cir_coord_conv function

Transforming between polar and Cartesian coordinates

Transformation between a matrix Theta containing M circular samples of size n on $[0, 2\pi)$ and an array X containing the associated Cartesian coordinates on $S^1:={x\in R^2:||x||=1}$.

Theta_to_X(Theta)

X_to_Theta(X)

Arguments

• Theta: a matrix of size c(n, M) with M samples of size n of circular data on $[0, 2\pi)$. Must not contain NA's.
• X: an array of size c(n, 2, M) containing the Cartesian coordinates of M samples of size n of directions on $S^{1}$. Must not contain NA's.

Returns

• Theta_to_X: the corresponding X.
• X_to_Theta: the corresponding Theta.

Examples

# Sample
Theta <- r_unif_cir(n = 10, M = 2)
X <- r_unif_sph(n = 10, p = 2, M = 2)

# Check equality
sum(abs(X - Theta_to_X(X_to_Theta(X))))
sum(abs(Theta - X_to_Theta(Theta_to_X(Theta))))