A pair object contains information defining pairs of points contained in a point object. A pair object is a list containing five
vectors: from, to, lags, dist, and bins. The length of each of these vectors (except bins) is equal to the number of pairs of
points being represented, say k. The vectors from and to contain pointers into the vectors of a point object, pointing to each
member of the pair of points (e.g., from[k] points to si and to[k] points to sj). The vector dist contains the distance between the
pairs of points. The vector lags contains the lag number to which each pair of points has been assigned. The vector bins contains
the spatial midpoint between each lag and is used for plotting.
the number of lags into which to divide the pairs of points in the pair object. The lags are all of equal size.
type
either
'isotropic' or 'anisotropic'. If 'isotropic' then all n choose 2 possible pairs of points are represented in the pair
object. If 'anisotropic', then the arguments theta and dtheta are used to determine which pairs of points to include.
theta
an angle, measured in degrees from the horizontal x axis, that determines pairs of points to be included in the pair
object (see Notes below).
dtheta
a tolerance angle, around theta, measured in degrees that determines pairs of points to be included in the pair
object (see Notes below).
maxdist
the distance beyond which not to consider pairs of points. A large number of spatial locations can cause the
pair function to consume a considerable amount of computation time. In most cases, spatial dependence can be
adaquately characterized without examining the entire spaital extent of the data set.
Value
A pair object:
from
vector of indices into the point object for "from" point
to
vector of indices into the point object for "to" point
lags
vector of spatial lags of each pair
dist
vector of distances between each pair
bins
vector of spatial midpoints of each lag (used for plotting)
NOTE
Name of this function changed from pairs to pair to avoid conflicts with R's pairs function!!
Note
When creating an anisotropic pair object, the assumption is that the direction, as well as the distance, between pairs of
points is important in describing the variation. Using the theta and dtheta arguments, pairs of points that meet direction
requirements can be selected. A pair of points will be included when the angle between the positive x axis and the vector
formed by the pair of points falls within the tolerance angle given by
(theta-dtheta,theta+dtheta)