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//! Implementation of ?gesdd - SVD factorization via divide-and-conquer
use lapack::{cgesdd, dgesdd, sgesdd, zgesdd};
use crate::base_types::{LapackError, c32, c64};
use crate::{base_types::LapackResult, traits::rlst_num::RlstScalar};
use crate::dense::linalg::lapack::interface::lapack_return;
use num::{Zero, complex::ComplexFloat};
/// JobZ specifies the computation of the left and right singular vectors.
#[derive(Clone, Copy)]
#[repr(u8)]
pub enum JobZ {
/// Return all singular vectors.
A = b'A',
/// Return the first `min(m, n)` singular vectors.
S = b'S',
/// Do not compute singular vectors.
N = b'N',
}
/// ?gesdd - SVD factorization via divide-and-conquer
pub trait Gesdd: RlstScalar {
/// Perform a singular value decomposition (SVD) of a matrix `a` with dimensions `m` x `n`.
/// If `jobz` is `JobZ::N`, the singular vectors are not computed and `u` and `vt` can be
/// `None`.
#[allow(clippy::too_many_arguments)]
fn gesdd(
jobz: JobZ,
m: usize,
n: usize,
a: &mut [Self],
lda: usize,
s: &mut [Self::Real],
u: Option<&mut [Self]>,
ldu: usize,
vt: Option<&mut [Self]>,
ldvt: usize,
) -> LapackResult<()>;
}
macro_rules! implement_gesdd {
($scalar:ty, $gesdd:expr) => {
impl Gesdd for $scalar {
fn gesdd(
jobz: JobZ,
m: usize,
n: usize,
a: &mut [Self],
lda: usize,
s: &mut [Self::Real],
u: Option<&mut [Self]>,
ldu: usize,
vt: Option<&mut [Self]>,
ldvt: usize,
) -> LapackResult<()> {
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, m),
"Require `lda` {} >= `max(1, m)` {}.",
lda,
std::cmp::max(1, m)
);
let mut info = 0;
let k = std::cmp::min(m, n);
assert_eq!(
s.len(),
k,
"Require `s.len()` {} == `min(m, n)` {}.",
s.len(),
k
);
// These are only needed if the user requests no singular vectors.
// The reason is that Lapack always requires some reference to a singular vector slice,
// even if it is not referenced in the computation.
let mut u_temp = Vec::<$scalar>::new();
let mut vt_temp = Vec::<$scalar>::new();
let (u, vt) = match jobz {
JobZ::A => {
let u = u.expect("JobU::A requires u to be Some");
let vt = vt.expect("JobVt::A requires vt to be Some");
assert_eq!(
u.len(),
ldu * m,
"Require `u.len()` {} == `ldu * m` {}.",
u.len(),
ldu * m
);
assert!(
ldu >= std::cmp::max(1, m),
"Require `ldu` {} >= `max(1, m)` {}.",
ldu,
std::cmp::max(1, m)
);
assert_eq!(
vt.len(),
ldvt * n,
"Require `vt.len()` {} == `ldvt * n` {}.",
vt.len(),
ldvt * n
);
assert!(
ldvt >= std::cmp::max(1, n),
"Require `ldvt` {} >= `max(1, n)` {}.",
ldvt,
std::cmp::max(1, n)
);
(u, vt)
}
JobZ::S => {
let u = u.expect("JobU::S requires u to be Some");
let vt = vt.expect("JobVt::S requires vt to be Some");
assert_eq!(
u.len(),
ldu * k,
"Require `u.len()` {} == `ldu * min(m, n)` {}.",
u.len(),
ldu * k
);
assert!(
ldu >= std::cmp::max(1, m),
"Require `ldu` {} >= `max(1, m)` {}.",
ldu,
std::cmp::max(1, m)
);
assert_eq!(
vt.len(),
ldvt * n,
"Require `vt.len()` {} == `ldvt * n` {}.",
vt.len(),
ldvt * n
);
assert!(
ldvt >= std::cmp::max(1, k),
"Require `ldvt` {} >= `max(1, min(m, n))` {}.",
ldvt,
std::cmp::max(1, k)
);
(u, vt)
}
JobZ::N => {
let u = &mut u_temp;
let vt = &mut vt_temp;
assert!(ldu >= 1, "Require `ldu` {} >= 1.", ldu);
assert!(ldvt >= 1, "Require `ldvt` {} >= 1.", ldvt);
(u.as_mut_slice(), vt.as_mut_slice())
}
};
let mut iwork = vec![0 as i32; 8 * k];
let mut work = vec![<$scalar>::zero(); 1];
unsafe {
$gesdd(
jobz as u8,
m as i32,
n as i32,
a,
lda as i32,
s,
u,
ldu as i32,
vt,
ldvt as i32,
&mut work,
-1,
&mut iwork,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0].re() as i32;
let mut work = vec![<$scalar>::zero(); lwork as usize];
unsafe {
$gesdd(
jobz as u8,
m as i32,
n as i32,
a,
lda as i32,
s,
u,
ldu as i32,
vt,
ldvt as i32,
&mut work,
lwork,
&mut iwork,
&mut info,
);
}
lapack_return(info, ())
}
}
};
}
macro_rules! implement_gesdd_complex {
($scalar:ty, $gesdd:expr) => {
impl Gesdd for $scalar {
fn gesdd(
jobz: JobZ,
m: usize,
n: usize,
a: &mut [Self],
lda: usize,
s: &mut [Self::Real],
u: Option<&mut [Self]>,
ldu: usize,
vt: Option<&mut [Self]>,
ldvt: usize,
) -> LapackResult<()> {
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, m),
"Require `lda` {} >= `max(1, m)` {}.",
lda,
std::cmp::max(1, m)
);
let mut info = 0;
let k = std::cmp::min(m, n);
assert_eq!(
s.len(),
k,
"Require `s.len()` {} == `min(m, n)` {}.",
s.len(),
k
);
// These are only needed if the user requests no singular vectors.
// The reason is that Lapack always requires some reference to a singular vector slice,
// even if it is not referenced in the computation.
let mut u_temp = Vec::<$scalar>::new();
let mut vt_temp = Vec::<$scalar>::new();
let (u, vt) = match jobz {
JobZ::A => {
let u = u.expect("JobU::A requires u to be Some");
let vt = vt.expect("JobVt::A requires vt to be Some");
assert_eq!(
u.len(),
ldu * m,
"Require `u.len()` {} == `ldu * m` {}.",
u.len(),
ldu * m
);
assert!(
ldu >= std::cmp::max(1, m),
"Require `ldu` {} >= `max(1, m)` {}.",
ldu,
std::cmp::max(1, m)
);
assert_eq!(
vt.len(),
ldvt * n,
"Require `vt.len()` {} == `ldvt * n` {}.",
vt.len(),
ldvt * n
);
assert!(
ldvt >= std::cmp::max(1, n),
"Require `ldvt` {} >= `max(1, n)` {}.",
ldvt,
std::cmp::max(1, n)
);
(u, vt)
}
JobZ::S => {
let u = u.expect("JobU::S requires u to be Some");
let vt = vt.expect("JobVt::S requires vt to be Some");
assert_eq!(
u.len(),
ldu * k,
"Require `u.len()` {} == `ldu * min(m, n)` {}.",
u.len(),
ldu * k
);
assert!(
ldu >= std::cmp::max(1, m),
"Require `ldu` {} >= `max(1, m)` {}.",
ldu,
std::cmp::max(1, m)
);
assert_eq!(
vt.len(),
ldvt * n,
"Require `vt.len()` {} == `ldvt * n` {}.",
vt.len(),
ldvt * n
);
assert!(
ldvt >= std::cmp::max(1, k),
"Require `ldvt` {} >= `max(1, min(m, n))` {}.",
ldvt,
std::cmp::max(1, k)
);
(u, vt)
}
JobZ::N => {
let u = &mut u_temp;
let vt = &mut vt_temp;
assert!(ldu >= 1, "Require `ldu` {} >= 1.", ldu);
assert!(ldvt >= 1, "Require `ldvt` {} >= 1.", ldvt);
(u.as_mut_slice(), vt.as_mut_slice())
}
};
let mx = std::cmp::max(m, n);
let mn = std::cmp::min(m, n);
// The formula for the optimal workspace size is taken from the LAPACK
// documentation.
// In old versions of LAPACK, at least 7 * mn is required, but in newer versions
// it is 5 * mn. The formula below is a compromise that works for both at the cost
// of a slightly larger workspace.
let lrwork = std::cmp::max(5 * mn * mn + 7 * mn, 2 * mx * mn + 2 * mn * mn + mn);
let mut rwork =
vec![<<$scalar as RlstScalar>::Real as Zero>::zero(); lrwork as usize];
let mut iwork = vec![0 as i32; 8 * mn];
let mut work = vec![<$scalar>::zero(); 1];
unsafe {
$gesdd(
jobz as u8,
m as i32,
n as i32,
a,
lda as i32,
s,
u,
ldu as i32,
vt,
ldvt as i32,
&mut work,
-1,
&mut rwork,
&mut iwork,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0].re() as i32;
let mut work = vec![<$scalar>::zero(); lwork as usize];
unsafe {
$gesdd(
jobz as u8,
m as i32,
n as i32,
a,
lda as i32,
s,
u,
ldu as i32,
vt,
ldvt as i32,
&mut work,
lwork,
&mut rwork,
&mut iwork,
&mut info,
);
}
lapack_return(info, ())
}
}
};
}
implement_gesdd!(f32, sgesdd);
implement_gesdd!(f64, dgesdd);
implement_gesdd_complex!(c32, cgesdd);
implement_gesdd_complex!(c64, zgesdd);