SPDE Spatial Field (Matern via Triangular Mesh)

Specify a continuous Matern spatial field using the SPDE approach (Lindgren, Rue & Lindstrom 2011). Builds a triangular mesh from observation coordinates, computes FEM matrices, and passes them to tulpa's SPDE Laplace engine with CHOLMOD sparse solver.

Usage

spatial_spde(
  coords,
  data = NULL,
  mesh = NULL,
  boundary = NULL,
  max_edge = NULL,
  cutoff = 0,
  nu = 1,
  prior_range = c(0.5, 0.5),
  prior_sigma = c(1, 0.5)
)

Arguments

coords: A formula ~ x + y or a two-column matrix of coordinates.
data: Optional data.frame for formula evaluation.
mesh: A pre-built tulpa_mesh object. If NULL (default), a mesh is built automatically from coords.
boundary: Optional boundary: a two-column matrix of polygon vertices, an sf polygon, or NULL for convex hull with extension.
max_edge: Maximum edge length for mesh refinement. A single value or c(inner, outer).
cutoff: Minimum distance between mesh vertices. Default 0.
nu: Matern smoothness parameter. A positive number. Integer nu (1, 2, 3, ...) gives an exact FEM construction (operator order alpha = nu + 1). Fractional nu (e.g. 0.5, 1.5) uses the operator-based rational SPDE approximation with BRASIL best-rational coefficients (Bolin & Kirchner 2020; Hofreither 2021); supported by the Laplace fitter fit_spde() (single-point and nested over range/sigma). NUTS and analytic marginal SEs remain integer-only. Default 1.
prior_range: Prior for the spatial range. A numeric vector c(U, alpha) where P(range < U) = alpha. Default c(0.5, 0.5).
prior_sigma: Prior for the marginal standard deviation. A numeric vector c(U, alpha) where P(sigma > U) = alpha. Default c(1, 0.5).

Value

A tulpa_spatial object with type "spde".

Examples

set.seed(42)
coords <- cbind(runif(50), runif(50))
spec <- spatial_spde(coords)
print(spec)