Re: [eigen] Progress and plans

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On Thu, 18 Feb 2010, Benoit Jacob wrote:

I think the module is usable at the moment. However, there are some problems
if the matrices have clustered eigenvalues (this is the most difficult
case). One issue is that ComplexSchur often reaches the maximum number of
iterations. I don't know whether that's an inherent weakness in the algoritm
or only in the implementation - it may be as simple as increasing the
maximum number of iterations.

It'd be interesting to know if increasing the number of iterations helps.

It helps but not a lot. The algorithm starts fine but gets stuck before it reaches the termination condition. It seems that either the condition is too strict, or there is an instability in some part of the computation. I'll look further into it.

There seems to be another issue in matrix_function_3, which I haven't investigated yet.

I solved this. The mistake was not in the computation of the matrix function, but in the computation of the supposedly exact value I compared the result with. :-/


That's certainly the most elegant possible syntax!

OK, I can agree with that. The only worry is that array.exp() means something else: apply the exponential function entry-wise. So there is a source of confusion. On the other hand, array * array and matrix * matrix already have different meanings.

I will change the code to the matrix.exp() syntax soon if nobody argues against it.

* related, what needs to be done to get the module out of unstable/ ?

You're doing pretty much exactly what you have to :)
1) say that you want it out of unstable/ ---> check
2) make sure the API is ready for prime time ---> in progress
3) tests, documentation ----> check
4) commit to maintaining that stuff in the future ? ;)

Ad 4) Of course. Otherwise it's not worth writing in the first place.


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