pkern_sample_pt: Sub-grid point sampler for grid data

In deankoch/pkern: Fast Kriging with Product Kernels

Sub-grid point sampler for grid data

Description

Sample n locations from the non-NA points in the input grid g, optionally using them as centers to place n sub-grids of the specified size and resolution.

Usage

pkern_sample_pt(g, n = 100, lag_max = 0, interval = 1L, over = FALSE)

Arguments

g	any grid object accepted or returned by pkern_grid
n	integer > 0, the maximum number of center points to sample
lag_max	integer, Moore neighborhood radius (ie the maximum queen's distance)
interval	integer > 0, the down-scaling factor for sub-grids of g
over	logical, indicates to allow overlapping sub-grids (when they can be avoided)

Details

The function draws a sample of n locations (uniformly at random) from the non-NA points in the input grid g, and returns their vector index. If there are fewer than n locations available, they are all returned.

When lag_max > 1, the function also identifies a regular sub-grid of the Moore neighbourhood of (integer) radius lag_max around each of the sample points, with interval-1 grid lines separating each sub-grid line. interval is the factor by which the resolution of the sub-grid is scaled to get the original grid resolution; It must evenly divide lag_max.

For a given interval, the grid g can be partitioned into interval^2 distinct non-overlapping sub-grids. When over=FALSE (the default), the function apportions its n point samples as evenly as possible among these disjoint subsets. This ensures that if n is less than or equal to interval^2, and there are no NAs, there can be no repetition (overlap) of points in the returned sub-grids.

Value

If lag_max=0 (the default), the function returns the sample indices as a length-n integer vector. If lag_max is positive, the function returns a list of n+1 indexing vectors; the first locates the n sub-grid center points, and the following n vectors locate the points in each sub-grid (including the center points itself)

Examples

# define a grid
gdim = c(100, 100)
ng = prod(gdim)

# get an ordinary random sample with default settings
idx_sample = pkern_sample_pt(g=gdim)
pkern_plot(seq(ng) %in% idx_sample, gdim)

# reduce or increase number of center points from default 100
idx_sample = pkern_sample_pt(gdim, n=10)
pkern_plot(seq(ng) %in% idx_sample, gdim)

# sampled from Moore neighbourhoods of radius 6
n = 10
idx_sample = pkern_sample_pt(gdim, n=n, lag_max=6L)
pkern_plot(seq(ng) %in% unlist(idx_sample), gdim, col_grid='white')

# plot each list element a different color
group_sample = rep(0L, prod(gdim))
for(i in seq(1 + n)[-1]) group_sample[ idx_sample[[i]] ] = i-1L
pkern_plot(group_sample, gdim, breaks=c('not sampled', seq(n)), zlab='sub-grid')

# When interval > 1, the function attempts to avoid overlap whenever possible
interval = 2
n = interval^2 # to get disjoint results n must be less than or equal to interval^2
lag_max = 10 * interval # vary to get larger/smaller subsets. max allowable: min(gdim)/2
idx_sample = pkern_sample_pt(gdim, n=n, interval=interval, lag_max=lag_max)
idx_overlap = rowSums( sapply(idx_sample[-1], function(i) seq(ng) %in% i) )
pkern_plot(as.integer(idx_overlap), gdim, zlab='times sampled')

# plot each list element a different color
group_sample = rep(0L, prod(gdim))
for(i in seq(1 + interval^2)[-1]) group_sample[ idx_sample[[i]] ] = i-1L
pkern_plot(group_sample, gdim, breaks=c('not sampled', seq(interval^2)), zlab='sub-grid')

# compare with over=TRUE (usually results in overlap - try running a few times)
idx_sample_compare = pkern_sample_pt(gdim, n=n, interval=interval, lag_max=lag_max, over=TRUE)
idx_overlap_compare = rowSums( sapply(idx_sample_compare[-1], function(i) seq(ng) %in% i) )
pkern_plot(as.integer(idx_overlap_compare), gdim, zlab='times sampled')

# only non-NA points are eligible in initial sample of center points
g = pkern_grid(gdim)
g$gval = rep(NA, ng)
idx_obs = sample.int(ng, ng/1e2)
g$gval[idx_obs] = 'non-NA'
pkern_plot(g)

# draw a sample of center points and indicate sub-grids in color
idx_sample = pkern_sample_pt(g, n=10, lag_max=6L, interval=2)
g$gval[unlist(idx_sample[-1])] = 'sub-grid'
g$gval[idx_sample[[1]]] = 'center point'
pkern_plot(g)

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