crossCy_sm: 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

crossCy_sm(
  Xdists,
  coords,
  Pcoords,
  d,
  n1,
  n2,
  r0,
  s0,
  cstat_opt,
  normalize,
  bumpLocs,
  rads,
  ampls,
  shps,
  Xdist1_sq,
  Xdist2_sq,
  Xdist12,
  Sigma11,
  Sigma22,
  Sigma12,
  PSigma11,
  PSigma22,
  PSigma12,
  nu,
  log_sigma_vec,
  Plog_sigma_vec
)

Value

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

Arguments

Xdists: N x N matrix of Euclidean distances
coords: N x d matrix of coordinate/input locations
Pcoords: N x d matrix of coordinate/input locations
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 (1 = TRUE)
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 \(b_{ij}\))
Xdist1_sq: N x N matrix; contains values of pairwise squared distances in the x-coordinate.
Xdist2_sq: N x N matrix; contains values of pairwise squared distances in the y-coordinate.
Xdist12: 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.
PSigma11: Vector of length N; contains the 1-1 element of the anisotropy process for each station.
PSigma22: Vector of length N; contains the 2-2 element of the anisotropy process for each station.
PSigma12: 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.
Plog_sigma_vec: Vector of length N; log of the signal standard deviation.