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
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
use crate::prelude::*;
use serde::{Deserialize, Serialize};
#[derive(ArgminSolver, Serialize, Deserialize)]
pub struct Dogleg<O>
where
O: ArgminOp<Output = f64>,
O::Param: ArgminMul<f64, O::Param>
+ ArgminWeightedDot<O::Param, f64, O::Hessian>
+ ArgminNorm<f64>
+ ArgminDot<O::Param, f64>
+ ArgminAdd<O::Param, O::Param>
+ ArgminSub<O::Param, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
{
radius: f64,
base: ArgminBase<O>,
}
impl<O> Dogleg<O>
where
O: ArgminOp<Output = f64>,
O::Param: ArgminMul<f64, O::Param>
+ ArgminWeightedDot<O::Param, f64, O::Hessian>
+ ArgminNorm<f64>
+ ArgminDot<O::Param, f64>
+ ArgminAdd<O::Param, O::Param>
+ ArgminSub<O::Param, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
{
pub fn new(operator: O) -> Self {
let base = ArgminBase::new(operator, O::Param::default());
Dogleg {
radius: std::f64::NAN,
base,
}
}
}
impl<O> ArgminIter for Dogleg<O>
where
O: ArgminOp<Output = f64>,
O::Param: ArgminMul<f64, O::Param>
+ ArgminWeightedDot<O::Param, f64, O::Hessian>
+ ArgminNorm<f64>
+ ArgminDot<O::Param, f64>
+ ArgminAdd<O::Param, O::Param>
+ ArgminSub<O::Param, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
{
type Param = O::Param;
type Output = O::Output;
type Hessian = O::Hessian;
fn init(&mut self) -> Result<(), Error> {
self.base_reset();
self.set_max_iters(1);
Ok(())
}
fn next_iter(&mut self) -> Result<ArgminIterData<Self::Param>, Error> {
let g = self.cur_grad();
let h = self.cur_hessian();
let pstar;
let pb = (self.cur_hessian().inv()?)
.dot(&self.cur_grad())
.mul(&(-1.0));
if pb.norm() <= self.radius {
pstar = pb;
} else {
let pu = g.mul(&(-g.dot(&g) / g.weighted_dot(&h, &g)));
let utu = pu.dot(&pu);
let btb = pb.dot(&pb);
let utb = pu.dot(&pb);
let delta = self.radius.powi(2);
let t1 = 3.0 * utb - btb - 2.0 * utu;
let t2 =
(utb.powi(2) - 2.0 * utb * delta + delta * btb - btb * utu + delta * utu).sqrt();
let t3 = -2.0 * utb + btb + utu;
let tau1: f64 = -(t1 + t2) / t3;
let tau2: f64 = -(t1 - t2) / t3;
let mut tau = tau1.max(tau2);
if tau.is_nan() {
tau = (delta + btb - 2.0 * utu) / (btb - utu);
}
if tau >= 0.0 && tau < 1.0 {
pstar = pu.mul(&tau);
} else if tau >= 1.0 && tau <= 2.0 {
pstar = pu.add(&pb.sub(&pu).mul(&(tau - 1.0)));
} else {
return Err(ArgminError::ImpossibleError {
text: "tau is bigger than 2, this is not supposed to happen.".to_string(),
}
.into());
}
}
let out = ArgminIterData::new(pstar, 0.0);
Ok(out)
}
}
impl<O> ArgminTrustRegion for Dogleg<O>
where
O: ArgminOp<Output = f64>,
O::Param: ArgminMul<f64, O::Param>
+ ArgminWeightedDot<O::Param, f64, O::Hessian>
+ ArgminNorm<f64>
+ ArgminDot<O::Param, f64>
+ ArgminAdd<O::Param, O::Param>
+ ArgminSub<O::Param, O::Param>,
O::Hessian: ArgminInv<O::Hessian> + ArgminDot<O::Param, O::Param>,
{
fn set_radius(&mut self, radius: f64) {
self.radius = radius;
}
fn set_grad(&mut self, grad: O::Param) {
self.set_cur_grad(grad);
}
fn set_hessian(&mut self, hessian: O::Hessian) {
self.set_cur_hessian(hessian);
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::send_sync_test;
#[cfg(feature = "ndarrayl")]
send_sync_test!(
dogleg,
Dogleg<NoOperator<ndarray::Array1<f64>, f64, ndarray::Array2<f64>>>
);
}