tulpa_spde_precision_Q: Rebuild the SPDE/Matern field precision matrix

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Rebuild the SPDE/Matern field precision matrix

Description

Rebuilds the sparse precision matrix Q(kappa, tau) of an SPDE/Matern field from its mesh geometry and a ⁠(kappa, tau)⁠ hyperparameter pair, mirroring the compiled builder (src/spde_qbuilder.h) that tulpa_nuts_spde() and fit_spde() use internally. Intended for a caller running its own outer-grid loop over ⁠(range, sigma)⁠ around a coupled model tulpa's own SPDE front doors (fit_spde(), spatial_spde()) do not fit directly – e.g. a per-species community layer sharing one spatial field.

Usage

tulpa_spde_precision_Q(spatial, kappa, tau_spde)

Arguments

spatial	A spatial_spde() / spatial_spde_custom() spec, carrying n_mesh, C0_diag, G and nu.
kappa	Spatial frequency kappa = sqrt(8*nu) / range.
tau_spde	SPDE precision scale (see tulpa_spde_log_hyperprior()'s ⁠(range, sigma)⁠ -> ⁠(kappa, tau)⁠ mapping via .spde_kappa_tau()).

Value

A sparse ⁠n_mesh x n_mesh⁠ precision matrix.

See Also

tulpa_spde_log_hyperprior(), fit_spde(), spatial_spde()

Examples

n <- 6L
G <- Matrix::bandSparse(n, k = c(-1, 0, 1),
                        diagonals = list(rep(-1, n - 1), c(1, rep(2, n - 2), 1),
                                         rep(-1, n - 1)))
sp <- spatial_spde_custom(Matrix::Diagonal(n), G, Matrix::Diagonal(n),
                          prior_range = c(1, 0.5), prior_sigma = c(1, 0.01))
Q <- tulpa_spde_precision_Q(sp, kappa = sqrt(8) / 1, tau_spde = 1)
dim(Q)

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.