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//! Implementation of ?geev - Compute the eigenvalues and, optionally, the eigenvectors of a
//! general matrix.
use lapack::{cgeev, dgeev, sgeev, zgeev};
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 itertools::izip;
use num::{Zero, complex::ComplexFloat};
/// The job options for the left eigenvectors.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
#[repr(u8)]
pub enum JobVl {
/// Do not compute the left eigenvectors.
None = b'N',
/// Compute the left eigenvectors.
Compute = b'V',
}
/// The job options for the right eigenvectors.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
#[repr(u8)]
pub enum JobVr {
/// Do not compute the right eigenvectors.
None = b'N',
/// Compute the right eigenvectors.
Compute = b'V',
}
/// ?geev - Compute the eigenvalues and, optionally, the eigenvectors of a general matrix.
pub trait Geev: RlstScalar {
/// Compute the eigenvalues and, optionally, the eigenvectors of a general matrix.
#[allow(clippy::too_many_arguments)]
fn geev(
jobvl: JobVl,
jobvr: JobVr,
n: usize,
a: &mut [Self],
lda: usize,
w: &mut [Self::Complex],
vl: Option<&mut [Self::Complex]>,
ldvl: usize,
vr: Option<&mut [Self::Complex]>,
ldvr: usize,
) -> LapackResult<()>;
}
macro_rules! implement_geev {
($scalar:ty, $geev:expr) => {
impl Geev for $scalar {
fn geev(
jobvl: JobVl,
jobvr: JobVr,
n: usize,
a: &mut [Self],
lda: usize,
w: &mut [Self::Complex],
mut vl: Option<&mut [Self::Complex]>,
ldvl: usize,
mut vr: Option<&mut [Self::Complex]>,
ldvr: usize,
) -> LapackResult<()> {
let mut info = 0;
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, n),
"Require `lda` {} >= `max(1, n)` {}.",
lda,
std::cmp::max(1, n)
);
assert_eq!(w.len(), n, "Require `wr.len()` {} == `n` {}.", w.len(), n);
let mut wr = vec![<$scalar>::zero(); n];
let mut wi = vec![<$scalar>::zero(); n];
let (mut vlr, ldvlr) = match jobvl {
JobVl::Compute => {
let vl = vl.as_ref().expect("vl must be Some when jobvl is V");
assert_eq!(
vl.len(),
ldvl * n,
"Require `vl.len()` {} == `ldvl * n` {}.",
vl.len(),
ldvl * n
);
assert!(
ldvl >= std::cmp::max(1, n),
"Require `ldvl` {} >= `max(1, n)` {}.",
ldvl,
std::cmp::max(1, n)
);
(vec![<$scalar>::zero(); n * n], n)
}
JobVl::None => {
assert_eq!(ldvl, 1, "Require `ldvl` {} == 1.", ldvl);
(Vec::<$scalar>::new(), 1)
}
};
let (mut vrr, ldvrr) = match jobvr {
JobVr::Compute => {
let vr = vr.as_ref().expect("vr must be Some when jobvr is V");
assert_eq!(
vr.len(),
ldvr * n,
"Require `vr.len()` {} == `ldvr * n` {}.",
vr.len(),
ldvr * n
);
assert!(
ldvr >= std::cmp::max(1, n),
"Require `ldvr` {} >= `max(1, n)` {}.",
ldvr,
std::cmp::max(1, n)
);
(vec![<$scalar>::zero(); n * n], n)
}
JobVr::None => {
assert_eq!(ldvr, 1, "Require `ldvr` {} == 1.", ldvr);
(Vec::<$scalar>::new(), 1)
}
};
let mut work = vec![<$scalar>::zero(); 1];
unsafe {
$geev(
jobvl as u8,
jobvr as u8,
n as i32,
a,
lda as i32,
&mut wr,
&mut wi,
&mut vlr,
ldvlr as i32,
&mut vrr,
ldvrr as i32,
&mut work,
-1,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0].re() as usize;
let mut work = vec![<$scalar>::zero(); lwork];
unsafe {
$geev(
jobvl as u8,
jobvr as u8,
n as i32,
a,
lda as i32,
&mut wr,
&mut wi,
&mut vlr,
ldvlr as i32,
&mut vrr,
ldvrr as i32,
&mut work,
lwork as i32,
&mut info,
);
}
for (w_elem, wr_elem, wi_elem) in izip!(w.iter_mut(), wr.iter(), wi.iter()) {
*w_elem = <<$scalar as RlstScalar>::Complex>::new(*wr_elem, *wi_elem);
}
if jobvl == JobVl::Compute {
let mut count = 0;
while count < n {
if count < n - 1 && w[count] == w[1 + count].conj() {
for row in 0..n {
unsafe {
*vl.as_mut().unwrap().get_unchecked_mut(row + count * ldvl) =
<<$scalar as RlstScalar>::Complex>::new(
*vlr.get_unchecked(row + count * n),
*vlr.get_unchecked(row + (1 + count) * n),
)
};
unsafe {
*vl.as_mut()
.unwrap()
.get_unchecked_mut(row + (1 + count) * ldvl) =
<<$scalar as RlstScalar>::Complex>::new(
*vlr.get_unchecked(row + count * n),
-*vlr.get_unchecked(row + (1 + count) * n),
)
};
}
count += 2;
} else {
for row in 0..n {
unsafe {
*vl.as_mut().unwrap().get_unchecked_mut(row + count * ldvl) =
<<$scalar as RlstScalar>::Complex>::from_real(
*vlr.get_unchecked(row + count * n),
)
};
}
count += 1;
}
}
}
if jobvr == JobVr::Compute {
let mut count = 0;
while count < n {
if count < n - 1 && w[count] == w[1 + count].conj() {
for row in 0..n {
unsafe {
*vr.as_mut().unwrap().get_unchecked_mut(row + count * ldvr) =
<<$scalar as RlstScalar>::Complex>::new(
*vrr.get_unchecked(row + count * n),
*vrr.get_unchecked(row + (1 + count) * n),
)
};
unsafe {
*vr.as_mut()
.unwrap()
.get_unchecked_mut(row + (1 + count) * ldvr) =
<<$scalar as RlstScalar>::Complex>::new(
*vrr.get_unchecked(row + count * n),
-*vrr.get_unchecked(row + (1 + count) * n),
)
};
}
count += 2;
} else {
for row in 0..n {
unsafe {
*vr.as_mut().unwrap().get_unchecked_mut(row + count * ldvr) =
<<$scalar as RlstScalar>::Complex>::from_real(
*vrr.get_unchecked(row + count * n),
)
};
}
count += 1;
}
}
}
lapack_return(info, ())
}
}
};
}
macro_rules! implement_geev_complex {
($scalar:ty, $geev:expr) => {
impl Geev for $scalar {
fn geev(
jobvl: JobVl,
jobvr: JobVr,
n: usize,
a: &mut [Self],
lda: usize,
w: &mut [Self::Complex],
vl: Option<&mut [Self::Complex]>,
ldvl: usize,
vr: Option<&mut [Self::Complex]>,
ldvr: usize,
) -> LapackResult<()> {
let mut info = 0;
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, n),
"Require `lda` {} >= `max(1, n)` {}.",
lda,
std::cmp::max(1, n)
);
assert_eq!(w.len(), n, "Require `wr.len()` {} == `n` {}.", w.len(), n);
let mut vl_temp = Vec::<$scalar>::new();
let mut vr_temp = Vec::<$scalar>::new();
let vl = match jobvl {
JobVl::Compute => {
let vl = vl.expect("vl must be Some when jobvl is V");
assert_eq!(
vl.len(),
ldvl * n,
"Require `vl.len()` {} == `ldvl * n` {}.",
vl.len(),
ldvl * n
);
vl
}
JobVl::None => {
assert_eq!(ldvl, 1, "Require `ldvl` {} == 1.", ldvl);
vl_temp.as_mut_slice()
}
};
let vr = match jobvr {
JobVr::Compute => {
let vr = vr.expect("vr must be Some when jobvr is V");
assert_eq!(
vr.len(),
ldvr * n,
"Require `vr.len()` {} == `ldvr * n` {}.",
vr.len(),
ldvr * n
);
vr
}
JobVr::None => {
assert_eq!(ldvr, 1, "Require `ldvr` {} == 1.", ldvr);
vr_temp.as_mut_slice()
}
};
let mut rwork = vec![<<$scalar as RlstScalar>::Real as Zero>::zero(); 2 * n];
let mut work = vec![<$scalar>::zero(); 1];
unsafe {
$geev(
jobvl as u8,
jobvr as u8,
n as i32,
a,
lda as i32,
w,
vl,
ldvl as i32,
vr,
ldvr as i32,
&mut work,
-1,
&mut rwork,
&mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0].re() as usize;
let mut work = vec![<$scalar>::zero(); lwork];
unsafe {
$geev(
jobvl as u8,
jobvr as u8,
n as i32,
a,
lda as i32,
w,
vl,
ldvl as i32,
vr,
ldvr as i32,
&mut work,
lwork as i32,
&mut rwork,
&mut info,
);
}
lapack_return(info, ())
}
}
};
}
implement_geev!(f32, sgeev);
implement_geev!(f64, dgeev);
implement_geev_complex!(c32, cgeev);
implement_geev_complex!(c64, zgeev);