[R] invert 160000x160000 matrix
Jiao Yang
yj316 at gwu.edu
Tue Aug 14 16:00:37 CEST 2007
Tir,
Thank you very much for the note. I'm using an algorithm to analyze a data set of 400 variables and the algorithm uses the inverse of a 160000x160000 positive definite matrix. The matrix is stored as a text file.
Can you please give some reference to in-place inverse technique? I googled it, yet did not get any good results. Thank you for your time.
Best regards,
Jiao
----- Original Message -----
From: "Patnaik, Tirthankar " <tirthankar.patnaik at citi.com>
Date: Tuesday, August 14, 2007 2:07 am
Subject: RE: [R] invert 160000x160000 matrix
To: Moshe Olshansky <m_olshansky at yahoo.com>, Paul Gilbert <pgilbert at bank-banque-canada.ca>, Jiao Yang <yj316 at gwu.edu>
Cc: r-help at stat.math.ethz.ch
> A variety of tricks would need to be used to invert a matrix of this
> size. If there are any other properties of the matrix that you know
> (symmetric, positive definite, etc, sparse) then they could be useful
> too. You could partition the matrix first, then use an in-place
> inverse technique for each block to individually calculate the
> blocks-inverses, then combine to get the inverse of the initial
> matrix. Again, if the implementation is actually solving an Ax-B = 0
> system of equations, then there are specific methods for these too,
> like an LU decomp, for instance. You might also want to check out some
> texts for this, like the Numerical Recipes.
> How's the matrix stored right now?
>
> Best,
> -Tir
>
>
>
> Tirthankar Patnaik
> India Strategy
> Citigroup Investment Research
> +91-22-6631 9887
>
> For important disclosures regarding Citigroup Investment Research,
> including with respect to any issuers mentioned herein, please refer
> to the Citigroup Investment Research disclosure website at
>
>
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch
> > [ On Behalf Of Moshe Olshansky
> > Sent: Tuesday, August 14, 2007 6:40 AM
> > To: Paul Gilbert; Jiao Yang
> > Cc: r-help at stat.math.ethz.ch
> > Subject: Re: [R] invert 160000x160000 matrix
> >
> > While inverting the matrix may be a problem, if you need to
> > solve an equation A*x = b you do not need to invert A, there
> > exist iterative methods which do need A or inv(A) - all you
> > need to provide is a function that computes A*x for an
> > arbitrary vector x.
> > For such a large matrix this may be slow but possible.
> >
> > --- Paul Gilbert <pgilbert at bank-banque-canada.ca>
> > wrote:
> >
> > > I don't think you can define a matrix this large in R, even if you
>
> > > have the memory. Then, of course, inverting it there may be other
>
> > > programs that have limitations.
> > >
> > > Paul
> > >
> > > Jiao Yang wrote:
> > > > Can R invert a 160000x160000 matrix with all
> > > positive numbers? Thanks a lot!
> > > >
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