# scontour: Plotting spherical depth contours In depth: Nonparametric Depth Functions for Multivariate Analysis

## Description

Traces spherical depth contours of a multivariate data set. Supports data on the circle or on the sphere.

## Usage

 ```1 2 3 4``` ```scontour(P, tracepoints=FALSE, colpoints="black", tracemed=TRUE, maxdepth=FALSE, xlim=c(0,2*pi), displaymed=FALSE, title="Circular Tukey contours", ylab="Tukey's circular depth", xlab=expression(theta), colmed=2, colarc="red", sizepoints=3) ```

## Arguments

 `P` The data as a vector, a matrix, a data frame or a list. `tracepoints` Logical; if TRUE, data points are added to the plot. `colpoints` A specification for the color of the data points. `tracemed` Logical; if TRUE, the Tukey median is added to the plot. `maxdepth` Logical; On the circle only; if TRUE, the maximum depth is printed on the plot. `xlim` Numeric vectors of length 2, giving the `x` coordinate range. `displaymed` Logical; On the circle only; if TRUE, the median value is printed on the plot. `title` On the circle only, a specification for the plot title. `ylab` On the circle only, a specification for the y axis title. `xlab` On the circle only, a specification for the x axis title. `colmed` Color of the Tukey median on the plot. `colarc` On the sphere only, color of the spherical depth contours on the plot. `sizepoints` Size of plotted points.

## Details

Supports data on the circle or the sphere. For data on the circle, data must be expressed in polar coordinates as a angle in radians with values between 0 and . Data on the sphere can be expressed in Euclidean coordinates (n by 3 matrix) or in spherical coordinates (n by 2 matrix) where the first column contains θ and the second column φ. The type of coordinates is determined automatically based on the dimensions of the input.

## Value

 `plot` A plot of Tukey spherical depth if the input data are on the circle, or the Tukey spherical depth contours if the input data are on the sphere.

If data are on the sphere only, a list of 3 elements is also outputted.

 `1` A sorted vector giving the depths of the plotted contours. `2` A list of matrices with the vertices of every contour. `3` The Euclidean coordinates of the Tukey median

Maxime Genest.

## References

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 783–858.

Mardia, K.V. and Jupp, E.J. (1999). Directional Statistics, Wiley.

`sdepth` for calculation of the depth of a point, `smed` for Tukey's spherical median.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## Plot of Tukey spherical depth for data on the circle. set.seed(2011) scontour(runif(30,min=0,max=2*pi)) ## Tukey spherical depth contours for data ## on the shpere expressed in spherical coordinates. scontour(cbind(runif(20,min=0,max=2*pi),runif(20,min=0,max=pi))) ## Tukey spherical depth contours for data ## on the sphere expressed in Euclidean coordinates. x=matrix(rnorm(60),ncol=3) x=t(apply(x,1,function(y){y/sqrt(sum(y^2))})) scontour(x) ```