Rolling user-defined function

Fast rolling user-defined function (UDF) to calculate on a sliding window. Experimental. Please read, at least, caveats section below. For "time-aware" (irregularly spaced time series) rolling function see frolladapt.

Usage

frollapply(X, N, FUN, ..., by.column=TRUE, fill=NA,
    align=c("right","left","center"), adaptive=FALSE, partial=FALSE,
    give.names=FALSE, simplify=TRUE, x, n)

Arguments

X: Atomic vector, data.frame, data.table or a list on which sliding window calculates FUN function. How the X is handled depends on the by.column argument. It supports vectorized input, for by.column=TRUE it needs to be a data.table, data.frame or a list, and for by.column=FALSE list of data.frames/data.tables, but not a list of lists.
N: Integer, non-negative, non-NA, rolling window size. This is the total number of included values in aggregate function. In case of an adaptive rolling function window size has to be provided as a vector for each individual value of X. It supports vectorized input, then it needs to be a vector, or in case of an adaptive rolling a list of vectors.
FUN: The function to be applied on subsets of X.
...: Extra arguments passed to FUN. Note that argument names passed to ... should not overlap with arguments of frollapply.
by.column: Logical. When TRUE (default) then X of types list/data.frame/data.table is treated as vectorized input rather an object to apply rolling window on. Setting to FALSE allows rolling window to be applied on multiple variables, using data.frame, data.table or a list, as a whole. For details see by.column argument section below.
fill: An object; value to pad by for an incomplete window iteration. Defaults to NA. When partial=TRUE this argument is ignored.
align: Character, specifying the "alignment" of the rolling window, defaulting to "right". For details see froll.
adaptive: Logical, default FALSE. Should the rolling function be calculated adaptively? For details see froll.
partial: Logical, default FALSE. Should the rolling window size(s) provided in N be trimmed to available observations? For details see froll.
give.names: Logical, default FALSE. When TRUE, names are automatically generated corresponding to names of X and names of N. If answer is an atomic vector, then the argument is ignored, see examples.
simplify: Logical or a function. When TRUE (default) then internal simplifylist function is applied on a list storing results of all computations. When FALSE then list is returned without any post-processing. Argument can take a function as well, then the function is applied to a list that would have been returned when simplify=FALSE. If results are not automatically simplified when simplify=TRUE then, for backward compatibility, one should use simplify=FALSE explicitly. See simplify argument section below for details.
x: Deprecated, use X instead.
n: Deprecated, use N instead.

Value

Argument simplify impacts the type returned. Its default value TRUE is set for convenience and backward compatibility, but it is advised to use simplify=unlist (or other desired function) instead.

simplify=FALSE will always return list where each element will be a result of each iteration.
simplify=unlist (or any other function) will return object returned by provided function as supplied with results of frollapply using simplify=FALSE.
simplify=TRUE will try to simplify results by unlist, rbind or other functions, its behavior is subject to change, see simplify argument section below for more details.

`by.column` argument

Setting by.column to FALSE allows to apply function on multiple variables rather than a single vector. Then X expects to be data.table, data.frame or a list of equal length vectors, and window size provided in N refers to number of rows (or length of a vectors in a list). See examples for use cases. Error "incorrect number of dimensions" can be commonly observed when by.column was not set to FALSE when FUN expects its input to be a data.table or data.frame.

`simplify` argument

When set to TRUE (default), then results from rolling function which are normally stored in a list may be simplified either with unlist or rbindlist. It also attempts to match type, size and names of fill argument to the results of a function. One should avoid simplify=TRUE when writing robust code. One reason is performance, as explained in Performance consideration section below. Another is backward compatibility. For backward compatibility and performance one should always provide desired function to simplify explicitly. In future version we may change internal simplifylist function, then simplify=TRUE may return object of a different type, breaking downstream code.

Caveats

With great power comes great responsibility.

An optimization used to avoid repeated allocation of window subsets (explained more deeply in Implementation section below) may, in special cases, return rather surprising results:


setDTthreads(1)
frollapply(c(1, 9), N=1L, FUN=identity) ## unexpected
#[1] 9 9
frollapply(c(1, 9), N=1L, FUN=list) ## unexpected
#      V1
#   <num>
#1:     9
#2:     9
setDTthreads(2, throttle=1) ## disable throttle
frollapply(c(1, 9), N=1L, FUN=identity) ## good only because threads >= input
#[1] 1 9                                ## on Linux and Macos
frollapply(c(1, 5, 9), N=1L, FUN=identity) ## unexpected again
#[1] 5 5 9

Problem occurs, in rather unlikely scenarios for rolling computations, when objects returned from a function can be its input (i.e. identity), or a reference to it (i.e. list), then one has to add extra copy call:


setDTthreads(1)
frollapply(c(1, 9), N=1L, FUN=function(x) copy(identity(x))) ## only 'copy' would be equivalent here
#[1] 1 9
frollapply(c(1, 9), N=1L, FUN=function(x) copy(list(x)))
#      V1
#   <num>
#1:     1
#2:     9

FUN calls are internally passed to parallel::mcparallel to evaluate them in parallel. We inherit few limitations from parallel package explained below. This optimization can be disabled completely by calling setDTthreads(1), in which case the limitations listed below do not apply because all evaluations of FUN will be made sequentially without use of parallel package. Note that on Windows platform this optimization is always disabled due to lack of fork used by parallel package. One can use options(datatable.verbose=TRUE) to get extra information if frollapply is running multithreaded or not.
- Warnings produced inside the function are silently ignored; for consistency we ignore warnings also when running single threaded path.
- FUN should not use any on-screen devices, GUI elements, tcltk, multithreaded libraries.
- setDTthreads(1L) is passed to forked processes, therefore any data.table code inside FUN will be forced to be single threaded. It is advised not to call setDTthreads inside FUN. frollapply is already parallelized, and nested parallelism is rarely a good idea.
- Any operation that could misbehave when run in parallel has to be handled. For example, writing to the same file from multiple CPU threads.
```
old = setDTthreads(1L)
frollapply(iris, 5L, by.column=FALSE, FUN=fwrite, file="rolling-data.csv", append=TRUE)
setDTthreads(old)
```
- Objects returned from forked processes, FUN, are serialized. This may cause problems for objects that are meant not to be serialized, like data.table. We are handling that for data.table class internally in frollapply whenever FUN is returning data.table (which is checked on the results of the first FUN call so it assumes function is type stable). If data.table is nested in another object returned from FUN then the problem may still manifest, in such case one has to call setDT on objects returned from FUN. This can be also nicely handled via simplify argument when passing a function that calls setDT on nested data.table objects returned from FUN. Anyway, returning data.table from FUN should, in majority of cases, be avoided from the performance reasons, see UDF optimization section for details.
```
setDTthreads(2, throttle=1) ## disable throttle
## frollapply will fix DT in most cases
ans = frollapply(1:2, 2, data.table)
.selfref.ok(ans)
#[1] TRUE
ans = frollapply(1:2, 2, data.table, simplify=FALSE)
.selfref.ok(ans[[2L]])
#[1] TRUE

## nested DT not fixed
ans = frollapply(1:2, 2, function(x) list(data.table(x)), fill=list(data.table(NA)), simplify=FALSE)
.selfref.ok(ans[[2L]][[1L]])
#[1] FALSE
#### now if we want to use it
set(ans[[2L]][[1L]],, "newcol", 1L)
#Error in set(ans[[2L]][[1L]], , "newcol", 1L) :
#  This data.table has either been loaded from disk (e.g. using readRDS()/load()) or constructed manually (e.g. using structure()). Please run setDT() or setalloccol() on it first (to pre-allocate space for new columns) before assigning by reference to it.
#### fix as explained in error message
ans = lapply(ans, lapply, setDT)
.selfref.ok(ans[[2L]][[1L]])
#[1] TRUE

## fix inside frollapply via simplify
simplifix = function(x) lapply(x, lapply, setDT)
ans = frollapply(1:2, 2, function(x) list(data.table(x)), fill=list(data.table(NA)), simplify=simplifix)
.selfref.ok(ans[[2L]][[1L]])
#[1] TRUE

## automatic fix may not work for a non-type stable function
f = function(x) (if (x[1L]==1L) data.frame else data.table)(x)
ans = frollapply(1:3, 2, f, fill=data.table(NA), simplify=FALSE)
.selfref.ok(ans[[3L]])
#[1] FALSE
#### fix inside frollapply via simplify
simplifix = function(x) lapply(x, function(y) if (is.data.table(y)) setDT(y) else y)
ans = frollapply(1:3, 2, f, fill=data.table(NA), simplify=simplifix)
.selfref.ok(ans[[3L]])
#[1] TRUE

setDTthreads(2, throttle=1024) ## enable throttle
```
Due to possible future improvements of handling simplification of results returned from rolling function, the default simplify=TRUE may not be backward compatible for functions that produce results that haven't been already automatically simplified. See the simplify argument section for details.

Performance consideration

frollapply is meant to run any UDF function. If one needs to use a common function like mean, sum, max, etc., then we have highly optimized, implemented in C language, rolling functions described in froll manual.
Most crucial optimizations are the ones to be applied on UDF. Those are discussed below in section UDF optimization.

When using by.column=FALSE, subset the dataset before passing it to X to keep only columns relevant for the computation:


x = setDT(lapply(1:1000, function(x) as.double(rep.int(x,1e4L))))
f = function(x) sum(x$V1 * x$V2)
system.time(frollapply(x, 100, f, by.column=FALSE))
#   user  system elapsed
#  0.373   0.069   0.234
system.time(frollapply(x[, c("V1","V2"), with=FALSE], 100, f, by.column=FALSE))
#   user  system elapsed
#  0.050   0.058   0.061

Avoid partial argument, see partial argument section of froll manual.

Avoid simplify=TRUE and provide a function instead:


x = rnorm(1e5)
system.time(frollapply(x, 2, function(x) 1L, simplify=TRUE))
#   user  system elapsed
#  0.227   0.095   0.236
system.time(frollapply(x, 2, function(x) 1L, simplify=unlist))
#   user  system elapsed
#  0.054   0.049   0.091

CPU threads utilization in frollapply can be controlled by setDTthreads, which by default uses half of available CPU threads. Usage of multiple CPU threads will be throttled for small input, as described in setDTthreads manual.
Parallel computation of FUN is handled by parallel package (part of R core since 2.14.0) and its fork mechanism. Fork is not available on Windows OS, therefore computations will always be single-threaded on that platform.

UDF optimization

FUN will be evaluated many times so should be highly optimized. Tips below are not specific to frollapply and can be applied to any code meant to run in many iterations.

It is usually better to return the most lightweight objects from FUN, for example it will be faster to return a list rather a data.table. In the case presented below, simplify=TRUE is calling rbindlist on the results anyway, which makes the results equal:


fun1 = function(x) {tmp=range(x); data.table(min=tmp[1L], max=tmp[2L])}
fun2 = function(x) {tmp=range(x); list(min=tmp[1L], max=tmp[2L])}
fill1 = data.table(min=NA_integer_, max=NA_integer_)
fill2 = list(min=NA_integer_, max=NA_integer_)
system.time(a<-frollapply(1:1e4, 100, fun1, fill=fill1, simplify=rbindlist))
#   user  system elapsed
#  0.934   0.347   0.706
system.time(b<-frollapply(1:1e4, 100, fun2, fill=fill2, simplify=rbindlist))
#   user  system elapsed
#  0.010   0.033   0.094
all.equal(a, b)
#[1] TRUE

Code that is not dependent on a rolling window should be taken out as pre or post computation:


x = c(1L,3L)
system.time(for (i in 1:1e6) sum(x+1L))
#   user  system elapsed
#  0.218   0.002   0.221
system.time({y = x+1L; for (i in 1:1e6) sum(y)})
#   user  system elapsed
#  0.160   0.001   0.161

Being strict about data types removes the need for R to handle them automatically:


x = vector("integer", 1e6)
system.time(for (i in 1:1e6) x[i] = NA)
#   user  system elapsed
#  0.114   0.000   0.114
system.time(for (i in 1:1e6) x[i] = NA_integer_)
#   user  system elapsed
#  0.029   0.000   0.030

If a function calls another function under the hood, it is usually better to call the latter one directly:


x = matrix(c(1L,2L,3L,4L), c(2L,2L))
system.time(for (i in 1:1e4) colSums(x))
#   user  system elapsed
#  0.033   0.000   0.033
system.time(for (i in 1:1e4) .colSums(x, 2L, 2L))
#   user  system elapsed
#  0.010   0.002   0.012

There are many functions that may be optimized for scaling up with larger input, yet for a small input they may incur bigger overhead comparing to simpler counterparts. One may need to experiment on own data, but low overhead functions are likely to be faster when evaluated over many iterations:


## uniqueN
x = c(1L,3L,5L)
system.time(for (i in 1:1e4) uniqueN(x))
#   user  system elapsed
#  0.078   0.001   0.080
system.time(for (i in 1:1e4) length(unique(x)))
#   user  system elapsed
#  0.018   0.000   0.018
## column subset
x = data.table(v1 = c(1L,3L,5L))
system.time(for (i in 1:1e4) x[, v1])
#   user  system elapsed
#  1.952   0.011   1.964
system.time(for (i in 1:1e4) x[["v1"]])
#   user  system elapsed
#  0.036   0.000   0.035

Implementation

Evaluation of UDF comes with very limited capabilities for optimizations, therefore speed improvements in frollapply should not be expected as good as in other data.table fast functions. frollapply is implemented almost exclusively in R, rather than C. Its speed improvement comes from two optimizations that have been applied:

No repeated allocation of a rolling window subset.
Object (type of X and size of N) is allocated once (for each CPU thread), and then for each iteration this object is being re-used by copying expected subset of data into it. This means we still have to subset data on each iteration, but we only copy data into pre-allocated window object, instead of allocating in each iteration. Allocation is carrying much bigger overhead than copy. The faster the FUN evaluates the more relative speedup we are getting, because allocation of a subset does not depend on how fast or slow FUN evaluates. See caveats section for possible edge cases caused by this optimization.
Parallel evaluation of FUN calls.
Until September 2025 all the multithreaded code in data.table was using OpenMP. It can be used only in C language and it has very low overhead. Unfortunately it could not be applied in frollapply because to evaluate UDF from C code one has to call R's C api that is not thread safe (can be run only from single threaded C code). Therefore frollapply uses parallel-package, which is included in base R, to provide parallelism at the R language level. It uses fork parallelism, which has low overhead as well (unless results of computation are big in size which is not an issue for rolling statistics). Fork is not available on Windows OS. See caveats section for limitations caused by using this optimization.

Note

Be aware that rolling functions operate on the physical order of input. If the intent is to roll values in a vector by a logical window, for example an hour, or a day, then one has to ensure that there are no gaps in the input, or use an adaptive rolling function to handle gaps, for which we provide helper function frolladapt to generate adaptive window size.

Examples

frollapply(1:16, 4, median)
#>  [1]   NA   NA   NA  2.5  3.5  4.5  5.5  6.5  7.5  8.5  9.5 10.5 11.5 12.5 13.5
#> [16] 14.5
frollapply(1:9, 3, toString)
#> [1] NA        NA        "1, 2, 3" "2, 3, 4" "3, 4, 5" "4, 5, 6" "5, 6, 7"
#> [8] "6, 7, 8" "7, 8, 9"

## vectorized input
x = list(1:10, 10:1)
n = c(3, 4)
frollapply(x, n, sum)
#> [[1]]
#>  [1] NA NA  6  9 12 15 18 21 24 27
#> 
#> [[2]]
#>  [1] NA NA NA 10 14 18 22 26 30 34
#> 
#> [[3]]
#>  [1] NA NA 27 24 21 18 15 12  9  6
#> 
#> [[4]]
#>  [1] NA NA NA 34 30 26 22 18 14 10
#> 
## give names
x = list(data1 = 1:10, data2 = 10:1)
n = c(small = 3, big = 4)
frollapply(x, n, sum, give.names=TRUE)
#> $data1_small
#>  [1] NA NA  6  9 12 15 18 21 24 27
#> 
#> $data1_big
#>  [1] NA NA NA 10 14 18 22 26 30 34
#> 
#> $data2_small
#>  [1] NA NA 27 24 21 18 15 12  9  6
#> 
#> $data2_big
#>  [1] NA NA NA 34 30 26 22 18 14 10
#> 

## by.column=FALSE
x = as.data.table(iris)
flow = function(x) {
  v1 = x[[1L]]
  v2 = x[[2L]]
  (v1[2L] - v1[1L] * (1+v2[2L])) / v1[1L]
}
x[, "flow" := frollapply(.(Sepal.Length, Sepal.Width), 2L, flow, by.column=FALSE),
  by = Species][]
#>      Sepal.Length Sepal.Width Petal.Length Petal.Width   Species      flow
#>             <num>       <num>        <num>       <num>    <fctr>     <num>
#>   1:          5.1         3.5          1.4         0.2    setosa        NA
#>   2:          4.9         3.0          1.4         0.2    setosa -3.039216
#>   3:          4.7         3.2          1.3         0.2    setosa -3.240816
#>   4:          4.6         3.1          1.5         0.2    setosa -3.121277
#>   5:          5.0         3.6          1.4         0.2    setosa -3.513043
#>  ---                                                                      
#> 146:          6.7         3.0          5.2         2.3 virginica -3.000000
#> 147:          6.3         2.5          5.0         1.9 virginica -2.559701
#> 148:          6.5         3.0          5.2         2.0 virginica -2.968254
#> 149:          6.2         3.4          5.4         2.3 virginica -3.446154
#> 150:          5.9         3.0          5.1         1.8 virginica -3.048387

## rolling regression: by.column=FALSE
f = function(x) coef(lm(v2 ~ v1, data=x))
x = data.table(v1=rnorm(120), v2=rnorm(120))
frollapply(x, 4, f, by.column=FALSE)
#>      (Intercept)         v1
#>            <num>      <num>
#>   1:          NA         NA
#>   2:          NA         NA
#>   3:          NA         NA
#>   4:  -0.7689705 -0.6347718
#>   5:  -0.4903080 -1.5062131
#>  ---                       
#> 116:   0.3520692  1.2413190
#> 117:  -0.5799706  0.5531221
#> 118:  -0.4525830  0.5763709
#> 119:  -0.8670370 -0.3124939
#> 120:  -0.6700778 -0.3203630