Draws a Halton Lattice sample from a SpatialLines* object.
hal.line(x, n, J = NULL, eta = c(1, 1), bases = c(2, 3), balance = "1D",
frame.spacing = NULL)A SpatialLines or SpatialLinesDataFrame object. This object must contain at least 1 line. If it contains more than 1 line, the HAL sample is drawn from the union of all lines.
Sample size. Number of locations to draw from the set of all lines
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 Halton boxes are as square as possible.
When balance is "2D", eta is 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. Size and shape of Halton boxes is controlled
by J parameter.
If balance == "2D", this is a 2X1 vector of co-prime Halton bases.
If balance == "1D", this is the single (scalar) Halton base to use.
If length(bases) == 2 and balance == "1D", the first element of
bases is used.
Option specifying how spatial balance is maintained. The options are "1D" or "2D".
Under "1D" all lines in x are stretched straight
and laid end-to-end in the order the appear in x and a 1-dimensional
BAS sample is taken from the amalgamated line. Sample locations are then
mapped back to two dimensional space and appear on the original lines. This
method maintains 1D spatial balance, but not 2D balance. Spatially
balanced samples in 1D may not look spatially balanced when plotted
in 2 dimensions.
Under "2D" a systematic sample of points along the union of all lines
in x is drawn first, and a 2-dimensional BAS sample of the points
is drawn (see bas.point). This maintains 2D spatial
balance of sample locations on the lines, but is slower than "1D".
If balance == "2D", this is the desired spacing of
points on lines prior to sampling via
HAL. If balance == "2D", the first step is discretization of lines by
placing
equally-spaced points on all lines. Then, points are sampled using Halton sampling
(see hal.point) for points. This parameter controls spacing of points during the
discretization of lines. For example, specifying 50, and assuming
x is projected to UTM meters, means points will be placed every 50
meters along all lines in x before sampling. x should be projected before
sampling so that pt.spacing makes sense. If pt.spacing is not
specified and balance == "2D", 1000*n points will be placed along
all lines during
discretization.
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. sampleID's, in the HAL case, are not
consecutive. sampleID's are usually the Halton
indices for the Halton boxes
containing the point, after adding random cycles for 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.
geometryID: The ID of the line in x on which each
sample point falls. The
ID of lines in x are row.names(x).
Any attributes of the original lines (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., "line").
sample.type: Type of sample drawn. (i.e., "BAS").
balance: The type of balance ("1d" or "2d").
random.start: The random seed for the random-start
1D or 2D Halton sequence
that produced the sample.
If balance=="1D",
random.start: The random start of the sample in the
1D or 2D 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. If balance=="2D",
this is a random number between 0 and the number of points
in the discretization of x (see frame.spacing).
If balance=="1D", this is a random number between 0
and the number of points in the 1D Halton lattice
discretization of x (see parameters J and eta).
The sample consists of the
n consecutive units starting at random.start+1 in
the sorted Halton frame.
A HAL sample is drawn from the union of all lines in x by
discretization of lines using points spaced pt.spacing apart. The
discretized points are then sampled using the HAL method
for points (see hal.point).
# NOT RUN {
# Default sample of Hawaii coastline. 1D balance
samp <- hal.line( HI.coast, 100 )
# Desire frame with spacing = 500 meters
# Frame has ~3144 points = lineLength(HI.coast)/500
samp <- hal.line( HI.coast, 100, balance="2D", frame.spacing=500)
# Desire 2000 points in frame
# Set frame.spacing = lineLength / 2000
# Set Halton lattice to contain
# 2592 boxes = prod(c(2,3)^c(5,4))
samp <- hal.line( HI.coast, 100, J=c(5,4), balance="2D",
frame.spacing=lineLength(HI.coast)/2000)
# }
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