angles_to_polysph

polysph_to_angles

Obtain the angular coordinates of points on a polysphere
\(\mathcal{S}^{d_1}\times\cdots\times\mathcal{S}^{d_r}\), 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_polysph function

<dl><dt>theta</dt>
<dd>matrix of size <code>c(n, sum(d))</code> with the angles.</dd>
<dt>d</dt>
<dd>vector with the dimensions of the polysphere.</dd>
<dt>x</dt>
<dd>matrix of size <code>c(n, sum(d + 1))</code> with the Cartesian
coordinates on \(\mathcal{S}^{d_1}\times\cdots\times\mathcal{S}^{d_r}\).
Assumed to be of unit norm by blocks of coordinates in the rows.</dd></dl>

Arguments

Conversion between the angular and Cartesian coordinates of the
polysphere — angles_to_polysph

<dl>

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


<dt>d</dt>
<dd>vector with the dimensions of the polysphere.</dd>


<dt>x</dt>
<dd>matrix of size <code>c(n, sum(d + 1))</code> with the Cartesian
coordinates on \(\mathcal{S}^{d_1}\times\cdots\times\mathcal{S}^{d_r}\).
Assumed to be of unit norm by blocks of coordinates in the rows.</dd>

</dl>

angles_to_polysph: Conversion between the angular and Cartesian coordinates of the polysphere

Description

Usage

Value

Arguments

Examples