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

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

/// Specifies how many of the columns of *U* and rows of *V*ᵀ are computed and returned.
///
/// For an input array of shape *m*×*n*, the following are computed:
#[derive(Clone, Copy, Eq, PartialEq)]
#[repr(u8)]
pub enum UVTFlag {
    /// All *m* columns of *U* and all *n* rows of *V*ᵀ.
    Full = b'A',
    /// The first min(*m*,*n*) columns of *U* and the first min(*m*,*n*) rows of *V*ᵀ.
    Some = b'S',
    /// No columns of *U* or rows of *V*ᵀ.
    None = b'N',
}

pub trait SVDDC_: Scalar {
    fn svddc(l: MatrixLayout, jobz: UVTFlag, a: &mut [Self]) -> Result<SVDOutput<Self>>;
}

macro_rules! impl_svddc {
    (@real, $scalar:ty, $gesdd:path) => {
        impl_svddc!(@body, $scalar, $gesdd, );
    };
    (@complex, $scalar:ty, $gesdd:path) => {
        impl_svddc!(@body, $scalar, $gesdd, rwork);
    };
    (@body, $scalar:ty, $gesdd:path, $($rwork_ident:ident),*) => {
        impl SVDDC_ for $scalar {
            fn svddc(l: MatrixLayout, jobz: UVTFlag, mut a: &mut [Self],) -> Result<SVDOutput<Self>> {
                let m = l.lda();
                let n = l.len();
                let k = m.min(n);
                let mut s = unsafe { vec_uninit( k as usize) };

                let (u_col, vt_row) = match jobz {
                    UVTFlag::Full | UVTFlag::None => (m, n),
                    UVTFlag::Some => (k, k),
                };
                let (mut u, mut vt) = match jobz {
                    UVTFlag::Full => (
                        Some(unsafe { vec_uninit( (m * m) as usize) }),
                        Some(unsafe { vec_uninit( (n * n) as usize) }),
                    ),
                    UVTFlag::Some => (
                        Some(unsafe { vec_uninit( (m * u_col) as usize) }),
                        Some(unsafe { vec_uninit( (n * vt_row) as usize) }),
                    ),
                    UVTFlag::None => (None, None),
                };

                $( // for complex only
                let mx = n.max(m) as usize;
                let mn = n.min(m) as usize;
                let lrwork = match jobz {
                    UVTFlag::None => 7 * mn,
                    _ => std::cmp::max(5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn),
                };
                let mut $rwork_ident = unsafe { vec_uninit( lrwork) };
                )*

                // eval work size
                let mut info = 0;
                let mut iwork = unsafe { vec_uninit( 8 * k as usize) };
                let mut work_size = [Self::zero()];
                unsafe {
                    $gesdd(
                        jobz as u8,
                        m,
                        n,
                        &mut a,
                        m,
                        &mut s,
                        u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
                        m,
                        vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
                        vt_row,
                        &mut work_size,
                        -1,
                        $(&mut $rwork_ident,)*
                        &mut iwork,
                        &mut info,
                    );
                }
                info.as_lapack_result()?;

                // do svd
                let lwork = work_size[0].to_usize().unwrap();
                let mut work = unsafe { vec_uninit( lwork) };
                unsafe {
                    $gesdd(
                        jobz as u8,
                        m,
                        n,
                        &mut a,
                        m,
                        &mut s,
                        u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
                        m,
                        vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
                        vt_row,
                        &mut work,
                        lwork as i32,
                        $(&mut $rwork_ident,)*
                        &mut iwork,
                        &mut info,
                    );
                }
                info.as_lapack_result()?;

                match l {
                    MatrixLayout::F { .. } => Ok(SVDOutput { s, u, vt }),
                    MatrixLayout::C { .. } => Ok(SVDOutput { s, u: vt, vt: u }),
                }
            }
        }
    };
}

impl_svddc!(@real, f32, lapack::sgesdd);
impl_svddc!(@real, f64, lapack::dgesdd);
impl_svddc!(@complex, c32, lapack::cgesdd);
impl_svddc!(@complex, c64, lapack::zgesdd);