angles_to_sph {polykde} | R Documentation |
Conversion between the angular and Cartesian coordinates of the (hyper)sphere
Description
Transforms the angles (\theta_1,\ldots,\theta_d)
in
[0,\pi)^{d-1}\times[-\pi,\pi)
into the Cartesian coordinates
(\cos(x_1),\sin(x_1)\cos(x_2),\ldots,
\sin(x_1)\cdots\sin(x_{d-1})\cos(x_d),
\sin(x_1)\cdots\sin(x_{d-1})\sin(x_d))
of the sphere \mathcal{S}^{d}
, and vice versa.
Usage
angles_to_sph(theta)
sph_to_angles(x)
Arguments
theta |
matrix of size |
x |
matrix of size |
Value
angles_to_sph
: the matrixx
.sph_to_angles
: the matrixtheta
.
Examples
# Check changes of coordinates
sph_to_angles(angles_to_sph(c(pi / 2, 0, pi)))
sph_to_angles(angles_to_sph(rbind(c(pi / 2, 0, pi), c(pi, pi / 2, 0))))
angles_to_sph(sph_to_angles(c(0, sqrt(0.5), sqrt(0.1), sqrt(0.4))))
angles_to_sph(sph_to_angles(rbind(c(0, sqrt(0.5), sqrt(0.1), sqrt(0.4)),
c(0, sqrt(0.5), sqrt(0.5), 0),
c(0, 1, 0, 0),
c(0, 0, 0, -1),
c(0, 0, 1, 0))))
[Package polykde version 1.1.4 Index]