```  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
```
```// Copyright 2018-2020 argmin developers
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE 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::de::DeserializeOwned;
use serde::{Deserialize, Serialize};
use std::default::Default;
use std::fmt::Debug;

/// The conjugate gradient method is a solver for systems of linear equations with a symmetric and
/// positive-definite matrix.
///
///
/// # References:
///
/// [0] Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization.
/// Springer. ISBN 0-387-30303-0.
#[derive(Clone, Serialize, Deserialize)]
pub struct ConjugateGradient<P, S> {
/// b (right hand side)
b: P,
/// residual
r: P,
/// p
p: P,
/// previous p
p_prev: P,
/// r^T * r
#[serde(skip)]
rtr: S,
/// alpha
#[serde(skip)]
alpha: S,
/// beta
#[serde(skip)]
beta: S,
}

impl<P, S> ConjugateGradient<P, S>
where
P: Clone + Default,
S: Default,
{
/// Constructor
///
/// Parameters:
///
/// `b`: right hand side of `A * x = b`
pub fn new(b: P) -> Result<Self, Error> {
b,
r: P::default(),
p: P::default(),
p_prev: P::default(),
rtr: S::default(),
alpha: S::default(),
beta: S::default(),
})
}

/// Return the current search direction (This is needed by NewtonCG for instance)
pub fn p(&self) -> P {
self.p.clone()
}

/// Return the previous search direction (This is needed by NewtonCG for instance)
pub fn p_prev(&self) -> P {
self.p_prev.clone()
}

/// Return the current residual (This is needed by NewtonCG for instance)
pub fn residual(&self) -> P {
self.r.clone()
}
}

impl<P, O, S, F> Solver<O> for ConjugateGradient<P, S>
where
O: ArgminOp<Param = P, Output = P, Float = F>,
P: Clone
+ Serialize
+ DeserializeOwned
+ ArgminDot<O::Param, S>
+ ArgminSub<O::Param, O::Param>
+ ArgminScaledAdd<O::Param, S, O::Param>
+ ArgminConj
+ ArgminMul<O::Float, O::Param>,
S: Debug + ArgminDiv<S, S> + ArgminNorm<O::Float> + ArgminConj,
F: ArgminFloat,
{
const NAME: &'static str = "Conjugate Gradient";

fn init(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<Option<ArgminIterData<O>>, Error> {
let init_param = state.get_param();
let ap = op.apply(&init_param)?;
let r0 = self.b.sub(&ap).mul(&(F::from_f64(-1.0).unwrap()));
self.r = r0.clone();
self.p = r0.mul(&(F::from_f64(-1.0).unwrap()));
self.rtr = self.r.dot(&self.r.conj());
Ok(None)
}

/// Perform one iteration of CG algorithm
fn next_iter(
&mut self,
op: &mut OpWrapper<O>,
state: &IterState<O>,
) -> Result<ArgminIterData<O>, Error> {
self.p_prev = self.p.clone();
let apk = op.apply(&self.p)?;
self.alpha = self.rtr.div(&self.p.dot(&apk.conj()));
let new_param = state.get_param().scaled_add(&self.alpha, &self.p);
self.r = self.r.scaled_add(&self.alpha, &apk);
let rtr_n = self.r.dot(&self.r.conj());
self.beta = rtr_n.div(&self.rtr);
self.rtr = rtr_n;
self.p = self
.r
.mul(&(F::from_f64(-1.0).unwrap()))
let norm = self.r.dot(&self.r.conj());

Ok(ArgminIterData::new()
.param(new_param)
// .cost(norm.sqrt())
.cost(norm.norm())
.kv(make_kv!("alpha" => self.alpha; "beta" => self.beta;)))
}
}

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