forked from M-Labs/nalgebra
390 lines
11 KiB
Rust
390 lines
11 KiB
Rust
#[cfg(feature = "serde-serialize")]
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use serde::{Deserialize, Serialize};
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use num::Zero;
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use num_complex::Complex;
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use simba::scalar::RealField;
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use crate::ComplexHelper;
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use na::allocator::Allocator;
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use na::dimension::{Const, Dim};
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use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
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use lapack;
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/// Eigendecomposition of a real square matrix with real eigenvalues.
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#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
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#[cfg_attr(
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feature = "serde-serialize",
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serde(
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bound(serialize = "DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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OVector<T, D>: Serialize,
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OMatrix<T, D, D>: Serialize")
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)
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)]
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#[cfg_attr(
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feature = "serde-serialize",
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serde(
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bound(deserialize = "DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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OVector<T, D>: Serialize,
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OMatrix<T, D, D>: Deserialize<'de>")
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)
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)]
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#[derive(Clone, Debug)]
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pub struct Eigen<T: Scalar, D: Dim>
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where
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DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,
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{
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/// The eigenvalues of the decomposed matrix.
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pub eigenvalues: OVector<T, D>,
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/// The (right) eigenvectors of the decomposed matrix.
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pub eigenvectors: Option<OMatrix<T, D, D>>,
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/// The left eigenvectors of the decomposed matrix.
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pub left_eigenvectors: Option<OMatrix<T, D, D>>,
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}
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impl<T: Scalar + Copy, D: Dim> Copy for Eigen<T, D>
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where
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DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,
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OVector<T, D>: Copy,
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OMatrix<T, D, D>: Copy,
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{
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}
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impl<T: EigenScalar + RealField, D: Dim> Eigen<T, D>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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{
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/// Computes the eigenvalues and eigenvectors of the square matrix `m`.
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///
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/// If `eigenvectors` is `false` then, the eigenvectors are not computed explicitly.
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pub fn new(
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mut m: OMatrix<T, D, D>,
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left_eigenvectors: bool,
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eigenvectors: bool,
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) -> Option<Eigen<T, D>> {
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assert!(
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m.is_square(),
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"Unable to compute the eigenvalue decomposition of a non-square matrix."
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);
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let ljob = if left_eigenvectors { b'V' } else { b'T' };
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let rjob = if eigenvectors { b'V' } else { b'T' };
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let (nrows, ncols) = m.shape_generic();
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let n = nrows.value();
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let lda = n as i32;
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// TODO: avoid the initialization?
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let mut wr = Matrix::zeros_generic(nrows, Const::<1>);
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// TODO: Tap into the workspace.
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let mut wi = Matrix::zeros_generic(nrows, Const::<1>);
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let mut info = 0;
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let mut placeholder1 = [T::zero()];
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let mut placeholder2 = [T::zero()];
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let lwork = T::xgeev_work_size(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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n as i32,
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&mut placeholder2,
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n as i32,
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&mut info,
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);
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lapack_check!(info);
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let mut work = vec![T::zero(); lwork as usize];
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match (left_eigenvectors, eigenvectors) {
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(true, true) => {
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// TODO: avoid the initializations?
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let mut vl = Matrix::zeros_generic(nrows, ncols);
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let mut vr = Matrix::zeros_generic(nrows, ncols);
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T::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut vl.as_mut_slice(),
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n as i32,
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&mut vr.as_mut_slice(),
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n as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Self {
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eigenvalues: wr,
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left_eigenvectors: Some(vl),
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eigenvectors: Some(vr),
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});
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}
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}
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(true, false) => {
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// TODO: avoid the initialization?
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let mut vl = Matrix::zeros_generic(nrows, ncols);
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T::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut vl.as_mut_slice(),
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n as i32,
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&mut placeholder2,
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1 as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Self {
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eigenvalues: wr,
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left_eigenvectors: Some(vl),
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eigenvectors: None,
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});
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}
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}
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(false, true) => {
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// TODO: avoid the initialization?
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let mut vr = Matrix::zeros_generic(nrows, ncols);
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T::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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1 as i32,
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&mut vr.as_mut_slice(),
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n as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Self {
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eigenvalues: wr,
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left_eigenvectors: None,
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eigenvectors: Some(vr),
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});
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}
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}
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(false, false) => {
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T::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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1 as i32,
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&mut placeholder2,
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1 as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Self {
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eigenvalues: wr,
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left_eigenvectors: None,
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eigenvectors: None,
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});
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}
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}
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}
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None
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}
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/// The complex eigenvalues of the given matrix.
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///
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/// Panics if the eigenvalue computation does not converge.
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pub fn complex_eigenvalues(mut m: OMatrix<T, D, D>) -> OVector<Complex<T>, D>
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where
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DefaultAllocator: Allocator<Complex<T>, D>,
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{
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assert!(
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m.is_square(),
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"Unable to compute the eigenvalue decomposition of a non-square matrix."
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);
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let nrows = m.shape_generic().0;
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let n = nrows.value();
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let lda = n as i32;
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// TODO: avoid the initialization?
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let mut wr = Matrix::zeros_generic(nrows, Const::<1>);
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let mut wi = Matrix::zeros_generic(nrows, Const::<1>);
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let mut info = 0;
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let mut placeholder1 = [T::zero()];
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let mut placeholder2 = [T::zero()];
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let lwork = T::xgeev_work_size(
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b'T',
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b'T',
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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n as i32,
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&mut placeholder2,
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n as i32,
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&mut info,
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);
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lapack_panic!(info);
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let mut work = vec![T::zero(); lwork as usize];
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T::xgeev(
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b'T',
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b'T',
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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1 as i32,
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&mut placeholder2,
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1 as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_panic!(info);
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let mut res = Matrix::zeros_generic(nrows, Const::<1>);
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for i in 0..res.len() {
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res[i] = Complex::new(wr[i], wi[i]);
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}
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res
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}
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/// The determinant of the decomposed matrix.
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#[inline]
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#[must_use]
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pub fn determinant(&self) -> T {
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let mut det = T::one();
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for e in self.eigenvalues.iter() {
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det *= *e;
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}
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det
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}
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}
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/*
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*
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* Lapack functions dispatch.
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*
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*/
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/// Trait implemented by scalar type for which Lapack function exist to compute the
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/// eigendecomposition.
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pub trait EigenScalar: Scalar {
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#[allow(missing_docs)]
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fn xgeev(
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jobvl: u8,
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jobvr: u8,
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n: i32,
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a: &mut [Self],
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lda: i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vl: &mut [Self],
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ldvl: i32,
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vr: &mut [Self],
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ldvr: i32,
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work: &mut [Self],
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lwork: i32,
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info: &mut i32,
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);
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#[allow(missing_docs)]
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fn xgeev_work_size(
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jobvl: u8,
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jobvr: u8,
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n: i32,
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a: &mut [Self],
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lda: i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vl: &mut [Self],
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ldvl: i32,
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vr: &mut [Self],
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ldvr: i32,
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info: &mut i32,
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) -> i32;
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}
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macro_rules! real_eigensystem_scalar_impl (
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($N: ty, $xgeev: path) => (
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impl EigenScalar for $N {
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#[inline]
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fn xgeev(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
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wr: &mut [Self], wi: &mut [Self],
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vl: &mut [Self], ldvl: i32, vr: &mut [Self], ldvr: i32,
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work: &mut [Self], lwork: i32, info: &mut i32) {
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unsafe { $xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info) }
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}
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#[inline]
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fn xgeev_work_size(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
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wr: &mut [Self], wi: &mut [Self], vl: &mut [Self], ldvl: i32,
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vr: &mut [Self], ldvr: i32, info: &mut i32) -> i32 {
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let mut work = [ Zero::zero() ];
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let lwork = -1 as i32;
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unsafe { $xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, &mut work, lwork, info) };
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ComplexHelper::real_part(work[0]) as i32
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}
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}
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)
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);
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real_eigensystem_scalar_impl!(f32, lapack::sgeev);
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real_eigensystem_scalar_impl!(f64, lapack::dgeev);
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//// TODO: decomposition of complex matrix and matrices with complex eigenvalues.
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// eigensystem_complex_impl!(f32, lapack::cgeev);
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// eigensystem_complex_impl!(f64, lapack::zgeev);
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