Calculate the cross k and g functions for a set of points on a network. (maturing)

cross_kfunctions(
lines,
pointsA,
pointsB,
start,
end,
step,
width,
nsim,
conf_int = 0.05,
digits = 2,
tol = 0.1,
resolution = NULL,
agg = NULL,
verbose = TRUE,
return_sims = FALSE
)

## Arguments

lines

A feature collection of linestrings representing the underlying network. The geometries must be simple Linestrings (may crash if some geometries are invalid) without MultiLineSring

pointsA

A feature collection of points representing the points to which the distances are calculated.

pointsB

A feature collection of points representing the points from which the distances are calculated.

start

A double, the lowest distance used to evaluate the k and g functions

end

A double, the highest distance used to evaluate the k and g functions

step

A double, the step between two evaluations of the k and g function. start, end and step are used to create a vector of distances with the function seq

width

The width of each donut for the g-function. Half of the width is applied on both sides of the considered distance

nsim

An integer indicating the number of Monte Carlo simulations to perform for inference

conf_int

A double indicating the width confidence interval (default = 0.05) calculated on the Monte Carlo simulations

digits

An integer indicating the number of digits to retain from the spatial coordinates

tol

When adding the points to the network, specify the minimum distance between these points and the lines' extremities. When points are closer, they are added at the extremity of the lines

resolution

When simulating random points on the network, selecting a resolution will reduce greatly the calculation time. When resolution is null the random points can occur everywhere on the graph. If a value is specified, the edges are split according to this value and the random points can only be vertices on the new network

agg

A double indicating if the events must be aggregated within a distance. If NULL, the events are aggregated only by rounding the coordinates

verbose

A Boolean indicating if progress messages should be displayed

return_sims

a boolean indicating if the simulated k and g values must also be returned as matrices

## Value

A list with the following values :

• plotk A ggplot2 object representing the values of the cross k-function

• plotg A ggplot2 object representing the values of the cross g-function

• values A DataFrame with the values used to build the plots

## Details

The cross k-function is a method to characterize the dispersion of a set of points (A) around a second set of points (B). For each point in B, the numbers of other points in A in subsequent radii are calculated. This empirical cross k-function can be more or less clustered than a cross k-function obtained if the points in A were randomly located around points in B. In a network, the network distance is used instead of the Euclidean distance. This function uses Monte Carlo simulations to assess if the points are clustered or dispersed and gives the results as a line plot. If the line of the observed cross k-function is higher than the shaded area representing the values of the simulations, then the points in A are more clustered around points in B than what we can expect from randomness and vice-versa. The function also calculates the cross g-function, a modified version of the cross k-function using rings instead of disks. The width of the ring must be chosen. The main interest is to avoid the cumulative effect of the classical k-function. Note that the cross k-function of points A around B is not necessarily the same as the cross k-function of points B around A. This function is maturing, it works as expected (unit tests) but will probably be modified in the future releases (gain speed, advanced features, etc.).

## Examples

# \donttest{
data(main_network_mtl)
data(mtl_libraries)
data(mtl_theatres)
result <- cross_kfunctions(main_network_mtl, mtl_theatres, mtl_libraries,
start = 0, end = 2500, step = 10, width = 250,
nsim = 50, conf_int = 0.05, digits = 2,
tol = 0.1, agg = NULL, verbose = FALSE)
# }