# rsmed: Bivariate RS median In rsdepth: Ray Shooting Depth (i.e. RS Depth) functions for bivariate analysis

## Description

Computes the Ray Shooting median of a bivariate data set.

## Usage

 `1` ```rsmed(pt, eps=c(0),...) ```

## Arguments

 `pt` The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations). Only 2-dimensional data is acceptable in this version. `eps` eps is an optional parameter used for approximating a median in case of large data sets. It takes valye of a real between 0 and 1 and is by default set to 0 which means no approximation is used if eps is not given. `...` Reserved for future use.

## Details

Finds out the an arbitrary point among the Ray Shooting median set of given point set. Current uses the brute-force algorithm on all O(n^4) possible points in the arrangment of all possible lines in complete graph on `pt`. For each point O(n log n) is used to find out depth so overall complexity of this algorithm is O(n^5 log n). When approximation parameter is provided then algorithm tries to approximate by finding median of a uniform sample subset of pt of size 1/eps^2*log(1/eps). If this constant is more than the size of original set then eps value is ignored and exact median is calculate on original point set.

## Value

A point in two dimension is returned as a single row two column vector

## Author(s)

Nabil Mustafa, Saurabh Ray, and Mudassir Shabbir.

## References

N. Mustafa, S. Ray, and M. Shabbir, Statistical Data Depth of Pointsets in the Plane,in prep..

`rsdepth` for depth function
 ```1 2 3 4``` ```## RS median of a two-dimensional data set set.seed(617) zz <- matrix(rnorm(120), nc = 2) rsmed(zz,eps=0.2) ```