cir_gaps {sphunif}

Circular gaps

Description

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

\Theta_{(2)} - \Theta_{(1)},\ldots,\Theta_{(n)} - \Theta_{(n - 1)}, 2\pi - \Theta_{(n)} - \Theta_{(1)},

where

0 \le \Theta_{(1)} \le \Theta_{(2)} \le \ldots \le \Theta_{(n)} \le 2\pi.

Usage

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.

Value

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

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)