Donut-shaped 2-D target

A rotationally symmetric annulus on \(\mathbb{R}^2\), with density $$f(x) \propto \exp\!\left(-\tfrac{(\Vert x \Vert - r_0)^2}{2 \sigma^2}\right).$$ Numerical integration in polar coordinates fixes the normaliser; the returned target exposes a normalised log_density.

Usage

donut_target(r0 = 2.5, sigma = 0.5, with_samples = FALSE, n = 2000L, seed = 1L)

Arguments

r0

Centre radius of the annulus.

sigma

Annulus width.

with_samples

If TRUE, attach n exact samples via polar change-of-variables and a one-dimensional rejection step.

n

Number of samples to attach when with_samples = TRUE.

seed

Optional integer seed used when drawing the samples.

Value

A gmm_target in dimension 2.

See also

Other targets: banana_target(), epanechnikov_target(), gmm_target_from_samples(), maxent_target(), mixture_target()

Examples

d <- donut_target()
d
#> <gmm_target>: "donut" in p = 2 dimensions
#>   log_density : supplied
#>   samples     : <absent>
#>   normalised  : TRUE
#>   log Z(f)    : 0