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chore: add comment providing details on the householder fix.

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Sébastien Crozet 2024-03-28 15:07:05 +01:00
parent dd44414a8a
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src/linalg/householder.rs
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@ -34,7 +34,17 @@ pub fn reflection_axis_mut<T: ComplexField, D: Dim, S: StorageMut<T, D>>(
if !factor.is_zero() { if !factor.is_zero() {
column.unscale_mut(factor.sqrt()); column.unscale_mut(factor.sqrt());
// Normalize again, making sure the vector is unit-sized.
// If `factor` had a very small value, the first normalization
// (dividing by `factor.sqrt()`) might end up with a slightly
// non-unit vector (especially when using 32-bits float).
// Decompositions strongly rely on that unit-vector property,
// so we run a second normalization (that is much more numerically
// stable since the norm is close to 1) to ensure it has a unit
// size.
let _ = column.normalize_mut(); let _ = column.normalize_mut();
(-signed_norm, true) (-signed_norm, true)
} else { } else {
// TODO: not sure why we don't have a - sign here. // TODO: not sure why we don't have a - sign here.