[MATH-1045] EigenDecomposition.Solver should consider tiny values 0 for purposes of determining singularity

• Type: Bug
• Status: Closed
• Priority: Minor
• Resolution: Fixed
• Affects Version/s: 3.2
• Fix Version/s: 3.3
• Labels: eigenvalue singular
• Assignee: Unassigned
• Reporter: Sean R. Owen
• Created: 22/Oct/13 13:10
• Updated: 19/May/14 15:13
• Resolved: 29/Oct/13 15:55

Description

EigenDecomposition.Solver tests for singularity by comparing eigenvalues to 0 for exact equality. Elsewhere in the class and in the code, of course, very small values are considered 0. This causes the solver to consider some singular matrices as non-singular.

The patch here includes a test as well showing the behavior – the matrix is clearly singular but isn't considered as such since one eigenvalue are ~1e-14 rather than exactly 0.

(What I am not sure of is whether we should really be evaluating the norm of the imaginary eigenvalues rather than real/imag components separately. But the javadoc says the solver only supports real eigenvalues anyhow, so it's kind of moot since imag=0 for all eigenvalues.)

Issue Links

• relates to: MATH-1049 Matrix decomposition and solver