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
use num::{One, Zero};
use simba::scalar::ComplexField;
use crate::base::constraint::{DimEq, ShapeConstraint};
use crate::base::dimension::{Dim, U2};
use crate::base::storage::{Storage, StorageMut};
use crate::base::{Matrix, Vector};
#[derive(Debug, Clone, Copy)]
pub struct GivensRotation<T: ComplexField> {
c: T::RealField,
s: T,
}
impl<T: ComplexField> GivensRotation<T> {
pub fn identity() -> Self {
Self {
c: T::RealField::one(),
s: T::zero(),
}
}
pub fn new_unchecked(c: T::RealField, s: T) -> Self {
Self { c, s }
}
pub fn new(c: T, s: T) -> (Self, T) {
Self::try_new(c, s, T::RealField::zero())
.unwrap_or_else(|| (GivensRotation::identity(), T::zero()))
}
pub fn try_new(c: T, s: T, eps: T::RealField) -> Option<(Self, T)> {
let (mod0, sign0) = c.to_exp();
let denom = (mod0.clone() * mod0.clone() + s.clone().modulus_squared()).sqrt();
if denom > eps {
let norm = sign0.scale(denom.clone());
let c = mod0 / denom;
let s = s.clone() / norm.clone();
Some((Self { c, s }, norm))
} else {
None
}
}
pub fn cancel_y<S: Storage<T, U2>>(v: &Vector<T, U2, S>) -> Option<(Self, T)> {
if !v[1].is_zero() {
let (mod0, sign0) = v[0].clone().to_exp();
let denom = (mod0.clone() * mod0.clone() + v[1].clone().modulus_squared()).sqrt();
let c = mod0 / denom.clone();
let s = -v[1].clone() / sign0.clone().scale(denom.clone());
let r = sign0.scale(denom);
Some((Self { c, s }, r))
} else {
None
}
}
pub fn cancel_x<S: Storage<T, U2>>(v: &Vector<T, U2, S>) -> Option<(Self, T)> {
if !v[0].is_zero() {
let (mod1, sign1) = v[1].clone().to_exp();
let denom = (mod1.clone() * mod1.clone() + v[0].clone().modulus_squared()).sqrt();
let c = mod1 / denom.clone();
let s = (v[0].clone().conjugate() * sign1.clone()).unscale(denom.clone());
let r = sign1.scale(denom);
Some((Self { c, s }, r))
} else {
None
}
}
#[must_use]
pub fn c(&self) -> T::RealField {
self.c.clone()
}
#[must_use]
pub fn s(&self) -> T {
self.s.clone()
}
#[must_use = "This function does not mutate self."]
pub fn inverse(&self) -> Self {
Self {
c: self.c.clone(),
s: -self.s.clone(),
}
}
pub fn rotate<R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>>(
&self,
rhs: &mut Matrix<T, R2, C2, S2>,
) where
ShapeConstraint: DimEq<R2, U2>,
{
assert_eq!(
rhs.nrows(),
2,
"Unit complex rotation: the input matrix must have exactly two rows."
);
let s = self.s.clone();
let c = self.c.clone();
for j in 0..rhs.ncols() {
unsafe {
let a = rhs.get_unchecked((0, j)).clone();
let b = rhs.get_unchecked((1, j)).clone();
*rhs.get_unchecked_mut((0, j)) =
a.clone().scale(c.clone()) - s.clone().conjugate() * b.clone();
*rhs.get_unchecked_mut((1, j)) = s.clone() * a + b.scale(c.clone());
}
}
}
pub fn rotate_rows<R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>>(
&self,
lhs: &mut Matrix<T, R2, C2, S2>,
) where
ShapeConstraint: DimEq<C2, U2>,
{
assert_eq!(
lhs.ncols(),
2,
"Unit complex rotation: the input matrix must have exactly two columns."
);
let s = self.s.clone();
let c = self.c.clone();
for j in 0..lhs.nrows() {
unsafe {
let a = lhs.get_unchecked((j, 0)).clone();
let b = lhs.get_unchecked((j, 1)).clone();
*lhs.get_unchecked_mut((j, 0)) = a.clone().scale(c.clone()) + s.clone() * b.clone();
*lhs.get_unchecked_mut((j, 1)) = -s.clone().conjugate() * a + b.scale(c.clone());
}
}
}
}