Draws a Halton Lattice sample from a
Sample size. Number of locations to draw from the set of points
A 2X1 vector of base powers.
2X1 vector of Halton bases. These must be co-prime.
A brief description of Halton Lattice sampling for points:
Given a set of Halton Lattice parameters
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
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.
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
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
are in the same Halton box, and are "close" in space.
geometryID: The ID of the sampled point in
ID of points in
Any attributes of the original points (in
Additional attributes of the output object, beyond those which
make it a
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
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
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
the sorted Halton frame.
1 2 3 4 5 6 7 8
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