Type:	Package
Title:	Multi-Resolution Thin-Plate Splines on the Sphere
Version:	0.1.2
Description:	Constructs multi-resolution thin-plate spline basis functions on the sphere for use in spatial regression and large-scale spatial prediction problems. Implements the basis system described in Huang, Huang, and Ing (2025) "Multi-Resolution Spatial Methods on the Sphere: Efficient Prediction for Global Data", Environmetrics, <doi:10.1002/env.70092>. Heavy computations are written in 'C++' via 'Rcpp' with optional 'OpenMP' parallelism.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
Depends:	R (≥ 4.0)
Imports:	Rcpp, RSpectra
LinkingTo:	Rcpp, RcppEigen, RcppNumerical
Suggests:	fields, testthat (≥ 3.0.0)
SystemRequirements:	GNU make
RoxygenNote:	7.3.2
URL:	https://github.com/STLABTW/multi-resolution-sphere
BugReports:	https://github.com/STLABTW/multi-resolution-sphere/issues
Config/testthat/edition:	3
NeedsCompilation:	yes
Packaged:	2026-04-28 23:07:49 UTC; hyhuang
Author:	Hao-Yun Huang [aut, cre], Hsin-Cheng Huang [aut], Ching-Kang Ing [aut]
Maintainer:	Hao-Yun Huang <hhuscout@gmail.com>
Repository:	CRAN
Date/Publication:	2026-04-29 18:40:07 UTC

mrtsSphere: Multi-Resolution Thin-Plate Splines on the Sphere

Description

Constructs multi-resolution thin-plate spline basis functions on the sphere for use in spatial regression and large-scale spatial prediction problems.

Details

The main user-facing function is mrts_sphere().

Author(s)

Maintainer: Hao-Yun Huang hhuscout@gmail.com (ORCID)

Authors:

• Hsin-Cheng Huang (ORCID)

• Ching-Kang Ing (ORCID)

References

Multi-resolution approximations of Gaussian processes for large spatial datasets on the sphere. Environmetrics, 2025. doi:10.1002/env.70092

See Also

Useful links:

• https://github.com/STLABTW/multi-resolution-sphere

• Report bugs at https://github.com/STLABTW/multi-resolution-sphere/issues

Multi-resolution thin-plate spline basis on the sphere

Description

Builds a set of k multi-resolution thin-plate spline (MRTS) basis functions on the sphere from a set of knot locations, and evaluates them at the prediction locations X.

Usage

mrts_sphere(knot, k, X)

Arguments

Details

The first basis function is constant (sqrt(1/n)); the remaining k - 1 basis functions are obtained from the eigen-decomposition of the centered knot kernel matrix, following the construction described in the reference.

Value

A list with one element:

mrts

An ⁠nrow(X) x k⁠ numeric matrix whose columns are the basis functions evaluated at the rows of X.

References

Multi-resolution approximations of Gaussian processes for large spatial datasets on the sphere. Environmetrics, 2025. doi:10.1002/env.70092

Examples

## Build a small global grid in (lat, lon) degrees.
n_lon <- 12
n_lat <- 8
lon_seq <- seq(-180, 150, length.out = n_lon)
lat_seq <- seq( -80,  80, length.out = n_lat)
grid <- as.matrix(expand.grid(lat = lat_seq, lon = lon_seq))

## Pick 30 knots and evaluate the MRTS basis at every grid point.
set.seed(1)
knots <- grid[sample(nrow(grid), 30), ]
res <- mrts_sphere(knots, k = 5, X = grid)
dim(res$mrts)   # nrow(grid) x k

## Recovering a simulated spherical exponential field with the basis.
if (requireNamespace("fields", quietly = TRUE)) {
  # Great-circle distance (km) -> exponential covariance.
  d_grid    <- fields::rdist.earth(grid[, 2:1], miles = FALSE)
  cov_field <- exp(-d_grid / 2000)
  y_true    <- as.numeric(t(chol(cov_field + diag(1e-8, nrow(grid)))) %*%
                          rnorm(nrow(grid)))

  # Noisy observations at the knot locations.
  obs_idx <- match(data.frame(t(knots)), data.frame(t(grid)))
  z_obs   <- y_true[obs_idx] + rnorm(nrow(knots), sd = 0.3)

  # Project into the MRTS basis (least squares) and predict on the grid.
  B_obs    <- res$mrts[obs_idx, , drop = FALSE]
  beta_hat <- qr.solve(B_obs, z_obs)
  y_hat    <- res$mrts %*% beta_hat
  sqrt(mean((y_hat - y_true)^2))   # RMSE
}