In atime: Asymptotic Timing

Custom Plots

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

The goal of this vignette is to demonstrate how to create custom ggplots (instead of always using the plot method). In particular, we would like to display the best fit asymptotic complexity class in the direct label, along side the expression name. We use optimal segmentation algorithms as an example.

library(data.table)
viz.data <- function(get.seg.means, data.per.seg=10, penalty=1){
  no.labels <- data.table(
    start=integer(), end=integer(), changes=integer())
  expr.list <- c(
    if(requireNamespace("changepoint"))atime::atime_grid(
      "changepoint::cpt.mean"=changepoint::cpt.mean(
        data.vec, method="PELT", penalty="Manual", pen.value=penalty)),
    if(requireNamespace("binsegRcpp"))atime::atime_grid(
      "binsegRcpp::binseg_normal"=binsegRcpp::binseg_normal(data.vec, N)),
    if(requireNamespace("fpop"))atime::atime_grid(
      "fpop::Fpop"=fpop::Fpop(data.vec, penalty)),
    if(requireNamespace("LOPART"))atime::atime_grid(
      "LOPART::LOPART"=LOPART::LOPART(data.vec, no.labels, penalty)),
    atime::atime_grid(mean=mean(data.vec)))
  atime.list <- atime::atime(
    N=2^seq(1, 20),
    setup={
      seg.means <- get.seg.means(N)
      mean.vec <- rep(seg.means, each=data.per.seg)
      set.seed(1)
      data.vec <- rnorm(data.per.seg*N, mean.vec, 0.2)
    },
    expr.list=expr.list,
    times=5)
  best.list <- atime::references_best(atime.list)
  if(require(ggplot2)){
    hline.df <- with(atime.list, data.frame(seconds.limit, unit="seconds"))
    gg <- ggplot()+
      theme_bw()+
      facet_grid(unit ~ ., scales="free")+
      geom_hline(aes(
        yintercept=seconds.limit),
        color="grey",
        data=hline.df)+
      geom_line(aes(
        N, empirical, color=expr.name),
        data=best.list$meas)+
      geom_ribbon(aes(
        N, ymin=min, ymax=max, fill=expr.name),
        data=best.list$meas[unit=="seconds"],
        alpha=0.5)+
      scale_x_log10()+
      scale_y_log10("median line, min/max band")
    if(require(directlabels)){
      gg+
        directlabels::geom_dl(aes(
          N, empirical, color=expr.name, label=expr.class),
          method="right.polygons",
          data=best.list$meas)+
        theme(legend.position="none")+
        coord_cartesian(xlim=c(2,1e7))
    }else{
      gg
    }
  }
}
viz.data(function(N.segs)rep(0:1,l=N.segs))

The plots above show some speed differences between segmentation algorithms. It is clear that LOPART and binseg algorithms are slow/quadratic in these data (ten points up, ten points down, ten points up, ...), whereas FPOP and PELT (changepoint pkg) are fast/log-linear. This is the worst case for binseg.

viz.data(function(N.segs)1:N.segs)

Results above show a more typical result: LOPART is slow/quadratic whereas others are fast/log-linear.

viz.data(function(N.segs)1:N.segs, data.per.seg=1, penalty=1e10)

Results above show a highly unusual/pathological result: FPOP and PELT are quadratic time for a data sequence which is always increasing with a large penalty.