Computes an approximation to the value of the heat kernel on a network evaluated at its source location.
heatkernelapprox(X, sigma, nmax = 20, floored=TRUE)Point pattern on a linear network (object of class "lpp").
Numeric. Bandwidth for kernel.
Number of terms to be used in the sum.
Logical. If TRUE, all values are constrained to be
greater than or equal to \(1/L\) where \(L\) is the total
length of the network. This the exact value of the heat kernel
when the bandwidth is infinite.
Numeric vector with one entry for each point in X.
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 \(\kappa(u,v)\) for a source location \(u\) evaluated at location \(v\) can be expressed as an infinite sum of contributions from all possible paths from \(u\) to \(v\). This algorithm applies to the special case \(u=v\) where the source point and the query point are the same.
The algorithm computes an approximation to \(\kappa(u,u)\)
by taking only the contributions from paths
which (a) remain in the line segment containing the point \(u\) and
(b) visit a vertex at most nmax times.
# NOT RUN {
X <- runiflpp(3,simplenet)
heatkernelapprox(X, 0.5)
# }
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