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//! Implementation of ?gees - Compute the eigenvalues and, optionally, the Schur form of a general
//! matrix.
use lapack::{cgees, dgees, sgees, zgees};
use itertools::izip;
use num::{Zero, complex::ComplexFloat};
use crate::base_types::{LapackError, c32, c64};
use crate::{base_types::LapackResult, traits::rlst_num::RlstScalar};
use crate::dense::linalg::lapack::interface::lapack_return;
/// The job options for the Schur vectors.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
#[repr(u8)]
pub enum JobVs {
/// Do not compute the Schur vectors.
None = b'N',
/// Compute the Schur vectors.
Compute = b'V',
}
/// ?gees - Compute the eigenvalues and, optionally, the Schur form of a general matrix.
pub trait Gees: RlstScalar {
/// Compute the eigenvalues and, optionally, the Schur form of a general matrix.
fn gees(
jobvs: JobVs,
n: usize,
a: &mut [Self],
lda: usize,
w: &mut [Self::Complex],
vs: Option<&mut [Self]>,
ldvs: usize,
) -> LapackResult<()>;
}
macro_rules! implement_gees {
($scalar:ty, $gees:expr) => {
impl Gees for $scalar {
fn gees(
jobvs: JobVs,
n: usize,
a: &mut [Self],
lda: usize,
w: &mut [Self::Complex],
vs: Option<&mut [Self]>,
ldvs: usize,
) -> LapackResult<()> {
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, n),
"Require `lda` {} >= `max(1, n)` {}.",
lda,
std::cmp::max(1, n)
);
assert_eq!(w.len(), n, "Require `w.len()` {} == `n` {}.", w.len(), n);
let mut vs_temp = Vec::<$scalar>::new();
let vs = match jobvs {
JobVs::Compute => {
let vs = vs.expect("If `jobvs` is Compute, `vs` must be Some.");
assert!(
ldvs >= std::cmp::max(1, n),
"Require `ldvs` {} >= `max(1, n)` {}.",
ldvs,
std::cmp::max(1, n)
);
assert_eq!(
vs.len(),
ldvs * n,
"Require `vs.len()` {} == `ldvs * n` {}.",
vs.len(),
ldvs * n
);
vs
}
JobVs::None => {
assert!(ldvs >= 1, "Require `ldvs` {} >= 1.", ldvs);
vs_temp.as_mut_slice()
}
};
let mut info = 0;
let mut work = vec![<$scalar>::zero(); 1];
let mut wr = vec![<$scalar>::zero(); n];
let mut wi = vec![<$scalar>::zero(); n];
let mut bwork = Vec::<i32>::new();
let mut sdim = 0;
unsafe {
$gees(
jobvs as u8,
b'N',
None,
n as i32,
a,
lda as i32,
&mut sdim,
&mut wr,
&mut wi,
vs,
ldvs as i32,
&mut work,
-1,
&mut bwork,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0].re() as usize;
let mut work = vec![<$scalar>::zero(); lwork];
unsafe {
$gees(
jobvs as u8,
b'N',
None,
n as i32,
a,
lda as i32,
&mut sdim,
&mut wr,
&mut wi,
vs,
ldvs as i32,
&mut work,
lwork as i32,
&mut bwork,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
// Fill the output complex eigenvalues
izip!(w.iter_mut(), wr.iter(), wi.iter()).for_each(|(w, &r, &i)| {
*w = <<$scalar as RlstScalar>::Complex>::new(r, i);
});
lapack_return(info, ())
}
}
};
}
macro_rules! implement_gees_complex {
($scalar:ty, $gees:expr) => {
impl Gees for $scalar {
fn gees(
jobvs: JobVs,
n: usize,
a: &mut [Self],
lda: usize,
w: &mut [Self::Complex],
vs: Option<&mut [Self]>,
ldvs: usize,
) -> LapackResult<()> {
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, n),
"Require `lda` {} >= `max(1, n)` {}.",
lda,
std::cmp::max(1, n)
);
assert_eq!(w.len(), n, "Require `w.len()` {} == `n` {}.", w.len(), n);
let mut vs_temp = Vec::<$scalar>::new();
let vs = match jobvs {
JobVs::Compute => {
let vs = vs.expect("If `jobvs` is Compute, `vs` must be Some.");
assert!(
ldvs >= std::cmp::max(1, n),
"Require `ldvs` {} >= `max(1, n)` {}.",
ldvs,
std::cmp::max(1, n)
);
assert_eq!(
vs.len(),
ldvs * n,
"Require `vs.len()` {} == `ldvs * n` {}.",
vs.len(),
ldvs * n
);
vs
}
JobVs::None => {
assert!(ldvs >= 1, "Require `ldvs` {} >= 1.", ldvs);
vs_temp.as_mut_slice()
}
};
let mut info = 0;
let mut work = vec![<$scalar>::zero(); 1];
let mut bwork = Vec::<i32>::new();
let mut sdim = 0;
let mut rwork = vec![<<$scalar as RlstScalar>::Real as Zero>::zero(); n];
unsafe {
$gees(
jobvs as u8,
b'N',
None,
n as i32,
a,
lda as i32,
&mut sdim,
w,
vs,
ldvs as i32,
&mut work,
-1,
&mut rwork,
&mut bwork,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0].re() as usize;
let mut work = vec![<$scalar>::zero(); lwork];
unsafe {
$gees(
jobvs as u8,
b'N',
None,
n as i32,
a,
lda as i32,
&mut sdim,
w,
vs,
ldvs as i32,
&mut work,
lwork as i32,
&mut rwork,
&mut bwork,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
lapack_return(info, ())
}
}
};
}
implement_gees!(f32, sgees);
implement_gees!(f64, dgees);
implement_gees_complex!(c32, cgees);
implement_gees_complex!(c64, zgees);