density.lpp: Kernel Estimate of Intensity on a Linear Network

Description

Estimates the intensity of a point process on a linear network by applying kernel smoothing to the point pattern data, using the equal-split continuous algorithm.

Usage

## S3 method for class 'lpp':
density(x, sigma, \dots,
        kernel="gaussian", continuous=TRUE,
        epsilon = 1e-06, verbose = TRUE, debug = FALSE, savehistory = TRUE)
## S3 method for class 'splitppx':
density(x, sigma, \dots)

Arguments

Point pattern on a linear network (object of class "lpp") to be smoothed.

sigma

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.

kernel

Character string specifying the smoothing kernel. See dkernel for possible options.

continuous

Logical value indicating whether to compute the equal-split continuous smoother (continuous=TRUE, the default) or the equal-split discontinuous smoother (continuous=FALSE).

epsilon

Tolerance value. A tail of the kernel with total mass less than epsilon may be deleted.

verbose

Logical value indicating whether to print progress reports.

debug

Logical value indicating whether to print debugging information.

savehistory

Logical value indicating whether to save the entire history of the algorithm, for the purposes of evaluating performance.

Value

Pixel image on the linear network (class "linim").

WARNING

THIS ALGORITHM CAN BE EXTREMELY SLOW for large values of sigma.

The computational complexity increases exponentially with sigma. You Have Been Warned.

Details

Kernel smoothing is applied to the points of x using one of the algorithms described in Okabe and Sugihara (2012). The result is a pixel image on the linear network (class "linim") which can be plotted.

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). This algorithm is faster, but the resulting function is not continuous.

There is also a method for split point patterns on a linear network (class "splitppx") which will return a list of pixel images.

References

Okabe, A. and Sugihara, K. (2012) Spatial analysis along networks. Wiley.

Examples

Run this code

X <- runiflpp(3, simplenet)
  D <- density(X, 0.2, verbose=FALSE)
  plot(D, style="w", main="", adjust=2)
  De <- density(X, 0.2, kernel="epanechnikov", verbose=FALSE)
  Ded <- density(X, 0.2, kernel="epanechnikov", continuous=FALSE, verbose=FALSE)

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