nalgebra/nalgebra-lapack/src/symmetric_eigen.rs

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#[cfg(feature = "serde-serialize")]
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use serde::{Deserialize, Serialize};
use num::Zero;
use std::ops::MulAssign;
use alga::general::Real;
use na::allocator::Allocator;
use na::dimension::{Dim, U1};
use na::storage::Storage;
use na::{DefaultAllocator, Matrix, MatrixN, Scalar, VectorN};
use ComplexHelper;
use lapack;
/// Eigendecomposition of a real square symmetric matrix with real eigenvalues.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize",
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serde(bound(
serialize = "DefaultAllocator: Allocator<N, D, D> +
Allocator<N, D>,
VectorN<N, D>: Serialize,
MatrixN<N, D>: Serialize"
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))
)]
#[cfg_attr(
feature = "serde-serialize",
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serde(bound(
deserialize = "DefaultAllocator: Allocator<N, D, D> +
Allocator<N, D>,
VectorN<N, D>: Deserialize<'de>,
MatrixN<N, D>: Deserialize<'de>"
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))
)]
#[derive(Clone, Debug)]
pub struct SymmetricEigen<N: Scalar, D: Dim>
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where DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>
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{
/// The eigenvectors of the decomposed matrix.
pub eigenvectors: MatrixN<N, D>,
/// The unsorted eigenvalues of the decomposed matrix.
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pub eigenvalues: VectorN<N, D>,
}
impl<N: Scalar, D: Dim> Copy for SymmetricEigen<N, D>
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where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
MatrixN<N, D>: Copy,
VectorN<N, D>: Copy,
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{}
impl<N: SymmetricEigenScalar + Real, D: Dim> SymmetricEigen<N, D>
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where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
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{
/// Computes the eigenvalues and eigenvectors of the symmetric matrix `m`.
///
/// Only the lower-triangular part of `m` is read. If `eigenvectors` is `false` then, the
/// eigenvectors are not computed explicitly. Panics if the method did not converge.
pub fn new(m: MatrixN<N, D>) -> Self {
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let (vals, vecs) =
Self::do_decompose(m, true).expect("SymmetricEigen: convergence failure.");
SymmetricEigen {
eigenvalues: vals,
eigenvectors: vecs.unwrap(),
}
}
/// Computes the eigenvalues and eigenvectors of the symmetric matrix `m`.
///
/// Only the lower-triangular part of `m` is read. If `eigenvectors` is `false` then, the
/// eigenvectors are not computed explicitly. Returns `None` if the method did not converge.
pub fn try_new(m: MatrixN<N, D>) -> Option<Self> {
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Self::do_decompose(m, true).map(|(vals, vecs)| SymmetricEigen {
eigenvalues: vals,
eigenvectors: vecs.unwrap(),
})
}
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fn do_decompose(
mut m: MatrixN<N, D>,
eigenvectors: bool,
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) -> Option<(VectorN<N, D>, Option<MatrixN<N, D>>)>
{
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assert!(
m.is_square(),
"Unable to compute the eigenvalue decomposition of a non-square matrix."
);
let jobz = if eigenvectors { b'V' } else { b'N' };
let nrows = m.data.shape().0;
let n = nrows.value();
let lda = n as i32;
let mut values = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
let mut info = 0;
let lwork = N::xsyev_work_size(jobz, b'L', n as i32, m.as_mut_slice(), lda, &mut info);
lapack_check!(info);
let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
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N::xsyev(
jobz,
b'L',
n as i32,
m.as_mut_slice(),
lda,
values.as_mut_slice(),
&mut work,
lwork,
&mut info,
);
lapack_check!(info);
let vectors = if eigenvectors { Some(m) } else { None };
Some((values, vectors))
}
/// Computes only the eigenvalues of the input matrix.
///
/// Panics if the method does not converge.
pub fn eigenvalues(m: MatrixN<N, D>) -> VectorN<N, D> {
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Self::do_decompose(m, false)
.expect("SymmetricEigen eigenvalues: convergence failure.")
.0
}
/// Computes only the eigenvalues of the input matrix.
///
/// Returns `None` if the method does not converge.
pub fn try_eigenvalues(m: MatrixN<N, D>) -> Option<VectorN<N, D>> {
Self::do_decompose(m, false).map(|res| res.0)
}
/// 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
}
/// Rebuild the original matrix.
///
/// This is useful if some of the eigenvalues have been manually modified.
pub fn recompose(&self) -> MatrixN<N, D> {
let mut u_t = self.eigenvectors.clone();
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for i in 0..self.eigenvalues.len() {
let val = self.eigenvalues[i];
u_t.column_mut(i).mul_assign(val);
}
u_t.transpose_mut();
&self.eigenvectors * u_t
}
}
/*
*
* Lapack functions dispatch.
*
*/
/// Trait implemented by scalars for which Lapack implements the eigendecomposition of symmetric
/// real matrices.
pub trait SymmetricEigenScalar: Scalar {
#[allow(missing_docs)]
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fn xsyev(
jobz: u8,
uplo: u8,
n: i32,
a: &mut [Self],
lda: i32,
w: &mut [Self],
work: &mut [Self],
lwork: i32,
info: &mut i32,
);
#[allow(missing_docs)]
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fn xsyev_work_size(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32)
-> i32;
}
macro_rules! real_eigensystem_scalar_impl (
($N: ty, $xsyev: path) => (
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) {
unsafe { $xsyev(jobz, uplo, n, a, lda, w, work, lwork, info) }
}
#[inline]
fn xsyev_work_size(jobz: u8, uplo: u8, n: i32, a: &mut [Self], lda: i32, info: &mut i32) -> i32 {
let mut work = [ Zero::zero() ];
let mut w = [ Zero::zero() ];
let lwork = -1 as i32;
unsafe { $xsyev(jobz, uplo, n, a, lda, &mut w, &mut work, lwork, info); }
ComplexHelper::real_part(work[0]) as i32
}
}
)
);
real_eigensystem_scalar_impl!(f32, lapack::ssyev);
real_eigensystem_scalar_impl!(f64, lapack::dsyev);