polykde (version 1.1.7)

r_path_s1r: Samplers of one-dimensional modes of variation for polyspherical data

Description

Functions for sampling data on \((\mathcal{S}^d)^r\), for \(d=1,2\), using one-dimensional modes of variation.

Usage

r_path_s1r(n, r, alpha = runif(r, -pi, pi), k = sample(-2:2, size = r,
  replace = TRUE), sigma = 0.25, angles = FALSE)
r_path_s2r(n, r, t = 0, c = 1, Theta = t(rotasym::r_unif_sphere(n = r, p
  = 3)), kappa = 0, sigma = 0.25, spiral = FALSE)

Value

An array of size c(n, d, r) with samples on \((\mathcal{S}^d)^r\). If angles = TRUE for r_path_s1r, then a matrix of size c(n ,r) with angles is returned.

Arguments

n

sample size.

r

number of spheres in the polysphere \((\mathcal{S}^d)^r\).

alpha

a vector of size r valued in \([-\pi,\pi)\) with the initial angles for the linear trend. Chosen at random by default.

k

a vector of size r with the integer slopes defining the angular linear trend. Chosen at random by default.

sigma

standard deviation of the noise about the one-dimensional mode of variation. Defaults to 0.25.

angles

return angles in \([-\pi, \pi)\)? Defaults to FALSE.

t

latitude, with respect to Theta, of the small circle. Defaults to 0 (equator).

c

Clélie curve parameter, changing the spiral wrappings. Defaults to 1.

Theta

a matrix of size c(3, r) giving the north poles for \(\mathcal{S}^2\). Useful for rotating the sample. Chosen at random by default.

kappa

concentration von Mises--Fisher parameter for longitudes in small circles. Defaults to 0 (uniform).

spiral

consider a spiral (or, more precisely, a Clélie curve) instead of a small circle? Defaults to FALSE.

Examples

# Straight trends on (S^1)^2
n <- 100
samp_1 <- r_path_s1r(n = n, r = 2, k = c(1, 2), angles = TRUE)
plot(samp_1, xlim = c(-pi, pi), ylim = c(-pi, pi), col = rainbow(n),
     axes = FALSE, xlab = "", ylab = "", pch = 16)
sdetorus::torusAxis()

# Straight trends on (S^1)^3
n <- 100
samp_2 <- r_path_s1r(n = n, r = 3, angles = TRUE)
pairs(samp_2, xlim = c(-pi, pi), ylim = c(-pi, pi), col = rainbow(n),
      pch = 16)
sdetorus::torusAxis()
scatterplot3d::scatterplot3d(
  samp_2, xlim = c(-pi, pi), ylim = c(-pi, pi), zlim = c(-pi, pi),
  xlab = "", ylab = "", zlab = "", color = rainbow(n), pch = 16
)

# Small-circle trends on (S^2)^2
n <- 100
samp_3 <- r_path_s2r(n = n, r = 2, sigma = 0.1, kappa = 5)
old_par <- par(mfrow = c(1, 2))
scatterplot3d::scatterplot3d(
  samp_3[, , 1], xlim = c(-1, 1), ylim = c(-1, 1), zlim = c(-1, 1),
  xlab = "", ylab = "", zlab = "", color = rainbow(n), pch = 16
)
scatterplot3d::scatterplot3d(
  samp_3[, , 2], xlim = c(-1, 1), ylim = c(-1, 1), zlim = c(-1, 1),
  xlab = "", ylab = "", zlab = "", color = rainbow(n), pch = 16
)
par(old_par)

# Spiral trends on (S^2)^2
n <- 100
samp_4 <- r_path_s2r(n = n, r = 2, c = 3, spiral = TRUE, sigma = 0.01)
old_par <- par(mfrow = c(1, 2))
scatterplot3d::scatterplot3d(
  samp_4[, , 1], xlim = c(-1, 1), ylim = c(-1, 1), zlim = c(-1, 1),
  xlab = "", ylab = "", zlab = "", color = rainbow(n), pch = 16
)
scatterplot3d::scatterplot3d(
  samp_4[, , 2], xlim = c(-1, 1), ylim = c(-1, 1), zlim = c(-1, 1),
  xlab = "", ylab = "", zlab = "", color = rainbow(n), pch = 16
)
par(old_par)