nalgebra-lapack: merge both Eigen decomposition function into a single one.
This commit is contained in:
Sébastien Crozet
parent
a0412c39f2
commit
3d52327f82
|
|
@ -13,7 +13,7 @@ use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
|
|||
|
||||
use lapack;
|
||||
|
||||
/// Eigendecomposition of a real square matrix with real eigenvalues.
|
||||
/// Eigendecomposition of a real square matrix with real or complex eigenvalues.
|
||||
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
|
||||
#[cfg_attr(
|
||||
feature = "serde-serialize",
|
||||
|
|
@ -36,8 +36,10 @@ pub struct Eigen<T: Scalar, D: Dim>
|
|||
where
|
||||
DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,
|
||||
{
|
||||
/// The eigenvalues of the decomposed matrix.
|
||||
pub eigenvalues: OVector<T, D>,
|
||||
/// The real parts of eigenvalues of the decomposed matrix.
|
||||
pub eigenvalues_re: OVector<T, D>,
|
||||
/// The imaginary parts of the eigenvalues of the decomposed matrix.
|
||||
pub eigenvalues_im: OVector<T, D>,
|
||||
/// The (right) eigenvectors of the decomposed matrix.
|
||||
pub eigenvectors: Option<OMatrix<T, D, D>>,
|
||||
/// The left eigenvectors of the decomposed matrix.
|
||||
|
|
@ -104,169 +106,27 @@ where
|
|||
lapack_check!(info);
|
||||
|
||||
let mut work = vec![T::zero(); lwork as usize];
|
||||
let mut vl = if left_eigenvectors {
|
||||
Some(Matrix::zeros_generic(nrows, ncols))
|
||||
} else {
|
||||
None
|
||||
};
|
||||
let mut vr = if eigenvectors {
|
||||
Some(Matrix::zeros_generic(nrows, ncols))
|
||||
} else {
|
||||
None
|
||||
};
|
||||
|
||||
match (left_eigenvectors, eigenvectors) {
|
||||
(true, true) => {
|
||||
// TODO: avoid the initializations?
|
||||
let mut vl = Matrix::zeros_generic(nrows, ncols);
|
||||
let mut vr = Matrix::zeros_generic(nrows, ncols);
|
||||
let vl_ref = vl
|
||||
.as_mut()
|
||||
.map(|m| m.as_mut_slice())
|
||||
.unwrap_or(&mut placeholder1);
|
||||
let vr_ref = vr
|
||||
.as_mut()
|
||||
.map(|m| m.as_mut_slice())
|
||||
.unwrap_or(&mut placeholder2);
|
||||
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut vl.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut vr.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_check!(info);
|
||||
|
||||
if wi.iter().all(|e| e.is_zero()) {
|
||||
return Some(Self {
|
||||
eigenvalues: wr,
|
||||
left_eigenvectors: Some(vl),
|
||||
eigenvectors: Some(vr),
|
||||
});
|
||||
}
|
||||
}
|
||||
(true, false) => {
|
||||
// TODO: avoid the initialization?
|
||||
let mut vl = Matrix::zeros_generic(nrows, ncols);
|
||||
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut vl.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut placeholder2,
|
||||
1 as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_check!(info);
|
||||
|
||||
if wi.iter().all(|e| e.is_zero()) {
|
||||
return Some(Self {
|
||||
eigenvalues: wr,
|
||||
left_eigenvectors: Some(vl),
|
||||
eigenvectors: None,
|
||||
});
|
||||
}
|
||||
}
|
||||
(false, true) => {
|
||||
// TODO: avoid the initialization?
|
||||
let mut vr = Matrix::zeros_generic(nrows, ncols);
|
||||
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut placeholder1,
|
||||
1 as i32,
|
||||
&mut vr.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_check!(info);
|
||||
|
||||
if wi.iter().all(|e| e.is_zero()) {
|
||||
return Some(Self {
|
||||
eigenvalues: wr,
|
||||
left_eigenvectors: None,
|
||||
eigenvectors: Some(vr),
|
||||
});
|
||||
}
|
||||
}
|
||||
(false, false) => {
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut placeholder1,
|
||||
1 as i32,
|
||||
&mut placeholder2,
|
||||
1 as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_check!(info);
|
||||
|
||||
if wi.iter().all(|e| e.is_zero()) {
|
||||
return Some(Self {
|
||||
eigenvalues: wr,
|
||||
left_eigenvectors: None,
|
||||
eigenvectors: None,
|
||||
});
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
None
|
||||
}
|
||||
|
||||
/// The complex eigen decomposition of the given matrix.
|
||||
///
|
||||
/// Panics if the eigenvalue computation does not converge.
|
||||
pub fn complex_eigen_decomposition(
|
||||
mut m: OMatrix<T, D, D>,
|
||||
left_eigenvectors: bool,
|
||||
eigenvectors: bool,
|
||||
) -> (
|
||||
OVector<Complex<T>, D>,
|
||||
Option<OMatrix<T, D, D>>,
|
||||
Option<OMatrix<T, D, D>>,
|
||||
)
|
||||
where
|
||||
DefaultAllocator: Allocator<Complex<T>, D> + Allocator<Complex<T>, D, D>,
|
||||
{
|
||||
assert!(
|
||||
m.is_square(),
|
||||
"Unable to compute the eigenvalue decomposition of a non-square matrix."
|
||||
);
|
||||
|
||||
let ljob = if left_eigenvectors { b'V' } else { b'N' };
|
||||
let rjob = if eigenvectors { b'V' } else { b'N' };
|
||||
|
||||
let (nrows, ncols) = m.shape_generic();
|
||||
let n = nrows.value();
|
||||
|
||||
let lda = n as i32;
|
||||
|
||||
// TODO: avoid the initialization?
|
||||
let mut wr = Matrix::zeros_generic(nrows, Const::<1>);
|
||||
// TODO: Tap into the workspace.
|
||||
let mut wi = Matrix::zeros_generic(nrows, Const::<1>);
|
||||
|
||||
let mut info = 0;
|
||||
let mut placeholder1 = [T::zero()];
|
||||
let mut placeholder2 = [T::zero()];
|
||||
|
||||
let lwork = T::xgeev_work_size(
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
|
|
@ -274,142 +134,36 @@ where
|
|||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut placeholder1,
|
||||
n as i32,
|
||||
&mut placeholder2,
|
||||
n as i32,
|
||||
vl_ref,
|
||||
if left_eigenvectors { n as i32 } else { 1 },
|
||||
vr_ref,
|
||||
if eigenvectors { n as i32 } else { 1 },
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_check!(info);
|
||||
|
||||
lapack_panic!(info);
|
||||
Some(Self {
|
||||
eigenvalues_re: wr,
|
||||
eigenvalues_im: wi,
|
||||
left_eigenvectors: vl,
|
||||
eigenvectors: vr,
|
||||
})
|
||||
}
|
||||
|
||||
let mut work = vec![T::zero(); lwork as usize];
|
||||
|
||||
match (left_eigenvectors, eigenvectors) {
|
||||
(true, true) => {
|
||||
// TODO: avoid the initializations?
|
||||
let mut vl = Matrix::zeros_generic(nrows, ncols);
|
||||
let mut vr = Matrix::zeros_generic(nrows, ncols);
|
||||
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut vl.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut vr.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_panic!(info);
|
||||
|
||||
let mut res = Matrix::zeros_generic(nrows, Const::<1>);
|
||||
|
||||
for i in 0..res.len() {
|
||||
res[i] = Complex::new(wr[i].clone(), wi[i].clone());
|
||||
}
|
||||
(res, Some(vl), Some(vr))
|
||||
}
|
||||
(true, false) => {
|
||||
// TODO: avoid the initialization?
|
||||
let mut vl = Matrix::zeros_generic(nrows, ncols);
|
||||
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut vl.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut placeholder2,
|
||||
1 as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_panic!(info);
|
||||
|
||||
let mut res = Matrix::zeros_generic(nrows, Const::<1>);
|
||||
|
||||
for i in 0..res.len() {
|
||||
res[i] = Complex::new(wr[i].clone(), wi[i].clone());
|
||||
}
|
||||
(res, Some(vl), None)
|
||||
}
|
||||
(false, true) => {
|
||||
// TODO: avoid the initialization?
|
||||
let mut vr = Matrix::zeros_generic(nrows, ncols);
|
||||
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut placeholder1,
|
||||
1 as i32,
|
||||
&mut vr.as_mut_slice(),
|
||||
n as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_panic!(info);
|
||||
|
||||
let mut res = Matrix::zeros_generic(nrows, Const::<1>);
|
||||
|
||||
for i in 0..res.len() {
|
||||
res[i] = Complex::new(wr[i].clone(), wi[i].clone());
|
||||
}
|
||||
(res, None, Some(vr))
|
||||
}
|
||||
(false, false) => {
|
||||
T::xgeev(
|
||||
ljob,
|
||||
rjob,
|
||||
n as i32,
|
||||
m.as_mut_slice(),
|
||||
lda,
|
||||
wr.as_mut_slice(),
|
||||
wi.as_mut_slice(),
|
||||
&mut placeholder1,
|
||||
1 as i32,
|
||||
&mut placeholder2,
|
||||
1 as i32,
|
||||
&mut work,
|
||||
lwork,
|
||||
&mut info,
|
||||
);
|
||||
lapack_panic!(info);
|
||||
|
||||
let mut res = Matrix::zeros_generic(nrows, Const::<1>);
|
||||
|
||||
for i in 0..res.len() {
|
||||
res[i] = Complex::new(wr[i].clone(), wi[i].clone());
|
||||
}
|
||||
(res, None, None)
|
||||
}
|
||||
}
|
||||
/// Returns `true` if all the eigenvalues are real.
|
||||
pub fn eigenvalues_are_real(&self) -> bool {
|
||||
self.eigenvalues_im.iter().all(|e| e.is_zero())
|
||||
}
|
||||
|
||||
/// The determinant of the decomposed matrix.
|
||||
#[inline]
|
||||
#[must_use]
|
||||
pub fn determinant(&self) -> T {
|
||||
let mut det = T::one();
|
||||
for e in self.eigenvalues.iter() {
|
||||
det *= e.clone();
|
||||
pub fn determinant(&self) -> Complex<T> {
|
||||
let mut det: Complex<T> = na::one();
|
||||
for (re, im) in self.eigenvalues_re.iter().zip(self.eigenvalues_im.iter()) {
|
||||
det *= Complex::new(re.clone(), im.clone());
|
||||
}
|
||||
|
||||
det
|
||||
|
|
|
|||
Loading…
Reference in New Issue