# Re: [R] a question about box counting

From: Deepayan Sarkar <deepayan_at_stat.wisc.edu>
Date: Tue 05 Apr 2005 - 04:52:48 EST

On Monday 04 April 2005 13:22, Rajarshi Guha wrote:
> Hi,
> I have a set of x,y data points and each data point lies between
> (0,0) and (1,1). Of this set I have selected all those that lie in
> the lower triangle (of the plot of these points).
>
> What I would like to do is to divide the region (0,0) to (1,1) into
> cells of say, side = 0.01 and then count the number of cells that
> contain a point.
>
> My first approach is to generate the coordinates of these cells and
> then loop over the point list to see whether a point lies in a cell
> or not.
>
> However this seems to be very inefficient esepcially since I will
> have 1000's of points.
>
> Has anybody dealt with this type of problem and are there routines to
> handle it?

A combination of cut and table/xtabs should do it, e.g.:

x <- runif(3000)
y <- runif(3000)

fx <- cut(x, breaks = seq(0, 1, length = 101)) fy <- cut(y, breaks = seq(0, 1, length = 101))

txy <- xtabs(~ fx + fy)
image(txy > 0)
sum(txy > 0)

Deepayan

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