First attempt at xgges (qz decomposition), passing tests. Serialization failing across many modules
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metric-space
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@ -86,6 +86,7 @@ mod eigen;
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mod hessenberg;
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mod lu;
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mod qr;
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mod qz;
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mod schur;
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mod svd;
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mod symmetric_eigen;
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@ -97,6 +98,7 @@ pub use self::eigen::Eigen;
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pub use self::hessenberg::Hessenberg;
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pub use self::lu::{LUScalar, LU};
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pub use self::qr::QR;
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pub use self::qz::QZ;
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pub use self::schur::Schur;
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pub use self::svd::SVD;
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pub use self::symmetric_eigen::SymmetricEigen;
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@ -0,0 +1,288 @@
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#[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 complex 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 QZ<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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alphar: OVector<T, D>,
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alphai: OVector<T, D>,
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beta: OVector<T,D>,
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vsl: OMatrix<T, D, D>,
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s: OMatrix<T, D, D>,
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vsr: OMatrix<T, D, D>,
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t: OMatrix<T, D, D>
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}
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impl<T: Scalar + Copy, D: Dim> Copy for QZ<T, D>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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OMatrix<T, D, D>: Copy,
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OVector<T, D>: Copy,
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{
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}
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impl<T: QZScalar + RealField, D: Dim> QZ<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 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(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Self {
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Self::try_new(a,b).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 a: OMatrix<T, D, D>, mut b: OMatrix<T, D, D>) -> Option<Self> {
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assert!(
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a.is_square() && b.is_square(),
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"Unable to compute the qz decomposition of non-square matrices."
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);
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// another assert to compare shape?
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let (nrows, ncols) = a.shape_generic();
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let n = nrows.value();
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let lda = n as i32;
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let ldb = lda.clone();
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let mut info = 0;
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let mut alphar = Matrix::zeros_generic(nrows, Const::<1>);
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let mut alphai = Matrix::zeros_generic(nrows, Const::<1>);
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let mut beta = Matrix::zeros_generic(nrows, Const::<1>);
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let mut vsl = Matrix::zeros_generic(nrows, ncols);
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let mut vsr = Matrix::zeros_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 = T::xgges_work_size(
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b'V',
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b'V',
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b'N',
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n as i32,
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a.as_mut_slice(),
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n as i32,
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b.as_mut_slice(),
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n as i32,
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&mut unused,
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alphar.as_mut_slice(),
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alphai.as_mut_slice(),
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beta.as_mut_slice(),
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vsl.as_mut_slice(),
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n as i32,
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vsr.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 = vec![T::zero(); lwork as usize];
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T::xgges(
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b'V',
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b'V',
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b'N',
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n as i32,
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a.as_mut_slice(),
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n as i32,
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b.as_mut_slice(),
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n as i32,
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&mut unused,
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alphar.as_mut_slice(),
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alphai.as_mut_slice(),
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beta.as_mut_slice(),
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vsl.as_mut_slice(),
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n as i32,
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vsr.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(QZ {alphar, alphai, beta,
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vsl, s:a,
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vsr, t:b})
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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) -> (OMatrix<T, D, D>, OMatrix<T, D, D>, OMatrix<T, D, D>, OMatrix<T, D, D>){
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(self.vsl, self.s, self.t, self.vsr)
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}
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/// computes the generalized eigenvalues
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#[must_use]
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pub fn eigenvalues(&self) -> 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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let mut out = Matrix::zeros_generic(self.t.shape_generic().0, Const::<1>);
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for i in 0..out.len() {
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out[i] = Complex::new(self.alphar[i].clone()/self.beta[i].clone(),
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self.alphai[i].clone()/self.beta[i].clone())
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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 QZ decomposition.
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pub trait QZScalar: Scalar {
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#[allow(missing_docs)]
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fn xgges(
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jobvsl: u8,
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jobvsr: 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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b: &mut [Self],
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ldb: i32,
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sdim: &mut i32,
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alphar: &mut [Self],
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alphai: &mut [Self],
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beta : &mut [Self],
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vsl: &mut [Self],
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ldvsl: i32,
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vsr: &mut [Self],
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ldvsr: 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 xgges_work_size(
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jobvsl: u8,
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jobvsr: 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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b: &mut [Self],
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ldb: i32,
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sdim: &mut i32,
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alphar: &mut [Self],
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alphai: &mut [Self],
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beta : &mut [Self],
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vsl: &mut [Self],
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ldvsl: i32,
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vsr: &mut [Self],
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ldvsr: 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, $xgges: path) => (
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impl QZScalar for $N {
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#[inline]
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fn xgges(jobvsl: u8,
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jobvsr: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [$N],
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lda: i32,
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b: &mut [$N],
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ldb: i32,
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sdim: &mut i32,
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alphar: &mut [$N],
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alphai: &mut [$N],
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beta : &mut [$N],
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vsl: &mut [$N],
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ldvsl: i32,
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vsr: &mut [$N],
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ldvsr: 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 { $xgges(jobvsl, jobvsr, sort, None, n, a, lda, b, ldb, sdim, alphar, alphai, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, bwork, info); }
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}
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#[inline]
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fn xgges_work_size(jobvsl: u8,
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jobvsr: u8,
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sort: u8,
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// select: ???
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n: i32,
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a: &mut [$N],
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lda: i32,
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b: &mut [$N],
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ldb: i32,
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sdim: &mut i32,
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alphar: &mut [$N],
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alphai: &mut [$N],
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beta : &mut [$N],
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vsl: &mut [$N],
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ldvsl: i32,
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vsr: &mut [$N],
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ldvsr: 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 { $xgges(jobvsl, jobvsr, sort, None, n, a, lda, b, ldb, sdim, alphar, alphai, beta, vsl, ldvsl, vsr, ldvsr, &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::sgges);
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real_eigensystem_scalar_impl!(f64, lapack::dgges);
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@ -1,6 +1,7 @@
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mod cholesky;
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mod lu;
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mod qr;
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mod qz;
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mod real_eigensystem;
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mod schur;
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mod svd;
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@ -0,0 +1,27 @@
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use na::DMatrix;
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use nl::QZ;
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use std::cmp;
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use crate::proptest::*;
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use proptest::{prop_assert, proptest};
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proptest! {
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#[test]
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fn qz(n in PROPTEST_MATRIX_DIM) {
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let n = cmp::max(1, cmp::min(n, 10));
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let a = DMatrix::<f64>::new_random(n, n);
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let b = DMatrix::<f64>::new_random(n, n);
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let (vsl,s,t,vsr) = QZ::new(a.clone(), b.clone()).unpack();
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prop_assert!(relative_eq!(&vsl * s * vsr.transpose(), a, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(vsl * t * vsr.transpose(), b, epsilon = 1.0e-7))
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}
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#[test]
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fn qz_static(a in matrix4(), b in matrix4()) {
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let (vsl,s,t,vsr) = QZ::new(a.clone(), b.clone()).unpack();
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prop_assert!(relative_eq!(&vsl * s * vsr.transpose(), a, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(vsl * t * vsr.transpose(), b, epsilon = 1.0e-7))
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}
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}
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