From a matrix of locations and covariance parameters of the form (variance, range, smoothness, nugget, <nonstat variance parameters>), return the square matrix of all pairwise covariances.
matern_nonstat_var(covparms, Z)d_matern_nonstat_var(covparms, Z)
A matrix with n
rows and n
columns, with the i,j entry
containing the covariance between observations at locs[i,]
and
locs[j,]
.
A vector with covariance parameters
in the form (variance, range, smoothness, nugget, <nonstat variance parameters>).
The number of nonstationary variance parameters should equal p
.
A matrix with n
rows and 2
columns for spatial
locations + p
columns describing spatial basis functions.
Each row of locs gives a point in R^2 (two dimensions only!) + the value
of p
spatial basis functions.
d_matern_nonstat_var()
: Derivatives with respect to parameters
This covariance function multiplies the isotropic Matern covariance
by a nonstationary variance function. The form of the covariance is
$$ C(x,y) = exp( \phi(x) + \phi(y) ) M(x,y) $$
where M(x,y) is the isotropic Matern covariance, and
$$ \phi(x) = c_1 \phi_1(x) + ... + c_p \phi_p(x) $$
where \(\phi_1,...,\phi_p\) are the spatial basis functions
contained in the last p
columns of Z
, and
\(c_1,...,c_p\) are the nonstationary variance parameters.