New code and modified tests for qz
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@ -176,36 +176,19 @@ 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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/// outputs the unprocessed (almost) version of generalized eigenvalues ((alphar, alpai), beta)
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/// straight from LAPACK
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#[must_use]
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pub fn eigenvalues(&self) -> OVector<Complex<T>, D>
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pub fn raw_eigenvalues(&self) -> OVector<(Complex<T>, T), D>
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where
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DefaultAllocator: Allocator<Complex<T>, D>,
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DefaultAllocator: Allocator<(Complex<T>, 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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let mut out = Matrix::from_element_generic(self.vsl.shape_generic().0, Const::<1>, (Complex::zero(), T::RealField::zero()));
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for i in 0..out.len() {
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out[i] = if self.beta[i].clone().abs() < T::RealField::default_epsilon() {
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Complex::zero()
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} else {
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let mut cr = self.alphar[i].clone();
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let mut ci = self.alphai[i].clone();
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let b = self.beta[i].clone();
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if cr.clone().abs() < T::RealField::default_epsilon() {
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cr = T::RealField::zero()
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} else {
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cr = cr / b.clone()
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};
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if ci.clone().abs() < T::RealField::default_epsilon() {
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ci = T::RealField::zero()
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} else {
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ci = ci / b
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};
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Complex::new(cr, ci)
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}
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out[i] = (Complex::new(self.alphar[i].clone(),
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self.alphai[i].clone()),
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self.beta[i].clone())
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}
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out
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@ -1,5 +1,7 @@
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use na::DMatrix;
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use nl::{GE, QZ};
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use na::{DMatrix, EuclideanNorm, Norm};
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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 std::cmp;
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use crate::proptest::*;
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@ -14,28 +16,59 @@ 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 ge = GE::new(a.clone(), b.clone());
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let eigenvalues2 = ge.eigenvalues();
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let eigenvalues = qz.raw_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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prop_assert!(eigenvalues == eigenvalues2);
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let a_condition_no = a.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&a)));
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let b_condition_no = b.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&b)));
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if a_condition_no.unwrap_or(200000.0) < 5.0 && b_condition_no.unwrap_or(200000.0) < 5.0 {
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let a_c = a.clone().map(|x| Complex::new(x, 0.0));
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let b_c = b.clone().map(|x| Complex::new(x, 0.0));
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for (alpha,beta) in eigenvalues.iter() {
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let l_a = a_c.clone() * Complex::new(*beta, 0.0);
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let l_b = b_c.clone() * *alpha;
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prop_assert!(
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relative_eq!(
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(&l_a - &l_b).determinant().modulus(),
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0.0,
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epsilon = 1.0e-7));
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};
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};
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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 eigenvalues2 = ge.eigenvalues();
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let eigenvalues = qz.raw_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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prop_assert!(eigenvalues == eigenvalues2);
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let a_condition_no = a.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&a)));
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let b_condition_no = b.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&b)));
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if a_condition_no.unwrap_or(200000.0) < 5.0 && b_condition_no.unwrap_or(200000.0) < 5.0 {
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let a_c =a.clone().map(|x| Complex::new(x, 0.0));
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let b_c = b.clone().map(|x| Complex::new(x, 0.0));
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for (alpha,beta) in eigenvalues.iter() {
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let l_a = a_c.clone() * Complex::new(*beta, 0.0);
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let l_b = b_c.clone() * *alpha;
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prop_assert!(
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relative_eq!(
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(&l_a - &l_b).determinant().modulus(),
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0.0,
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epsilon = 1.0e-7));
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}
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};
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}
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}
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