knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
The goal of this vignette is to explain how to estimate asymptotic complexity for custom units (other than the defaults, seconds and kilobytes).
The time complexity of the Dynamic Programming algorithm implemented in the PeakSegDisk package depends on the number of intervals (candidate changepoints stored). Here we compute the mean number of intervals for real Mono27ac data, and synthetic count data which are always increasing.
old.opt <- options(width=100) data(Mono27ac, package="PeakSegDisk", envir=environment()) library(data.table) penalty <- 1e6 expr.list <- c( if(requireNamespace("PeakSegDisk"))atime::atime_grid( real=PeakSegDisk::PeakSegFPOP_df(real, penalty), synthetic=PeakSegDisk::PeakSegFPOP_df(synthetic, penalty)), atime::atime_grid(mean=mean(real$count))) atime.list <- atime::atime( N=as.integer(10^seq(1, 3, by=0.5)), setup={ real <- Mono27ac$coverage[1:N] synthetic <- data.table(real)[, count := 1:.N] }, expr.list=expr.list, seconds.limit=Inf, result=TRUE) plot(atime.list)
The plot above shows the timings in both kinds of data. Clearly the algorithm is much faster in real data than in synthetic increasing data. The code below creates a new column for the mean number of intervals computing during the algorithm, then computes the best asymptotic references:
atime.list$measurements[, intervals := sapply( result, function(L)if(is.numeric(L))NA else L$loss$mean.intervals)] best.list <- atime::references_best(atime.list, more.units="intervals") plot(best.list)
Note in the code above the more.units="intervals"
argument, which
says to use the intervals column as an additional unit. The plot above
shows plots of all three units as a function of data size. It is clear
that there is a substantial difference in the number of intervals
stored by the algorithm, between real and synthetic increasing
data. From the plot above it is clear that
Exercise for the reader: to see the expected asymptotic time complexity in the last plot, re-do the previous analyses, increasing the penalty as well as the max data size N.
options(old.opt)
atime_grid
Note in the original atime
call above, the only difference between
real and synthetic is the data, so the atime_grid
function could be
used to create an expression list in this case. The advantage is that
the code below avoids the repetition of the PeakSegFPOP_df
function
call, which would be even more beneficial if there were more than two
data sets:
(data.grid.exprs <- c( if(requireNamespace("PeakSegDisk"))atime::atime_grid( list(DATA=c("real","synthetic")), PeakSegDisk=PeakSegDisk::PeakSegFPOP_df(data.list[[DATA]], penalty)), atime::atime_grid(mean=mean(data.list$real$count)))) data.grid.result <- atime::atime( N=as.integer(10^seq(1, 3, by=0.5)), setup={ real <- Mono27ac$coverage[1:N] data.list <- list( real=real, synthetic=data.table(real)[, count := 1:.N]) }, seconds.limit = Inf, expr.list=data.grid.exprs) plot(data.grid.result)
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