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Fix default rank-detection threshold in QR and LU decompositions

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libeigen/eigen!2232

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
This commit is contained in:
Rasmus Munk Larsen
2026-03-03 18:44:22 -08:00
parent d36a7db7b5
commit b0ebf966a5
5 changed files with 118 additions and 10 deletions
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7
Eigen/src/LU/FullPivLU.h
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@@ -321,9 +321,10 @@ class FullPivLU : public SolverBase<FullPivLU<MatrixType_, PermutationIndex_> >
RealScalar threshold() const {
eigen_assert(m_isInitialized || m_usePrescribedThreshold);
return m_usePrescribedThreshold ? m_prescribedThreshold
// this formula comes from experimenting (see "LU precision tuning" thread on the
// list) and turns out to be identical to Higham's formula used already in LDLt.
: NumTraits<Scalar>::epsilon() * RealScalar(m_lu.diagonalSize());
// Higham's backward error bound for Gaussian elimination with
// complete pivoting (Theorem 9.4) is ||ΔA||₂ ≤ c·min(m,n)·u·||A||₂.
// The factor of 4 covers the constant c.
: NumTraits<Scalar>::epsilon() * RealScalar(4 * m_lu.diagonalSize());
}
/** \returns the rank of the matrix of which *this is the LU decomposition.