torus_dist {ridgetorus}

Toroidal distances

Description

Computation of distances on [-\pi, \pi)^d, d\geq 1, between two sets of observations.

Usage

torus_dist(x, y, squared = FALSE)

Arguments

x

a matrix of size c(nx, d) with angles on [-\pi, \pi).

y

either a matrix with the same size as x or a vector of size nx.

squared

return the squared distance? Defaults to FALSE.

Details

The maximal distance on [-\pi, \pi)^d is \sqrt{d}\pi.

Value

A vector of size nx with the distances between the observations of x and y.

Examples

# Illustration of torus distances
n <- 10
x <- matrix(runif(2 * n, -pi, pi), nrow = n, ncol = 2)
y <- c(pi / 2, pi / 3)
col <- rainbow(n)
plot(x, xlim = c(-pi, pi), ylim = c(-pi, pi), axes = FALSE, col = col,
     xlab = expression(theta[1]), ylab = expression(theta[2]), pch = 16)
sdetorus::torusAxis()
points(y[1], y[2], col = 1, pch = 17)
for (i in 1:n) {

  sdetorus::linesTorus(x = c(x[i, 1], y[1]),
                       y = c(x[i, 2], y[2]), lty = 2, col = col[i])

}
text(x = x, labels = sprintf("%.2f", torus_dist(x, y)), col = col, pos = 1)