Rec2Polar {KEPTED}

Rectangular to polar coordinates

Description

Given a d-dimensional vector X in rectangular coordinate, this function compute its polar coordinate (R,Theta), where R is the length of X and the (d-1)-dimensional vector Theta contains the d-1 angles of X.

Usage

Rec2Polar(X)

Arguments

X

A vector in rectangular coordinate. Suppose the dimension of X is d.

Details

The formula corresponds to theta=g(v) as in Lemma 1 of Tang and Li (2024). See also Anderson (2003). Note that when d=2, V will be (sin(Theta),cos(Theta)).

Value

A list of the following:

R

The length of X.

Theta

A vector of length d-1, containing the angles of X.

References

Tang, Y. and Li, B. (2024), “A nonparametric test for elliptical distribution based on kernel embedding of probabilities,” https://arxiv.org/abs/2306.10594 Anderson, T. W. (2003). An Introduction to Multivariate Statistical Analysis. John Wiley & Suns, Inc. Huboken, New Jersey.

Examples

X=c(3,1,3)
Rec2Polar(X)