nalgebra/nalgebra-lapack/src/eigen.rs

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use num::Zero;
use num_complex::Complex;
use alga::general::Real;
use ::ComplexHelper;
use na::{Scalar, DefaultAllocator, Matrix, VectorN, MatrixN};
use na::dimension::{Dim, U1};
use na::storage::Storage;
use na::allocator::Allocator;
use lapack::fortran as interface;
/// Eigendecomposition of a real square matrix with real eigenvalues.
pub struct Eigen<N: Scalar, D: Dim>
where DefaultAllocator: Allocator<N, D> +
Allocator<N, D, D> {
/// The eigenvalues of the decomposed matrix.
pub eigenvalues: VectorN<N, D>,
/// The (right) eigenvectors of the decomposed matrix.
pub eigenvectors: Option<MatrixN<N, D>>,
/// The left eigenvectors of the decomposed matrix.
pub left_eigenvectors: Option<MatrixN<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<Eigen<N, 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.data.shape();
let n = nrows.value();
let lda = n as i32;
let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
// FIXME: Tap into the workspace.
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(ljob, rjob, 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_check!(info);
let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
match (left_eigenvectors, eigenvectors) {
(true, true) => {
let mut vl = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
let mut vr = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
N::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(Eigen {
eigenvalues: wr, left_eigenvectors: Some(vl), eigenvectors: Some(vr)
})
}
},
(true, false) => {
let mut vl = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
N::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(Eigen {
eigenvalues: wr, left_eigenvectors: Some(vl), eigenvectors: None
});
}
},
(false, true) => {
let mut vr = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
N::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(Eigen {
eigenvalues: wr, left_eigenvectors: None, eigenvectors: Some(vr)
});
}
},
(false, false) => {
N::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(Eigen {
eigenvalues: wr, left_eigenvectors: None, eigenvectors: None
});
}
}
}
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 = m.data.shape().0;
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 {
let mut det = N::one();
for e in self.eigenvalues.iter() {
det *= *e;
}
det
}
}
/*
*
* Lapack functions dispatch.
*
*/
/// Trait implemented by scalar type for which Lapack funtion exist to compute the
/// eigendecomposition.
pub trait EigenScalar: Scalar {
#[allow(missing_docs)]
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,
work: &mut [Self], lwork: i32, info: &mut i32);
#[allow(missing_docs)]
fn xgeev_work_size(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, info: &mut i32) -> i32;
}
macro_rules! real_eigensystem_scalar_impl (
($N: ty, $xgeev: path) => (
impl EigenScalar for $N {
#[inline]
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,
work: &mut [Self], lwork: i32, info: &mut i32) {
$xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)
}
#[inline]
fn xgeev_work_size(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, info: &mut i32) -> i32 {
let mut work = [ Zero::zero() ];
let lwork = -1 as i32;
$xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, &mut work, lwork, info);
ComplexHelper::real_part(work[0]) as i32
}
}
)
);
real_eigensystem_scalar_impl!(f32, interface::sgeev);
real_eigensystem_scalar_impl!(f64, interface::dgeev);
//// FIXME: decomposition of complex matrix and matrices with complex eigenvalues.
// eigensystem_complex_impl!(f32, interface::cgeev);
// eigensystem_complex_impl!(f64, interface::zgeev);