LUDecompositionNR detects singular matrix, but ignores it

[Luke Nezda]

Hello,

In LUDecompositionNR, lines 80 and 81 (below) might as well just throw
a SingularMatrixException because indx is invalid (i.e., invert calls
LUDecompositionBase._solveVectorInternal which falls over on line
220):
// TODO flag as singular
indx[k] = -1;

Can this be put into v22? For now, I'm gonna catch
ArrayIndexOutOfBoundsException and throw SingularMatrixException
myself.

Please advise,
- Luke

[Peter A]

That is a bug and will be fixed, but it's not recommended that you use LUDecompositionNR.  Instead use whatever DecompositionFactory.lu() returns, which will always be LUDecompositionAlt.  I'm going to push LUDecompositionNR into the experimental code directory since there is no real reason to use it, but I don't want to delete it for benchmarking purposes.

- Peter

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[Luke Nezda]

Hmm, for many of the matrices I've been inverting, LUDecompositionAlt
(default via path CommonOps.invert) often failed while
LUDecompositionNR usually worked. I'll have to do some more
testing... maybe I can provide some test matrices to illustrate.

- Luke

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[Peter A]

Having test matrices would be helpful.  I just ran the build in stability tests and those results show that they are comparable.  How do you detect the failure case?  For example, do you consider it a failure only when the algorithm detects a failure or the matrix is incorrect based on some error metric?

If you are trying to invert nearly singular matrices, you might want to consider using the pseudo inverse (QR with pivot) or SVD instead.

- Peter

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