Applying functions to partitions

How are the blocks defined? As a priori index ranges? By factors? By
some property of i,j? Or...?
Ok, I should have been more specific.

The blocks are defined by factors.  There's a factor for the columns and
a factor for the rows.  In the example below the column factor would be
c(1,1,1,2,3,3) and the row factor c(1,1,1,2,2,3).  In the particular
case I'm working on the matrix is square and symmetric and there's only
one factor for both.

I can figure out ways to subset the matrix, similar to what Jorge
proposed, but I'm looking for a way to get the means more or less at
once because the matrix is pretty large and doing it block-wise is too
slow.

Thanks again!

 Titus
On 2/16/09, Titus von der Malsburg <malsburg at gmail.com> wrote:
Hi list!  I have a large matrix which I'd like to partition into blocks
and for each block I'd like to compute the mean.  Following a example
where each letter marks a block of the partition:

     a a a d g g
     a a a d g g
     a a a d g g
     b b b e h h
     b b b e h h
     c c c f i i

I'm only interested in the resulting matrix of means.  How can this be
done efficiently?

Thanks!  Titus

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On Mon, Feb 16, 2009 at 01:45:52PM -0500, Stavros Macrakis wrote:
How are the blocks defined? As a priori index ranges? By factors? By
some property of i,j? Or...?
Ok, I should have been more specific.

The blocks are defined by factors.  There's a factor for the columns and
a factor for the rows.  In the example below the column factor would be
c(1,1,1,2,3,3) and the row factor c(1,1,1,2,2,3).  In the particular
case I'm working on the matrix is square and symmetric and there's only
one factor for both.
If the number of factor levels is manageable and if as.numeric( 
your.factor ) orders the blocks properly something like this

mat <- model.matrix( ~ 0 + your.factor )

tab <- table( your.factor )

means <- (t(mat) %*% your.block.matrix %*% mat) / outer( tab, tab )

Alternatively, use

means <-
    sapply(split.data.frame(your.block.matrix,your.factor),function(x)
 		sapply(split(colMeans(x),your.factor),mean))

HTH,

Chuck
I can figure out ways to subset the matrix, similar to what Jorge
proposed, but I'm looking for a way to get the means more or less at
once because the matrix is pretty large and doing it block-wise is too
slow.

Thanks again!

Titus

On 2/16/09, Titus von der Malsburg <malsburg at gmail.com> wrote:
Hi list!  I have a large matrix which I'd like to partition into blocks
and for each block I'd like to compute the mean.  Following a example
where each letter marks a block of the partition:

     a a a d g g
     a a a d g g
     a a a d g g
     b b b e h h
     b b b e h h
     c c c f i i

I'm only interested in the resulting matrix of means.  How can this be
done efficiently?

Thanks!  Titus

______________________________________________
R-help at 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.

Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901