[R] invert 160000x160000 matrix

[Jiao Yang]

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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