Draws a Halton Lattice sample from a SpatialPoints* object.
hal.point(x, n, J = NULL, bases = c(2, 3))A SpatialPoints or SpatialPointsDataFrame object.
This object must contain at least 1 point.
Sample size. Number of locations to draw from the set of points
contained in x.
A 2X1 vector of base powers. J[1] is for horizontal,
J[2] for vertical dimension. J determines the size and shape
of the smallest Halton boxes. There are bases[1]^J[1] vertical columns
of Halton boxes over x's bounding box, and bases[2]^J[2]
horizontal rows of Halton boxes over the bounding box, for a total
of prod(bases^J) boxes. The dimension of each box is
c(dx,dy)/(bases^J), where c(dx,dy) are the horizontal and
vertical extents of x's bounding box. If J=NULL (the default),
J is chosen so that Halton boxes are as square as possible.
2X1 vector of Halton bases. These must be co-prime.
A SpatialPointsDataFrame containing locations in the HAL sample,
in HAL order.
Attributes of the sample points are:
sampleID: A unique identifier for every sample point that
encodes the HAL order. return[order(return$sampleID),] will sort the
returned object in HAL order. sampleID's, in the HAL case, are not
consecutive. sampleID's are the Halton indices for the Halton boxes
containing the point, after adding random cycles to multiple points in
the same box (see halton.frame). If the sample cycled around
to the beginning of the frame, because random start
fell at the end, the sample number is appended
to the beginning of the normal sampleID's so they
will sort the frame in the proper order.
HaltonIndex: The index of the Halton box containing the point.
This column is not, in general, unique. Points with the same HaltonIndex
are in the same Halton box, and are "close" in space.
geometryID: The ID of the sampled point in x The
ID of points in x are row.names(x).
Any attributes of the original points (in x).
Additional attributes of the output object, beyond those which
make it a SpatialPointsDataFrame, are:
frame: Name of the input sampling frame.
frame.type: Type of resource in sampling frame. (i.e., "point").
sample.type: Type of sample drawn. (i.e., "HAL").
J: Exponents of the bases used to form the lattice of
Halton boxes. This is either the input J, or the J vector
computed by halton.indices.
bases: Bases of the Halton sequence used to draw the sample.
hl.box: The bounding box around points in x used to
draw the sample. See halton.indices.
random.start: The random start of the sample in the Halton
frame. The Halton frame is a list of all points sorted in
Halton order. Halton order is the Halton index of each point, with
random cycles added to multiple points
in the same Halton box.
This is a random number between 0 and the number of points in
x minus 1 .
The sample consists of the
n consecutive units starting at random.start+1 in
the sorted Halton frame.
A brief description of Halton Lattice sampling for points:
Given a set of Halton Lattice parameters J and bases,
a lattice of Halton boxes is constructed over the bounding box of the input points.
This results in prod(bases^J) Halton boxes on the bounding box.
The Halton index of all boxes is computed and assigned to points that lie
in each box. Points that lie in the same Halton box are randomly assigned
unique Halton cycle numbers. This separates points in the same Halton box by
at least prod(bases^J) units when indices are mapped to the real line.
Finally, a random number between 1 and the largest Halton (index+cycle) is
drawn, and the next n units in the mapped real numbers are taken as
the sample, restarting from the beginning if necessary.
# NOT RUN {
# Draw sample of Hawaii coastline
# This takes approximately 30 seconds to run
data(WA.cities)
samp <- hal.point( WA.cities, 100 )
# Different lattice topology
samp <- hal.point( WA.cities, 100, J=c(10,4))
# }
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