pkern_corr: Stationary 1D correlation kernels

In deankoch/pkern: Fast Kriging with Product Kernels

Stationary 1D correlation kernels

Description

Computes stationary correlation function values for the n (non-negative) 1-dimensional distances in d. Parameter list entry pars$kp supplies the kernel parameter(s).

Usage

pkern_corr(pars, d = NA)

Arguments

pars	list with elements 'k', the kernel name, and 'kp' the parameter vector
d	numeric vector of length n, the distances to evaluate

Details

pars$k must be one of the following kernel names:

• 'exp': exponential (special case of 'gex' with shape p=1)

• 'gau': gaussian/stable (special case of 'gex' with shape p=2)

• 'sph': spherical (AKA stable/Gaussian for p=2)

• 'gex': gamma-exponential (with shape p)

• 'mat': Whittle-Matern (Handcock and Wallis parameterization, with shape kap)

where the first three kernels have only a range parameters, and the last two have both a range and shape parameter.

For the 1-parameter kernels, pars$kp is the range parameter value ('rho'); For the 2-parameter kernels, pars$kp is a vector whose first element is 'rho', and second element is the shape parameter ('p' or 'kap'). The names in pars$kp are ignored and only the order matters - the range parameter always comes first.

Note that this function will not accept parameter lists pars of the form returned by pkern_pars(...) etc, as these include a pair of 1d kernels (however the sub-lists pars$y and pars$x are accepted).

Value

length-n vector or a list of parameters and bounds (see details)

Examples

# define test distances, grid, and example kernel
n_test = 100
d_test = seq(n_test)-1
g_example = pkern_grid(n_test)
pars = pkern_pars(g_example, c('mat', 'gau'))
pars_x = pars[['x']]

# compute and plot the x component of the correlogram function
corr_x_example = pkern_corr(pars_x, d=d_test)
plot(d_test, corr_x_example, pch=NA)
lines(d_test, corr_x_example)

## show how this function gets used to build more complicated objects

# get the other component correlation, take product
pars_y = pars[['y']]
corr_y_example = pkern_corr(pars_y, d=d_test)
corr_example = corr_y_example * corr_x_example

# variogram
variogram_example = pkern_vario_fun(pars, d=list(y=d_test, x=d_test))
variogram_compare = 2 * pars$eps + pars$psill * (1 - corr_example)
max(abs( variogram_example - variogram_compare ))

# Toeplitz component matrices built entirely from these correlation vectors
variance_matrix_example = pkern_var(g_example, pars)
max(abs( variance_matrix_example[['y']][,1L] - corr_y_example ))
max(abs( variance_matrix_example[['x']][,1L] - corr_x_example ))

deankoch/pkern documentation built on Oct. 26, 2023, 8:54 p.m.