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//! Eigenvalue decomposition for general matrices
use lapacke;
use num_traits::Zero;
use crate::error::*;
use crate::layout::MatrixLayout;
use crate::types::*;
use super::into_result;
/// Wraps `*geev` for real/complex
pub trait Eig_: Scalar {
unsafe fn eig(
calc_v: bool,
l: MatrixLayout,
a: &mut [Self],
) -> Result<(Vec<Self::Complex>, Vec<Self::Complex>)>;
}
macro_rules! impl_eig_complex {
($scalar:ty, $ev:path) => {
impl Eig_ for $scalar {
unsafe fn eig(
calc_v: bool,
l: MatrixLayout,
mut a: &mut [Self],
) -> Result<(Vec<Self::Complex>, Vec<Self::Complex>)> {
let (n, _) = l.size();
let jobvr = if calc_v { b'V' } else { b'N' };
let mut w = vec![Self::Complex::zero(); n as usize];
let mut vl = Vec::new();
let mut vr = vec![Self::Complex::zero(); (n * n) as usize];
let info = $ev(
l.lapacke_layout(),
b'N',
jobvr,
n,
&mut a,
n,
&mut w,
&mut vl,
n,
&mut vr,
n,
);
into_result(info, (w, vr))
}
}
};
}
macro_rules! impl_eig_real {
($scalar:ty, $ev:path) => {
impl Eig_ for $scalar {
unsafe fn eig(
calc_v: bool,
l: MatrixLayout,
mut a: &mut [Self],
) -> Result<(Vec<Self::Complex>, Vec<Self::Complex>)> {
let (n, _) = l.size();
let jobvr = if calc_v { b'V' } else { b'N' };
let mut wr = vec![Self::Real::zero(); n as usize];
let mut wi = vec![Self::Real::zero(); n as usize];
let mut vl = Vec::new();
let mut vr = vec![Self::Real::zero(); (n * n) as usize];
let info = $ev(
l.lapacke_layout(),
b'N',
jobvr,
n,
&mut a,
n,
&mut wr,
&mut wi,
&mut vl,
n,
&mut vr,
n,
);
let w: Vec<Self::Complex> = wr
.iter()
.zip(wi.iter())
.map(|(&r, &i)| Self::Complex::new(r, i))
.collect();
// If the j-th eigenvalue is real, then
// eigenvector = [ vr[j], vr[j+n], vr[j+2*n], ... ].
//
// If the j-th and (j+1)-st eigenvalues form a complex conjugate pair,
// eigenvector(j) = [ vr[j] + i*vr[j+1], vr[j+n] + i*vr[j+n+1], vr[j+2*n] + i*vr[j+2*n+1], ... ] and
// eigenvector(j+1) = [ vr[j] - i*vr[j+1], vr[j+n] - i*vr[j+n+1], vr[j+2*n] - i*vr[j+2*n+1], ... ].
//
// Therefore, if eigenvector(j) is written as [ v_{j0}, v_{j1}, v_{j2}, ... ],
// you have to make
// v = vec![ v_{00}, v_{10}, v_{20}, ..., v_{jk}, v_{(j+1)k}, v_{(j+2)k}, ... ] (v.len() = n*n)
// based on wi and vr.
// After that, v is converted to Array2 (see ../eig.rs).
let n = n as usize;
let mut flg = false;
let conj: Vec<i8> = wi
.iter()
.map(|&i| {
if flg {
flg = false;
-1
} else if i != 0.0 {
flg = true;
1
} else {
0
}
})
.collect();
let v: Vec<Self::Complex> = (0..n * n)
.map(|i| {
let j = i % n;
match conj[j] {
1 => Self::Complex::new(vr[i], vr[i + 1]),
-1 => Self::Complex::new(vr[i - 1], -vr[i]),
_ => Self::Complex::new(vr[i], 0.0),
}
})
.collect();
into_result(info, (w, v))
}
}
};
}
impl_eig_real!(f64, lapacke::dgeev);
impl_eig_real!(f32, lapacke::sgeev);
impl_eig_complex!(c64, lapacke::zgeev);
impl_eig_complex!(c32, lapacke::cgeev);