for<'b> &'b A::Observable : std::ops::Neg<Output=A::Observable>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
450 //+ std::ops::Mul<F, Output=A::Observable>, <-- FIXME: compiler overflow
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
451 A::Observable : std::ops::MulAssign<F>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
452 GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
453 A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
454 + Lipschitz<𝒟, FloatType=F>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
455 BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
456 G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
457 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
458 𝒟::Codomain : RealMapping<F, N>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
459 S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
460 K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
461 BTNodeLookup: BTNode<F, usize, Bounds<F>, N>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
462 Cube<F, N>: P2Minimise<Loc<F, N>, F>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
463 PlotLookup : Plotting<N>,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
464 DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F> {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
465
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
466 let initial_residual = -b;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
467 let τ = config.τ0/opA.lipschitz_factor(&op𝒟).unwrap();
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
468
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
469 match config.meta {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
470 FBMetaAlgorithm::None => generic_pointsource_fb(
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
471 opA, α, op𝒟, τ, &config.insertion, iterator, plotter, initial_residual,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
472 BasicFB{ b, opA }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
473 ),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
474 FBMetaAlgorithm::InertiaFISTA => generic_pointsource_fb(
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
475 opA, α, op𝒟, τ, &config.insertion, iterator, plotter, initial_residual,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
476 FISTA{ b, opA, λ : 1.0, μ_prev : DiscreteMeasure::new() }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
477 ),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
478 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
479 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
480
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
481 /// Generic implementation of [`pointsource_fb`].
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
482 ///
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
483 /// The method can be specialised to even primal-dual proximal splitting through the
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
484 /// [`FBSpecialisation`] parameter `specialisation`.
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parents:
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485 /// The settings in `config` have their [respective documentation](FBGenericConfig). `opA` is the
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Tuomo Valkonen <tuomov@iki.fi>
parents:
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486 /// forward operator $A$, $b$ the observable, and $\lambda$ the regularisation weight.
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Tuomo Valkonen <tuomov@iki.fi>
parents:
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487 /// The operator `op𝒟` is used for forming the proximal term. Typically it is a convolution
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parents:
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488 /// operator. Finally, the `iterator` is an outer loop verbosity and iteration count control
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Tuomo Valkonen <tuomov@iki.fi>
parents:
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489 /// as documented in [`alg_tools::iterate`].
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parents:
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490 ///
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491 /// The implementation relies on [`alg_tools::bisection_tree::BTFN`] presentations of
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Tuomo Valkonen <tuomov@iki.fi>
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492 /// sums of simple functions usign bisection trees, and the related
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493 /// [`alg_tools::bisection_tree::Aggregator`]s, to efficiently search for component functions
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494 /// active at a specific points, and to maximise their sums. Through the implementation of the
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495 /// [`alg_tools::bisection_tree::BT`] bisection trees, it also relies on the copy-on-write features
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parents:
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496 /// of [`std::sync::Arc`] to only update relevant parts of the bisection tree when adding functions.
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497 ///
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498 /// Returns the final iterate.
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diff changeset
499 #[replace_float_literals(F::cast_from(literal))]
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Tuomo Valkonen <tuomov@iki.fi>
parents:
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500 pub fn generic_pointsource_fb<'a, F, I, A, GA, 𝒟, BTA, G𝒟, S, K, Spec, const N : usize>(
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501 opA : &'a A,
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Tuomo Valkonen <tuomov@iki.fi>
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diff changeset
502 α : F,
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Tuomo Valkonen <tuomov@iki.fi>
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503 op𝒟 : &'a 𝒟,
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504 mut τ : F,
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Tuomo Valkonen <tuomov@iki.fi>
parents:
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505 config : &FBGenericConfig<F>,
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Tuomo Valkonen <tuomov@iki.fi>
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506 iterator : I,
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Tuomo Valkonen <tuomov@iki.fi>
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507 mut plotter : SeqPlotter<F, N>,
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Tuomo Valkonen <tuomov@iki.fi>
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508 mut residual : A::Observable,
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509 mut specialisation : Spec,
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Tuomo Valkonen <tuomov@iki.fi>
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510 ) -> DiscreteMeasure<Loc<F, N>, F>
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Tuomo Valkonen <tuomov@iki.fi>
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511 where F : Float + ToNalgebraRealField,
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
512 I : AlgIteratorFactory<IterInfo<F, N>>,
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Tuomo Valkonen <tuomov@iki.fi>
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513 Spec : FBSpecialisation<F, A::Observable, N>,
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Tuomo Valkonen <tuomov@iki.fi>
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514 A::Observable : std::ops::MulAssign<F>,
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Tuomo Valkonen <tuomov@iki.fi>
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515 GA : SupportGenerator<F, N, SupportType = S, Id = usize> + Clone,
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516 A : ForwardModel<Loc<F, N>, F, PreadjointCodomain = BTFN<F, GA, BTA, N>>
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517 + Lipschitz<𝒟, FloatType=F>,
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518 BTA : BTSearch<F, N, Data=usize, Agg=Bounds<F>>,
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519 G𝒟 : SupportGenerator<F, N, SupportType = K, Id = usize> + Clone,
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520 𝒟 : DiscreteMeasureOp<Loc<F, N>, F, PreCodomain = PreBTFN<F, G𝒟, N>>,
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521 𝒟::Codomain : RealMapping<F, N>,
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Tuomo Valkonen <tuomov@iki.fi>
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522 S: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>,
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Tuomo Valkonen <tuomov@iki.fi>
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523 K: RealMapping<F, N> + LocalAnalysis<F, Bounds<F>, N>,
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Tuomo Valkonen <tuomov@iki.fi>
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524 BTNodeLookup: BTNode<F, usize, Bounds<F>, N>,
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Tuomo Valkonen <tuomov@iki.fi>
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525 Cube<F, N>: P2Minimise<Loc<F, N>, F>,
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Tuomo Valkonen <tuomov@iki.fi>
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diff changeset
526 PlotLookup : Plotting<N>,
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Tuomo Valkonen <tuomov@iki.fi>
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diff changeset
527 DiscreteMeasure<Loc<F, N>, F> : SpikeMerging<F> {
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Tuomo Valkonen <tuomov@iki.fi>
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528
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
529 // Set up parameters
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
530 let quiet = iterator.is_quiet();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
531 let op𝒟norm = op𝒟.opnorm_bound();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
532 // We multiply tolerance by τ for FB since
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
533 // our subproblems depending on tolerances are scaled by τ compared to the conditional
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
534 // gradient approach.
8
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
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diff changeset
535 let tolerance = config.tolerance * τ * α;
0
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Tuomo Valkonen <tuomov@iki.fi>
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536 let mut ε = tolerance.initial();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
537
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
538 // Initialise operators
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
539 let preadjA = opA.preadjoint();
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
540
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
541 // Initialise iterates
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
542 let mut μ = DiscreteMeasure::new();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
543
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
544 let mut inner_iters = 0;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
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545 let mut this_iters = 0;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
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546 let mut pruned = 0;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
547 let mut merged = 0;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
548
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
549 let μ_diff = |μ_new : &DiscreteMeasure<Loc<F, N>, F>,
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
550 μ_base : &DiscreteMeasure<Loc<F, N>, F>| {
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
551 let mut ν : DiscreteMeasure<Loc<F, N>, F> = match config.insertion_style {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
552 InsertionStyle::Reuse => {
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
553 μ_new.iter_spikes()
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
554 .zip(μ_base.iter_masses().chain(std::iter::repeat(0.0)))
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
555 .map(|(δ, α_base)| (δ.x, α_base - δ.α))
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
556 .collect()
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
557 },
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
558 InsertionStyle::Zero => {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
559 μ_new.iter_spikes()
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
560 .map(|δ| -δ)
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
561 .chain(μ_base.iter_spikes().copied())
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
562 .collect()
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
563 }
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
564 };
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
565 ν.prune(); // Potential small performance improvement
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
566 ν
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
567 };
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
568
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
569 // Run the algorithm
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
570 iterator.iterate(|state| {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
571 // Calculate subproblem tolerances, and update main tolerance for next iteration
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
572 let τα = τ * α;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
573 let target_bounds = Bounds(τα - ε, τα + ε);
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
574 let merge_tolerance = config.merge_tolerance_mult * ε;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
575 let merge_target_bounds = Bounds(τα - merge_tolerance, τα + merge_tolerance);
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
576 let inner_tolerance = ε * config.inner.tolerance_mult;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
577 let refinement_tolerance = ε * config.refinement.tolerance_mult;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
578 let maximise_above = τα + ε * config.insertion_cutoff_factor;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
579 let ε_prev = ε;
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
580 ε = tolerance.update(ε, state.iteration());
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
581
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
582 // Maximum insertion count and measure difference calculation depend on insertion style.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
583 let (m, warn_insertions) = match (state.iteration(), config.bootstrap_insertions) {
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
584 (i, Some((l, k))) if i <= l => (k, false),
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
585 _ => (config.max_insertions, !quiet),
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
586 };
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
587 let max_insertions = match config.insertion_style {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
588 InsertionStyle::Zero => {
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
589 todo!("InsertionStyle::Zero does not currently work with FISTA, so diabled.");
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
590 // let n = μ.len();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
591 // μ = DiscreteMeasure::new();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
592 // n + m
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
593 },
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
594 InsertionStyle::Reuse => m,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
595 };
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
596
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
597 // Calculate smooth part of surrogate model.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
598 // Using `std::mem::replace` here is not ideal, and expects that `empty_observable`
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
599 // has no significant overhead. For some reosn Rust doesn't allow us simply moving
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
600 // the residual and replacing it below before the end of this closure.
7
c32171f7cce5 Remove ergodic tolerance; it's not useful.
Tuomo Valkonen <tuomov@iki.fi>
parents: 0
diff changeset
601 residual *= -τ;
0
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
602 let r = std::mem::replace(&mut residual, opA.empty_observable());
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
603 let minus_τv = preadjA.apply(r); // minus_τv = -τA^*(Aμ^k-b)
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
604 // TODO: should avoid a second copy of μ here; μ_base already stores a copy.
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
605 let ω0 = op𝒟.apply(μ.clone()); // 𝒟μ^k
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
606 //let g = &minus_τv + ω0; // Linear term of surrogate model
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
607
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
608 // Save current base point
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
609 let μ_base = μ.clone();
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
610
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
611 // Add points to support until within error tolerance or maximum insertion count reached.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
612 let mut count = 0;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
613 let (within_tolerances, d) = 'insertion: loop {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
614 if μ.len() > 0 {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
615 // Form finite-dimensional subproblem. The subproblem references to the original μ^k
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
616 // from the beginning of the iteration are all contained in the immutable c and g.
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
617 let à = op𝒟.findim_matrix(μ.iter_locations());
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
618 let g̃ = DVector::from_iterator(μ.len(),
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
619 μ.iter_locations()
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
620 .map(|ζ| minus_τv.apply(ζ) + ω0.apply(ζ))
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
621 .map(F::to_nalgebra_mixed));
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
622 let mut x = μ.masses_dvector();
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
623
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
624 // The gradient of the forward component of the inner objective is C^*𝒟Cx - g̃.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
625 // We have |C^*𝒟Cx|_2 = sup_{|z|_2 ≤ 1} ⟨z, C^*𝒟Cx⟩ = sup_{|z|_2 ≤ 1} ⟨Cz|𝒟Cx⟩
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
626 // ≤ sup_{|z|_2 ≤ 1} |Cz|_ℳ |𝒟Cx|_∞ ≤ sup_{|z|_2 ≤ 1} |Cz|_ℳ |𝒟| |Cx|_ℳ
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
627 // ≤ sup_{|z|_2 ≤ 1} |z|_1 |𝒟| |x|_1 ≤ sup_{|z|_2 ≤ 1} n |z|_2 |𝒟| |x|_2
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Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
628 // = n |𝒟| |x|_2, where n is the number of points. Therefore
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
629 let inner_τ = config.inner.τ0 / (op𝒟norm * F::cast_from(μ.len()));
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
630
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
631 // Solve finite-dimensional subproblem.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
632 let inner_it = config.inner.iterator_options.stop_target(inner_tolerance);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
633 inner_iters += quadratic_nonneg(config.inner.method, &Ã, &g̃, τ*α, &mut x,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
634 inner_τ, inner_it);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
635
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
636 // Update masses of μ based on solution of finite-dimensional subproblem.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
637 μ.set_masses_dvector(&x);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
638 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
639
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
640 // Form d = ω0 - τv - 𝒟μ = -𝒟(μ - μ^k) - τv for checking the proximate optimality
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
641 // conditions in the predual space, and finding new points for insertion, if necessary.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
642 let mut d = &minus_τv + op𝒟.preapply(μ_diff(&μ, &μ_base));
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
643
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
644 // If no merging heuristic is used, let's be more conservative about spike insertion,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
645 // and skip it after first round. If merging is done, being more greedy about spike
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
646 // insertion also seems to improve performance.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
647 let may_break = if let SpikeMergingMethod::None = config.merging {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
648 false
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
649 } else {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
650 count > 0
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
651 };
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
652
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
653 // If preliminary check indicates that we are in bonds, and if it otherwise matches
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
654 // the insertion strategy, skip insertion.
7
c32171f7cce5 Remove ergodic tolerance; it's not useful.
Tuomo Valkonen <tuomov@iki.fi>
parents: 0
diff changeset
655 if may_break && target_bounds.superset(&d.bounds()) {
0
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
656 break 'insertion (true, d)
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
657 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
658
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
659 // If the rough check didn't indicate stopping, find maximising point, maintaining for
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
660 // the calculations in the beginning of the loop that v_ξ = (ω0-τv-𝒟μ)(ξ) = d(ξ),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
661 // where 𝒟μ is now distinct from μ0 after the insertions already performed.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
662 // We do not need to check lower bounds, as a solution of the finite-dimensional
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
663 // subproblem should always satisfy them.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
664
8
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
Tuomo Valkonen <tuomov@iki.fi>
parents: 7
diff changeset
665 // If μ has some spikes, only find a maximum of d if it is above a threshold
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
Tuomo Valkonen <tuomov@iki.fi>
parents: 7
diff changeset
666 // defined by the refinment tolerance.
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
Tuomo Valkonen <tuomov@iki.fi>
parents: 7
diff changeset
667 let (ξ, v_ξ) = match d.maximise_above(maximise_above, refinement_tolerance,
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
Tuomo Valkonen <tuomov@iki.fi>
parents: 7
diff changeset
668 config.refinement.max_steps) {
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
Tuomo Valkonen <tuomov@iki.fi>
parents: 7
diff changeset
669 None => break 'insertion (true, d),
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
Tuomo Valkonen <tuomov@iki.fi>
parents: 7
diff changeset
670 Some(res) => res,
0
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
671 };
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
672
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
673 // Break if maximum insertion count reached
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
674 if count >= max_insertions {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
675 let in_bounds2 = target_bounds.upper() >= v_ξ;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
676 break 'insertion (in_bounds2, d)
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
677 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
678
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
679 // No point in optimising the weight here; the finite-dimensional algorithm is fast.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
680 μ += DeltaMeasure { x : ξ, α : 0.0 };
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
681 count += 1;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
682 };
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
683
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
684 if !within_tolerances && warn_insertions {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
685 // Complain (but continue) if we failed to get within tolerances
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
686 // by inserting more points.
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
687 let err = format!("Maximum insertions reached without achieving \
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
688 subproblem solution tolerance");
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
689 println!("{}", err.red());
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
690 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
691
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
692 // Merge spikes
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
693 if state.iteration() % config.merge_every == 0 {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
694 let n_before_merge = μ.len();
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
695 μ.merge_spikes(config.merging, |μ_candidate| {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
696 let mut d = &minus_τv + op𝒟.preapply(μ_diff(&μ_candidate, &μ_base));
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
697
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
698 if merge_target_bounds.superset(&d.bounds()) {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
699 return Some(())
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
700 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
701
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
702 let d_min_supp = μ_candidate.iter_spikes().filter_map(|&DeltaMeasure{ α, ref x }| {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
703 (α != 0.0).then(|| d.apply(x))
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
704 }).reduce(F::min);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
705
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
706 if d_min_supp.map_or(true, |b| b >= merge_target_bounds.lower()) &&
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
707 d.has_upper_bound(merge_target_bounds.upper(), refinement_tolerance,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
708 config.refinement.max_steps) {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
709 Some(())
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
710 } else {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
711 None
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
712 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
713 });
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
714 debug_assert!(μ.len() >= n_before_merge);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
715 merged += μ.len() - n_before_merge;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
716 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
717
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
718 let n_before_prune = μ.len();
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
719 (residual, τ) = match specialisation.update(&mut μ, &μ_base) {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
720 (r, None) => (r, τ),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
721 (r, Some(new_τ)) => (r, new_τ)
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
722 };
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
723 debug_assert!(μ.len() <= n_before_prune);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
724 pruned += n_before_prune - μ.len();
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
725
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
726 this_iters += 1;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
727
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
728 // Give function value if needed
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
729 state.if_verbose(|| {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
730 let value_μ = specialisation.value_μ(&μ);
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
731 // Plot if so requested
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
732 plotter.plot_spikes(
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
733 format!("iter {} end; {}", state.iteration(), within_tolerances), &d,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
734 "start".to_string(), Some(&minus_τv),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
735 Some(target_bounds), value_μ,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
736 );
8
ea3ca78873e8 Clean up / remove various unused FB algorithm family hacks.
Tuomo Valkonen <tuomov@iki.fi>
parents: 7
diff changeset
737 // Calculate mean inner iterations and reset relevant counters.
0
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
738 // Return the statistics
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
739 let res = IterInfo {
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
740 value : specialisation.calculate_fit(&μ, &residual) + α * value_μ.norm(Radon),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
741 n_spikes : value_μ.len(),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
742 inner_iters,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
743 this_iters,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
744 merged,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
745 pruned,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
746 ε : ε_prev,
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
747 postprocessing: config.postprocessing.then(|| value_μ.clone()),
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
748 };
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
749 inner_iters = 0;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
750 this_iters = 0;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
751 merged = 0;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
752 pruned = 0;
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
753 res
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
754 })
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
755 });
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
756
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
757 specialisation.postprocess(μ, config.final_merging)
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
758 }
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
759
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
760
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
761
eb3c7813b67a Initial version
Tuomo Valkonen <tuomov@iki.fi>
parents:
diff changeset
762

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