In this vignette we compare computational requirements (time and memory) of common operations using data.table and tidyverse functions.
Setup
library(data.table)
hostname <- system("hostname",intern=TRUE)
(max.threads <- as.integer(Sys.getenv("SLURM_JOB_CPUS_PER_NODE", "1")))
#> [1] 4
threads.vec <- unique(as.integer(c(1, ceiling(max.threads/2), max.threads)))
seconds.limit <- 1
cache.list <- list()
cache <- function(symbol, code){
cache.symb <- substitute(symbol)
suffix <- if(grepl("devel",R.version.string)){
"devel"
}else{
gsub("R version | .*", "", R.version.string)
}
cache.dir <- paste0("~/R/atime-cache-",suffix)
cache.rds <- file.path(cache.dir, paste0(cache.symb, ".RDS"))
if(file.exists(cache.rds)){
value <- readRDS(cache.rds)
}else{
to.eval <- substitute(code)
value <- eval(to.eval)
value$hostname <- hostname
if(dir.exists(cache.dir))saveRDS(value, cache.rds)
}
cache.list[[paste(cache.symb)]] <<- value
assign(paste(cache.symb), value, parent.frame())
}
aplot <- function(atime.list, my.title, xmax, max.seconds, xlab, color.vec=NULL){
best.list <- atime::references_best(atime.list)
blank.dt <- data.table(x=best.list$meas$N[1], y=max.seconds, unit="seconds")
if(require(ggplot2)){
hline.df <- with(atime.list, data.frame(seconds.limit, unit="seconds"))
gg <- ggplot()+
ggtitle(tit <<- paste(my.title,"on",hostname))+
theme_bw()+
geom_blank(aes(
x, y),
data=blank.dt)+
facet_grid(unit ~ ., scales="free")+
geom_hline(aes(
yintercept=seconds.limit),
color="grey",
data=hline.df)+
geom_line(aes(
N, empirical, color=expr.name),
data=best.list$meas)+
geom_ribbon(aes(
N, ymin=q25, ymax=q75, fill=expr.name),
data=best.list$meas[unit=="seconds"],
alpha=0.5)+
scale_x_log10(xlab)+
scale_y_log10("median line, quartiles band")
if(!is.null(color.vec)){
gg <- gg+
scale_color_manual(values=color.vec)+
scale_fill_manual(values=color.vec)
}
if(require(directlabels)){
gg+
directlabels::geom_dl(aes(
N, empirical, color=expr.name, label=expr.name),
method="right.polygons",
data=best.list$meas)+
theme(legend.position="none")+
coord_cartesian(xlim=c(NA,xmax))
}else{
gg
}
}
}Writing CSV
First we define some code which will be used in all of the writing benchmarks,
atime_write <- function(make.input.fun, fmt){
grid.args <- list(
list(THREADS=threads.vec),
"data.table::fwrite"=quote({
data.table::setDTthreads(THREADS)
data.table::fwrite(input, name.list[["fwrite"]], showProgress = FALSE)
}))
small.input <- make.input.fun(2,2)
if(requireNamespace("arrow") && is.data.frame(small.input)){
grid.args[["write_csv_arrow"]] <- quote({
arrow::set_cpu_count(THREADS)
arrow::write_csv_arrow(input, name.list[["write_csv_arrow"]])
})
}
if(requireNamespace("readr") && is.data.frame(small.input)){
##readr can't handle matrix input.
grid.args[["readr::write_csv"]] <- quote({
readr::write_csv(
input, name.list[["write_csv"]], progress = FALSE, num_threads = THREADS)
})
}
expr.list <- do.call(atime::atime_grid, grid.args)
atime::atime(
N=as.integer(10^seq(0, 6, by=0.5)),
setup={
input <- make.input.fun(N)
name.list <- list()
for(fun in c("fwrite", "write_csv", "write_csv_arrow", "write.csv")){
name.list[[fun]] <- file.path(
tempdir(), sprintf(fmt, fun, N))
}
},
seconds.limit = seconds.limit,
expr.list=expr.list,
"utils::write.csv"=utils::write.csv(input, name.list[["write.csv"]]))
}
one.thread <- function(DT)DT[grepl("utils|scan|THREADS=1$", expr.name)]
facetPlot <- function(atime.list, fun.name.vec=c("N^2","N"), N.min=1e2){
best.list <- atime::references_best(atime.list)
meas.dt <- one.thread(best.list$meas)
ref.dt <- one.thread(best.list$ref)[
fun.name %in% fun.name.vec & N >= N.min]
if(require(ggplot2)){
hline.df <- with(write.real.vary.rows, data.frame(
seconds.limit, unit="seconds"))
gg <- ggplot()+
ggtitle(paste0(tit,", asymptotic complexity"))+
theme_bw()+
facet_grid(unit ~ expr.name, scales="free")+
geom_hline(aes(
yintercept=seconds.limit),
color="grey",
data=hline.df)+
geom_line(aes(
N, reference, group=paste(expr.name, fun.name)),
linewidth=2,
data=ref.dt)+
geom_line(aes(
N, empirical, color=expr.name),
linewidth=1,
data=meas.dt)+
geom_ribbon(aes(
N, ymin=q25, ymax=q75, fill=expr.name),
data=meas.dt[unit=="seconds"],
alpha=0.5)+
scale_x_log10("N = Number of columns")+
scale_y_log10("median line, quartiles band")+
scale_color_manual(values=write.colors)+
scale_fill_manual(values=write.colors)
if(require(directlabels)){
gg+
directlabels::geom_dl(aes(
N, reference,
label.group=paste(expr.name, fun.name),
label=fun.name),
method="left.polygons",
data=ref.dt)+
theme(legend.position="none")
}else{
gg
}
}
}
if(FALSE){
RColorBrewer::display.brewer.all()
dput(RColorBrewer::brewer.pal(Inf, "Set2"))
dput(RColorBrewer::brewer.pal(Inf, "RdGy"))
}
NAME <- function(prefix, ...){
structure(
c(...)[1:length(threads.vec)],
names=sprintf("%sTHREADS=%d", prefix, threads.vec))
}
write.colors <- c(
NAME("readr::write_csv ", "#9970AB","#762A83", "#40004B"), #purple
"#5AAE61", "#1B7837", "#00441B",#green
NAME("data.table::fwrite ", "#D6604D", "#B2182B", "#67001F"),#reds
"#878787", "#4D4D4D", "#1A1A1A",#greys
NAME("write_csv_arrow ", "#BF812D", "#8C510A", "#543005"),#browns
"#35978F", "#01665E", "#003C30",#teal polars
"utils::write.csv"="deepskyblue")
(write.colors <- write.colors[names(write.colors)!=""])
#> readr::write_csv THREADS=1 readr::write_csv THREADS=2
#> "#9970AB" "#762A83"
#> readr::write_csv THREADS=4 data.table::fwrite THREADS=1
#> "#40004B" "#D6604D"
#> data.table::fwrite THREADS=2 data.table::fwrite THREADS=4
#> "#B2182B" "#67001F"
#> write_csv_arrow THREADS=1 write_csv_arrow THREADS=2
#> "#BF812D" "#8C510A"
#> write_csv_arrow THREADS=4 utils::write.csv
#> "#543005" "deepskyblue"Writing CSV with real numbers
The code below is for real numbers with a constant number of columns, and a variable number of rows.
random_real <- function(N.rows, N.cols){
set.seed(1)
matrix(rnorm(N.rows*N.cols), N.rows, N.cols)
}
cache(write.real.vary.rows, atime_write(
function(N.rows, N.cols=10)random_real(N.rows, N.cols),
"10_real_cols_%s_%d.csv"))
aplot(write.real.vary.rows, "Write CSV with 10 random normal real columns", 1e9, 1e1, "Number of rows", write.colors)
#> Loading required package: ggplot2
#> Loading required package: directlabels
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
The plot above shows that all methods are the same, except utils::write.csv memory is increasing with data size, and others are contant.
facetPlot(write.real.vary.rows)
#> Warning: Transformation introduced infinite values in continuous y-axis
The plot above shows that the memory usage of utils::write.csv is linear.
The code below writes real numbers with a constant number of rows, and a variable number of columns.
cache(write.real.vary.cols, atime_write(
function(N.cols, N.rows=10)random_real(N.rows, N.cols),
"10_real_rows_%s_%d.csv"))
aplot(write.real.vary.cols, "Write CSV with 10 random normal real rows", 1e9, 1e1, "Number of columns", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
The plot above shows that data.table::fread uses asymptotically less time and memory than the others.
Write CSV from character matrix
The code below is for a character data matrix with a constant number of columns, and a variable number of rows.
chr_mat <- function(N.rows, N.cols){
data.vec <- paste0("'quoted", c(" ", "_"), "data'")
matrix(data.vec, N.rows, N.cols)
}
cache(write.chrmat.vary.rows, atime_write(
function(N.rows,N.cols=10)chr_mat(N.rows, N.cols),
"10_chrmat_cols_%s_%d.csv"))
aplot(write.chrmat.vary.rows, "Write CSV from matrix with 10 character columns", 1e9, 1e1, "Number of rows", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
TODO
facetPlot(write.chrmat.vary.rows)
#> Warning: Transformation introduced infinite values in continuous y-axis
TODO
cache(write.chrmat.vary.cols, atime_write(
function(N.cols, N.rows=10)chr_mat(N.rows, N.cols),
"10_chrmat_rows_%s_%d.csv"))
aplot(write.chrmat.vary.cols, "Write CSV from matrix with 10 character rows", 1e9, 1e1, "Number of columns", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
TODO
facetPlot(write.chrmat.vary.cols)
#> Warning: Transformation introduced infinite values in continuous y-axis
TODO
Write CSV from character data.table
The code below is for a character data.table with a constant number of columns, and a variable number of rows.
chr_dt <- function(N.rows, N.cols){
data.table(chr_mat(N.rows, N.cols))
}
cache(write.chr.vary.rows, atime_write(
function(N.rows,N.cols=10)chr_dt(N.rows, N.cols),
"10_chr_cols_%s_%d.csv"))
aplot(write.chr.vary.rows, "Write CSV from data.table with 10 character columns", 1e9, 1e1, "Number of rows", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
The figure above is useful for comparing different functions, and shows that all have the same asymptotic time complexity class. However, we observe a difference in memory usage: linear for write.csv and constant for others. Below, we draw reference lines, so we can see the complexity class.
facetPlot(write.chr.vary.rows)
#> Warning: Transformation introduced infinite values in continuous y-axis
The figure above shows that all functions are linear time, and write.csv is linear memory. The code below is for a character data.frame with a constant number of rows, and a variable number of columns.
cache(write.chr.vary.cols, atime_write(
function(N.cols, N.rows=10)chr_dt(N.rows, N.cols),
"10_chr_rows_%s_%d.csv"))
aplot(write.chr.vary.cols, "Write CSV from data.table with 10 character rows", 1e9, 1e1, "Number of columns", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
The figure above shows that data.table::fwrite clearly has a smaller slope (linear complexity in number of columns) than the other methods (quadratic complexity), as shown in the plot below, which includes best reference lines above and below each empirical measurement asymptote.
facetPlot(write.chr.vary.cols)
#> Warning: Transformation introduced infinite values in continuous y-axis
The comparisons above show significant advantages for data.table for writing CSV data with a large number of columns: asymptotically less time and memory (linear rather than quadratic in number of columns).
Write CSV from data.table with factor columns
The code below is for factor data with a constant number of columns, and a variable number of rows.
fac_dt <- function(N.rows, N.cols){
data.vec <- factor(paste0("'quoted", c(" ", "_"), "data'"))
as.data.table(lapply(1:N.cols, function(col.i)rep(data.vec,l=N.rows)))
}
cache(write.fac.vary.rows, atime_write(
function(N.rows,N.cols=10)fac_dt(N.rows, N.cols),
"10_fac_cols_%s_%d.csv"))
aplot(write.fac.vary.rows, "Write CSV from data.table with 10 factor columns", 1e9, 1e1, "Number of rows", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
TODO. Below, we draw reference lines, so we can see the complexity class.
facetPlot(write.fac.vary.rows)
#> Warning: Transformation introduced infinite values in continuous y-axis
TODO The code below is for factor data with a constant number of rows, and a variable number of columns.
cache(write.fac.vary.cols, atime_write(
function(N.cols, N.rows=10)fac_dt(N.rows, N.cols),
"10_fac_rows_%s_%d.csv"))
aplot(write.fac.vary.cols, "Write CSV with 10 factor rows", 1e9, 1e1, "Number of columns", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
TODO. In the plot below, we include best reference lines above and below each empirical measurement asymptote.
facetPlot(write.fac.vary.cols)
#> Warning: Transformation introduced infinite values in continuous y-axis
TODO
Write CSV from data.table with POSIXct columns
The code below is for factor data with a constant number of columns, and a variable number of rows.
POSIXct_dt <- function(N.rows, N.cols){
as.data.table(lapply(1:N.cols, function(col.i)rep(Sys.time(),l=N.rows)))
}
cache(write.POSIXct.vary.rows, atime_write(
function(N.rows,N.cols=10)POSIXct_dt(N.rows, N.cols),
"10_fac_cols_%s_%d.csv"))
aplot(write.POSIXct.vary.rows, "Write CSV from data.table with 10 POSIXct columns", 1e9, 1e1, "Number of rows", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
TODO. Below, we draw reference lines, so we can see the complexity class.
facetPlot(write.POSIXct.vary.rows)
#> Warning: Transformation introduced infinite values in continuous y-axis
TODO The code below is for factor data with a constant number of rows, and a variable number of columns.
cache(write.POSIXct.vary.cols, atime_write(
function(N.cols, N.rows=10)POSIXct_dt(N.rows, N.cols),
"10_POSIXct_rows_%s_%d.csv"))
aplot(write.POSIXct.vary.cols, "Write CSV with 10 POSIXct rows", 1e9, 1e1, "Number of columns", write.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
TODO. In the plot below, we include best reference lines above and below each empirical measurement asymptote.
facetPlot(write.POSIXct.vary.cols)
#> Warning: Transformation introduced infinite values in continuous y-axis
TODO
Reading CSV
First we define a function which we will use for all of the read benchmarks,
read.expr.list <- c(
if(requireNamespace("readr"))atime::atime_grid(
list(LAZY=c(TRUE, FALSE), THREADS=threads.vec),
"readr::read_csv"={
readr::read_csv(
f.csv, num_threads = THREADS, lazy = LAZY,
show_col_types=FALSE, progress=FALSE)
}),
atime::atime_grid(
list(THREADS=threads.vec),
"data.table::fread"={
data.table::setDTthreads(THREADS)
data.table::fread(f.csv, showProgress=FALSE)
}),
if(FALSE && requireNamespace("polars"))atime::atime_grid(
##TODO wait until we know how to set max number of threads.
"polars::pl$read_csv"={
},
"polars::pl$read_csv_lazy"={
}),
if(requireNamespace("arrow"))atime::atime_grid(
list(THREADS=threads.vec),
"read_csv_arrow"={
arrow::set_cpu_count(THREADS)#https://github.com/apache/arrow/issues/30205#issuecomment-1378060874
arrow::read_csv_arrow(f.csv)
}),
atime::atime_grid(
"utils::read.csv"={
utils::read.csv(f.csv)
}))
#> Loading required namespace: readr
#> Loading required namespace: arrow
atime_read <- function(glob, compute=FALSE, colClasses, N.col){
fmt <- sub("[*]", "%d", glob)
csv.dt <- nc::capture_first_vec(
Sys.glob(file.path(tempdir(), glob)),
N="[0-9]+", as.integer,
".csv")[order(N)]
read.more.list <- c(
read.expr.list,
if(!missing(colClasses))list(
"read.csv(colClasses)"=substitute(
utils::read.csv(f.csv, colClasses = CLASS),
list(CLASS=colClasses)),
"list2DF(scan)"=substitute({
what <- `names<-`(
rep(list(FUN()), NCOL),
paste0("V",seq_len(NCOL))
)
list2DF(scan(f.csv, what=what, sep=",", skip=1, multi.line=FALSE))
}, list(
FUN=as.symbol(colClasses),
NCOL=if(missing(N.col))quote(N) else N.col)
)))
expr.list <- if(compute){
read.compute.expr.list <- list()
for(expr.name in names(read.more.list)){
lang.list <- as.list(read.more.list[[expr.name]])
LAST <- length(lang.list)
lang.list[[LAST]] <- as.call(c(
quote(`<-`),
quote(DF),
lang.list[[LAST]]))
read.compute.expr.list[[expr.name]] <- as.call(c(
lang.list,
quote(apply(DF, 1, paste, collapse=","))))
}
read.compute.expr.list
}else{
read.more.list
}
atime::atime(
N=csv.dt$N,
setup={
f.csv <- file.path(tempdir(), sprintf(fmt, N))
},
seconds.limit = seconds.limit,
expr.list=expr.list)
}
PRGn <- c(
NAME("readr::read_csv LAZY=FALSE,", "#9970AB","#762A83", "#40004B"), #purple
"#5AAE61", "#1B7837", "#00441B",#green
NAME("data.table::fread ", "#D6604D", "#B2182B", "#67001F"),#reds
NAME("readr::read_csv LAZY=TRUE,", "#878787", "#4D4D4D", "#1A1A1A"),#greys
NAME("read_csv_arrow ", "#BF812D", "#8C510A", "#543005"),#browns
"#35978F", "#01665E", "#003C30",#teal polars
"utils::read.csv"="#00FFFF",#"deepskyblue",
"read.csv(colClasses)"="#00CCCC",
"list2DF(scan)"="#009999")
(read.colors <- PRGn[names(PRGn)!=""&!is.na(names(PRGn))])
#> readr::read_csv LAZY=FALSE,THREADS=1 readr::read_csv LAZY=FALSE,THREADS=2
#> "#9970AB" "#762A83"
#> readr::read_csv LAZY=FALSE,THREADS=4 data.table::fread THREADS=1
#> "#40004B" "#D6604D"
#> data.table::fread THREADS=2 data.table::fread THREADS=4
#> "#B2182B" "#67001F"
#> readr::read_csv LAZY=TRUE,THREADS=1 readr::read_csv LAZY=TRUE,THREADS=2
#> "#878787" "#4D4D4D"
#> readr::read_csv LAZY=TRUE,THREADS=4 read_csv_arrow THREADS=1
#> "#1A1A1A" "#BF812D"
#> read_csv_arrow THREADS=2 read_csv_arrow THREADS=4
#> "#8C510A" "#543005"
#> utils::read.csv read.csv(colClasses)
#> "#00FFFF" "#00CCCC"
#> list2DF(scan)
#> "#009999"Below we read real numbers with a constant number of columns, and a variable number of rows.
cache(read.real.vary.rows, atime_read("10_real_cols_fwrite_*.csv", compute=FALSE, colClasses="numeric",N.col=10))
aplot(read.real.vary.rows, "Read CSV with 10 real columns", 1e9, 1e1, "Number of rows", read.colors)
It can be seen in the plot above that the green results, read_csv with LAZY=TRUE are fastest, which is normal because lazy reading does not actually read the data values into memory. A more fair comparison is below, which computes a text string for every row after reading the CSV,
cache(compute.real.vary.rows, atime_read("10_real_cols_fwrite_*.csv", compute=TRUE))
aplot(compute.real.vary.rows, "Read CSV with 10 real columns, then collapse each row", 1e9, 1e1, "Number of rows", read.colors)
Below we read real numbers with a constant number of rows, and a variable number of columns.
cache(read.real.vary.cols, atime_read("10_real_rows_fwrite_*.csv", compute=FALSE, colClasses="numeric"))
aplot(read.real.vary.cols, "Read CSV with 10 real rows", 1e8, 1e1, "Number of columns", read.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
The plot above shows that all functions have the same asymptotic memory usage, but read.csv has a larger asymptotic time complexity class than the others. The plot below shows that the time complexity class of read.csv is in fact quadratic, whereas the others are linear.
facetPlot(read.real.vary.cols,c("N^2","N log N", "N"))
#> Warning: Transformation introduced infinite values in continuous y-axis
Below we read character data with a constant number of columns, and a variable number of rows.
cache(read.chr.vary.rows, atime_read("10_chr_cols_fwrite_*.csv", compute=FALSE, colClasses="character",N.col=10))
aplot(read.chr.vary.rows, "Read CSV with 10 character columns", 1e9, 1e1, "Number of rows", read.colors)
As with the previous result for real data, the green results above, read_csv with LAZY=TRUE are fastest, which is normal because lazy reading does not actually read the data values into memory. A more fair comparison is below, which computes a text string for every row after reading the CSV,
cache(compute.chr.vary.rows, atime_read("10_chr_cols_fwrite_*.csv", compute=TRUE))
aplot(compute.chr.vary.rows, "Read CSV with 10 character columns, then collapse each row", 1e9, 1e1, "Number of rows", read.colors)
Below we read character data with a constant number of rows, and a variable number of columns.
cache(read.chr.vary.cols, atime_read("10_chr_rows_fwrite_*.csv", compute=FALSE, colClasses="character"))
aplot(read.chr.vary.cols, "Read CSV with 10 character rows", 1e8, 1e1, "Number of columns", read.colors)
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
From the comparisons above, it can be seen that for a small number of columns, and a large number of rows, all the methods are about the same (constant factor differences, using more than one thread also results in small constant factor speedups). However for a small number of rows and a large number of columns, data.table::fread is clearly the most efficient:
data.table::freaduses constant factors less time and memory thanreadr::read_csv.utils::read.csvuses asymptotically more time (super-linear in the number of columns).
facetPlot(read.chr.vary.cols,c("N^2","N log N", "N"))
#> Warning: Transformation introduced infinite values in continuous y-axis
Total time
Sys.time() - time.begin
#> Time difference of 1.811833 mins
seconds.vec <- sapply(cache.list, function(L){
do.call(sum, L$meas$time)
})
sum(seconds.vec)+time.begin-time.begin
#> Time difference of 1.118916 hourssession info
sessionInfo()
#> R version 4.3.0 (2023-04-21)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Red Hat Enterprise Linux 8.7 (Ootpa)
#>
#> Matrix products: default
#> BLAS: /projects/genomic-ml/R/R-4.3.0/lib/libRblas.so
#> LAPACK: /projects/genomic-ml/R/R-4.3.0/lib/libRlapack.so; LAPACK version 3.11.0
#>
#> locale:
#> [1] C
#>
#> time zone: America/Phoenix
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] directlabels_2021.1.13 ggplot2_3.4.2 data.table_1.14.8
#>
#> loaded via a namespace (and not attached):
#> [1] bit_4.0.5 gtable_0.3.3 jsonlite_1.8.4 dplyr_1.1.2
#> [5] compiler_4.3.0 highr_0.10 tidyselect_1.2.0 assertthat_0.2.1
#> [9] jquerylib_0.1.4 arrow_11.0.0.3 scales_1.2.1 fastmap_1.1.1
#> [13] lattice_0.21-8 readr_2.1.4 R6_2.5.1 generics_0.1.3
#> [17] knitr_1.42 tibble_3.2.1 munsell_0.5.0 atime_2023.4.27
#> [21] tzdb_0.3.0 bslib_0.4.2 pillar_1.9.0 rlang_1.1.0
#> [25] utf8_1.2.3 cachem_1.0.7 xfun_0.39 quadprog_1.5-8
#> [29] sass_0.4.5 bit64_4.0.5 cli_3.6.1 withr_2.5.0
#> [33] magrittr_2.0.3 digest_0.6.31 grid_4.3.0 hms_1.1.3
#> [37] lifecycle_1.0.3 vctrs_0.6.2 evaluate_0.20 glue_1.6.2
#> [41] farver_2.1.1 fansi_1.0.4 colorspace_2.1-1 purrr_1.0.1
#> [45] rmarkdown_2.21 tools_4.3.0 pkgconfig_2.0.3 htmltools_0.5.5