angles_to_sph

sph_to_angles

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.

Kernel density estimation on the polysphere, (hyper)sphere, and
circle. Includes functions for density estimation, regression estimation,
ridge estimation, bandwidth selection, kernels, samplers, and homogeneity
tests. Companion package to García-Portugués and Meilán-Vila (2025)
<doi:10.1080/01621459.2025.2521898> and García-Portugués and Meilán-Vila
(2023) <doi:10.1007/978-3-031-32729-2_4>.

Eduardo Portugues

polykde

Polyspherical Kernel Density Estimation

Eduardo García-Portugués

Andrea Meilán-Vila

angles_to_sph function

<dl><dt>theta</dt>
<dd>matrix of size <code>c(n, d)</code> with the angles.</dd>
<dt>x</dt>
<dd>matrix of size <code>c(n, d + 1)</code> with the Cartesian coordinates
on $\mathcal{S}^{d}$. Assumed to be of unit norm by rows.</dd></dl>

Arguments

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

<dl>

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


<dt>x</dt>
<dd>matrix of size <code>c(n, d + 1)</code> with the Cartesian coordinates
on $\mathcal{S}^{d}$. Assumed to be of unit norm by rows.</dd>

</dl>

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

Description

Usage

Value

Arguments

Examples