polykde (version 1.1.7)

r_kde_polysph: Sample from polyspherical kernel density estimator

Description

Simulates from the distribution defined by a polyspherical kernel density estimator on \(\mathcal{S}^{d_1} \times \ldots \times \mathcal{S}^{d_r}\).

Usage

r_kde_polysph(n, X, d, h, kernel = 1, kernel_type = 1, k = 10,
  intrinsic = FALSE, norm_X = FALSE)

Value

A matrix of size c(n, sum(d) + r) with the sample.

Arguments

n

sample size.

X

a matrix of size c(n, sum(d) + r) with the sample.

d

vector of size r with dimensions.

h

vector of size r with bandwidths.

kernel

kernel employed: 1 for von Mises--Fisher (default); 2 for Epanechnikov; 3 for softplus.

kernel_type

type of kernel employed: 1 for product kernel (default); 2 for spherically symmetric kernel.

k

softplus kernel parameter. Defaults to 10.0.

intrinsic

use the intrinsic distance, instead of the extrinsic-chordal distance, in the kernel? Defaults to FALSE.

norm_X

ensure a normalization of the data?

Details

The function uses r_kern_polysph to sample from the considered kernel.

Examples

# Simulated data on (S^1)^2
n <- 50
samp <- r_path_s1r(n = n, r = 2, k = c(1, 2), angles = TRUE)
plot(samp, xlim = c(-pi, pi), ylim = c(-pi, pi), col = rainbow(n),
     axes = FALSE, xlab = "", ylab = "", pch = 16, cex = 0.75)
points(torus_to_angles(r_kde_polysph(n = 10 * n, X = angles_to_torus(samp),
                                     d = c(1, 1), h = c(0.1, 0.1))),
       col = "black", pch = 16, cex = 0.2)
sdetorus::torusAxis()

# Simulated data on S^2
n <- 50
samp <- r_path_s2r(n = n, r = 1, sigma = 0.1, kappa = 5,
                   spiral = TRUE)[, , 1]
sc3d <- scatterplot3d::scatterplot3d(
  samp, xlim = c(-1, 1), ylim = c(-1, 1), zlim = c(-1, 1),
  xlab = "", ylab = "", zlab = "", color = rainbow(n), pch = 16
)
xyz <- r_kde_polysph(n = 10 * n, X = samp, d = 2, h = 0.1)
sc3d$points3d(xyz[, 1], xyz[, 2], xyz[, 3], col = "black", pch = 16,
              cex = 0.2)