Simulation from an Isotropic Spatial Kernel via Polar Coordinates
To sample points from isotropic spatial kernels
f_2(s) = f(||s||) such as siaf.powerlaw on a
bounded domain (i.e., ||s|| < \code{ub}), it is
convenient to switch to polar coordinates (r,θ),
which have a density proportional to
r f_2((r \cos(θ), r \sin(θ))) = r f(r)
(independent of the angle θ due to isotropy).
The angle is thus simply drawn uniformly in [0,2π), and
r can be sampled by the inversion method, where numeric root
finding is used for the quantiles (since the quantile function is not
available in closed form).
siaf.simulatePC(intrfr)
intrfr |
a function computing the integral of r f(r) from 0 to |
a function with arguments (n, siafpars, type, ub), which
samples n points from the spatial kernel f_2(s) within the
disc of radius ub, where siafpars and type are
passed as second and third argument to intrfr.
The environment of the returned function will be the caller's environment.
Sebastian Meyer
simfun <- siaf.powerlaw()$simulate ## is internally generated as siaf.simulatePC(intrfr.powerlaw) set.seed(1) simfun(n=10, siafpars=log(c(sigma=1, d=2)), ub=5)
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