Add non-naive way of calculate generalized eigenvalue, write spotty test for generalized eigenvalues
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@ -176,10 +176,17 @@ where
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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(
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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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let b = self.beta[i].clone();
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out[i] = {
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if b < T::RealField::zero() {
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Complex::<T>::zero()
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} else {
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Complex::new(
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self.alphar[i].clone() / b.clone(),
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self.alphai[i].clone() / b.clone(),
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)
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}
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}
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}
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out
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@ -1,5 +1,6 @@
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use na::DMatrix;
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use na::{zero, DMatrix, Normed};
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use nl::QZ;
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use num_complex::Complex;
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use std::cmp;
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use crate::proptest::*;
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@ -12,10 +13,19 @@ proptest! {
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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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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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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!(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 eiegenvalue 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().norm(), 0.0, epsilon = 1.0e-6));
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}
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}
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#[test]
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