| Abstract | Objectives | Installation | Functions | Usage | Plotting | Benchmarking | Testing | Resources |
|---|
R package developers currently use ad-hoc tests of asymptotic computational complexity via empirical timings of functions and visual diagnostic plots. However, there is no framework in R for systematically testing the empirical computational complexity of functions, which tends to be a problem because such a testing framework could be essential for identifying big speed gains in R code as well. In response to this, testComplexity provides a suite of functions that will be useful for testing and thereby improving the speed of various algorithms/functions in R.
- Primary objectives include quantification of runtimes for an algorithm/function (against a set of user-provided data sizes), classification of the corresponding asymptotic time complexity class it belongs to (based on the computed benchmarks) and testing for the same against an expected time complexity class for verification of empirically observed results, based upon the initial idea as staged here.
- Additionally (or as per my proposal), I thought of covering memory complexity testing as well, which in terms of resources, goes hand-in-hand when dealing with 'complexity' in Computer Science.
- Furthermore, @tdhock suggested classifying complexity for user-defined output parameters (i.e. a measure of a parameter apart from timings/memory), which would eventually make the package more flexible in terms of use-cases.
Since algorithms are used in every sphere of research, this package potentially caters to all sorts of R-users, following different fields of study. At its current state, it has been tested on algorithms pertaining to changepoint detection, sorting, constrained optimal segmentation/partitioning, plus a few common ones from base R such as substring and gregexpr.
Use devtools or remotes to fetch the package from this repository:
if(!require(devtools)) install.packages("devtools")
devtools::install_github("Anirban166/testComplexity")if(!require(remotes)) install.packages("remotes")
remotes::install_github("Anirban166/testComplexity")__________________ R Files _______________________________________ Additional Details _____________________________
testComplexity @ returns @ type @ commit-branch(es)
├──> asymptoticTimings : data.frame timings quantifier master
│ ├──> asymptoticTimeComplexityClass : ├──> string ↑ complexity classifier master
│ └──> plotTimings : └──> ggplot object ↑ plotter master/Plotfunc
│
├──> asymptoticMemoryUsage : data.frame memory-usage quantifier Memtest
│ ├──> asymptoticMemoryComplexityClass : ├──> string ↑ complexity classifier Memtest
│ └──> plotMemoryUsage : └──> ggplot object ↑ plotter Memtest/Plotfunc
│
├──> asymptoticComplexityClass : string complexity classifier Generalizedcomplexity
│ └──> asymptoticComplexityClassifier : ↑ string ↑ complexity classifier Generalizedcomplexity
│
├──> expect_complexity_class : -/- test function Testfunc
│ └──> expect_time_complexity : -/- ↑ test function Testfunc
│ ├──> expect_linear_time : -/- ↑↑ test function Testfunc
│ ├──> expect_loglinear_time : -/- ↑↑ test function Testfunc
│ └──> expect_quadratic_time : -/- ↑↑ test function Testfunc
│
└──> testthat
├──> testsfortestComplexity unit-tester All branches
├──> testsforConstrainedchangepointmodelalgos unit-tester Testfunc
└──> testsforRegularfunctions unit-tester Testfunc
____________________________________________________________________________________________________________________To get started, please check the general vignette which highlights all the features, enlists the different types of function categories existent in the package and describes the functionality offered by the underlying user-oriented functions via a set of textual elucidations with one example taken to be discussed throughout for each of them.
For a quick overview of the main functionality (obtaining quantified benchmarks and subsequently computing the time/memory complexity class), please check the examples below.
- To obtain the benchmarked timings/memory-allocations against specified data sizes, pass the required algorithm as a function of
NtoasymptoticTimings()/asymptoticMemoryUsage():
library(data.table)
# Example 1 | Applying the bubble sort algorithm to a sample of 100 elements: (expected quadratic time complexity & constant memory complexity)
bubble.sort <- function(elements.vec) {
n <- length(elements.vec)
for(i in 1:(n - 1)) {
for(j in 1:(n - i)) {
if(elements.vec[j + 1] < elements.vec[j]) {
temp <- elements.vec[j]
elements.vec[j] <- elements.vec[j + 1]
elements.vec[j + 1] <- temp
}
}
}
return(elements.vec)
}
df.bubble.time <- asymptoticTimings(bubble.sort(sample(1:100, N, replace = TRUE)), data.sizes = 10^seq(1, 3, by = 0.5))
data.table(df.bubble.time)
Timings Data sizes
1: 91902 10
2: 39402 10
3: 34701 10
4: 33101 10
5: 33201 10
---
496: 64490501 1000
497: 59799101 1000
498: 63452200 1000
499: 62807201 1000
500: 59757102 1000
df.bubble.memory <- asymptoticMemoryUsage(bubble.sort(sample(1:100, N, replace = TRUE)), data.sizes = 10^seq(1, 3, by = 0.1))
data.table(df.bubble.memory)
Memory usage Data sizes
1: 87800 10.00000
2: 2552 12.58925
3: 2552 15.84893
4: 2552 19.95262
5: 2552 25.11886
---
17: 7472 398.10717
18: 8720 501.18723
19: 10256 630.95734
20: 12224 794.32823
21: 14696 1000.00000# Example 2 | Testing PeakSegPDPA, an algorithm for constrained changepoint detection: (expected log-linear time and memory complexity)
data.vec <- rpois(N, 1)
df.PDPA.time <- asymptoticTimings(PeakSegOptimal::PeakSegPDPA(count.vec = data.vec, max.segments = 3L), data.sizes = 10^seq(1, 4, by = 0.1))
data.table(df.PDPA.time)
Timings Data sizes
1: 248701 10
2: 120302 10
3: 125701 10
4: 133301 10
5: 146500 10
---
696: 405597501 10000
697: 408335001 10000
698: 338544401 10000
699: 404081901 10000
700: 399575501 10000
df.PDPA.memory <- asymptoticMemoryUsage(PeakSegOptimal::PeakSegPDPA(count.vec = data.vec, max.segments = 3L), data.sizes = 10^seq(1, 4, by = 0.1))
data.table(df.PDPA.memory)
Memory usage Data sizes
1: 6256 10.00000
2: 7024 12.58925
3: 7432 15.84893
4: 8560 19.95262
5: 9496 25.11886
---
25: 447792 2511.88643
26: 562336 3162.27766
27: 706512 3981.07171
28: 887792 5011.87234
29: 1116240 6309.57344- To estimate the corresponding time/memory complexity class, pass the obtained data frame onto
asymptoticTimeComplexityClass()/asymptoticMemoryComplexityClass():
# Example 1 | Applying the bubble sort algorithm to a sample of 100 elements: (expected quadratic time complexity & constant memory complexity)
asymptoticTimeComplexityClass(df.bubble.time)
[1] "quadratic"
asymptoticMemoryComplexityClass(df.bubble.memory)
[1] "constant"# Example 2 | Testing PeakSegPDPA, an algorithm for constrained changepoint detection: (expected log-linear time and memory complexity)
asymptoticTimeComplexityClass(df.PDPA.time)
[1] "loglinear"
asymptoticMemoryComplexityClass(df.PDPA.memory)
[1] "loglinear"- Combine the functions if you only require the complexity class:
# Example 3 | Testing the time complexity of the quick sort algorithm: (expected log-linear time complexity)
asymptoticTimeComplexityClass(asymptoticTimings(sort(sample(1:100, N, replace = TRUE), method = "quick" , index.return = TRUE), data.sizes = 10^seq(1, 3, by = 0.5)))
[1] "loglinear"# Example 4 | Allocating a square matrix (N*N dimensions): (expected quadratic memory complexity)
asymptoticMemoryComplexityClass(asymptoticMemoryUsage(matrix(data = N:N, nrow = N, ncol = N), data.sizes = 10^seq(1, 3, by = 0.1)))
[1] "quadratic"Check this screencast for a demonstration of time complexity testing on different sorting algorithms over a test session. For more examples with functions from specific packages, please check the table with relevant contents in the testing section.
For obtaining a visual description of the trend followed between runtimes/memory-usage vs data sizes so as to diagnose the complexity result(s) (the traditional method, for visual verification say), simple plots can be crafted. They are roughly grouped into:
- Single Plots
Individual plots can be obtained by passing the data frame returned by the quantifying functions toplotTimings()/plotMemoryUsage()for time/memory cases respectively:
# Timings plot for PeakSegDP::cDPA
df <- asymptoticTimings(PeakSegDP::cDPA(rpois(N, 1), rep(1, length(rpois(N, 1))), 3L), data.sizes = 10^seq(1, 4))
plotTimings(df.time, titles = list("Timings", "PeakSegDP::cDPA"), line.color = "#ffec1b", point.color = "#ffec1b", line.size = 1, point.size = 1.5)
# Equivalent ggplot object:
df <- asymptoticTimings(PeakSegDP::cDPA(rpois(data.sizes, 1), rep(1, length(rpois(data.sizes, 1))), 3L), data.sizes = 10^seq(1, 4))
ggplot(df, aes(x = `Data sizes`, y = Timings)) + geom_point(color = ft_cols$yellow, size = 1.5) + geom_line(color = ft_cols$yellow, size = 1) + labs(x = "Data sizes", y = "Runtime (in nanoseconds)") + scale_x_log10() + scale_y_log10() + ggtitle("Timings", "PeakSegDP::cDPA") + hrbrthemes::theme_ft_rc()# Memory Usage plot for PeakSegDP::cDPA
df <- asymptoticMemoryUsage(PeakSegDP::cDPA(rpois(N, 1), rep(1, length(rpois(N, 1))), 3L), data.sizes = 10^seq(1, 6, by = 0.1))
plotMemoryUsage(df.memory, titles = list("Memory Usage", "PeakSegDP::cDPA"), line.color = "#ffec1b", point.color = "#ffec1b", line.size = 1, point.size = 2)
# Equivalent ggplot object:
ggplot(df, aes(x = `Data sizes`, y = `Memory usage`)) + geom_point(color = ft_cols$yellow, size = 2) + geom_line(color = ft_cols$yellow, size = 1) labs(x = "Data sizes", y = "Memory usage (in bytes)") + scale_x_log10() + scale_y_log10() + ggtitle("Memory Usage", "PeakSegDP::cDPA") + hrbrthemes::theme_ft_rc()
- Comparison Plots
In order to visually compare different algorithms based on the benchmarked metrics returned as a data frame by the quantifiers, one can appropriately add a third column (to help distinguish by aesthetics based on it) with a unique value for each of the data frames, combine them using anrbind()and then plot the resultant data frame using suitable aesthetics, geometry, scale, labels/titles etcetera via a ggplot:
df.substring <- asymptoticTimings(substring(paste(rep("A", N), collapse = ""), 1:N, 1:N), data.sizes = 10^seq(1, 4, by = 0.5))
asymptoticTimeComplexityClass(df.substring)
[1] "linear"
df.PeakSegPDPA <- asymptoticTimings(PeakSegOptimal::PeakSegPDPA(rpois(N, 1),rep(1, length(rpois(N, 1))), 3L), data.sizes = 10^seq(1, 4, by = 0.5), max.seconds = 1)
asymptoticTimeComplexityClass(df.PeakSegPDPA)
[1] "loglinear"
df.cDPA <- asymptoticTimings(PeakSegDP::cDPA(rpois(N, 1), rep(1, length(rpois(N, 1))), 3L), data.sizes = 10^seq(1, 4, by = 0.5), max.seconds = 5)
asymptoticTimeComplexityClass(df.cDPA)
[1] "quadratic"
df.gregexpr <- asymptoticTimings(gregexpr("a", paste(collapse = "", rep("ab", N)), perl = TRUE), data.sizes = 10^seq(1, 4, by = 0.5))
asymptoticTimeComplexityClass(df.gregexpr)
[1] "linear"
df.fpop <- asymptoticTimings(fpop::Fpop(rnorm(N), 1), data.sizes = 10^seq(1, 4, by = 0.5))
asymptoticTimeComplexityClass(df.fpop)
[1] "loglinear"
df.opart <- asymptoticTimings(opart::opart_gaussian(rnorm(N), 1), data.sizes = 10^seq(1, 4, by = 0.5))
asymptoticTimeComplexityClass(df.opart)
[1] "quadratic"
df.substring$expr = "substring"
df.PeakSegPDPA$expr = "PeakSegPDPA"
df.cDPA$expr = "cDPA"
df.gregexpr$expr = "gregexpr"
df.fpop$expr = "fpop"
df.opart$expr = "opart"
plot.df <- rbind(df.substring, df.PeakSegPDPA, df.cDPA, df.gregexpr, df.fpop, df.opart)
ggplot(plot.df, aes(x = `Data sizes`, y = Timings)) + geom_point(aes(color = expr)) + geom_line(aes(color = expr)) + labs(x = "Data sizes", y = "Runtime (in nanoseconds)") + scale_x_log10() + scale_y_log10() + ggtitle("Timings comparison plot", subtitle = "Linear vs Log-linear vs Quadratic complexities") + ggthemes::theme_pander()
Feel free to include more functions and increase the number of data sizes for a more comprehensive outlook:
- Generalized Linear Model based Plots
ggfortify, an extension ofggplot2, can be used to produce diagnostic plots for generalized linear models with the same formulae as used in the complexity classification functions:
library(ggfortify)
df <- asymptoticTimings(PeakSegDP::cDPA(rpois(N, 1), rep(1, length(rpois(N, 1))), 3L), data.sizes = 10^seq(1, 4 by = 0.1))
glm.plot.obj <- glm(Timings~`Data sizes`, data = df)
ggplot2::autoplot(stats::glm(glm.plot.obj)) + ggthemes::theme_gdocs()
Among a few options,
microbenchmark::microbenchmark()is used to compute the benchmarks to obtain the time results intestComplexity::asymptoticTimings(), for the added convenience of having the benchmarked results as a data frame plus for the precision or time scale it produces the results on. (usually in nanoseconds, as can be found from here)bench::bench_memory()is used to compute the allocated memory size in order to obtain the memory use metrics intestComplexity::asymptoticMemoryUsage().
- Functions
Current set of functions taken into consideration for testing our functionality, plus a dedicated vignette-based article for each can be found below:
| Source Package | Function | Article Link |
|---|---|---|
| base | gregexpr | Quadratic to linear transition for substring and gregexpr |
| base | substring | Quadratic to linear transition for substring and gregexpr |
| fpop | Fpop | fpop::Fpop(), a log-linear time segmentation algorithm |
| gfpop | gfpop | gfpop::gfpop(), a log-linear time algorithm for constrained changepoint detection |
| opart | gaussian | opart::gaussian(), a quadratic time optimal partioning algorithm |
| PeakSegDP | cDPA | PeakSegDP::cDPA, a quadratic time constrained dynamic programming algorithm |
| changepoint | cpt.mean | PELT and SegNeigh algorithms for changepoint::cpt.mean() |
| PeakSegOptimal | PeakSegPDPA | PeakSegOptimal::PeakSegPDPA, a log-linear time algorithm for constrained changepoint detection |
A complexity-wise ordered list with functional instances for the aforementioned set of functions can be found here.
- Unit Testing
Test cases for testComplexity functions via testthat package can be found here. - Code Coverage
Tested usingcovr::package_coverage()both locally and via codecov, with 100% coverage attained. - OS Support
Windows is the native OS this package is developed and tested on, but in addition to that, RCMD checks are run on latest versions of MacOS and Ubuntu as well.
Note that the use ofbench::bench_memory()overcomes the drawback of windows-only OS limitation for memory complexity testing as observed inGuessCompx::CompEst()since it successfully runs on other operating systems.
In addition to the readme content, the web version includes quick reference to functions plus vignettes for some use-cases. For blog posts, please check the links below:
