polykde (version 1.1.7)

angles_to_torus: Conversion between the angular and Cartesian coordinates of the torus

Description

Transforms the angles \((\theta_1,\ldots,\theta_d)\) in \([-\pi,\pi)^d\) into the Cartesian coordinates $$(\cos(x_1), \sin(x_1),\ldots,\cos(x_d), \sin(x_d))$$ of the torus \((\mathcal{S}^1)^d\), and vice versa.

Usage

angles_to_torus(theta)
torus_to_angles(x)

Value

• angles_to_torus: the matrix x.

• torus_to_angles: the matrix theta.

Arguments

theta

matrix of size c(n, d) with the angles.

x

matrix of size c(n, 2 * d) with the Cartesian coordinates on \((\mathcal{S}^1)^d\). Assumed to be of unit norm by pairs of coordinates in the rows.

Examples

# Check changes of coordinates
torus_to_angles(angles_to_torus(c(0, pi / 3, pi / 2)))
torus_to_angles(angles_to_torus(rbind(c(0, pi / 3, pi / 2), c(0, 1, -2))))
angles_to_torus(torus_to_angles(c(0, 1, 1, 0)))
angles_to_torus(torus_to_angles(rbind(c(0, 1, 1, 0), c(0, 1, 0, 1))))