R help - Mar 2011 - *Building* a covariance matrix efficiently

deaRs,

I want to build a covariance matrix out of the data from a binary
file, that I can read in chunk by chunk, with each chunk containing a
single observation vector X. I wonder how to do that most efficiently,
avoiding the calculation of the full symmetric matrices XX'. The
trivial non-optimal approach boils down to something like:

Q <- matrix(rnorm(100000),ncol=200)
M <- matrix(0,ncol=200,nrow=200)
for (i in 1:nrow(Q))
  M <- M + tcrossprod(Q[i,])

I would appreciate pointers to help me fill this lacuna in my R skills :)

Cheers,

Tsjerk

-- 
Tsjerk A. Wassenaar, Ph.D.

post-doctoral researcher
Molecular Dynamics Group
* Groningen Institute for Biomolecular Research and Biotechnology
* Zernike Institute for Advanced Materials
University of Groningen
The Netherlands

Tjerk,
This is just a pseudo code outline of what you need to do:

M = matrix(0, number of variables, number of variables)
V = rep(0, number of variables)
N = 0
While (more observations to read) {
   X <- next observation
   V <- V + X
   M <- M + outer(X,X)
   N <- N+1
}
Compute covariance matrix from elements of V,M, and N

You just need to refer to the formula defining covariance.
Outlook seems to think all my variables should be upper case.

HTH
Rex


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Tsjerk Wassenaar
Sent: Monday, March 14, 2011 10:14 AM
To: R-help
Subject: [R] *Building* a covariance matrix efficiently

deaRs,

I want to build a covariance matrix out of the data from a binary
file, that I can read in chunk by chunk, with each chunk containing a
single observation vector X. I wonder how to do that most efficiently,
avoiding the calculation of the full symmetric matrices XX'. The
trivial non-optimal approach boils down to something like:

Q <- matrix(rnorm(100000),ncol=200)
M <- matrix(0,ncol=200,nrow=200)
for (i in 1:nrow(Q))
  M <- M + tcrossprod(Q[i,])

I would appreciate pointers to help me fill this lacuna in my R skills :)

Cheers,

Tsjerk

--
Tsjerk A. Wassenaar, Ph.D.

post-doctoral researcher
Molecular Dynamics Group
* Groningen Institute for Biomolecular Research and Biotechnology
* Zernike Institute for Advanced Materials
University of Groningen
The Netherlands

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Tsjerk,
It seems to me that memory and not time is your big efficiency problem, and
I've showed you how to avoid storing your entire input.
If you want to avoid doing each multiplication twice, you can replace the
"outer" with a function that computes each product only once and
accumulate sums of those products.
Iii = matrix(c(rep(1:200,200),rep(1:200,each=200)), ncol=2)
Iii = iii[ iii[,1]<=iii[,2]]

and at each step

V2 = v2+X[iii[,1]] * X[iii[,2]]

instead of M.

I would imagine that the internal cov does this anyway, as you are not the first
person to notice this symmetry, so I'm not sure of the point of this
exercise.

PS: I actually know how to spell and pronounce Tsjerk, but Tsj is not a very
familiar pattern for my fingers.

From: Tsjerk Wassenaar [mailto:tsjerkw@gmail.com]
Sent: Monday, March 14, 2011 1:41 PM
To: Dwyer Rex USRE
Subject: Re: RE: [R] *Building* a covariance matrix efficiently


Hi Rex,

Thanks for the reply. But it doesn't solve the issues of redundant
calculations due to symmetry, both in the outer product and in the summation.

Cheers,

Tsjerk (correct spelling, really)
On Mar 14, 2011 5:44 PM,
<rex.dwyer@syngenta.com<mailto:rex.dwyer@syngenta.com>> wrote:

Tjerk,
This is just a pseudo code outline of what you need to do:

M = matrix(0, number of variables, number of variables)
V = rep(0, number of variables)
N = 0
While (more observations to read) {
  X <- next observation
  V <- V + X
  M <- M + outer(X,X)
  N <- N+1
}
Compute covariance matrix from elements of V,M, and N

You just need to refer to the formula defining covariance.
Outlook seems to think all my variables should be upper case.

HTH
Rex

-----Original Message----- From:
r-help-bounces@r-project.org<mailto:r-help-bounces@r-project.org>
[mailto:r-help-bounces@r-project.org.<mailto:r-help-bounces@r-project.org.>..
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R-help@r-project.org<mailto:R-help@r-project.org> mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.




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recipient, please notify the sender immediately, and delete the original and any
copies. Any use of the message by you is prohibited.



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recipient, please notify the sender immediately, and delete the original and any
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