calculateU_ns: Calculate the (sparse) matrix U

Description

calculateU_ns calculates the (sparse) matrix U (i.e., the Cholesky of the inverse covariance matrix) using a nonstationary covariance function. The output only contains non-zero values and is stored as three vectors: (1) the row indices, (2) the column indices, and (3) the non-zero values. NOTE: this code assumes the all inputs correspond to the ORDERED locations.

Usage

calculateU_ns(
  dist1_3d,
  dist2_3d,
  dist12_3d,
  Sigma11,
  Sigma22,
  Sigma12,
  log_sigma_vec,
  log_tau_vec,
  nu,
  nID,
  cond_on_y,
  N,
  k,
  d,
  M = 0
)

Value

Returns a sparse matrix representation of the Cholesky of the precision matrix for a fixed set of covariance parameters.

Arguments

dist1_3d: N x (k+1) x (k+1) array of distances in the x-coordinate direction.
dist2_3d: N x (k+1) x (k+1) array of distances in the y-coordinate direction.
dist12_3d: N x (k+1) x (k+1) array of cross-distances.
Sigma11: N-vector; 1-1 element of the Sigma() process.
Sigma22: N-vector; 2-2 element of the Sigma() process.
Sigma12: N-vector; 1-2 element of the Sigma() process.
log_sigma_vec: N-vector; process standard deviation values.
log_tau_vec: N-vector; nugget standard deviation values.
nu: Scalar; Matern smoothness parameter.
nID: N x k matrix of (ordered) neighbor indices.
cond_on_y: A matrix indicating whether the conditioning set for each (ordered) location is on the latent process (y, 1) or the observed values (z, 0). Calculated in sgvSetup.
N: Scalar; number of data measurements.
k: Scalar; number of nearest neighbors.
d: Scalar; dimension of the spatial domain.
M: Scalar; number of prediction sites.