Re: [ojAlgo-user] BigDecimal EVD?

[Jacob M. <Jac...@cs...>]

Actually, the problem isn't that the numbers are too large or too small.  
Rather, it is that gaps between the numbers aren't small enough. 

Specifically, I don't get enough decimal places represented when using 
doubles.  

Thanks anyway for trying to help.  

Jake

On Monday 29 January 2007 16:59, Anders Peterson wrote:
> I'm no expert in this area, but if the problem is that the matrix
> generally has too large or too small elements (resulting in bad
> numerical behaviour) it seems to me it should be fixable by using
> equation 10, 11 and/or 12 on this page.
>
> http://mathworld.wolfram.com/Eigenvalue.html
>
> /Anders
>
> Jacob Martin wrote:
> >>> Can't you just scale the matrix before you calculate the eigenvalues?
> >
> > Hmm.  I'm not sure the best way to scale it?  Won't this remove the
> > accuracy I was looking for?
> >
> >>> I've never seen a BigDecimal eigenvalue or singular value
> >>> decomposition algorithm. They require rather heavy calculations and
> >>> using BigDecimal instead of double is MUCH slower.
> >>>
> >>>
> >>>
> >>>
> >>> In the future ojAlgo may get code that works with any kind of
> >>> numbers (like ArbitraryLU and ArbitraryQR) but this is currently
> >>> not high priority - don't hold your breath.
> >>>
> >>> /Anders
> >>>
> >>> jac...@gm... wrote:
> >>>> Hi Anders,
> >>>>
> >>>> I guess I'm just looking for a quick fix right now.   I may get
> >>>> the urge to implement it later when I have more time though, so
> >>>> thanks for the information.
> >>>>
> >>>> I'm working with around 1000x1000 matrices.  They could be
> >>>> bigger.  I have the time to wait for the right answer.  LAPACK and
> >>>> MTJ and others (Jama, JMSL, etc) are quick, but don't give me
> >>>> satistfactory answers with very large numbers for some reason.
> >>>> Maybe there is some tolerance or epsilon parameter somewhere that
> >>>> will help the convergence (if I only knew where to look).
> >>>>
> >>>> Anyway, I haven't found a BigDecimal eigenvalue solver
> >>>> implementation out there yet.  Maybe they don't exist?
> >>>>
> >>>> Well, thanks for your kindness.  It looks like you have the best
> >>>> start towards this functionality in Java.
> >>>>
> >>>> Kind regards,
> >>>> Jake
> >>>>
> >>>> On Saturday 27 January 2007 20:45, Anders Peterson wrote:
> >>>>> As you've noticed ojAlgo does not contain a BigDecimal
> >>>>> implementation
> >>>>> of Eigenvalue or SingularValue. You'll have to build it yourself...
> >>>>>
> >>>>> If you look at PrimitiveEigenvalue you'll "see" the algorithm, and
> >>>>> then study ArbitraryQR and ArbitraryLU for examples on how to use
> >>>>> PhysicalStore to develop an implementation that works with any
> >>>>> Number
> >>>>> type. I've been planning to move (some of) the Householder code from
> >>>>> ArbitraryQR to PhysicalStore or some utility class. That would
> >>>>> probably be useful for you.
> >>>>>
> >>>>> What size matrices are you working with? If they are large a
> >>>>> BigDecimal implementation will be very slow.
> >>>>>
> >>>>> /Anders
> >>>>>
> >>>>> On 27 jan 2007, at 19.11, jac...@gm... wrote:
> >>>>>> Hi,
> >>>>>>
> >>>>>> I'm trying to figure out how/if I can do a BigDecimal EVD with
> >>>>>> ojAlgo.  I
> >>>>>> would like all operations to be done with BigDecimal, so I can
> >>>>>> avoid rounding
> >>>>>> errors.
> >>>>>>
> >>>>>> Do all of the classes that implement the Eigenvalue interface round
> >>>>>> down to
> >>>>>> doubles?
> >>>>>>
> >>>>>> If so, is my only choice the BigQR, and then read off diagonal
> >>>>>> of R?
> >>>>>>
> >>>>>> Many thanks for any help!
> >>>>>>
> >>>>>> Jacob Martin
> >>>>>> -------------------------------------------------
> >>>>>> BasicMatrix tmpMatrix = BigMatrix.FACTORY.make(M);
> >>>>>> Eigenvalue tmpDecomposition = new PrimitiveEigenvalue();
> >>>>>> tmpDecomposition.compute(tmpMatrix);
> >>>>>> BasicArray ba =tmpDecomposition.getEigenvalues();
> >>>>>>
> >>>>>>
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