Cleanup of QZ module and added GE's calculation of eigenvalues as a test for QZ's calculation of eigenvalues
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@ -13,7 +13,11 @@ use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
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use lapack;
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/// Generalized eigendecomposition of a pair of N*N square matrices.
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/// QZ decomposition of a pair of N*N square matrices.
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/// Retrieves the left and right matrices of Schur Vectors (VSL and VSR)
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/// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
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/// decomposed input matrix `a` equals `VSL * S * VSL.transpose()` and
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/// decomposed input matrix `b` equals `VSL * T * VSL.transpose()`.
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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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@ -59,6 +63,11 @@ where
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{
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/// Attempts to compute the QZ decomposition of input square matrices `a` and `b`.
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///
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/// i.e retrieves the left and right matrices of Schur Vectors (VSL and VSR)
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/// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
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/// decomposed matrix `a` equals `VSL * S * VSL.transpose()` and
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/// decomposed matrix `b` equals `VSL * T * VSL.transpose()`.
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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("QZ decomposition: convergence failed.")
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@ -154,8 +163,8 @@ where
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/// Retrieves the left and right matrices of Schur Vectors (VSL and VSR)
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/// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
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/// decomposed matrix `A` equals `VSL * S * VSL.transpose()` and
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/// decomposed matrix `B` equals `VSL * T * VSL.transpose()`.
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/// decomposed input matrix `a` equals `VSL * S * VSL.transpose()` and
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/// decomposed input matrix `b` equals `VSL * T * VSL.transpose()`.
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pub fn unpack(
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self,
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) -> (
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@ -167,8 +176,6 @@ where
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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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@ -1,7 +1,5 @@
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use na::{zero, DMatrix, SMatrix};
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use nl::QZ;
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use num_complex::Complex;
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use simba::scalar::ComplexField;
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use na::DMatrix;
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use nl::{GE, QZ};
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use std::cmp;
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use crate::proptest::*;
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@ -16,33 +14,28 @@ proptest! {
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let qz = QZ::new(a.clone(), b.clone());
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let (vsl,s,t,vsr) = qz.clone().unpack();
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//let eigenvalues = qz.eigenvalues();
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//let a_c = a.clone().map(|x| Complex::new(x, zero::<f64>()));
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let eigenvalues = qz.eigenvalues();
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let ge = GE::new(a.clone(), b.clone());
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let eigenvalues2 = ge.eigenvalues();
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prop_assert!(relative_eq!(&vsl * s * vsr.transpose(), a.clone(), epsilon = 1.0e-7));
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prop_assert!(relative_eq!(vsl * t * vsr.transpose(), b.clone(), epsilon = 1.0e-7));
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// spotty test that skips over the first eigenvalue which in some cases is extremely large relative to the other ones
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// and fails the condition
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//for i in 1..n {
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// let b_c = b.clone().map(|x| eigenvalues[i]*Complex::new(x,zero::<f64>()));
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// prop_assert!(relative_eq!((&a_c - &b_c).determinant().modulus(), 0.0, epsilon = 1.0e-6));
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//}
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prop_assert!(eigenvalues == eigenvalues2);
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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 qz = QZ::new(a.clone(), b.clone());
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let ge = GE::new(a.clone(), b.clone());
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let (vsl,s,t,vsr) = qz.unpack();
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//let eigenvalues = qz.eigenvalues();
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//let a_c = a.clone().map(|x| Complex::new(x, zero::<f64>()));
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let eigenvalues = qz.eigenvalues();
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let eigenvalues2 = ge.eigenvalues();
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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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//for i in 0..4 {
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// let b_c = b.clone().map(|x| eigenvalues[i]*Complex::new(x,zero::<f64>()));
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// println!("{}",eigenvalues);
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// prop_assert!(relative_eq!((&a_c - &b_c).determinant().modulus(), 0.0, epsilon = 1.0e-4))
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//}
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prop_assert!(eigenvalues == eigenvalues2);
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}
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}
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