angles_to_sphere

sphere_to_angles

Transforms the angles $(\theta_1,\ldots,\theta_{p-1})'$ in
$[0,\pi)^{p-2}\times[-\pi,\pi)$ into the Cartesian coordinates
$$(\cos(x_1),\sin(x_1)\cos(x_2),\ldots,
\sin(x_1)\cdots\sin(x_{p-2})\cos(x_{p-1}),
\sin(x_1)\cdots\sin(x_{p-2})\sin(x_{p-1}))'$$
of $S^{p-1}$, and vice versa.

Implementation of uniformity tests on the circle and
(hyper)sphere. The main function of the package is unif_test(), which
conveniently collects more than 35 tests for assessing uniformity on
S^{p-1} = {x in R^p : ||x|| = 1}, p >= 2. The test statistics are
implemented in the unif_stat() function, which allows computing several
statistics for different samples within a single call, thus facilitating
Monte Carlo experiments. Furthermore, the unif_stat_MC() function allows
parallelizing them in a simple way. The asymptotic null distributions of
the statistics are available through the function unif_stat_distr(). The
core of 'sphunif' is coded in C++ by relying on the 'Rcpp' package.
The package also provides several novel datasets and gives the replicability
for the data applications/simulations in García-Portugués et al. (2021)
<doi:10.1007/978-3-030-69944-4_12>, García-Portugués et al. (2023)
<doi:10.3150/21-BEJ1454>, Fernández-de-Marcos and
García-Portugués (2024) <doi:10.1016/j.spl.2024.110218>, and
García-Portugués et al. (2025) <doi:10.1080/01621459.2025.2566414>.

Eduardo Portugues

sphunif

Uniformity Tests on the Circle, Sphere, and Hypersphere

Eduardo García-Portugués

Thomas Verdebout

Alberto Fernández-de-Marcos

Paula Navarro

angles_to_sphere function

<dl><dt>theta</dt>
<dd>matrix of size <code>c(n, p - 1)</code> with the angles.</dd>
<dt>x</dt>
<dd>matrix of size <code>c(n, p)</code> with the Cartesian coordinates.
Assumed to be of unit norm by rows.</dd></dl>

Arguments

Conversion between angular and Cartesian coordinates of the
(hyper)sphere — angles_to_sphere

<dl>

<dt>theta</dt>
<dd>matrix of size <code>c(n, p - 1)</code> with the angles.</dd>


<dt>x</dt>
<dd>matrix of size <code>c(n, p)</code> with the Cartesian coordinates.
Assumed to be of unit norm by rows.</dd>

</dl>

angles_to_sphere: Conversion between angular and Cartesian coordinates of the (hyper)sphere

Description

Usage

Value

Arguments

Examples