# Re: [R] Seeking a more efficient way to find partition maxima

From: Gabor Grothendieck <ggrothendieck_at_gmail.com>
Date: Mon, 7 Jan 2008 13:49:13 -0500

Try testing the performance of transforming your series to one in which the values of each partition are larger than all prior partitions and the untransforming back:

# test data
myseq <- c(1, 4, 2, 6, 7, 5)
part <- c(1, 4, 5)

M <- max(myseq)

# transform
myseq2 <- myseq + M * cumsum(replace(0 * myseq, part, 1))

# calcuate on transformed version
tmp <- partiCmax(myseq2, part)

# untransform
tmp - M * seq_along(tmp) # c(4, 6, 7)

Also you might check how it compares to the simpler

tapply(myseq, cumsum(replace(0 * myseq, part, 1)), max)

On Jan 7, 2008 11:18 AM, Talbot Katz <topkatz_at_msn.com> wrote:
>
> Hi.
>
> Suppose I have a vector that I partition into disjoint, contiguous subvectors. For example, let v = c(1,4,2,6,7,5), partition it into three subvectors, v1 = v[1:3], v2 = v, v3 = v[5:6]. I want to find the maximum element of each subvector. In this example, max(v1) is 4, max(v2) is 6, max(v3) is 7. If I knew that the successive subvector maxima would never decrease, as in the example, I could do the following:
>
> partiCmax <- function( values, seriesIdx ) {
> # assume seriesIdx is increasing integer sequence beginning with 1, ending at less than or equal to length(values)
> parti <- cbind( seriesIdx, c( ( seriesIdx[ -1 ] - 1 ), length( values ) ) )
> return( cummax( values )[ parti[ , 2 ] ] )
> }
>
>
> The use of cummax makes that pretty efficient, but if the subvector maxima are not non-decreasing, it doesn't work. The following function works (at least it did on the examples I tried):
>
> partiMax <- function( values, seriesIdx ) {
> # assume seriesIdx is increasing integer sequence beginning with 1, ending at less than or equal to length(values)
> parti <- cbind( seriesIdx, c( ( seriesIdx[ -1 ] - 1 ), length( values ) ) )
> return( sapply( ( 1:length(seriesIdx) ), function ( i ) {return( max( values[ parti[ i, 1 ]:parti[ i, 2 ] ] ) ) } ) )
> }
>
>
> but I figured someone out there could come up with something cleverer. Thanks!
>
> -- TMK --212-460-5430 home917-656-5351 cellt o p k a t z @ m s n . c o m
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