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
#[cfg(feature = "serde-serialize")]
use serde::{Deserialize, Serialize};
use alga::general::Real;
use allocator::Allocator;
use base::{DefaultAllocator, MatrixMN, MatrixN, SquareMatrix, VectorN};
use dimension::{DimDiff, DimSub, U1};
use storage::Storage;
use linalg::householder;
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(
serialize = "DefaultAllocator: Allocator<N, D, D> +
Allocator<N, DimDiff<D, U1>>,
MatrixN<N, D>: Serialize,
VectorN<N, DimDiff<D, U1>>: Serialize"
))
)]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(
deserialize = "DefaultAllocator: Allocator<N, D, D> +
Allocator<N, DimDiff<D, U1>>,
MatrixN<N, D>: Deserialize<'de>,
VectorN<N, DimDiff<D, U1>>: Deserialize<'de>"
))
)]
#[derive(Clone, Debug)]
pub struct SymmetricTridiagonal<N: Real, D: DimSub<U1>>
where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
{
tri: MatrixN<N, D>,
off_diagonal: VectorN<N, DimDiff<D, U1>>,
}
impl<N: Real, D: DimSub<U1>> Copy for SymmetricTridiagonal<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>,
MatrixN<N, D>: Copy,
VectorN<N, DimDiff<D, U1>>: Copy,
{}
impl<N: Real, D: DimSub<U1>> SymmetricTridiagonal<N, D>
where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
{
pub fn new(mut m: MatrixN<N, D>) -> Self {
let dim = m.data.shape().0;
assert!(
m.is_square(),
"Unable to compute the symmetric tridiagonal decomposition of a non-square matrix."
);
assert!(
dim.value() != 0,
"Unable to compute the symmetric tridiagonal decomposition of an empty matrix."
);
let mut off_diagonal = unsafe { MatrixMN::new_uninitialized_generic(dim.sub(U1), U1) };
let mut p = unsafe { MatrixMN::new_uninitialized_generic(dim.sub(U1), U1) };
for i in 0..dim.value() - 1 {
let mut m = m.rows_range_mut(i + 1..);
let (mut axis, mut m) = m.columns_range_pair_mut(i, i + 1..);
let (norm, not_zero) = householder::reflection_axis_mut(&mut axis);
off_diagonal[i] = norm;
if not_zero {
let mut p = p.rows_range_mut(i..);
p.gemv_symm(::convert(2.0), &m, &axis, N::zero());
let dot = axis.dot(&p);
p.axpy(-dot, &axis, N::one());
m.ger_symm(-N::one(), &p, &axis, N::one());
m.ger_symm(-N::one(), &axis, &p, N::one());
}
}
SymmetricTridiagonal {
tri: m,
off_diagonal: off_diagonal,
}
}
#[doc(hidden)]
pub fn internal_tri(&self) -> &MatrixN<N, D> {
&self.tri
}
pub fn unpack(self) -> (MatrixN<N, D>, VectorN<N, D>, VectorN<N, DimDiff<D, U1>>)
where DefaultAllocator: Allocator<N, D> {
let diag = self.diagonal();
let q = self.q();
(q, diag, self.off_diagonal)
}
pub fn unpack_tridiagonal(self) -> (VectorN<N, D>, VectorN<N, DimDiff<D, U1>>)
where DefaultAllocator: Allocator<N, D> {
let diag = self.diagonal();
(diag, self.off_diagonal)
}
pub fn diagonal(&self) -> VectorN<N, D>
where DefaultAllocator: Allocator<N, D> {
self.tri.diagonal()
}
pub fn off_diagonal(&self) -> &VectorN<N, DimDiff<D, U1>>
where DefaultAllocator: Allocator<N, D> {
&self.off_diagonal
}
pub fn q(&self) -> MatrixN<N, D> {
householder::assemble_q(&self.tri)
}
pub fn recompose(mut self) -> MatrixN<N, D> {
let q = self.q();
self.tri.fill_lower_triangle(N::zero(), 2);
self.tri.fill_upper_triangle(N::zero(), 2);
for i in 0..self.off_diagonal.len() {
self.tri[(i + 1, i)] = self.off_diagonal[i];
self.tri[(i, i + 1)] = self.off_diagonal[i];
}
&q * self.tri * q.transpose()
}
}
impl<N: Real, D: DimSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
{
pub fn symmetric_tridiagonalize(self) -> SymmetricTridiagonal<N, D> {
SymmetricTridiagonal::new(self.into_owned())
}
}