Estimates the intensity of a point process on a linear network by applying kernel smoothing to the point pattern data.
# S3 method for lpp
density(x, sigma=NULL, …,
weights=NULL,
distance=c("path", "euclidean"),
kernel="gaussian",
continuous=TRUE,
epsilon = 1e-06, verbose = TRUE,
debug = FALSE, savehistory = TRUE,
old=FALSE)# S3 method for splitppx
density(x, sigma=NULL, …)
Point pattern on a linear network (object of class "lpp")
to be smoothed.
Smoothing bandwidth (standard deviation of the kernel)
in the same units as the spatial coordinates of x.
Arguments passed to as.mask determining the
resolution of the result.
Optional. Numeric vector of weights associated with the
points of x. Weights may be positive, negative or zero.
Character string (partially matched) specifying whether to use
a kernel based on paths in the network (distance="path", the default)
or a two-dimensional kernel (distance="euclidean").
Character string specifying the smoothing kernel.
See dkernel for possible options.
Logical value indicating whether to compute the
“equal-split continuous” smoother (continuous=TRUE, the
default) or the “equal-split discontinuous” smoother
(continuous=FALSE). Applies only when distance="path".
Tolerance value. A tail of the kernel with total mass
less than epsilon may be deleted.
Logical value indicating whether to print progress reports.
Logical value indicating whether to print debugging information.
Logical value indicating whether to save the entire history of the algorithm, for the purposes of evaluating performance.
Logical value indicating whether to use the old, very slow algorithm for the equal-split continuous estimator.
A pixel image on the linear network (object of class "linim").
Kernel smoothing is applied to the points of x
using either a kernel based on path distances in the network,
or a two-dimensional kernel.
The result is a pixel image on the linear network (class
"linim") which can be plotted.
If distance="path" (the default)
then the smoothing is performed
using a kernel based on path distances in the network, as described in
described in Okabe and Sugihara (2012) and McSwiggan et al (2016).
If continuous=TRUE (the default), smoothing is performed
using the “equal-split continuous” rule described in
Section 9.2.3 of Okabe and Sugihara (2012).
The resulting function is continuous on the linear network.
If continuous=FALSE, smoothing is performed
using the “equal-split discontinuous” rule described in
Section 9.2.2 of Okabe and Sugihara (2012). The
resulting function is not continuous.
In the default case
(where distance="path" and
continuous=TRUE and kernel="gaussian"
and old=FALSE),
computation is performed rapidly by solving the classical heat equation
on the network, as described in McSwiggan et al (2016).
Computational time is short, but increases quadratically
with sigma.
The arguments epsilon,debug,verbose,savehistory are ignored.
In all other cases, computation is performed by path-tracing
as described in Okabe and Sugihara (2012);
computation can be extremely slow, and time
increases exponentially with sigma.
If distance="euclidean", the smoothing is performed
using a two-dimensional kernel. The arguments are passed to
densityQuick.lpp to perform the computation.
See the help for densityQuick.lpp for further details.
There is also a method for split point patterns on a linear network
(class "splitppx") which will return a list of pixel images.
McSwiggan, G., Baddeley, A. and Nair, G. (2016) Kernel density estimation on a linear network. Scandinavian Journal of Statistics 44, 324--345.
Okabe, A. and Sugihara, K. (2012) Spatial analysis along networks. Wiley.
# NOT RUN {
X <- runiflpp(3, simplenet)
D <- density(X, 0.2, verbose=FALSE)
plot(D, style="w", main="", adjust=2)
Dw <- density(X, 0.2, weights=c(1,2,-1), verbose=FALSE)
De <- density(X, 0.2, kernel="epanechnikov", verbose=FALSE)
Ded <- density(X, 0.2, kernel="epanechnikov", continuous=FALSE, verbose=FALSE)
# }
Run the code above in your browser using DataLab