pkern_sample_vg: Sample point pair absolute differences for use in...

In deankoch/pkern: Fast Kriging with Product Kernels

Sample point pair absolute differences for use in semi-variogram estimation

Description

Compute the absolute differences for point pairs in g, along with their separation distances. If no sample point index is supplied (in idx), the function samples points at random using pkern_sample_pt.

Usage

pkern_sample_vg(
  g,
  n_pp = 10000,
  idx = NULL,
  n_bin = 25,
  n_layer_max = NA,
  quiet = FALSE
)

Arguments

g	any grid object accepted or returned by pkern_grid, containing non-NA data
idx	optional integer vector indexing the points to sample
n_bin	integer number of distance bins to assign (passed to pkern_add_bins)
n_max	integer maximum number of point pairs to sample

Details

In a set of n points there are n_pp(n) = (n^2 - n) / 2 possible point pairs. This expression is inverted to determine the maximum number of sample points in g to use in order to satisfy the user-supplied argument n_pp. A random sub-sample of idx is taken as needed.

The mean of the point pair absolute values ('dabs') is the classical estimator of the variogram. This and two other robust methods are implemented in pkern_plot_vg.

Value

Results are returned in a data frame with each row representing one point pair. Fields include 'dabs' and 'd', the absolute difference and distance mentioned earlier, along with a number of indexing vectors for both point locations and relative separation. 'bin' is an integer splitting distances into n_bin categories.

Examples

# make example grid and reference covariance model
gdim = c(22, 15)
n = prod(gdim)
g_obs = pkern_grid(gdim)
pars = pkern_pars(g_obs, 'mat')

# generate sample data and sample semi-variogram
g_obs[['gval']] = pkern_sim(g=g_obs, pars)
vg = pkern_sample_vg(g_obs)
str(vg)

# pass to plotter and overlay the model that generated the data
pkern_plot_semi(vg, pars)

# repeat with smaller sample sizes
pkern_plot_semi(pkern_sample_vg(g_obs, 1e2), pars)
pkern_plot_semi(pkern_sample_vg(g_obs, 1e3), pars)

# use a set of specific points
n_sp = 10
( n_sp^2 - n_sp ) / 2 # the number of point pairs
vg = pkern_sample_vg(g_obs, idx=sample.int(n, n_sp))
pkern_plot_semi(vg, pars)

# repeat with all point pairs sampled (not recommended for big data sets)
vg = pkern_sample_vg(g_obs, n_pp=Inf)
pkern_plot_semi(vg, pars)
( n^2 - n ) / 2 # the number of point pairs

## example with multiple layers

# generate five layers
z_multi = sapply(seq(5), function(x) pkern_sim(g=g_obs, pars))
g_obs_multi = modifyList(g_obs, list(gval=z_multi, idx_grid=seq(n)))

# by default, a sub-sample of sqrt(n_layers) is selected
vg = pkern_sample_vg(g_obs_multi)
pkern_plot_semi(vg, pars)

# change this behaviour with n_layer_max
vg = pkern_sample_vg(g_obs_multi, n_layer_max=5)
pkern_plot_semi(vg, pars)

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