optimMKV  R Documentation 
Optimize a sample configuration for spatial interpolation with a 'known' linear mixed model, e.g. universal (external drift) kriging and regressionkriging with a linear regression model. A criterion is defined so that the sample configuration minimizes the mean or maximum kriging prediction error variance (MKV).
optimMKV(
points,
candi,
covars,
eqn,
vgm,
krige.stat = "mean",
...,
schedule,
plotit = FALSE,
track = FALSE,
boundary,
progress = "txt",
verbose = FALSE
)
objMKV(points, candi, covars, eqn, vgm, krige.stat = "mean", ...)
points 
Integer value, integer vector, data frame (or matrix), or list. The number of sampling points (sample size) or the starting sample configuration. Four options are available:
Most users will want to set an integer value simply specifying the required sample size. Using an integer vector or data frame (or matrix) will generally be helpful to users willing to evaluate starting sample configurations, test strategies to speed up the optimization, and finetune or thin an existing sample configuration. Users interested in augmenting a possibly existing realworld sample configuration or finetuning only a subset of the existing sampling points will want to use a list. 
candi 
Data frame (or matrix). The Cartesian x and ycoordinates (in this order) of the
cell centres of a spatially exhaustive, rectangular grid covering the entire spatial sampling
domain. The spatial sampling domain can be contiguous or composed of disjoint areas and contain
holes and islands. 
covars 
Data frame or matrix with the covariates in the columns. The number of rows of 
eqn 
Formula string that defines the dependent variable 
vgm 
Object of class 
krige.stat 
Character value defining the statistic that should be used to summarize the kriging
prediction error variance. Available options are 
... 
further arguments passed to 
schedule 
List with named subarguments setting the control parameters of the annealing
schedule. See 
plotit 
(Optional) Logical for plotting the evolution of the optimization. Plot updates
occur at each ten (10) spatial jitters. Defaults to

track 
(Optional) Logical value. Should the evolution of the energy state be recorded and
returned along with the result? If 
boundary 
(Optional) An object of class SpatialPolygons (see sp::SpatialPolygons()) with
the outer and inner limits of the spatial sampling domain (see 
progress 
(Optional) Type of progress bar that should be used, with options 
verbose 
(Optional) Logical for printing messages about the progress of the optimization.
Defaults to 
There are multiple mechanism to generate a new sample configuration out of an existing one. The main step consists of randomly perturbing the coordinates of a single sample, a process known as ‘jittering’. These mechanisms can be classified based on how the set of candidate locations for the samples is defined. For example, one could use an infinite set of candidate locations, that is, any location in the spatial domain can be selected as a new sample location after a sample is jittered. All that is needed is a polygon indicating the boundary of the spatial domain. This method is more computationally demanding because every time an existing sample is jittered, it is necessary to check if the new sample location falls in spatial domain.
Another approach consists of using a finite set of candidate locations for the samples. A finite set of candidate locations is created by discretising the spatial domain, that is, creating a fine (regular) grid of points that serve as candidate locations for the jittered sample. This is a less computationally demanding jittering method because, by definition, the new sample location will always fall in the spatial domain.
Using a finite set of candidate locations has two important inconveniences. First, not all locations in the spatial domain can be selected as the new location for a jittered sample. Second, when a sample is jittered, it may be that the new location already is occupied by another sample. If this happens, another location has to be iteratively sought for, say, as many times as the size of the sample configuration. In general, the larger the size of the sample configuration, the more likely it is that the new location already is occupied by another sample. If a solution is not found in a reasonable time, the the sample selected to be jittered is kept in its original location. Such a procedure clearly is suboptimal.
spsann uses a more elegant method which is based on using a finite set of candidate locations
coupled with a form of twostage random sampling as implemented in spcosa::spsample()
.
Because the candidate locations are placed on a finite regular grid, they can be taken as the
centre nodes of a finite set of grid cells (or pixels of a raster image). In the first stage, one
of the “grid cells” is selected with replacement, i.e. independently of already being
occupied by another sample. The new location for the sample chosen to be jittered is selected
within that “grid cell” by simple random sampling. This method guarantees that virtually
any location in the spatial domain can be selected. It also discards the need to check if the new
location already is occupied by another sample, speeding up the computations when compared to the
first two approaches.
The search graph corresponds to the set of effective candidate locations for a sample location selected to be jittered. The size of the search graph, i.e. area within which a sample location can be moved around, is related to the concept of temperature. A larger search graph is equivalent to higher temperatures, which potentially result in more movement – or ‘agitation’ – of the set of sample locations.
The current version of the spsannpackage uses a linear cooling schedule which depends upon the number of jitters to control the size of the search graph. The equations are
x_max = x_max0  (chains_i / chains) * (x_max0  x_min) + x_cellsize + x_min0
and
y_max = y_max0  (chains_i / chains) * (y_max0  y_min) + y_cellsize + y_min0
,
where $x_max0$ and $y_max0$ are the maximum allowed shifts in the x and ycoordinates in the first chain, $x_min$ and $y_min$ are the minimum required shifts in the x and ycoordinates, $x_max$ and $y_max$ are the maximum allowed shifts in the x and ycoordinates during the next chain, $chains$ and $chain_i$ are the total and current chains, and $x_cellsize$ and $y_cellsize$ are the grid spacing in the x and ycoordinates. Because $x_cellsize$ and $y_cellsize$ can be equal to zero when a finite set of candidate locations is used, $x_min0$ and $y_min0$ are the maximum nearest neighbour distance in the x and ycoordinates between candidate locations.
optimMKV
returns an object of class OptimizedSampleConfiguration
: the optimized sample
configuration with details about the optimization.
objMKV
returns a numeric value: the energy state of the sample configuration – the objective
function value.
spsann always computes the distance between two locations (points) as the Euclidean distance between them. This computation requires the optimization to operate in the twodimensional Euclidean space, i.e. the coordinates of the sample, candidate and evaluation locations must be Cartesian coordinates, generally in metres or kilometres. spsann has no mechanism to check if the coordinates are Cartesian: you are the sole responsible for making sure that this requirement is attained.
This function is based on the method originally proposed by Heuvelink, Brus and de Gruijter (2006) and implemented in the Rpackage intamapInteractive by Edzer Pebesma and Jon Skoien.
Alessandro SamuelRosa alessandrosamuelrosa@gmail.com
Brus, D. J.; Heuvelink, G. B. M. Optimization of sample patterns for universal kriging of environmental variables. Geoderma. v. 138, p. 8695, 2007.
Heuvelink, G. B. M.; Brus, D. J.; de Gruijter, J. J. Optimization of sample configurations for digital mapping of soil properties with universal kriging. In: Lagacherie, P.; McBratney, A. & Voltz, M. (Eds.) Digital soil mapping  an introductory perspective. Elsevier, v. 31, p. 137151, 2006.
#####################################################################
# NOTE: The settings below are unlikely to meet your needs. #
#####################################################################
## Not run:
data(meuse.grid, package = "sp")
candi < meuse.grid[1:1000, 1:2]
covars < as.data.frame(meuse.grid)[1:1000, ]
vgm < gstat::vgm(psill = 10, model = "Exp", range = 500, nugget = 8)
schedule < scheduleSPSANN(
initial.temperature = 10, chains = 1, x.max = 1540, y.max = 2060,
x.min = 0, y.min = 0, cellsize = 40)
set.seed(2001)
res < optimMKV(
points = 10, candi = candi, covars = covars, eqn = z ~ dist,
vgm = vgm, schedule = schedule)
data.frame(
expected = 15.37137,
objSPSANN = objSPSANN(res),
objMKV = objMKV(
points = res, candi = candi, covars = covars, eqn = z ~ dist, vgm = vgm)
)
## End(Not run)
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