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POLapply slows with increasing loops
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Introduction I've been writing a program that processes some Raw data and then passes it through several statistical processes. All in all it uses several instances of "lapply". For example: in one part of the script I use a function known as Maxstat (note the function only takes data either as data.frame or data.table - will not accept a matrix). ** <ul> <li>REPRODUCIBLE SAMPLE below - just copy all sample data, and two parts of the code</li> </ul> ** Sample data: The first two columns are neccesary. This is the large data sample seen below --> please read on after the sample <pre><code>Genedata <- structure(list(time = c(120, 120, 28.96, 119.21, 59.53, 68.81, 82.29, 110.82, 65.88, 84.13, 16.47, 89.75, 76.07, 67.82, 52.24, 64.1, 55.13, 57.79, 50.1, 43.79, 30.27, 3.64, 36.59, 20.02, 118.58, 55.33, 120, 120, 120, 106.94, 11.7, 28.79, 26.82, 52.5, 24.03, 88.99, 102.44, 33.73, 85.28, 26.53, 37.31, 86.43, 55.92, 70.65, 76.04, 79.13, 83.99, 80.25, 40.6, 95.37, 31.06, 37.31, 22.02, 63.25, 34.09, 52.14, 66.04, 59.96, 47.86, 58.45, 45.99, 60.42, 37.67, 15.71, 39.25, 49.87, 25.24, 44.97, 35.9, 26.66, 36.78, 41.52, 22.22, 33.2, 39.68, 25.61, 83.99, 15.05, 8.38, 18.18, 27.15, 24.26, 105.17, 11.76, 70.45, 95.07, 112.33, 27.51, 45.92, 54.04, 103.98, 6.11, 99.51, 20.44, 76.6, 10.02, 41.45, 96.26, 85.61, 78.87, 22.25, 74.53, 59.07, 47.8, 5.68, 79.39, 74.07, 50.76, 67.82, 70.84, 50.59, 34.58, 38.72, 54.9, 67.92, 58.45, 59.34, 54.54, 19.03, 26.26, 52.86, 32.05, 55.95, 56.67, 50.43, 4.24, 49.11, 49.57, 50.49, 63.05, 49.24, 0.92, 31.36, 40.3, 116.64, 31.92, 19.98, 24.62, 18.54, 120, 17.62, 5.32, 2.36, 5.72, 15.28, 95.07, 4.96, 28.89, 3.25, 0.92, 18.77, 57.73, 14.39, 5.12, 4.99, 33.17, 50.53, 5.72, 8.02, 34.02, 1.44, 36.95, 60.75, 37.44, 23.07, 19.85, 31.85, 8.61, 42.27, 15.25, 14.56, 9.96, 8.94, 32.67, 2.07, 22.78, 22.35), cens = c(0L, 0L, NA, 0L, 0L, 1L, 0L, 0L, NA, 0L, NA, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, NA, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, NA, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, NA, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, NA, 1L, 1L, 1L, 0L, 0L, 0L, NA, 0L, NA, NA, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, NA, NA, 0L, 0L, 0L, 0L, 1L, NA, 0L, 1L, 0L, 0L, 0L, NA, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, NA, 1L, 1L, 1L, 1L, NA, 0L, NA, 1L, 1L, 0L, 1L, 0L, 1L, 1L, NA, 1L, 0L, 1L, 1L, 0L)), .Names = c("time", "cens"), class = "data.frame", row.names = c(NA, -177L)) </code></pre> To generate a larger set -> First define the sample above as Genedata then the additional code (to change variable/column length, just change 1000 to 5000 or 50000 etc. <pre><code> data <- replicate(1000, abs(rnorm(177))) Genedata <- data.frame(Genedata, data) library(data.table) Genedata2 <- data.table(Genedata) </code></pre> Then to calculate <pre><code> #Calculating Maxstat library(maxstat) maxstat.genes <- as.list( names(Genedata) )[-c(1:3)] #generate a list of column numbers system.time(maxstat.estimate <-lapply( maxstat.genes, function (x) {maxstat.test(Surv(time, cens) ~ get (x), data=Genedata2, smethod="LogRank", pmethod="Lau94")})) </code></pre> I originally planned on using the for statement, as i'm familiar with it having a background in python. However, research has told me that using apply should be faster. I also originally used data.frame, but switched to data.table as someone suggested this should be better for performance. However, it seems there is still a significant problem with processing large datasets. Below is an explanation of why. Running 25 variables <pre><code> user system elapsed 0.04 0.00 0.05 </code></pre> Running 1000 variables <pre><code> user system elapsed 6.54 0.00 6.57 </code></pre> Running 5000 variables <pre><code> user system elapsed 132.89 0.00 133.02 </code></pre> As you can see, the processing speed is not linear but rather begins to fall off at a staggering rate. Given that the dataset is 43000 variables long, I can only guess that it would take on the order of hours. Interestingly, if i manually divided the tables into small sets, and ran them individually, it would be faster. I think it has something to do with copying increasingly larger data, but I' not sure how this could be fixed. I already tried the data.table and lapply. Any suggestions? Update 1: Added sample data. Note to reproduce a larger dataset. You can copy columns 4 onwards and paste. Rows can also be copied down. Should work as far as i know. Update 2: Rprof on 1000 variables <pre><code>> Rprof(NULL) > summaryRprof() $by.self self.time self.pct total.time total.pct terms.formula 0.50 15.82 0.50 15.82 eval 0.34 10.76 1.92 60.76 Surv 0.12 3.80 0.20 6.33 .deparseOpts 0.12 3.80 0.18 5.70 deparse 0.08 2.53 0.32 10.13 na.omit.data.frame 0.08 2.53 0.30 9.49 lapply 0.06 1.90 3.16 100.00 maxstat.test 0.06 1.90 3.16 100.00 maxstat.test.data.frame 0.06 1.90 3.10 98.10 model.frame.default 0.06 1.90 1.68 53.16 cmaxstat 0.06 1.90 0.38 12.03 match.arg 0.06 1.90 0.30 9.49 ifelse 0.06 1.90 0.06 1.90 is.matrix 0.06 1.90 0.06 1.90 length 0.06 1.90 0.06 1.90 match 0.06 1.90 0.06 1.90 pmatch 0.06 1.90 0.06 1.90 FUN 0.04 1.27 3.16 100.00 maxstat 0.04 1.27 0.90 28.48 terms 0.04 1.27 0.62 19.62 [.data.frame 0.04 1.27 0.20 6.33 order 0.04 1.27 0.08 2.53 [.formula 0.04 1.27 0.06 1.90 [.Surv 0.04 1.27 0.06 1.90 attr.all.equal 0.04 1.27 0.06 1.90 makepredictcall 0.04 1.27 0.06 1.90 unique 0.04 1.27 0.06 1.90 unlist 0.04 1.27 0.06 1.90 <Anonymous> 0.04 1.27 0.04 1.27 is.data.frame 0.04 1.27 0.04 1.27 names 0.04 1.27 0.04 1.27 NextMethod 0.04 1.27 0.04 1.27 sum 0.04 1.27 0.04 1.27 model.frame 0.02 0.63 1.70 53.80 na.omit 0.02 0.63 0.32 10.13 [ 0.02 0.63 0.30 9.49 cscores 0.02 0.63 0.28 8.86 cscores.Surv 0.02 0.63 0.26 8.23 all.equal 0.02 0.63 0.14 4.43 all.equal.numeric 0.02 0.63 0.12 3.80 paste 0.02 0.63 0.12 3.80 [[ 0.02 0.63 0.08 2.53 sort 0.02 0.63 0.08 2.53 [[.data.frame 0.02 0.63 0.06 1.90 sort.int 0.02 0.63 0.06 1.90 as.list 0.02 0.63 0.04 1.27 as.vector 0.02 0.63 0.04 1.27 get 0.02 0.63 0.04 1.27 - 0.02 0.63 0.02 0.63 $<- 0.02 0.63 0.02 0.63 / 0.02 0.63 0.02 0.63 anyDuplicated 0.02 0.63 0.02 0.63 as.environment 0.02 0.63 0.02 0.63 as.list.data.frame 0.02 0.63 0.02 0.63 attr 0.02 0.63 0.02 0.63 attr<- 0.02 0.63 0.02 0.63 c 0.02 0.63 0.02 0.63 cbind 0.02 0.63 0.02 0.63 data.class 0.02 0.63 0.02 0.63 is.array 0.02 0.63 0.02 0.63 makepredictcall.default 0.02 0.63 0.02 0.63 mode 0.02 0.63 0.02 0.63 pLausen94 0.02 0.63 0.02 0.63 sys.function 0.02 0.63 0.02 0.63 $by.total total.time total.pct self.time self.pct lapply 3.16 100.00 0.06 1.90 maxstat.test 3.16 100.00 0.06 1.90 FUN 3.16 100.00 0.04 1.27 maxstat.test.data.frame 3.10 98.10 0.06 1.90 eval 1.92 60.76 0.34 10.76 model.frame 1.70 53.80 0.02 0.63 model.frame.default 1.68 53.16 0.06 1.90 maxstat 0.90 28.48 0.04 1.27 do.call 0.90 28.48 0.00 0.00 terms 0.62 19.62 0.04 1.27 terms.formula 0.50 15.82 0.50 15.82 cmaxstat 0.38 12.03 0.06 1.90 sapply 0.34 10.76 0.00 0.00 deparse 0.32 10.13 0.08 2.53 na.omit 0.32 10.13 0.02 0.63 na.omit.data.frame 0.30 9.49 0.08 2.53 match.arg 0.30 9.49 0.06 1.90 [ 0.30 9.49 0.02 0.63 cscores 0.28 8.86 0.02 0.63 cscores.Surv 0.26 8.23 0.02 0.63 Surv 0.20 6.33 0.12 3.80 [.data.frame 0.20 6.33 0.04 1.27 .deparseOpts 0.18 5.70 0.12 3.80 all.equal 0.14 4.43 0.02 0.63 all.equal.numeric 0.12 3.80 0.02 0.63 paste 0.12 3.80 0.02 0.63 order 0.08 2.53 0.04 1.27 [[ 0.08 2.53 0.02 0.63 sort 0.08 2.53 0.02 0.63 ifelse 0.06 1.90 0.06 1.90 is.matrix 0.06 1.90 0.06 1.90 length 0.06 1.90 0.06 1.90 match 0.06 1.90 0.06 1.90 pmatch 0.06 1.90 0.06 1.90 [.formula 0.06 1.90 0.04 1.27 [.Surv 0.06 1.90 0.04 1.27 attr.all.equal 0.06 1.90 0.04 1.27 makepredictcall 0.06 1.90 0.04 1.27 unique 0.06 1.90 0.04 1.27 unlist 0.06 1.90 0.04 1.27 [[.data.frame 0.06 1.90 0.02 0.63 sort.int 0.06 1.90 0.02 0.63 %in% 0.06 1.90 0.00 0.00 simplify2array 0.06 1.90 0.00 0.00 sort.default 0.06 1.90 0.00 0.00 <Anonymous> 0.04 1.27 0.04 1.27 is.data.frame 0.04 1.27 0.04 1.27 names 0.04 1.27 0.04 1.27 NextMethod 0.04 1.27 0.04 1.27 sum 0.04 1.27 0.04 1.27 as.list 0.04 1.27 0.02 0.63 as.vector 0.04 1.27 0.02 0.63 get 0.04 1.27 0.02 0.63 - 0.02 0.63 0.02 0.63 $<- 0.02 0.63 0.02 0.63 / 0.02 0.63 0.02 0.63 anyDuplicated 0.02 0.63 0.02 0.63 as.environment 0.02 0.63 0.02 0.63 as.list.data.frame 0.02 0.63 0.02 0.63 attr 0.02 0.63 0.02 0.63 attr<- 0.02 0.63 0.02 0.63 c 0.02 0.63 0.02 0.63 cbind 0.02 0.63 0.02 0.63 data.class 0.02 0.63 0.02 0.63 is.array 0.02 0.63 0.02 0.63 makepredictcall.default 0.02 0.63 0.02 0.63 mode 0.02 0.63 0.02 0.63 pLausen94 0.02 0.63 0.02 0.63 sys.function 0.02 0.63 0.02 0.63 formals 0.02 0.63 0.00 0.00 is.na 0.02 0.63 0.00 0.00 is.na.Surv 0.02 0.63 0.00 0.00 rowSums 0.02 0.63 0.00 0.00 $sample.interval [1] 0.02 $sampling.time [1] 3.16 </code></pre> Update 3 - Rprof on 5000 variables - as you can see its not linear increase <pre><code>> Rprof(NULL) > summaryRprof() $by.self self.time self.pct total.time total.pct eval 11.28 32.83 23.40 68.10 terms.formula 11.00 32.01 11.08 32.25 model.frame.default 0.68 1.98 22.38 65.13 deparse 0.68 1.98 1.70 4.95 cmaxstat 0.46 1.34 2.38 6.93 .deparseOpts 0.44 1.28 0.74 2.15 na.omit.data.frame 0.40 1.16 1.74 5.06 [.data.frame 0.36 1.05 1.06 3.08 maxstat.test.data.frame 0.32 0.93 34.16 99.42 pmatch 0.32 0.93 0.34 0.99 match 0.28 0.81 0.60 1.75 NextMethod 0.28 0.81 0.28 0.81 na.omit 0.26 0.76 2.00 5.82 Surv 0.26 0.76 0.54 1.57 get 0.26 0.76 0.28 0.81 unique 0.24 0.70 0.46 1.34 makepredictcall 0.24 0.70 0.36 1.05 order 0.24 0.70 0.34 0.99 match.arg 0.22 0.64 1.26 3.67 [.Surv 0.22 0.64 0.40 1.16 lapply 0.20 0.58 34.36 100.00 paste 0.20 0.58 0.90 2.62 maxstat 0.18 0.52 4.50 13.10 [ 0.18 0.52 1.54 4.48 cscores 0.18 0.52 1.26 3.67 $<- 0.18 0.52 0.18 0.52 terms 0.16 0.47 11.46 33.35 sort.int 0.16 0.47 0.46 1.34 cbind 0.16 0.47 0.16 0.47 is.matrix 0.16 0.47 0.16 0.47 length 0.16 0.47 0.16 0.47 [[.data.frame 0.14 0.41 0.34 0.99 FUN 0.12 0.35 34.26 99.71 all.equal.numeric 0.12 0.35 0.24 0.70 c 0.12 0.35 0.12 0.35 ifelse 0.12 0.35 0.12 0.35 is.data.frame 0.12 0.35 0.12 0.35 makepredictcall.default 0.12 0.35 0.12 0.35 names 0.12 0.35 0.12 0.35 cscores.Surv 0.10 0.29 1.08 3.14 %in% 0.10 0.29 0.70 2.04 all.equal 0.10 0.29 0.40 1.16 mode 0.10 0.29 0.34 0.99 unlist 0.10 0.29 0.20 0.58 unique.default 0.10 0.29 0.16 0.47 as.list 0.10 0.29 0.10 0.29 dim 0.10 0.29 0.10 0.29 is.factor 0.10 0.29 0.10 0.29 parent.frame 0.10 0.29 0.10 0.29 model.frame 0.08 0.23 22.46 65.37 is.na 0.08 0.23 0.18 0.52 duplicated 0.08 0.23 0.12 0.35 maxstat.test 0.06 0.17 34.22 99.59 sapply 0.06 0.17 1.72 5.01 sort 0.06 0.17 0.52 1.51 pLausen94 0.06 0.17 0.22 0.64 anyDuplicated 0.06 0.17 0.10 0.29 which 0.06 0.17 0.10 0.29 ncol 0.06 0.17 0.08 0.23 rowSums 0.06 0.17 0.08 0.23 * 0.06 0.17 0.06 0.17 / 0.06 0.17 0.06 0.17 environment 0.06 0.17 0.06 0.17 is.ordered 0.06 0.17 0.06 0.17 list 0.06 0.17 0.06 0.17 do.call 0.04 0.12 4.56 13.27 [[ 0.04 0.12 0.38 1.11 attr.all.equal 0.04 0.12 0.10 0.29 formals 0.04 0.12 0.08 0.23 ! 0.04 0.12 0.04 0.12 .Call 0.04 0.12 0.04 0.12 <Anonymous> 0.04 0.12 0.04 0.12 anyDuplicated.default 0.04 0.12 0.04 0.12 duplicated.default 0.04 0.12 0.04 0.12 floor 0.04 0.12 0.04 0.12 is.array 0.04 0.12 0.04 0.12 match.fun 0.04 0.12 0.04 0.12 options 0.04 0.12 0.04 0.12 pnorm 0.04 0.12 0.04 0.12 seq.default 0.04 0.12 0.04 0.12 sys.call 0.04 0.12 0.04 0.12 simplify2array 0.02 0.06 0.52 1.51 [.formula 0.02 0.06 0.14 0.41 is.na.Surv 0.02 0.06 0.10 0.29 sys.function 0.02 0.06 0.04 0.12 & 0.02 0.06 0.02 0.06 .row_names_info 0.02 0.06 0.02 0.06 ^ 0.02 0.06 0.02 0.06 < 0.02 0.06 0.02 0.06 <= 0.02 0.06 0.02 0.06 == 0.02 0.06 0.02 0.06 as.environment 0.02 0.06 0.02 0.06 attr<- 0.02 0.06 0.02 0.06 baseenv 0.02 0.06 0.02 0.06 data.class 0.02 0.06 0.02 0.06 is.numeric 0.02 0.06 0.02 0.06 sqrt 0.02 0.06 0.02 0.06 sum 0.02 0.06 0.02 0.06 sys.parent 0.02 0.06 0.02 0.06 $by.total total.time total.pct self.time self.pct lapply 34.36 100.00 0.20 0.58 FUN 34.26 99.71 0.12 0.35 maxstat.test 34.22 99.59 0.06 0.17 maxstat.test.data.frame 34.16 99.42 0.32 0.93 eval 23.40 68.10 11.28 32.83 model.frame 22.46 65.37 0.08 0.23 model.frame.default 22.38 65.13 0.68 1.98 terms 11.46 33.35 0.16 0.47 terms.formula 11.08 32.25 11.00 32.01 do.call 4.56 13.27 0.04 0.12 maxstat 4.50 13.10 0.18 0.52 cmaxstat 2.38 6.93 0.46 1.34 na.omit 2.00 5.82 0.26 0.76 na.omit.data.frame 1.74 5.06 0.40 1.16 sapply 1.72 5.01 0.06 0.17 deparse 1.70 4.95 0.68 1.98 [ 1.54 4.48 0.18 0.52 match.arg 1.26 3.67 0.22 0.64 cscores 1.26 3.67 0.18 0.52 cscores.Surv 1.08 3.14 0.10 0.29 [.data.frame 1.06 3.08 0.36 1.05 paste 0.90 2.62 0.20 0.58 .deparseOpts 0.74 2.15 0.44 1.28 %in% 0.70 2.04 0.10 0.29 match 0.60 1.75 0.28 0.81 Surv 0.54 1.57 0.26 0.76 sort 0.52 1.51 0.06 0.17 simplify2array 0.52 1.51 0.02 0.06 unique 0.46 1.34 0.24 0.70 sort.int 0.46 1.34 0.16 0.47 sort.default 0.46 1.34 0.00 0.00 [.Surv 0.40 1.16 0.22 0.64 all.equal 0.40 1.16 0.10 0.29 [[ 0.38 1.11 0.04 0.12 makepredictcall 0.36 1.05 0.24 0.70 pmatch 0.34 0.99 0.32 0.93 order 0.34 0.99 0.24 0.70 [[.data.frame 0.34 0.99 0.14 0.41 mode 0.34 0.99 0.10 0.29 NextMethod 0.28 0.81 0.28 0.81 get 0.28 0.81 0.26 0.76 all.equal.numeric 0.24 0.70 0.12 0.35 pLausen94 0.22 0.64 0.06 0.17 unlist 0.20 0.58 0.10 0.29 $<- 0.18 0.52 0.18 0.52 is.na 0.18 0.52 0.08 0.23 cbind 0.16 0.47 0.16 0.47 is.matrix 0.16 0.47 0.16 0.47 length 0.16 0.47 0.16 0.47 unique.default 0.16 0.47 0.10 0.29 [.formula 0.14 0.41 0.02 0.06 c 0.12 0.35 0.12 0.35 ifelse 0.12 0.35 0.12 0.35 is.data.frame 0.12 0.35 0.12 0.35 makepredictcall.default 0.12 0.35 0.12 0.35 names 0.12 0.35 0.12 0.35 duplicated 0.12 0.35 0.08 0.23 as.list 0.10 0.29 0.10 0.29 dim 0.10 0.29 0.10 0.29 is.factor 0.10 0.29 0.10 0.29 parent.frame 0.10 0.29 0.10 0.29 anyDuplicated 0.10 0.29 0.06 0.17 which 0.10 0.29 0.06 0.17 attr.all.equal 0.10 0.29 0.04 0.12 is.na.Surv 0.10 0.29 0.02 0.06 ncol 0.08 0.23 0.06 0.17 rowSums 0.08 0.23 0.06 0.17 formals 0.08 0.23 0.04 0.12 as.vector 0.08 0.23 0.00 0.00 * 0.06 0.17 0.06 0.17 / 0.06 0.17 0.06 0.17 environment 0.06 0.17 0.06 0.17 is.ordered 0.06 0.17 0.06 0.17 list 0.06 0.17 0.06 0.17 nrow 0.06 0.17 0.00 0.00 ! 0.04 0.12 0.04 0.12 .Call 0.04 0.12 0.04 0.12 <Anonymous> 0.04 0.12 0.04 0.12 anyDuplicated.default 0.04 0.12 0.04 0.12 duplicated.default 0.04 0.12 0.04 0.12 floor 0.04 0.12 0.04 0.12 is.array 0.04 0.12 0.04 0.12 match.fun 0.04 0.12 0.04 0.12 options 0.04 0.12 0.04 0.12 pnorm 0.04 0.12 0.04 0.12 seq.default 0.04 0.12 0.04 0.12 sys.call 0.04 0.12 0.04 0.12 sys.function 0.04 0.12 0.02 0.06 getOption 0.04 0.12 0.00 0.00 irank 0.04 0.12 0.00 0.00 seq 0.04 0.12 0.00 0.00 & 0.02 0.06 0.02 0.06 .row_names_info 0.02 0.06 0.02 0.06 ^ 0.02 0.06 0.02 0.06 < 0.02 0.06 0.02 0.06 <= 0.02 0.06 0.02 0.06 == 0.02 0.06 0.02 0.06 as.environment 0.02 0.06 0.02 0.06 attr<- 0.02 0.06 0.02 0.06 baseenv 0.02 0.06 0.02 0.06 data.class 0.02 0.06 0.02 0.06 is.numeric 0.02 0.06 0.02 0.06 sqrt 0.02 0.06 0.02 0.06 sum 0.02 0.06 0.02 0.06 sys.parent 0.02 0.06 0.02 0.06 match.call 0.02 0.06 0.00 0.00 $sample.interval [1] 0.02 $sampling.time [1] 34.36 </code></pre>
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Lapply slows with increasing loops
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