forked from M-Labs/nalgebra
254 lines
7.0 KiB
Rust
254 lines
7.0 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::{Dim, U1};
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use na::storage::Storage;
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use na::{DefaultAllocator, Matrix, MatrixN, Scalar, VectorN};
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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<N, D, D> + Allocator<N, D>,
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VectorN<N, D>: Serialize,
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MatrixN<N, 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<N, D, D> + Allocator<N, D>,
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VectorN<N, D>: Serialize,
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MatrixN<N, D>: Deserialize<'de>")
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)
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)]
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#[derive(Clone, Debug)]
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pub struct Schur<N: Scalar, D: Dim>
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where DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>
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{
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re: VectorN<N, D>,
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im: VectorN<N, D>,
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t: MatrixN<N, D>,
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q: MatrixN<N, D>,
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}
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impl<N: Scalar + Copy, D: Dim> Copy for Schur<N, D>
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where
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DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
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MatrixN<N, D>: Copy,
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VectorN<N, D>: Copy,
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{
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}
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impl<N: SchurScalar + RealField, D: Dim> Schur<N, D>
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where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
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{
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/// Computes the eigenvalues and real Schur form of the matrix `m`.
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///
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/// Panics if the method did not converge.
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pub fn new(m: MatrixN<N, D>) -> Self {
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Self::try_new(m).expect("Schur decomposition: convergence failed.")
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}
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/// Computes the eigenvalues and real Schur form of the matrix `m`.
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///
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/// Returns `None` if the method did not converge.
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pub fn try_new(mut m: MatrixN<N, D>) -> Option<Self> {
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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, ncols) = m.data.shape();
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let n = nrows.value();
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let lda = n as i32;
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let mut info = 0;
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let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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let mut q = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
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// Placeholders:
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let mut bwork = [0i32];
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let mut unused = 0;
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let lwork = N::xgees_work_size(
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b'V',
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b'N',
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n as i32,
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m.as_mut_slice(),
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lda,
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&mut unused,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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q.as_mut_slice(),
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n as i32,
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&mut bwork,
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&mut info,
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);
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lapack_check!(info);
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let mut work = unsafe { crate::uninitialized_vec(lwork as usize) };
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N::xgees(
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b'V',
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b'N',
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n as i32,
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m.as_mut_slice(),
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lda,
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&mut unused,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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q.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 bwork,
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&mut info,
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);
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lapack_check!(info);
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Some(Schur {
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re: wr,
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im: wi,
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t: m,
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q: q,
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})
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}
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/// Retrieves the unitary matrix `Q` and the upper-quasitriangular matrix `T` such that the
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/// decomposed matrix equals `Q * T * Q.transpose()`.
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pub fn unpack(self) -> (MatrixN<N, D>, MatrixN<N, D>) {
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(self.q, self.t)
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}
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/// Computes the real eigenvalues of the decomposed matrix.
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///
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/// Return `None` if some eigenvalues are complex.
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pub fn eigenvalues(&self) -> Option<VectorN<N, D>> {
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if self.im.iter().all(|e| e.is_zero()) {
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Some(self.re.clone())
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} else {
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None
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}
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}
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/// Computes the complex eigenvalues of the decomposed matrix.
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pub fn complex_eigenvalues(&self) -> VectorN<Complex<N>, D>
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where DefaultAllocator: Allocator<Complex<N>, D> {
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let mut out = unsafe { VectorN::new_uninitialized_generic(self.t.data.shape().0, U1) };
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for i in 0..out.len() {
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out[i] = Complex::new(self.re[i], self.im[i])
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}
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out
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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 scalars for which Lapack implements the RealField Schur decomposition.
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pub trait SchurScalar: Scalar {
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#[allow(missing_docs)]
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fn xgees(
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jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [Self],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vs: &mut [Self],
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ldvs: i32,
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work: &mut [Self],
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lwork: i32,
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bwork: &mut [i32],
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info: &mut i32,
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);
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#[allow(missing_docs)]
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fn xgees_work_size(
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jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [Self],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vs: &mut [Self],
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ldvs: i32,
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bwork: &mut [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, $xgees: path) => (
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impl SchurScalar for $N {
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#[inline]
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fn xgees(jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [$N],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [$N],
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wi: &mut [$N],
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vs: &mut [$N],
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ldvs: i32,
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work: &mut [$N],
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lwork: i32,
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bwork: &mut [i32],
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info: &mut i32) {
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unsafe { $xgees(jobvs, sort, None, n, a, lda, sdim, wr, wi, vs, ldvs, work, lwork, bwork, info); }
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}
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#[inline]
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fn xgees_work_size(jobvs: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [$N],
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lda: i32,
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sdim: &mut i32,
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wr: &mut [$N],
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wi: &mut [$N],
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vs: &mut [$N],
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ldvs: i32,
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bwork: &mut [i32],
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info: &mut i32)
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-> i32 {
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let mut work = [ Zero::zero() ];
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let lwork = -1 as i32;
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unsafe { $xgees(jobvs, sort, None, n, a, lda, sdim, wr, wi, vs, ldvs, &mut work, lwork, bwork, 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::sgees);
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real_eigensystem_scalar_impl!(f64, lapack::dgees);
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