Subject: Help with very very slow determinant calcuation
From: Claudio Delpino
Date: Sat, 6 Aug 2011 23:49:12 -0300
Taking matrix "A" to a LU form (i don't know if there is anything pre-packed
in maxima to do this, but it shouldn't be difficult to do on your own [i can
help you if you need]), then for det(A)=det(LU)=det(L).det(U), and det(L)
and det(U) are straightforwardly the product of their diagonal elements.
Of course this is perhaps the approach that's packed in determinant(A), but
you could do it step-by-step on your own to grasp control of the
calculation.
Just a suggestion
Regards
Claudio
2011/8/6 Nghia Ho <nghiaho12 at yahoo.com>
> Can you elaborate more on how factorizing the matrix can help? My
> background isn't in mathematics, I only did basic engineering level maths.
>
> ------------------------------
> *From:* Claudio Delpino <cladelpino at gmail.com>
> *To:* Bernard Hurley <bernard at marcade.biz>
> *Cc:* Nghia Ho <nghiaho12 at yahoo.com>; "maxima at math.utexas.edu" <
> maxima at math.utexas.edu>
> *Sent:* Saturday, 6 August 2011 7:25 PM
> *Subject:* Re: [Maxima] Help with very very slow determinant calcuation
>
> Is there any reason you're not factorizing the matrix ?
>
> 2011/8/6 Bernard Hurley <bernard at marcade.biz>
>
> On Wed, 2011-08-03 at 19:26 -0700, Nghia Ho wrote:
> > Hi all,
> >
> >
> > I'm trying to run the determinant() function a 10x10 matrix that
> contains all symbolic values. I've searched through the mailing list to find
> a solution. I've tried ratmax:true and newdet(), but it is still taking
> forever. In fact, as of writing now it has been going for over 12 hours and
> still hasn't finished! Is the determinant doing other stuff besides doing
> the multiplication and addition? Is it trying to simplify/factorise as it
> goes along?
> >
> > Nghia
> >
> > _______________________________________________
>
> To evaluate a 10x10 determinant containing independent symbols requires
> 10! = 3628800 multiplications, as well as additions etc. I would expect
> this to take a very very long time. There are ways of cutting down on
> this in a numerical matrix or if there are relationships between the
> symbols.
>
> Bernard.
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>