A note about the speed of the functional form for rxode2
The functional form has the benefit that it is what is supported by nlmixr2 and therefore there is only one interface between solving and estimating, and it takes some computation time to get to the underlying “classic” simulation code.
These models are in the form of:
library(rxode2)
#> rxode2 3.0.2.9000 using 2 threads (see ?getRxThreads)
#> no cache: create with `rxCreateCache()`
mod1 <- function() {
ini({
KA <- 0.3
CL <- 7
V2 <- 40
Q <- 10
V3 <- 300
Kin <- 0.2
Kout <- 0.2
EC50 <- 8
})
model({
C2 = centr/V2
C3 = peri/V3
d/dt(depot) = -KA*depot
d/dt(centr) = KA*depot - CL*C2 - Q*C2 + Q*C3
d/dt(peri) = Q*C2 - Q*C3
d/dt(eff) = Kin - Kout*(1-C2/(EC50+C2))*eff
eff(0) = 1
})
}
Or you can also specify the end-points for simulation/estimation just
like nlmixr2
:
mod2f <- function() {
ini({
TKA <- 0.3
TCL <- 7
TV2 <- 40
TQ <- 10
TV3 <- 300
TKin <- 0.2
TKout <- 0.2
TEC50 <- 8
eta.cl + eta.v ~ c(0.09,
0.08, 0.25)
c2.prop.sd <- 0.1
eff.add.sd <- 0.1
})
model({
KA <- TKA
CL <- TCL*exp(eta.cl)
V2 <- TV2*exp(eta.v)
Q <- TQ
V3 <- TV3
Kin <- TKin
Kout <- TKout
EC50 <- TEC50
C2 = centr/V2
C3 = peri/V3
d/dt(depot) = -KA*depot
d/dt(centr) = KA*depot - CL*C2 - Q*C2 + Q*C3
d/dt(peri) = Q*C2 - Q*C3
d/dt(eff) = Kin - Kout*(1-C2/(EC50+C2))*eff
eff(0) = 1
C2 ~ prop(c2.prop.sd)
eff ~ add(eff.add.sd)
})
}
For every solve, there is a compile (or a cached compile) of the
underlying model. If you wish to speed this process up you can use the
two underlying rxode2
classic models. This takes two
steps:
Parsing/evaluating the model
Creating the simulation model
The first step can be done by rxode2(mod1)
or
mod1()
(or for the second model too).
mod1 <- mod1()
mod2f <- rxode2(mod2f)
#> ℹ parameter labels from comments are typically ignored in non-interactive mode
#> ℹ Need to run with the source intact to parse comments
The second step is to create the underlying “classic”
rxode2
model, which can be done with two different
methods:$simulationModel
and
$simulationIniModel
. The $simulationModel
will
provide the simulation code without the initial conditions pre-pended,
the $simulationIniModel
will pre-pend the values. When the
endpoints are specified, the simulation code for each endpoint is also
output. You can see the differences below:
summary(mod1$simulationModel)
#> rxode2 3.0.2.9000 model named rx_2f5cde500e9adc62e740eed3f87a558c model (✔ ready).
#> DLL: /tmp/RtmpAAiz4N/rxode2/rx_2f5cde500e9adc62e740eed3f87a558c__.rxd/rx_2f5cde500e9adc62e740eed3f87a558c_.so
#> NULL
#>
#> Calculated Variables:
#> [1] "C2" "C3"
#> ── rxode2 Model Syntax ──
#> rxode2({
#> param(KA, CL, V2, Q, V3, Kin, Kout, EC50)
#> C2 = centr/V2
#> C3 = peri/V3
#> d/dt(depot) = -KA * depot
#> d/dt(centr) = KA * depot - CL * C2 - Q * C2 + Q * C3
#> d/dt(peri) = Q * C2 - Q * C3
#> d/dt(eff) = Kin - Kout * (1 - C2/(EC50 + C2)) * eff
#> eff(0) = 1
#> })
summary(mod1$simulationIniModel)
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> rxode2 3.0.2.9000 model named rx_117da5916c65d8e6b6549770fa8b943a model (✔ ready).
#> DLL: /tmp/RtmpAAiz4N/rxode2/rx_117da5916c65d8e6b6549770fa8b943a__.rxd/rx_117da5916c65d8e6b6549770fa8b943a_.so
#> NULL
#>
#> Calculated Variables:
#> [1] "C2" "C3"
#> ── rxode2 Model Syntax ──
#> rxode2({
#> param(KA, CL, V2, Q, V3, Kin, Kout, EC50)
#> KA = 0.3
#> CL = 7
#> V2 = 40
#> Q = 10
#> V3 = 300
#> Kin = 0.2
#> Kout = 0.2
#> EC50 = 8
#> C2 = centr/V2
#> C3 = peri/V3
#> d/dt(depot) = -KA * depot
#> d/dt(centr) = KA * depot - CL * C2 - Q * C2 + Q * C3
#> d/dt(peri) = Q * C2 - Q * C3
#> d/dt(eff) = Kin - Kout * (1 - C2/(EC50 + C2)) * eff
#> eff(0) = 1
#> })
summary(mod2f$simulationModel)
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> rxode2 3.0.2.9000 model named rx_0daab0dfafd10d5c69d5c00c241bac5f model (✔ ready).
#> DLL: /tmp/RtmpAAiz4N/rxode2/rx_0daab0dfafd10d5c69d5c00c241bac5f__.rxd/rx_0daab0dfafd10d5c69d5c00c241bac5f_.so
#> NULL
#>
#> Calculated Variables:
#> [1] "KA" "CL" "V2" "Q" "V3" "Kin"
#> [7] "Kout" "EC50" "C2" "C3" "ipredSim" "sim"
#> ── rxode2 Model Syntax ──
#> rxode2({
#> param(TKA, TCL, TV2, TQ, TV3, TKin, TKout, TEC50, c2.prop.sd,
#> eff.add.sd, eta.cl, eta.v)
#> KA = TKA
#> CL = TCL * exp(eta.cl)
#> V2 = TV2 * exp(eta.v)
#> Q = TQ
#> V3 = TV3
#> Kin = TKin
#> Kout = TKout
#> EC50 = TEC50
#> C2 = centr/V2
#> C3 = peri/V3
#> d/dt(depot) = -KA * depot
#> d/dt(centr) = KA * depot - CL * C2 - Q * C2 + Q * C3
#> d/dt(peri) = Q * C2 - Q * C3
#> d/dt(eff) = Kin - Kout * (1 - C2/(EC50 + C2)) * eff
#> eff(0) = 1
#> if (CMT == 5) {
#> rx_yj_ ~ 2
#> rx_lambda_ ~ 1
#> rx_low_ ~ 0
#> rx_hi_ ~ 1
#> rx_pred_f_ ~ C2
#> rx_pred_ ~ rx_pred_f_
#> rx_r_ ~ (rx_pred_f_ * c2.prop.sd)^2
#> ipredSim = rxTBSi(rx_pred_, rx_lambda_, rx_yj_, rx_low_,
#> rx_hi_)
#> sim = rxTBSi(rx_pred_ + sqrt(rx_r_) * rxerr.C2, rx_lambda_,
#> rx_yj_, rx_low_, rx_hi_)
#> }
#> if (CMT == 4) {
#> rx_yj_ ~ 2
#> rx_lambda_ ~ 1
#> rx_low_ ~ 0
#> rx_hi_ ~ 1
#> rx_pred_f_ ~ eff
#> rx_pred_ ~ rx_pred_f_
#> rx_r_ ~ (eff.add.sd)^2
#> ipredSim = rxTBSi(rx_pred_, rx_lambda_, rx_yj_, rx_low_,
#> rx_hi_)
#> sim = rxTBSi(rx_pred_ + sqrt(rx_r_) * rxerr.eff, rx_lambda_,
#> rx_yj_, rx_low_, rx_hi_)
#> }
#> cmt(C2)
#> dvid(5, 4)
#> })
summary(mod2f$simulationIniModel)
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> rxode2 3.0.2.9000 model named rx_a2c224f7472dacc45308658038a067c2 model (✔ ready).
#> DLL: /tmp/RtmpAAiz4N/rxode2/rx_a2c224f7472dacc45308658038a067c2__.rxd/rx_a2c224f7472dacc45308658038a067c2_.so
#> NULL
#>
#> Calculated Variables:
#> [1] "KA" "CL" "V2" "Q" "V3" "Kin"
#> [7] "Kout" "EC50" "C2" "C3" "ipredSim" "sim"
#> ── rxode2 Model Syntax ──
#> rxode2({
#> param(TKA, TCL, TV2, TQ, TV3, TKin, TKout, TEC50, c2.prop.sd,
#> eff.add.sd, eta.cl, eta.v)
#> rxerr.C2 = 1
#> rxerr.eff = 1
#> TKA = 0.3
#> TCL = 7
#> TV2 = 40
#> TQ = 10
#> TV3 = 300
#> TKin = 0.2
#> TKout = 0.2
#> TEC50 = 8
#> c2.prop.sd = 0.1
#> eff.add.sd = 0.1
#> eta.cl = 0
#> eta.v = 0
#> KA = TKA
#> CL = TCL * exp(eta.cl)
#> V2 = TV2 * exp(eta.v)
#> Q = TQ
#> V3 = TV3
#> Kin = TKin
#> Kout = TKout
#> EC50 = TEC50
#> C2 = centr/V2
#> C3 = peri/V3
#> d/dt(depot) = -KA * depot
#> d/dt(centr) = KA * depot - CL * C2 - Q * C2 + Q * C3
#> d/dt(peri) = Q * C2 - Q * C3
#> d/dt(eff) = Kin - Kout * (1 - C2/(EC50 + C2)) * eff
#> eff(0) = 1
#> if (CMT == 5) {
#> rx_yj_ ~ 2
#> rx_lambda_ ~ 1
#> rx_low_ ~ 0
#> rx_hi_ ~ 1
#> rx_pred_f_ ~ C2
#> rx_pred_ ~ rx_pred_f_
#> rx_r_ ~ (rx_pred_f_ * c2.prop.sd)^2
#> ipredSim = rxTBSi(rx_pred_, rx_lambda_, rx_yj_, rx_low_,
#> rx_hi_)
#> sim = rxTBSi(rx_pred_ + sqrt(rx_r_) * rxerr.C2, rx_lambda_,
#> rx_yj_, rx_low_, rx_hi_)
#> }
#> if (CMT == 4) {
#> rx_yj_ ~ 2
#> rx_lambda_ ~ 1
#> rx_low_ ~ 0
#> rx_hi_ ~ 1
#> rx_pred_f_ ~ eff
#> rx_pred_ ~ rx_pred_f_
#> rx_r_ ~ (eff.add.sd)^2
#> ipredSim = rxTBSi(rx_pred_, rx_lambda_, rx_yj_, rx_low_,
#> rx_hi_)
#> sim = rxTBSi(rx_pred_ + sqrt(rx_r_) * rxerr.eff, rx_lambda_,
#> rx_yj_, rx_low_, rx_hi_)
#> }
#> cmt(C2)
#> dvid(5, 4)
#> })
If you wish to speed up multiple simualtions from the
rxode2
functions, you need to pre-calculate care of the
steps above:
mod1 <- mod1$simulationModel
mod2 <- mod2f$simulationModel
These functions then can act like a normal ui model to be solved. You
can convert them back to a UI as.rxUi()
or a function
as.function()
as needed.
To increase speed for multiple simulations from the same model you
should use the lower level simulation model (ie
$simulationModel
or $simulationIniModel
depending on what you need)
Increasing rxode2 speed by multi-subject parallel solving
Using the classic rxode2
model specification (which we
can convert from a functional/ui model style) we will continue the
discussion on rxode2
speed enhancements.
rxode2
originally developed as an ODE solver that
allowed an ODE solve for a single subject. This flexibility is still
supported.
The original code from the rxode2
tutorial is below:
library(rxode2)
library(microbenchmark)
library(ggplot2)
mod1 <- rxode2({
C2 = centr/V2
C3 = peri/V3
d/dt(depot) = -KA*depot
d/dt(centr) = KA*depot - CL*C2 - Q*C2 + Q*C3
d/dt(peri) = Q*C2 - Q*C3
d/dt(eff) = Kin - Kout*(1-C2/(EC50+C2))*eff
eff(0) = 1
})
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
## Create an event table
ev <- et() %>%
et(amt=10000, addl=9,ii=12) %>%
et(time=120, amt=20000, addl=4, ii=24) %>%
et(0:240) ## Add Sampling
nsub <- 100 # 100 sub-problems
sigma <- matrix(c(0.09,0.08,0.08,0.25),2,2) # IIV covariance matrix
mv <- rxRmvn(n=nsub, rep(0,2), sigma) # Sample from covariance matrix
CL <- 7*exp(mv[,1])
V2 <- 40*exp(mv[,2])
params.all <- cbind(KA=0.3, CL=CL, V2=V2, Q=10, V3=300,
Kin=0.2, Kout=0.2, EC50=8)
For Loop
The slowest way to code this is to use a for
loop. In
this example we will enclose it in a function to compare timing.
Running with apply
In general for R, the apply
types of functions perform
better than a for
loop, so the tutorial also suggests this
speed enhancement
runSapply <- function(){
res <- apply(params.all, 1, function(theta)
mod1$run(theta, ev)[, "eff"])
}
Run using a single-threaded solve
You can also have rxode2 solve all the subject simultaneously without collecting the results in R, using a single threaded solve.
The data output is slightly different here, but still gives the same information:
Run a 2 threaded solve
rxode2 supports multi-threaded solves, so another option is to have
2
threads (called cores
in the solve options,
you can see the options in rxControl()
or
rxSolve()
).
Compare the times between all the methods
Now the moment of truth, the timings:
bench <- microbenchmark(runFor(), runSapply(), runSingleThread(),run2Thread())
print(bench)
#> Unit: milliseconds
#> expr min lq mean median uq max
#> runFor() 377.01013 384.09838 403.17610 390.44411 410.46605 570.1512
#> runSapply() 378.44977 385.01763 397.54414 389.02789 393.56492 512.3124
#> runSingleThread() 31.19483 31.45187 32.59865 31.63691 32.04282 55.1383
#> run2Thread() 19.88603 20.16210 22.14530 20.37325 21.04637 34.8136
#> neval
#> 100
#> 100
#> 100
#> 100
autoplot(bench)
It is clear that the largest jump in performance
when using the solve
method and providing all the
parameters to rxode2 to solve without looping over each subject with
either a for
or a sapply
. The number of
cores/threads applied to the solve also plays a role in the solving.
We can explore the number of threads further with the following code:
runThread <- function(n){
solve(mod1, params.all, ev, cores=n)[,c("sim.id", "time", "eff")]
}
bench <- eval(parse(text=sprintf("microbenchmark(%s)",
paste(paste0("runThread(", seq(1, 2 * rxCores()),")"),
collapse=","))))
print(bench)
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> runThread(1) 31.20030 31.37967 32.51537 31.50170 31.90993 54.89426 100
#> runThread(2) 19.89671 20.20453 23.19236 20.45664 24.47766 38.80069 100
#> runThread(3) 21.13313 21.44681 22.91155 21.76893 24.77142 28.86559 100
#> runThread(4) 21.12162 21.43005 23.10094 21.56052 21.91201 43.32421 100
autoplot(bench)
There can be a suite spot in speed vs number or cores. The system type (mac, linux, windows and/or processor), complexity of the ODE solving and the number of subjects may affect this arbitrary number of threads. 4 threads is a good number to use without any prior knowledge because most systems these days have at least 4 threads (or 2 processors with 4 threads).
Increasing speed with compiler options
One of the way that allows faster ODE solving is to make some
approximations that make some math operators like exp()
faster but not technically accurate enough to follow the IEEE standard
for the math functions values (there are other implications that I will
not cover here).
While these are optimizations are opt-in for Julia since they compile everything each session, CRAN has a more conservative approach since individuals do not compile each R function before running it.
Still, rxode2
models can be compiled with this option
without disturbing CRAN policies. The key is to set an option. Here is
an example:
# Using the first example subset to PK
mod2f <- function() {
ini({
TKA <- 0.3
TCL <- 7
TV2 <- 40
TQ <- 10
TV3 <- 300
TKin <- 0.2
TKout <- 0.2
TEC50 <- 8
eta.cl + eta.v ~ c(0.09,
0.08, 0.25)
c2.prop.sd <- 0.1
})
model({
KA <- TKA
CL <- TCL*exp(eta.cl)
V2 <- TV2*exp(eta.v)
Q <- TQ
V3 <- TV3
Kin <- TKin
Kout <- TKout
EC50 <- TEC50
C2 = centr/V2
C3 = peri/V3
d/dt(depot) = -KA*depot
d/dt(centr) = KA*depot - CL*C2 - Q*C2 + Q*C3
d/dt(peri) = Q*C2 - Q*C3
C2 ~ prop(c2.prop.sd)
})
}
mod2f <- mod2f()
mod2s <- mod2f$simulationIniModel
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
ev <- et(amountUnits="mg", timeUnits="hours") %>%
et(amt=10000, addl=9,ii=12,cmt="depot") %>%
et(time=120, amt=2000, addl=4, ii=14, cmt="depot") %>%
et(0:240) # Add sampling
bench1 <- microbenchmark(standardCompile=rxSolve(mod2s, ev, nSub=1000))
# Now clear the cache of models so we can change the compile options for the same model
rxClean()
# Use withr to preserve the options
withr::with_options(list(rxode2.compile.O="fast"), {
mod2s <- mod2f$simulationIniModel
})
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
bench2 <- microbenchmark(fastCompile=rxSolve(mod2s, ev, nSub=1000))
bench <- rbind(bench1, bench2)
print(bench)
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> standardCompile 350.1249 360.9716 421.4276 397.9825 499.0685 558.8724 100
#> fastCompile 351.4854 362.2075 415.6193 375.1544 498.6084 556.2115 100
autoplot(bench)
Note compiler settings can be tricky and if you setup your system
wide Makevars
it may interact with this setting. For
example if you use ccache
the compile may not be produced
with the same options since it was cached with the other options.
For example, on the github runner (which generates this page), there
is no advantage to the "fast"
compile. However, on my
development laptop there is some
minimal speed increase. You should probably check before using this
yourself.
This is disabled by default since there is only minimum increase in speed.
A real life example
cBefore some of the parallel solving was implemented, the fastest way
to run rxode2
was with lapply
. This is how Rik
Schoemaker created the data-set for nlmixr
comparisons, but
reduced to run faster automatic building of the pkgdown website.
library(rxode2)
library(data.table)
#Define the rxode2 model
ode1 <- "
d/dt(abs) = -KA*abs;
d/dt(centr) = KA*abs-(CL/V)*centr;
C2=centr/V;
"
#Create the rxode2 simulation object
mod1 <- rxode2(model = ode1)
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#Population parameter values on log-scale
paramsl <- c(CL = log(4),
V = log(70),
KA = log(1))
#make 10,000 subjects to sample from:
nsubg <- 300 # subjects per dose
doses <- c(10, 30, 60, 120)
nsub <- nsubg * length(doses)
#IIV of 30% for each parameter
omega <- diag(c(0.09, 0.09, 0.09))# IIV covariance matrix
sigma <- 0.2
#Sample from the multivariate normal
set.seed(98176247)
rxSetSeed(98176247)
library(MASS)
mv <-
mvrnorm(nsub, rep(0, dim(omega)[1]), omega) # Sample from covariance matrix
#Combine population parameters with IIV
params.all <-
data.table(
"ID" = seq(1:nsub),
"CL" = exp(paramsl['CL'] + mv[, 1]),
"V" = exp(paramsl['V'] + mv[, 2]),
"KA" = exp(paramsl['KA'] + mv[, 3])
)
#set the doses (looping through the 4 doses)
params.all[, AMT := rep(100 * doses,nsubg)]
Startlapply <- Sys.time()
#Run the simulations using lapply for speed
s = lapply(1:nsub, function(i) {
#selects the parameters associated with the subject to be simulated
params <- params.all[i]
#creates an eventTable with 7 doses every 24 hours
ev <- eventTable()
ev$add.dosing(
dose = params$AMT,
nbr.doses = 1,
dosing.to = 1,
rate = NULL,
start.time = 0
)
#generates 4 random samples in a 24 hour period
ev$add.sampling(c(0, sort(round(sample(runif(600, 0, 1440), 4) / 60, 2))))
#runs the rxode2 simulation
x <- as.data.table(mod1$run(params, ev))
#merges the parameters and ID number to the simulation output
x[, names(params) := params]
})
#runs the entire sequence of 100 subjects and binds the results to the object res
res = as.data.table(do.call("rbind", s))
Stoplapply <- Sys.time()
print(Stoplapply - Startlapply)
#> Time difference of 13.23896 secs
By applying some of the new parallel solving concepts you can simply run the same simulation both with less code and faster:
rx <- rxode2({
CL = log(4)
V = log(70)
KA = log(1)
CL = exp(CL + eta.CL)
V = exp(V + eta.V)
KA = exp(KA + eta.KA)
d/dt(abs) = -KA*abs;
d/dt(centr) = KA*abs-(CL/V)*centr;
C2=centr/V;
})
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
omega <- lotri(eta.CL ~ 0.09,
eta.V ~ 0.09,
eta.KA ~ 0.09)
doses <- c(10, 30, 60, 120)
startParallel <- Sys.time()
ev <- do.call("rbind",
lapply(seq_along(doses), function(i){
et() %>%
et(amt=doses[i]) %>% # Add single dose
et(0) %>% # Add 0 observation
## Generate 4 samples in 24 hour period
et(lapply(1:4, function(...){c(0, 24)})) %>%
et(id=seq(1, nsubg) + (i - 1) * nsubg) %>%
## Convert to data frame to skip sorting the data
## When binding the data together
as.data.frame
}))
## To better compare, use the same output, that is data.table
res <- rxSolve(rx, ev, omega=omega, returnType="data.table")
endParallel <- Sys.time()
print(endParallel - startParallel)
#> Time difference of 0.1278534 secs
You can see a striking time difference between the two methods; A few things to keep in mind:
rxode2
use the thread-safe sitmothreefry
routines for simulation ofeta
values. Therefore the results are expected to be different (also the random samples are taken in a different order which would be different)This prior simulation was run in R 3.5, which has a different random number generator so the results in this simulation will be different from the actual nlmixr comparison when using the slower simulation.
This speed comparison used
data.table
.rxode2
usesdata.table
internally (when available) try to speed up sorting, so this would be different than installations wheredata.table
is not installed. You can force rxode2 to useorder()
when sorting by usingforderForceBase(TRUE)
. In this case there is little difference between the two, though in other examplesdata.table
’s presence leads to a speed increase (and less likely it could lead to a slowdown).
Want more ways to run multi-subject simulations
The version since the tutorial has even more ways to run
multi-subject simulations, including adding variability in sampling and
dosing times with et()
(see rxode2
events for more information), ability to supply both an
omega
and sigma
matrix as well as adding as a
thetaMat
to R to simulate with uncertainty in the
omega
, sigma
and theta
matrices;
see rxode2
simulation vignette.
Session Information
The session information:
sessionInfo()
#> R version 4.4.2 (2024-10-31)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 22.04.5 LTS
#>
#> Matrix products: default
#> BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
#>
#> locale:
#> [1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
#> [4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
#> [7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: UTC
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] MASS_7.3-61 data.table_1.16.4 ggplot2_3.5.1
#> [4] microbenchmark_1.5.0 rxode2_3.0.2.9000
#>
#> loaded via a namespace (and not attached):
#> [1] sass_0.4.9 utf8_1.2.4 generics_0.1.3
#> [4] lattice_0.22-6 digest_0.6.37 magrittr_2.0.3
#> [7] evaluate_1.0.1 grid_4.4.2 fastmap_1.2.0
#> [10] lotri_1.0.0.9000 jsonlite_1.8.9 rxode2ll_2.0.12
#> [13] backports_1.5.0 fansi_1.0.6 scales_1.3.0
#> [16] lazyeval_0.2.2 textshaping_0.4.1 jquerylib_0.1.4
#> [19] RApiSerialize_0.1.4 cli_3.6.3 symengine_0.2.6
#> [22] crayon_1.5.3 rlang_1.1.4 units_0.8-5
#> [25] munsell_0.5.1 withr_3.0.2 cachem_1.1.0
#> [28] yaml_2.3.10 tools_4.4.2 qs_0.27.2
#> [31] memoise_2.0.1 checkmate_2.3.2 dplyr_1.1.4
#> [34] colorspace_2.1-1 vctrs_0.6.5 R6_2.5.1
#> [37] lifecycle_1.0.4 fs_1.6.5 stringfish_0.16.0
#> [40] htmlwidgets_1.6.4 ragg_1.3.3 PreciseSums_0.7
#> [43] pkgconfig_2.0.3 desc_1.4.3 rex_1.2.1
#> [46] pkgdown_2.1.1 RcppParallel_5.1.9 pillar_1.9.0
#> [49] bslib_0.8.0 gtable_0.3.6 glue_1.8.0
#> [52] Rcpp_1.0.13-1 systemfonts_1.1.0 xfun_0.49
#> [55] tibble_3.2.1 tidyselect_1.2.1 sys_3.4.3
#> [58] knitr_1.49 farver_2.1.2 dparser_1.3.1-13
#> [61] htmltools_0.5.8.1 nlme_3.1-166 labeling_0.4.3
#> [64] rmarkdown_2.29 compiler_4.4.2