argmin 0.11.0

Numerical optimization in pure Rust
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138

// Copyright 2018-2024 argmin developers
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or
// http://opensource.org/licenses/MIT>, at your option. This file may not be
// copied, modified, or distributed except according to those terms.

//! # Landweber iteration
//!
//! The Landweber iteration is a solver for ill-posed linear inverse problems.
//! See [`Landweber`] for details.
//!
//! ## References
//!
//! Landweber, L. (1951): An iteration formula for Fredholm integral equations of the first
//! kind. Amer. J. Math. 73, 615–624
//!
//! <https://en.wikipedia.org/wiki/Landweber_iteration>

use crate::core::{ArgminFloat, Error, Gradient, IterState, Problem, Solver, KV};
use argmin_math::ArgminScaledSub;
#[cfg(feature = "serde1")]
use serde::{Deserialize, Serialize};

/// # Landweber iteration
///
/// The Landweber iteration is a solver for ill-posed linear inverse problems.
///
/// In iteration `k`, the new parameter vector `x_{k+1}` is calculated from the previous parameter
/// vector `x_k` and the gradient at `x_k` according to the following update rule:
///
/// `x_{k+1} = x_k - omega * \nabla f(x_k)`
///
/// ## Requirements on the optimization problem
///
/// The optimization problem is required to implement [`Gradient`].
///
/// ## References
///
/// Landweber, L. (1951): An iteration formula for Fredholm integral equations of the first
/// kind. Amer. J. Math. 73, 615–624
///
/// <https://en.wikipedia.org/wiki/Landweber_iteration>
#[derive(Clone, Copy)]
#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
pub struct Landweber<F> {
    /// omega
    omega: F,
}

impl<F> Landweber<F> {
    /// Construct a new instance of [`Landweber`]
    ///
    /// # Example
    ///
    /// ```
    /// # use argmin::solver::landweber::Landweber;
    /// let omega: f64 = 0.5;
    /// let landweber = Landweber::new(omega);
    /// ```
    pub fn new(omega: F) -> Self {
        Landweber { omega }
    }
}

impl<O, F, P, G> Solver<O, IterState<P, G, (), (), (), F>> for Landweber<F>
where
    O: Gradient<Param = P, Gradient = G>,
    P: Clone + ArgminScaledSub<G, F, P>,
    F: ArgminFloat,
{
    fn name(&self) -> &str {
        "Landweber"
    }

    fn next_iter(
        &mut self,
        problem: &mut Problem<O>,
        mut state: IterState<P, G, (), (), (), F>,
    ) -> Result<(IterState<P, G, (), (), (), F>, Option<KV>), Error> {
        let param = state.take_param().ok_or_else(argmin_error_closure!(
            NotInitialized,
            concat!(
                "`Landweber` requires an initial parameter vector. ",
                "Please provide an initial guess via `Executor`s `configure` method."
            )
        ))?;
        let grad = problem.gradient(&param)?;
        let new_param = param.scaled_sub(&self.omega, &grad);
        Ok((state.param(new_param), None))
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::core::{test_utils::TestProblem, ArgminError, State};
    use approx::assert_relative_eq;

    test_trait_impl!(landweber, Landweber<f64>);

    #[test]
    fn test_new() {
        let omega_in: f64 = 0.5;
        let Landweber { omega } = Landweber::new(omega_in);
        assert_eq!(omega.to_ne_bytes(), omega_in.to_ne_bytes());
    }

    #[test]
    fn test_next_iter_param_not_initialized() {
        let omega: f64 = 0.5;
        let mut landweber = Landweber::new(omega);
        let state = IterState::new();
        let res = landweber.next_iter(&mut Problem::new(TestProblem::new()), state);
        assert_error!(
            res,
            ArgminError,
            concat!(
                "Not initialized: \"`Landweber` requires an initial parameter vector. ",
                "Please provide an initial guess via `Executor`s `configure` method.\""
            )
        );
    }

    #[test]
    fn test_next_iter() {
        let omega: f64 = 0.5;
        let mut landweber = Landweber::new(omega);
        let state = IterState::new().param(vec![2.0, 4.0]);
        let (state, kv) = landweber
            .next_iter(&mut Problem::new(TestProblem::new()), state)
            .unwrap();
        assert!(kv.is_none());
        let new_param = state.get_param().unwrap();
        assert_relative_eq!(new_param[0], 1.0, epsilon = f64::EPSILON);
        assert_relative_eq!(new_param[1], 2.0, epsilon = f64::EPSILON);
    }
}