argmin 0.3.0

Mathematical 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
139
140
141
142
143
144
145
146

// Copyright 2018-2020 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.

//! # References:
//!
//! [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
//! Springer. ISBN 0-387-30303-0.

use crate::prelude::*;
use serde::{Deserialize, Serialize};
use std::default::Default;

/// Gauss-Newton method
///
/// [Example](https://github.com/argmin-rs/argmin/blob/master/examples/gaussnewton.rs)
///
/// # References:
///
/// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
/// Springer. ISBN 0-387-30303-0.
#[derive(Clone, Serialize, Deserialize)]
pub struct GaussNewton<F> {
    /// gamma
    gamma: F,
    /// Tolerance for the stopping criterion based on cost difference
    tol: F,
}

impl<F: ArgminFloat> GaussNewton<F> {
    /// Constructor
    pub fn new() -> Self {
        GaussNewton {
            gamma: F::from_f64(1.0).unwrap(),
            tol: F::epsilon().sqrt(),
        }
    }

    /// set gamma
    pub fn with_gamma(mut self, gamma: F) -> Result<Self, Error> {
        if gamma <= F::from_f64(0.0).unwrap() || gamma > F::from_f64(1.0).unwrap() {
            return Err(ArgminError::InvalidParameter {
                text: "Gauss-Newton: gamma must be in  (0, 1].".to_string(),
            }
            .into());
        }
        self.gamma = gamma;
        Ok(self)
    }

    /// Set tolerance for the stopping criterion based on cost difference
    pub fn with_tol(mut self, tol: F) -> Result<Self, Error> {
        if tol <= F::from_f64(0.0).unwrap() {
            return Err(ArgminError::InvalidParameter {
                text: "Gauss-Newton: tol must be positive.".to_string(),
            }
            .into());
        }
        self.tol = tol;
        Ok(self)
    }
}

impl<F: ArgminFloat> Default for GaussNewton<F> {
    fn default() -> GaussNewton<F> {
        GaussNewton::new()
    }
}

impl<O, F> Solver<O> for GaussNewton<F>
where
    O: ArgminOp<Float = F>,
    O::Param: Default
        + ArgminScaledSub<O::Param, O::Float, O::Param>
        + ArgminSub<O::Param, O::Param>
        + ArgminMul<O::Float, O::Param>,
    O::Output: ArgminNorm<O::Float>,
    O::Jacobian: ArgminTranspose
        + ArgminInv<O::Jacobian>
        + ArgminDot<O::Jacobian, O::Jacobian>
        + ArgminDot<O::Output, O::Param>
        + ArgminDot<O::Param, O::Param>,
    O::Hessian: Default,
    F: ArgminFloat,
{
    const NAME: &'static str = "Gauss-Newton method";

    fn next_iter(
        &mut self,
        op: &mut OpWrapper<O>,
        state: &IterState<O>,
    ) -> Result<ArgminIterData<O>, Error> {
        let param = state.get_param();
        let residuals = op.apply(&param)?;
        let jacobian = op.jacobian(&param)?;

        let p = jacobian
            .clone()
            .t()
            .dot(&jacobian)
            .inv()?
            .dot(&jacobian.t().dot(&residuals));

        let new_param = param.sub(&p.mul(&self.gamma));

        Ok(ArgminIterData::new()
            .param(new_param)
            .cost(residuals.norm()))
    }

    fn terminate(&mut self, state: &IterState<O>) -> TerminationReason {
        if (state.get_prev_cost() - state.get_cost()).abs() < self.tol {
            return TerminationReason::NoChangeInCost;
        }
        TerminationReason::NotTerminated
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::test_trait_impl;

    test_trait_impl!(gauss_newton_method, GaussNewton<f64>);

    #[test]
    fn test_tolerance() {
        let tol1: f64 = 1e-4;

        let GaussNewton { tol: t, .. } = GaussNewton::new().with_tol(tol1).unwrap();

        assert!((t - tol1).abs() < std::f64::EPSILON);
    }

    #[test]
    fn test_gamma() {
        let gamma: f64 = 0.5;

        let GaussNewton { gamma: g, .. } = GaussNewton::new().with_gamma(gamma).unwrap();

        assert!((g - gamma).abs() < std::f64::EPSILON);
    }
}