Estimate a density on the torus

Estimates a joint or conditional kernel density for circular-circular data on S1 x S1. Both components use von Mises weights.

Usage

estimate_toroidal_density(
  theta,
  phi,
  n_theta = 181,
  n_phi = 181,
  kappa_theta = 20,
  kappa_phi = 20,
  conditional = FALSE
)

Arguments

theta

First angle in radians.

phi

Second angle in radians.

n_theta

Number of theta grid points.

n_phi

Number of phi grid points.

kappa_theta

Kernel concentration for theta.

kappa_phi

Kernel concentration for phi.

conditional

If TRUE, rows are normalized to estimate f(phi | theta).

Value

A list with grids, a density matrix, a long data frame and smoothing metadata.

See also

Other toroidal dependence helpers: toroidal_flow_data(), toroidal_ridge_data(), toroidal_topography_data()

Examples

dat <- simulate_toroidal(n = 80, seed = 1)
est <- estimate_toroidal_density(dat$theta, dat$phi, n_theta = 24, n_phi = 24)
str(est$data)
#> 'data.frame':	576 obs. of  3 variables:
#>  $ theta  : num  0.131 0.393 0.654 0.916 1.178 ...
#>  $ phi    : num  0.131 0.131 0.131 0.131 0.131 ...
#>  $ density: num  3.43e-03 2.19e-03 8.09e-04 1.41e-04 9.08e-06 ...
#>  - attr(*, "out.attrs")=List of 2
#>   ..$ dim     : Named int [1:2] 24 24
#>   .. ..- attr(*, "names")= chr [1:2] "theta" "phi"
#>   ..$ dimnames:List of 2
#>   .. ..$ theta: chr [1:24] "theta=0.1308997" "theta=0.3926991" "theta=0.6544985" "theta=0.9162979" ...
#>   .. ..$ phi  : chr [1:24] "phi=0.1308997" "phi=0.3926991" "phi=0.6544985" "phi=0.9162979" ...