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//! Implementation of ?sygv/?hegv - Generalized Symmetric/Hermitian Eigenvalue Problem.
use lapack::{chegv, dsygv, ssygv, zhegv};
use crate::base_types::{LapackError, LapackResult, c32, c64};
use crate::dense::linalg::lapack::interface::lapack_return;
use crate::traits::rlst_num::RlstScalar;
use num::Zero;
use num::complex::ComplexFloat;
/// The job options for the eigenvectors.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
#[repr(u8)]
pub enum JobZ {
/// Compute eigenvalues only.
None = b'N',
/// Compute eigenvalues and eigenvectors.
ValuesAndVectors = b'V',
}
/// Use upper or lower triangular part of the matrix.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
#[repr(u8)]
pub enum SygvUplo {
/// Use the upper triangular part of the matrix.
Upper = b'U',
/// Use the lower triangular part of the matrix.
Lower = b'L',
}
/// ?sygv/?hegv - Generalized Symmetric/Hermitian Eigenvalue Problem.
pub trait Sygv: RlstScalar {
/// Compute generalized eigenvalues and optionally eigenvectors.
///
/// Depending on `itype`, solves:
/// 1: Ax = λBx
/// 2: ABx = λx
/// 3: BAx = λx
///
/// A and B are column-major `n x n` arrays and are overwritten; only the
/// triangle selected by `uplo` is read. B must be positive definite.
/// Eigenvalues are written to `w` in ascending order and, when requested,
/// eigenvectors overwrite A. Invalid storage dimensions panic; LAPACK
/// failures (including failure to factor B) are returned as errors.
#[allow(clippy::too_many_arguments)]
fn sygv(
itype: i32,
jobz: JobZ,
uplo: SygvUplo,
n: usize,
a: &mut [Self],
lda: usize,
b: &mut [Self],
ldb: usize,
w: &mut [Self::Real],
) -> LapackResult<()>;
}
macro_rules! implement_sygv_real {
($scalar:ty, $sygv:expr) => {
impl Sygv for $scalar {
fn sygv(
itype: i32,
jobz: JobZ,
uplo: SygvUplo,
n: usize,
a: &mut [Self],
lda: usize,
b: &mut [Self],
ldb: usize,
w: &mut [Self::Real],
) -> LapackResult<()> {
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, n),
"Require `lda` {} >= `max(1, n)` {}.",
lda,
std::cmp::max(1, n)
);
assert_eq!(
b.len(),
ldb * n,
"Require `b.len()` {} == `ldb * n` {}.",
b.len(),
ldb * n
);
assert!(
ldb >= std::cmp::max(1, n),
"Require `ldb` {} >= `max(1, n)` {}.",
ldb,
std::cmp::max(1, n)
);
assert_eq!(w.len(), n, "Require `w.len()` {} == `n` {}.", w.len(), n);
let mut info = 0;
let mut work = vec![<$scalar>::zero(); 1];
let itype = [itype];
unsafe {
$sygv(
&itype, jobz as u8, uplo as u8, n as i32, a, lda as i32, b, ldb as i32, w,
&mut work, -1, &mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0] as usize;
let mut work = vec![<$scalar>::zero(); lwork];
unsafe {
$sygv(
&itype,
jobz as u8,
uplo as u8,
n as i32,
a,
lda as i32,
b,
ldb as i32,
w,
&mut work,
lwork as i32,
&mut info,
);
}
lapack_return(info, ())
}
}
};
}
macro_rules! implement_hegv_complex {
($scalar:ty, $hegv:expr) => {
impl Sygv for $scalar {
fn sygv(
itype: i32,
jobz: JobZ,
uplo: SygvUplo,
n: usize,
a: &mut [Self],
lda: usize,
b: &mut [Self],
ldb: usize,
w: &mut [Self::Real],
) -> LapackResult<()> {
assert_eq!(
a.len(),
lda * n,
"Require `a.len()` {} == `lda * n` {}.",
a.len(),
lda * n
);
assert!(
lda >= std::cmp::max(1, n),
"Require `lda` {} >= `max(1, n)` {}.",
lda,
std::cmp::max(1, n)
);
assert_eq!(
b.len(),
ldb * n,
"Require `b.len()` {} == `ldb * n` {}.",
b.len(),
ldb * n
);
assert!(
ldb >= std::cmp::max(1, n),
"Require `ldb` {} >= `max(1, n)` {}.",
ldb,
std::cmp::max(1, n)
);
assert_eq!(w.len(), n, "Require `w.len()` {} == `n` {}.", w.len(), n);
let mut info = 0;
let mut work = vec![<$scalar>::zero(); 1];
let itype = [itype];
let mut rwork = vec![
<<$scalar as RlstScalar>::Real as Zero>::zero();
std::cmp::max(1, 3 * n - 2)
];
unsafe {
$hegv(
&itype, jobz as u8, uplo as u8, n as i32, a, lda as i32, b, ldb as i32, w,
&mut work, -1, &mut rwork, &mut info,
);
}
if info != 0 {
return Err(LapackError::LapackInfoCode(info));
}
let lwork = work[0].re() as usize;
let mut work = vec![<$scalar>::zero(); lwork];
unsafe {
$hegv(
&itype,
jobz as u8,
uplo as u8,
n as i32,
a,
lda as i32,
b,
ldb as i32,
w,
&mut work,
lwork as i32,
&mut rwork,
&mut info,
);
}
lapack_return(info, ())
}
}
};
}
implement_sygv_real!(f32, ssygv);
implement_sygv_real!(f64, dsygv);
implement_hegv_complex!(c32, chegv);
implement_hegv_complex!(c64, zhegv);