A simple tool for numerical optimization on the unit sphere. This is achieved by combining the spherical coordinating system with L-BFGS-B optimization. This algorithm is implemented in Kolkiewicz, A., Rice, G., & Xie, Y. (2020) <doi:10.1016/j.jspi.2020.07.001>.

Fitting dimension reduction methods to data lying on two-dimensional sphere.
    This package provides principal geodesic analysis, principal circle, principal curves 
    proposed by Hauberg, and spherical principal curves. Moreover, it offers the method of locally   
    defined principal geodesics which is underway. The detailed procedures 
    are described in Lee, J., Kim, J.-H. and Oh, H.-S. (2021) <doi:10.1109/TPAMI.2020.3025327>. 
    Also see Kim, J.-H., Lee, J. and Oh, H.-S. (2020) <arXiv:2003.02578>.

Various functions for creating spherical coordinate system plots via extensions to rgl.

Fitting a smooth path to a given set of noisy spherical data observed at known time points. It implements a piecewise geodesic curve fitting method on the unit sphere based on a velocity-based penalization scheme. The proposed approach is implemented using the Riemannian block coordinate descent algorithm. To understand the method and algorithm, one can refer to Bak, K. Y., Shin, J. K., & Koo, J. Y. (2023) <doi:10.1080/02664763.2022.2054962> for the case of order 1. Additionally, this package includes various functions necessary for handling spherical data.

Provides several methods to integrate functions over the unit
 sphere and ball in n-dimensional Euclidean space.  Routines for converting to/from
 multivariate polar/spherical coordinates are also provided.

Functions for fitting Cliff-Ord-type spatial autoregressive models with and without heteroskedastic innovations using Generalized Method of Moments estimation are provided. Some support is available for fitting spatial HAC models, and for fitting with non-spatial endogeneous variables using instrumental variables.

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. (2024) <doi:10.48550/arXiv.2108.09874>.