In hrvg/statisticalRoughness: Estimation of roughness exponents across scale for large areas

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 6, 
  fig.height = 6
)

Introduction

In statisticalRoughness, scale factorization is handled by the function get_all_R_L which returns a list with the values of $L$, and, for each value of $L$, the associated values of $R$. The calculation is constrained by a maximum for $L$, Lmax, which is independent of map units: it is just a number on the number line. The second parameter of get_all_R_L is the minimum number of factors that have to be found for a value of $L$ to be returned. Let's see one example:

library(statisticalRoughness)
get_all_R_L(20, 3, logfilter = FALSE)

There are r length(get_all_R_L(20, 3, logfilter = FALSE)[[1]]) numbers that have at least 3 factors between 1 and 20.

logfilter option

The logfilter = FALSE option, along with the options detailed below, handles a number of speed up factorization when $L$ becomes large.

logfilter = TRUE tries to find $n$ logarithmically spaced factors, with $n$ controlled by the len parameter Let's see it in action with Lmax = 1E4:

get_all_R_L(1e4, 55, logfilter = FALSE, len = 3)
get_all_R_L(1e4, 55, logfilter = TRUE, len = 3)

In the first case, len has no effect and r length(get_all_R_L(1e4, 55, logfilter = FALSE, len = 3)[[1]]) are returned. In the second case, only r length(get_all_R_L(1e4, 55, logfilter = TRUE, len = 3)[[1]]) logarithmically spaced values are returned.

only option

The only options speeds up the execution by looking directly at multiples of 6 and 10 if only = 610 and at multiples of 12 if only = 12. Because these numbers have the most numbers of factors at the start of the number line, their factors also do have a greater number of factors. Focusing on these only, speeds up the factorization. More details can be found here.

library(microbenchmark)
tm <- microbenchmark(
    get_all_R_L(1e4, 5, only = NULL),
    get_all_R_L(1e4, 5, only = 610),
    get_all_R_L(1e4, 5, only = 12),
    times = 10
)
ggplot2::autoplot(tm) + ggpubr::theme_pubr()

hrvg/statisticalRoughness documentation built on March 12, 2021, 4:55 p.m.