75 lines
2.8 KiB
Rust
75 lines
2.8 KiB
Rust
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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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 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.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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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 (vsl,s,t,vsr) = qz.unpack();
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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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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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