Abstract	Installation	Functions	Usage	Plotting	Benchmarking	Testing

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Abstract

R package developers traditionally rely on ad-hoc benchmarking (empirical timings and visual plots) to understand their code's asymptotic performance. We lack a framework for systematically testing the computational complexity of a function, which is crucial for identifying and implementing speed improvements in R code.

testComplexity attempts to address this by providing a suite of functions for asymptotic complexity classification.

Since algorithms are used in every sphere of research, this package potentially caters to all variants of R-users. It has been specifically tested on ones ranging from changepoint detection and sorting to constrained optimal segmentation and partitioning, besides common base R functions such as substring and gregexpr.

Installation

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")

Function Map

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

Usage

To get started, please check the general vignette which highlights all features, categorizes the different functions available, and describes their functionality through textual elucidations and a running example case.

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 N to asymptoticTimings()/asymptoticMemoryUsage():
  

library(data.table)
# Example 1 | Applying the bubble sort algorithm to a sample of 100 elements: (expected -> quadratic time & 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 & 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 examples with functions from selected packages, please check the table in the testing section.

Plotting

For obtaining a visual description of the trends followed between runtimes/memory-usage vs data sizes in order to visually diagnose/verify the complexity result(s), 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 to plotTimings()/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 an rbind() and then plot the resultant data frame using suitable aesthetics, geometry, scale, labels/titles etc. 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()

Including more functions (if applicable) and increasing the number of data sizes can lead to a more comprehensive outlook:

• Generalized Linear Model based Plots
  ggfortify (an extension of ggplot2) 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()

Benchmarking

• microbenchmark::microbenchmark() is used to obtain the time results in testComplexity::asymptoticTimings() for precision and convenience of having the benchmarks as a data frame.
  
• bench::bench_memory() is used to compute the size of memory allocation in testComplexity::asymptoticMemoryUsage().
  

Testing

• Functions
  The routines considered for testing the package's functionality along with a dedicated vignette-based article for each are listed 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

• Unit Testing
  Test cases for testComplexity functions that utilize testthat can be found here.
  
• Code Coverage
  Tested using covr::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. However, RCMD checks are run on latest versions of MacOS and Ubuntu as well.
  Note that the use of bench::bench_memory() overcomes the Windows-only OS limitation for memory complexity testing observed in GuessCompx::CompEst() as it successfully runs on other operating systems.