Fix numerical issue on SVD with near-identity matrix (#1369)
* fix: Normalize the column once more The column may not be normalized if the `factor` is on a scale of 1e-40. Possibly, f32 just runs out of precision. There is likely a better solution to the problem. * chore: Add test that fails before fix * chore: add comment providing details on the householder fix. * chore: rename regression test --------- Co-authored-by: Sébastien Crozet <sebcrozet@dimforge.com>
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@ -34,6 +34,17 @@ pub fn reflection_axis_mut<T: ComplexField, D: Dim, S: StorageMut<T, D>>(
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if !factor.is_zero() {
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column.unscale_mut(factor.sqrt());
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// Normalize again, making sure the vector is unit-sized.
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// If `factor` had a very small value, the first normalization
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// (dividing by `factor.sqrt()`) might end up with a slightly
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// non-unit vector (especially when using 32-bits float).
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// Decompositions strongly rely on that unit-vector property,
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// so we run a second normalization (that is much more numerically
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// stable since the norm is close to 1) to ensure it has a unit
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// size.
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let _ = column.normalize_mut();
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(-signed_norm, true)
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} else {
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// TODO: not sure why we don't have a - sign here.
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@ -1,4 +1,4 @@
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use na::DMatrix;
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use na::{DMatrix, Matrix3};
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#[cfg(feature = "proptest-support")]
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mod proptest_tests {
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@ -116,6 +116,31 @@ fn symmetric_eigen_singular_24x24() {
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);
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}
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// Regression test for #1368
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#[test]
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fn very_small_deviation_from_identity_issue_1368() {
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let m = Matrix3::<f32>::new(
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1.0,
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3.1575704e-23,
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8.1146196e-23,
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3.1575704e-23,
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1.0,
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1.7471054e-22,
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8.1146196e-23,
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1.7471054e-22,
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1.0,
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);
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for v in m
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.try_symmetric_eigen(f32::EPSILON, 0)
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.unwrap()
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.eigenvalues
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.into_iter()
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{
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assert_relative_eq!(*v, 1.);
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}
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}
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// #[cfg(feature = "arbitrary")]
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// quickcheck! {
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// TODO: full eigendecomposition is not implemented yet because of its complexity when some
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