cir_gaps function

Circular gaps

Computation of the circular gaps of an angular sample $\Theta_1,\ldots,\Theta_n$ on $[0, 2\pi)$, defined as [REMOVE_ME]$\Theta_{(2)} - \Theta_{(1)},\ldots,\Theta_{(n)} - \Theta_{(n - 1)},2\pi - \Theta_{(n)} - \Theta_{(1)}, [REMOVE_ME_2]$

where [REMOVE_ME]$0 \le \Theta_{(1)} \le \Theta_{(2)} \le \ldots \le\Theta_{(n)} \le 2\pi. [REMOVE_ME_2]$

cir_gaps(Theta, sorted = FALSE)

Arguments

• Theta: a matrix of size c(n, M) with M samples of size n of circular data on $[0, 2\pi)$. Must not contain NA's.
• sorted: are the columns of Theta sorted increasingly? If TRUE, performance is improved. If FALSE (default), each column of Theta is sorted internally.

Returns

A matrix of size c(n, M) containing the n circular gaps for each of the M circular samples.

Description

Computation of the circular gaps of an angular sample $\Theta_1,\ldots,\Theta_n$ on $[0, 2\pi)$, defined as

where

Warning

Be careful on avoiding the next bad usages of cir_gaps, which will produce spurious results:

• The entries of Theta are not in $[0, 2\pi)$.
• Theta is not sorted increasingly when data_sorted = TRUE.

Examples

Theta <- cbind(c(pi, 0, 3 * pi / 2), c(0, 3 * pi / 2, pi), c(5, 3, 1))
cir_gaps(Theta)