Cy_sm: Calculate sparse kernel, core kernel, and determine nonzero...

In BayesNSGP: Bayesian Analysis of Non-Stationary Gaussian Process Models

Calculate sparse kernel, core kernel, and determine nonzero entries

Description

Cy_sm calculates the normalized sparse kernel for a fixed set of bump function hyperparameters and returns the nonzero entries. Note that the matrix is calculated and returned in dense format.

Usage

Cy_sm(
  dists,
  coords,
  N,
  d,
  n1,
  n2,
  r0,
  s0,
  cstat_opt,
  normalize,
  bumpLocs,
  rads,
  ampls,
  shps,
  dist1_sq,
  dist2_sq,
  dist12,
  Sigma11,
  Sigma22,
  Sigma12,
  nu,
  log_sigma_vec,
  lognuggetSD
)

Arguments

dists	N x N matrix of Euclidean distances
coords	N x d matrix of coordinate/input locations
N	Scalar; number of data measurements.
d	Scalar; dimension of the spatial domain.
n1	Scalar; number of outer products.
n2	Scalar; number of bump functions in each outer product.
r0	Scalar; length-scale of sparse stationary kernel.
s0	Scalar; signal-variance of sparse stationary kernel.
cstat_opt	Scalar; determines the compactly supported kernel. See Details.
normalize	Logical; should C_sparse have 1's along the diagonal
bumpLocs	Array of bump function locations (n2*d x n1)
rads	Matrix of bump function radii (n1 x n2; denoted r_{ij})
ampls	Matrix of bump function amplitudes (n1 x n2; denoted a_{ij})
shps	Matrix of bump function shape parameters (n1 x n2; denoted b_{ij})
dist1_sq	N x N matrix; contains values of pairwise squared distances in the x-coordinate.
dist2_sq	N x N matrix; contains values of pairwise squared distances in the y-coordinate.
dist12	N x N matrix; contains values of pairwise signed cross- distances between the x- and y-coordinates. The sign of each element is important; see nsDist function for the details of this calculation. in the x-coordinate.
Sigma11	Vector of length N; contains the 1-1 element of the anisotropy process for each station.
Sigma22	Vector of length N; contains the 2-2 element of the anisotropy process for each station.
Sigma12	Vector of length N; contains the 1-2 element of the anisotropy process for each station.
nu	Scalar; Matern smoothness parameter. nu = 0.5 corresponds to the Exponential correlation; nu = Inf corresponds to the Gaussian correlation function.
log_sigma_vec	Vector of length N; log of the signal standard deviation.
lognuggetSD	Vector of length N; log of the error standard deviation.

Value

Returns a sparse matrix (N x 3) of the nonzero elements of the product between the core and sparse kernel.

BayesNSGP documentation built on Dec. 11, 2025, 5:08 p.m.