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nalgebra-lapack: add computation of complex eigenvalues. 

Also renames RealEigensystem -> Eigen
This commit is contained in:
Sébastien Crozet 2017-08-06 19:41:33 +02:00 committed by Sébastien Crozet
parent c616c3ddef
commit 89e8b49759
3 changed files with 59 additions and 16 deletions
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61
nalgebra-lapack/src/eigen.rs
View File

@ -1,4 +1,5 @@
use num::Zero;
use num_complex::Complex;
use alga::general::Real;
@ -11,7 +12,7 @@ use na::allocator::Allocator;
use lapack::fortran as interface;
/// Eigendecomposition of a real square matrix with real eigenvalues.
pub struct RealEigensystem<N: Scalar, D: Dim>
pub struct Eigen<N: Scalar, D: Dim>
where DefaultAllocator: Allocator<N, D> +
Allocator<N, D, D> {
pub eigenvalues: VectorN<N, D>,
@ -20,14 +21,14 @@ pub struct RealEigensystem<N: Scalar, D: Dim>
}
impl<N: RealEigensystemScalar + Real, D: Dim> RealEigensystem<N, D>
impl<N: EigenScalar + Real, D: Dim> Eigen<N, D>
where DefaultAllocator: Allocator<N, D, D> +
Allocator<N, D> {
/// Computes the eigenvalues and eigenvectors of the square matrix `m`.
///
/// If `eigenvectors` is `false` then, the eigenvectors are not computed explicitly.
pub fn new(mut m: MatrixN<N, D>, left_eigenvectors: bool, eigenvectors: bool)
-> Option<RealEigensystem<N, D>> {
-> Option<Eigen<N, D>> {
assert!(m.is_square(), "Unable to compute the eigenvalue decomposition of a non-square matrix.");
@ -67,7 +68,7 @@ impl<N: RealEigensystemScalar + Real, D: Dim> RealEigensystem<N, D>
lapack_check!(info);
if wi.iter().all(|e| e.is_zero()) {
return Some(RealEigensystem {
return Some(Eigen {
eigenvalues: wr, left_eigenvectors: Some(vl), eigenvectors: Some(vr)
})
}
@ -81,7 +82,7 @@ impl<N: RealEigensystemScalar + Real, D: Dim> RealEigensystem<N, D>
lapack_check!(info);
if wi.iter().all(|e| e.is_zero()) {
return Some(RealEigensystem {
return Some(Eigen {
eigenvalues: wr, left_eigenvectors: Some(vl), eigenvectors: None
});
}
@ -95,7 +96,7 @@ impl<N: RealEigensystemScalar + Real, D: Dim> RealEigensystem<N, D>
lapack_check!(info);
if wi.iter().all(|e| e.is_zero()) {
return Some(RealEigensystem {
return Some(Eigen {
eigenvalues: wr, left_eigenvectors: None, eigenvectors: Some(vr)
});
}
@ -107,7 +108,7 @@ impl<N: RealEigensystemScalar + Real, D: Dim> RealEigensystem<N, D>
lapack_check!(info);
if wi.iter().all(|e| e.is_zero()) {
return Some(RealEigensystem {
return Some(Eigen {
eigenvalues: wr, left_eigenvectors: None, eigenvectors: None
});
}
@ -117,6 +118,48 @@ impl<N: RealEigensystemScalar + Real, D: Dim> RealEigensystem<N, D>
None
}
/// The complex eigenvalues of the given matrix.
///
/// Panics if the eigenvalue computation does not converge.
pub fn complex_eigenvalues(mut m: MatrixN<N, D>) -> VectorN<Complex<N>, D>
where DefaultAllocator: Allocator<Complex<N>, D> {
assert!(m.is_square(), "Unable to compute the eigenvalue decomposition of a non-square matrix.");
let (nrows, ncols) = m.data.shape();
let n = nrows.value();
let lda = n as i32;
let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
let mut info = 0;
let mut placeholder1 = [ N::zero() ];
let mut placeholder2 = [ N::zero() ];
let lwork = N::xgeev_work_size(b'N', b'N', n as i32, m.as_mut_slice(), lda,
wr.as_mut_slice(), wi.as_mut_slice(), &mut placeholder1,
n as i32, &mut placeholder2, n as i32, &mut info);
lapack_panic!(info);
let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
N::xgeev(b'N', b'N', 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 = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
for i in 0 .. res.len() {
res[i] = Complex::new(wr[i], wi[i]);
}
res
}
/// The determinant of the decomposed matrix.
#[inline]
pub fn determinant(&self) -> N {
@ -138,7 +181,7 @@ impl<N: RealEigensystemScalar + Real, D: Dim> RealEigensystem<N, D>
* Lapack functions dispatch.
*
*/
pub trait RealEigensystemScalar: Scalar {
pub trait EigenScalar: Scalar {
fn xgeev(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
wr: &mut [Self], wi: &mut [Self],
vl: &mut [Self], ldvl: i32, vr: &mut [Self], ldvr: i32,
@ -150,7 +193,7 @@ pub trait RealEigensystemScalar: Scalar {
macro_rules! real_eigensystem_scalar_impl (
($N: ty, $xgeev: path) => (
impl RealEigensystemScalar for $N {
impl EigenScalar for $N {
#[inline]
fn xgeev(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
wr: &mut [Self], wi: &mut [Self],

8
nalgebra-lapack/src/symmetric_eigen.rs
View File

@ -11,7 +11,7 @@ use na::allocator::Allocator;
use lapack::fortran as interface;
/// Eigendecomposition of a real square matrix with real eigenvalues.
/// SymmetricEigendecomposition of a real square matrix with real eigenvalues.
pub struct SymmetricEigen<N: Scalar, D: Dim>
where DefaultAllocator: Allocator<N, D> +
Allocator<N, D, D> {
@ -20,7 +20,7 @@ pub struct SymmetricEigen<N: Scalar, D: Dim>
}
impl<N: RealEigensystemScalar + Real, D: Dim> SymmetricEigen<N, D>
impl<N: SymmetricEigenScalar + Real, D: Dim> SymmetricEigen<N, D>
where DefaultAllocator: Allocator<N, D, D> +
Allocator<N, D> {
@ -113,7 +113,7 @@ impl<N: RealEigensystemScalar + Real, D: Dim> SymmetricEigen<N, D>
* Lapack functions dispatch.
*
*/
pub trait RealEigensystemScalar: Scalar {
pub trait SymmetricEigenScalar: Scalar {
fn xsyev(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, w: &mut [Self], work: &mut [Self],
lwork: i32, info: &mut i32);
fn xsyev_work_size(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32) -> i32;
@ -121,7 +121,7 @@ pub trait RealEigensystemScalar: Scalar {
macro_rules! real_eigensystem_scalar_impl (
($N: ty, $xsyev: path) => (
impl RealEigensystemScalar for $N {
impl SymmetricEigenScalar for $N {
#[inline]
fn xsyev(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, w: &mut [Self], work: &mut [Self],
lwork: i32, info: &mut i32) {

6
nalgebra-lapack/tests/linalg/real_eigensystem.rs
View File

@ -1,6 +1,6 @@
use std::cmp;
use nl::RealEigensystem;
use nl::Eigen;
use na::{DMatrix, Matrix4};
quickcheck!{
@ -9,7 +9,7 @@ quickcheck!{
let n = cmp::min(n, 25);
let m = DMatrix::<f64>::new_random(n, n);
match RealEigensystem::new(m.clone(), true, true) {
match Eigen::new(m.clone(), true, true) {
Some(eig) => {
let eigvals = DMatrix::from_diagonal(&eig.eigenvalues);
let transformed_eigvectors = &m * eig.eigenvectors.as_ref().unwrap();
@ -30,7 +30,7 @@ quickcheck!{
}
fn eigensystem_static(m: Matrix4<f64>) -> bool {
match RealEigensystem::new(m, true, true) {
match Eigen::new(m, true, true) {
Some(eig) => {
let eigvals = Matrix4::from_diagonal(&eig.eigenvalues);
let transformed_eigvectors = m * eig.eigenvectors.unwrap();