Fig. 1
Empirical computing times for the Lomb-Scargle periodogram (LSP) for 2D time series of varying length, using different R-based routines on a 2.5GHZ i5 CPU. All time series featured 50 % randomly selected missing observations, so that the reported sample sizes are half the series’ lengths. “ctmm” corresponds to our new, fast algorithm. “lomb” corresponds to the implementation in the lomb R-package [22], “cts” is from [34], and “nlts” is from [35]. The steeper slope of the “lomb”, “cts”, and “nlts” curves is due to these being based on a O(N 2) algorithm, whereas “ctmm” is based on a O(N log N) algorithm (see main text) and therefore becomes increasingly faster than other R-based alternatives as the sample size increases. The different intercepts for “lomb”, “cts”, and “nlts” indicate a change in per-iteration efficiency across implementations of the same algorithm