heatkernelapprox {spatstat.linnet} | R Documentation |
Approximation to Heat Kernel on Linear Network at Source Point
Description
Computes an approximation to the value of the heat kernel on a network evaluated at its source location.
Usage
heatkernelapprox(X, sigma, nmax = 20, floored=TRUE)
Arguments
X |
Point pattern on a linear network (object of class |
sigma |
Numeric. Bandwidth for kernel. |
nmax |
Number of terms to be used in the sum. |
floored |
Logical. If |
Details
For each point X[i]
in the pattern X
, this algorithm computes an
approximation to the value of the heat kernel with source point
X[i]
evaluated at the same location.
The heat kernel for a source location
evaluated at location
can be expressed as an infinite sum of contributions
from all possible paths from
to
.
This algorithm applies to the special case
where the source
point and the query point are the same.
The algorithm computes an approximation to
by taking only the contributions from paths
which (a) remain in the line segment containing the point
and
(b) visit a vertex at most
nmax
times.
Value
Numeric vector with one entry for each point in X
.
Author(s)
Greg McSwiggan and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
See Also
Examples
X <- runiflpp(3,simplenet)
heatkernelapprox(X, 0.5)