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

//! QR decomposition

use crate::{error::*, layout::MatrixLayout, *};
use cauchy::*;
use num_traits::{ToPrimitive, Zero};

pub trait QR_: Sized {
    /// Execute Householder reflection as the first step of QR-decomposition
    ///
    /// For C-continuous array,
    /// this will call LQ-decomposition of the transposed matrix $ A^T = LQ^T $
    fn householder(l: MatrixLayout, a: &mut [Self]) -> Result<Vec<Self>>;

    /// Reconstruct Q-matrix from Householder-reflectors
    fn q(l: MatrixLayout, a: &mut [Self], tau: &[Self]) -> Result<()>;

    /// Execute QR-decomposition at once
    fn qr(l: MatrixLayout, a: &mut [Self]) -> Result<Vec<Self>>;
}

macro_rules! impl_qr {
    ($scalar:ty, $qrf:path, $lqf:path, $gqr:path, $glq:path) => {
        impl QR_ for $scalar {
            fn householder(l: MatrixLayout, mut a: &mut [Self]) -> Result<Vec<Self>> {
                let m = l.lda();
                let n = l.len();
                let k = m.min(n);
                let mut tau = unsafe { vec_uninit(k as usize) };

                // eval work size
                let mut info = 0;
                let mut work_size = [Self::zero()];
                unsafe {
                    match l {
                        MatrixLayout::F { .. } => {
                            $qrf(m, n, &mut a, m, &mut tau, &mut work_size, -1, &mut info);
                        }
                        MatrixLayout::C { .. } => {
                            $lqf(m, n, &mut a, m, &mut tau, &mut work_size, -1, &mut info);
                        }
                    }
                }
                info.as_lapack_result()?;

                // calc
                let lwork = work_size[0].to_usize().unwrap();
                let mut work = unsafe { vec_uninit(lwork) };
                unsafe {
                    match l {
                        MatrixLayout::F { .. } => {
                            $qrf(
                                m,
                                n,
                                &mut a,
                                m,
                                &mut tau,
                                &mut work,
                                lwork as i32,
                                &mut info,
                            );
                        }
                        MatrixLayout::C { .. } => {
                            $lqf(
                                m,
                                n,
                                &mut a,
                                m,
                                &mut tau,
                                &mut work,
                                lwork as i32,
                                &mut info,
                            );
                        }
                    }
                }
                info.as_lapack_result()?;

                Ok(tau)
            }

            fn q(l: MatrixLayout, mut a: &mut [Self], tau: &[Self]) -> Result<()> {
                let m = l.lda();
                let n = l.len();
                let k = m.min(n);
                assert_eq!(tau.len(), k as usize);

                // eval work size
                let mut info = 0;
                let mut work_size = [Self::zero()];
                unsafe {
                    match l {
                        MatrixLayout::F { .. } => {
                            $gqr(m, k, k, &mut a, m, &tau, &mut work_size, -1, &mut info)
                        }
                        MatrixLayout::C { .. } => {
                            $glq(k, n, k, &mut a, m, &tau, &mut work_size, -1, &mut info)
                        }
                    }
                };

                // calc
                let lwork = work_size[0].to_usize().unwrap();
                let mut work = unsafe { vec_uninit(lwork) };
                unsafe {
                    match l {
                        MatrixLayout::F { .. } => {
                            $gqr(m, k, k, &mut a, m, &tau, &mut work, lwork as i32, &mut info)
                        }
                        MatrixLayout::C { .. } => {
                            $glq(k, n, k, &mut a, m, &tau, &mut work, lwork as i32, &mut info)
                        }
                    }
                }
                info.as_lapack_result()?;
                Ok(())
            }

            fn qr(l: MatrixLayout, a: &mut [Self]) -> Result<Vec<Self>> {
                let tau = Self::householder(l, a)?;
                let r = Vec::from(&*a);
                Self::q(l, a, &tau)?;
                Ok(r)
            }
        }
    };
} // endmacro

impl_qr!(
    f64,
    lapack::dgeqrf,
    lapack::dgelqf,
    lapack::dorgqr,
    lapack::dorglq
);
impl_qr!(
    f32,
    lapack::sgeqrf,
    lapack::sgelqf,
    lapack::sorgqr,
    lapack::sorglq
);
impl_qr!(
    c64,
    lapack::zgeqrf,
    lapack::zgelqf,
    lapack::zungqr,
    lapack::zunglq
);
impl_qr!(
    c32,
    lapack::cgeqrf,
    lapack::cgelqf,
    lapack::cungqr,
    lapack::cunglq
);