nlmixr2/rxode2 user functions

By Matthew Fidler in nlmixr2 rxode2 user functions

May 8, 2024

One of the exciting new features of the recent rxode2 is user functions. This allows you to define your own R functions for use in nlmixr2 or rxode2. This new feature can really help make your code more concise by reusing custom transformations or apply more complex routines.

This can call R functions directly, but at a cost – single threaded and slower execution. However, you can reduce the cost by converting the R functions to C automatically with rxFun(). Most of this blog is simply restating a new vignette on user defined functions with an additional example of a slow running nlmixr2 model to show how much converting to C will save computation time. However since this opens up the flexibility of nlmixr2 and rxode2, I think it is exciting enough to share in the blog as well.

User Defined Functions

## rxode2 using 8 threads (see ?getRxThreads)
##   no cache: create with `rxCreateCache()`

When defining models you may have wished to write a small R function or make a function integrate into rxode2 somehow. This post discusses 2 ways to do this:

  • A R-based user function which can be loaded as a simple function or in certain circumstances translated to C to run more efficiently

  • A C function that you define and integrate into code

R based user functions

A R-based user function is the most convenient to include in the ODE, but is slower than what you could have done if it was written in C , C++ or some other compiled language. This was requested in github with an appropriate example; However, I will use a very simple example here to simply illustrate the concepts.

newAbs <- function(x) {
  if (x < 0) {
  } else {

f <- rxode2({
  a <- newAbs(time)
## using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
e <- et(-10, 10, length.out=40)

Now that the ODE has been compiled the R functions will be called while solving the ODE. Since this is calling R, this forces the parallization to be turned off since R is single-threaded. It also takes more time to solve since it is shuttling back and forth between R and C. Lets see how this very simple function performs:

mb1 <- microbenchmark::microbenchmark(withoutC=suppressWarnings(rxSolve(f,e)))

autoplot(mb1) + rxTheme()

Not terribly bad, even though it is shuffling between R and C.

You can make it a better by converting the functions to C:

# Create C functions automatically with `rxFun()`
## → finding duplicate expressions in d(newAbs)/d(x)...
## [====|====|====|====|====|====|====|====|====|====] 0:00:00
## → optimizing duplicate expressions in d(newAbs)/d(x)...
## [====|====|====|====|====|====|====|====|====|====] 0:00:00
## converted R function 'newAbs' to C (will now use in rxode2)
## converted R function 'rx_newAbs_d_x' to C (will now use in rxode2)
## Added derivative table for 'newAbs'
# Recompile to use the C functions
# Note it would recompile anyway if you didn't do this step,
# it just makes sure that it doesn't recompile every step in
# the benchmark
f <- rxode2({
  a <- newAbs(time)
## using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
mb2 <- microbenchmark::microbenchmark(withC=rxSolve(f,e, cores=1))

mb <- rbind(mb1, mb2)
autoplot(mb) + rxTheme() + xgxr::xgx_scale_y_log10()
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.

## Unit: milliseconds
##      expr      min       lq     mean   median       uq       max neval
##  withoutC 7.451945 7.582450 9.014079 7.773921 9.886330 18.919026   100
##     withC 2.354004 2.387503 2.604025 2.430683 2.533291  7.533218   100

The C version is almost twice as fast as the R version. You may have noticed the conversion also created C versions of the first derivative. This is done automatically and gives not just C versions of function, but C versions of the derivatives and registers them with rxode2. This allows the C versions to work with not only rxode2 but nlmixr2 models.

This function was setup in advance to allow this type of conversion. In general the derivatives will be calculated if there is not a return() statement in the user defined function. This means simply let R return the last value instead of explictly calling out the return(). Many people prefer this method of coding.

Even if there is a return function, the function could be converted to C. In the github issue, they used a function that would not convert the derivatives:

# Light
f_R <- function(actRad, k_0, a_k) {
  photfac <- a_k * actRad + k_0
  if (photfac > 1) {
    photfac = 1

## function contains return statement; derivatives not calculated
## converted R function 'f_R' to C (will now use in rxode2)

While this is still helpful because some functions have early returns, the nlmixr2 models requiring derivatives would be calculated be non-optimized finite differences when this occurs. While this gets into the internals of rxode2 and nlmixr2 you can see this more easily when calculating the derivatives:

rxFromSE("Derivative(f_R(actRad, k_0, a_k),k_0)")
## [1] "(f_R(actRad,(k_0)+6.05545445239334e-06,a_k)-f_R(actRad,k_0,a_k))/6.05545445239334e-06"

Whereas the originally defined function newAbs() would use the new derivatives calculated as well:

## [1] "rx_newAbs_d_x(x)"

In some circumstances, the conversion to C is not possible, though you can still use the R function.

There are some requirements for R functions to be integrated into the rxode2 system:

  • The function must have a set number of arguments, variable arguments like f(…) are currently not allowed.

  • The function is given each argument as a single number, and the function should return a single number

If these requirements are met you can use the R function in rxode2. Additional requirements for conversion to C include:

  • Any functions that you use within the R function must be understood and available to rxode2.

    • Practically speaking if you have fun2() which refers to fun1(), fun1() must be changed to C code and available to rxode2 before changing the function fun2() to C.
  • The functions can include if/else assignments or simple return statements (either by returning a value or having that value on a line by itself). Special R control structures and functions (like for and lapply) cannot be present.

  • The function cannot refer to any package functions

  • As mentioned, if the return() statement is present, the derivative C functions and rxode2’s derivative table is not updated.

C based functions

You can add your own C functions directly into rxode2 as well using rxFun():

fun <- "
 double fun(double a, double b, double c) {
   return a*a+b*a+c;
" ## C-code for function

rxFun("fun", c("a", "b", "c"), fun)

If you wanted you could also use C functions or expressions for the derivatives by using the rxD() function:

rxD("fun", list(
   function(a, b, c) { # derivative of arg1: a
     paste0("2*", a, "+", b)
   function(a, b, c) { # derivative of arg2: b
   function(a, b, c) { # derivative of arg3: c

Removing the function with rxRmFun() will also remove the derivative table:


A nlmixr2 example

We will also use a very artificial example to illustrate the differences in R and C evaluation in nlmixr2() in a very small example.

## Loading required package: nlmixr2data
gg <- function(x, y) {
  x * y

g <- function() {
    tke <- 0.5 <- sqrt(0.1)
    ke <- tke
    ipre <- gg(10, exp(-ke * t))
    lipre <- log(ipre)
    ipre ~ add(

dat <- nlmixr2data::Wang2007
dat$DV <- dat$Y

mbn1 <- microbenchmark::microbenchmark(withR=suppressMessages(nlmixr2(g, dat, "nlminb", control=list(print=0))))
## [====|====|====|====|====|====|====|====|====|====] 0:00:00

Now use the C versions of the function

rxClean() # Clean the cache just in case it uses the R instead of the C
# Convert the function (and derivates) to C
## → finding duplicate expressions in d(gg)/d(x)...
## [====|====|====|====|====|====|====|====|====|====] 0:00:00
## → finding duplicate expressions in d(gg)/d(y)...
## [====|====|====|====|====|====|====|====|====|====] 0:00:00
## converted R function 'gg' to C (will now use in rxode2)
## converted R function 'rx_gg_d_x' to C (will now use in rxode2)
## converted R function 'rx_gg_d_y' to C (will now use in rxode2)
## Added derivative table for 'gg'
mbn2 <- microbenchmark::microbenchmark(withC=suppressMessages(nlmixr2(g, dat, "nlminb", control=list(print=0))))
## [====|====|====|====|====|====|====|====|====|====] 0:00:00
mbn <- rbind(mbn1, mbn2)
autoplot(mb) + rxTheme() + xgxr::xgx_scale_y_log10()
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.

## Unit: seconds
##   expr      min       lq     mean   median       uq      max neval
##  withR 4.635311 4.799454 4.961371 4.916435 5.071639 6.860650   100
##  withC 1.583859 1.702866 1.824142 1.789773 1.945982 2.777273   100

You can clearly see the need for C function in nlmixr2 optimization


This is the first user function that is added to the rxode2/nlmixr2. It is powerful and can be fast if you convert your functions to C.

Posted on:
May 8, 2024
7 minute read, 1437 words
nlmixr2 rxode2 user functions
user functions
See Also: