Provides fast moving-window ("focal") and buffer-based extraction 
    for raster data using the 'terra' package. Automatically selects between 
    a 'C++' backend (via 'terra') and a Fast Fourier Transform (FFT) backend 
    depending on problem size. The FFT backend supports sum and mean, while 
    other statistics (e.g., median, min, max, standard deviation) are handled 
    by the 'terra' backend. Supports multiple kernel types (e.g., circle, 
    rectangle, gaussian), with NA handling consistent with 'terra' via 
    'na.rm' and 'na.policy'. Operates on 'SpatRaster' objects and returns 
    results with the same geometry.

Implements fast and exact computation of Gaussian stochastic process with the Matern kernel using forward filtering and backward smoothing algorithm. It includes efficient implementations of the inverse Kalman filter, with applications such as estimating particle interaction functions. These tools support models with or without noise. Additionally, the package offers algorithms for fast parameter estimation in latent factor models, where the factor loading matrix is orthogonal, and latent processes are modeled by Gaussian processes.  See the references: 1) Mengyang Gu and Yanxun Xu (2020), Journal of Computational and Graphical Statistics; 2) Xinyi Fang and Mengyang Gu (2024), <doi:10.48550/arXiv.2407.10089>; 3) Mengyang Gu and Weining Shen (2020), Journal of Machine Learning Research; 4) Yizi Lin, Xubo Liu, Paul Segall and Mengyang Gu (2025), <doi:10.48550/arXiv.2501.01324>.

Converts R data frames and 'sf' spatial objects into 'JSON' and 
    'GeoJSON' strings. The core encoders are implemented in 'Rust' using the 
    'extendr' framework and are designed to efficiently serialize large 
    tabular and spatial datasets. Returns serialized 'JSON' text, allowing 
    applications such as 'shiny' or web APIs to transfer data to 
    client-side 'JavaScript' libraries without additional encoding overhead.

Fast, numerically-stable Gauss-Hermite quadrature rules and
    utility functions for adaptive GH quadrature. See Liu, Q. and Pierce, D. A.
    (1994) <doi:10.2307/2337136> for a reference on these methods.