Draws a Halton Lattice sample from a SpatialPolygons* object.
hal.polygon(x, n, J = NULL, eta = c(1, 1), triangular = FALSE,
bases = c(2, 3), init.n.factor = 1000)A SpatialPoints or SpatialPointsDataFrame object.
This object must contain at least 1 polygon.
Sample size. Number of locations to draw from the union of all
polygons 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) total 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 approximately 1000*n Halton boxes are placed
in the bounding box of polygons, each as
square as possible and each containing one point,
A 2X1 vector specifying the number of points to add in the
horizontal and vertical dimensions of each Halton box. e.g., if
eta = c(3,2), a grid of 3 (horizontal) by 2 (vertical) points is
added inside each Halton box.
A boolean scalar. If TRUE, odd horizontal rows of the Halton lattice are moved one-quarter a Halton box width to the right, while even rows of the Halton lattice are moved one-quarter of a Halton box width to the left. This creates a triangular Halton lattice over the bounding box of the polygons. If FALSE, a rectangular Halton lattice is constructed.
2X1 vector of Halton bases. These must be co-prime.
A
scalar factor controlling the approximate number of points
in the Halton lattice to place inside the polygons before sampling.
If J is not specified, approximately init.n.factor*n
points are placed in the Halton lattice overlaid on the polygons
of x. Points in the Halton lattice are then sampled
using the HAL method for points. init.n.factor*n is the
approximate frame size.
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. This
encodes the HAL order. return[order(return$sampleID),] will sort the
returned object in HAL 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 polygon in x containing each
sample point. The
ID of polygons in x are row.names(geometry(x)).
Any attributes of the original polygons (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., "polygon").
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.lattice.
bases: Bases of the Halton sequence used to draw the sample.
eta: the eta vector used in the lattice.
hl.box: The bounding box around points in x used to
draw the sample. See halton.indices.
triangular: Whether the underlying lattice is triangular or square.
random.start: The random seed of the Halton lattice sample.
See hal.point.
A brief description of Halton Lattice sampling for polygons:
Given a set of Halton Lattice parameters J, bases, eta,
and triangular, the bounding box around all polygons is partitioned using
a Halton lattice of prod(bases^J) boxes, each containing prod(eta)
points. Points not inside at
least one polygon are
dropped. All this is done by halton.lattice.polygon.
The resulting points (the Halton lattice frame) are passed to hal.point
and sampled using the HAL method for points.
# NOT RUN {
samp <- hal.polygon( WA, 100, J=c(4,3) )
plot(WA)
points( samp, pch=16, col="red" )
# Different lattice topology
samp <- hal.polygon( WA, 100, J=c(8,2), eta=c(2,1), triangular=TRUE)
points( samp, pch=15, col="blue")
# }
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