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Implement absolute threshold for early deflation in Schur algorithm #1565

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Implement absolute threshold for early deflation in Schur algorithm #1565

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12 changes: 9 additions & 3 deletions src/linalg/schur.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -348,12 +348,15 @@ where
DefaultAllocator: Allocator<DimDiff<D, U1>>,
{
let mut n = end;
let absolute_threshold = eps.clone() * eps.clone();

while n > 0 {
let m = n - 1;
let off_diag_norm = t[(n, m)].clone().norm1();

if t[(n, m)].clone().norm1()
<= eps.clone() * (t[(n, n)].clone().norm1() + t[(m, m)].clone().norm1())
if off_diag_norm <= absolute_threshold
|| off_diag_norm
<= eps.clone() * (t[(n, n)].clone().norm1() + t[(m, m)].clone().norm1())
{
t[(n, m)] = T::zero();
} else {
Expand All @@ -372,8 +375,11 @@ where
let m = new_start - 1;

let off_diag = t[(new_start, m)].clone();
let off_diag_norm = off_diag.clone().norm1();

if off_diag.is_zero()
|| off_diag.norm1()
|| off_diag_norm <= absolute_threshold
|| off_diag_norm
<= eps.clone()
* (t[(new_start, new_start)].clone().norm1() + t[(m, m)].clone().norm1())
{
Expand Down
33 changes: 31 additions & 2 deletions tests/linalg/eigen.rs
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Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
use na::{DMatrix, Matrix3};
use na::{Complex, DMatrix, Matrix3};

#[cfg(feature = "proptest-support")]
mod proptest_tests {
Expand Down Expand Up @@ -141,6 +141,35 @@ fn very_small_deviation_from_identity_issue_1368() {
}
}

// Regression test for #1528
#[test]
#[rustfmt::skip]
fn eigenvalues_search_should_not_hang_issue_1528() {
let m = DMatrix::from_row_slice(
4,
4,
&[
0.0_f64, 0.5773502691896257, 0.0, 0.0,
0.5773502691896257, 0.0, 0.5163977794943222, 0.0,
0.0, 0.5163977794943222, 0.0, 0.50709255283711,
0.0, 0.0, 0.50709255283711, 0.0,
],
);
let complex_eigenvals = m.complex_eigenvalues();

assert_relative_eq!(
complex_eigenvals.iter().sum::<Complex<f64>>().re,
m.trace(),
epsilon = 1e-10
);

assert_relative_eq!(
complex_eigenvals.iter().product::<Complex<f64>>().re,
m.determinant(),
epsilon = 1e-10
);
}

// #[cfg(feature = "arbitrary")]
// quickcheck! {
// TODO: full eigendecomposition is not implemented yet because of its complexity when some
Expand Down Expand Up @@ -225,4 +254,4 @@ fn very_small_deviation_from_identity_issue_1368() {
// println!("{}{:.5}{:.5}", m, mv, eig.eigenvectors);
//
// relative_eq!(eig.eigenvectors, mv, epsilon = 1.0e-5)
// }
// }