Fast rolling functions to calculate aggregates on sliding windows. Function name and arguments are experimental.

frollmean(x, n, fill=NA, algo=c("fast", "exact"),
align=c("right", "left", "center"), na.rm=FALSE, hasNA=NA, adaptive=FALSE)
frollsum(x, n, fill=NA, algo=c("fast","exact"),
align=c("right", "left", "center"), na.rm=FALSE, hasNA=NA, adaptive=FALSE)
frollapply(x, n, FUN, ..., fill=NA, align=c("right", "left", "center"))

## Arguments

x

Vector, data.frame or data.table of integer, numeric or logical columns over which to calculate the windowed aggregations. May also be a list, in which case the rolling function is applied to each of its elements.

n

Integer vector giving rolling window size(s). This is the total number of included values. Adaptive rolling functions also accept a list of integer vectors.

fill

Numeric; value to pad by. Defaults to NA.

algo

Character, default "fast". When set to "exact", a slower (but more accurate) algorithm is used. It suffers less from floating point rounding errors by performing an extra pass, and carefully handles all non-finite values. It will use mutiple cores where available. See Details for more information.

align

Character, specifying the "alignment" of the rolling window, defaulting to "right". "right" covers preceding rows (the window ends on the current value); "left" covers following rows (the window starts on the current value); "center" is halfway in between (the window is centered on the current value, biased towards "left" when n is even).

na.rm

Logical, default FALSE. Should missing values be removed when calculating window? For details on handling other non-finite values, see Details.

hasNA

Logical. If it is known that x contains NA then setting this to TRUE will speed up calculation. Defaults to NA.

Logical, default FALSE. Should the rolling function be calculated adaptively? See Details below.

FUN

The function to be applied to the rolling window; see Details for restrictions.

...

Extra arguments passed to FUN in frollapply.

## Details

froll* functions accept vectors, lists, data.frames or data.tables. They always return a list except when the input is a vector and length(n)==1, in which case a vector is returned, for convenience. Thus, rolling functions can be used conveniently within data.table syntax.

Argument n allows multiple values to apply rolling functions on multiple window sizes. If adaptive=TRUE, then n must be a list. Each list element must be integer vector of window sizes corresponding to every single observation in each column; see Examples.

When algo="fast" an "on-line" algorithm is used, and all of NaN, +Inf, -Inf are treated as NA. Setting algo="exact" will make rolling functions to use a more computationally-intensive algorithm that suffers less from floating point rounding error (the same consideration applies to mean). algo="exact" also handles NaN, +Inf, -Inf consistently to base R. In case of some functions (like mean), it will additionally make extra pass to perform floating point error correction. Error corrections might not be truly exact on some platforms (like Windows) when using multiple threads.

Adaptive rolling functions are a special case where each observation has its own corresponding rolling window width. Due to the logic of adaptive rolling functions, the following restrictions apply:

• align only "right".

• if list of vectors is passed to x, then all vectors within it must have equal length.

When multiple columns or multiple windows width are provided, then they are run in parallel. The exception is for algo="exact", which runs in parallel already.

frollapply computes rolling aggregate on arbitrary R functions. The input x (first argument) to the function FUN is coerced to numeric beforehand and FUN has to return a scalar numeric value. Checks for that are made only during the first iteration when FUN is evaluated. Edge cases can be found in examples below. Any R function is supported, but it is not optimized using our own C implementation -- hence, for example, using frollapply to compute a rolling average is inefficient. It is also always single-threaded because there is no thread-safe API to R's C eval. Nevertheless we've seen the computation speed up vis-a-vis versions implemented in base R.

## Value

A list except when the input is a vector and

length(n)==1 in which case a vector is returned.

## Note

Users coming from most popular package for rolling functions zoo might expect following differences in data.table implementation.

• rolling function will always return result of the same length as input.

• fill defaults to NA.

• fill accepts only constant values. It does not support for na.locf or other functions.

• align defaults to "right".

• na.rm is respected, and other functions are not needed when input contains NA.

• integers and logical are always coerced to double.

• when adaptive=FALSE (default), then n must be a numeric vector. List is not accepted.

• when adaptive=TRUE, then n must be vector of length equal to nrow(x), or list of such vectors.

• partial window feature is not supported, although it can be accomplished by using adaptive=TRUE, see examples. NA is always returned for incomplete windows.

Be aware that rolling functions operates 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, one has to ensure that there are no gaps in input. For details see issue #3241.

shift, data.table

Round-off error

## Examples

d = as.data.table(list(1:6/2, 3:8/4))
# rollmean of single vector and single window
frollmean(d[, V1], 3)
#> [1]  NA  NA 1.0 1.5 2.0 2.5
# multiple columns at once
frollmean(d, 3)
#> [[1]]
#> [1]  NA  NA 1.0 1.5 2.0 2.5
#>
#> [[2]]
#> [1]   NA   NA 1.00 1.25 1.50 1.75
#>
# multiple windows at once
frollmean(d[, .(V1)], c(3, 4))
#> [[1]]
#> [1]  NA  NA 1.0 1.5 2.0 2.5
#>
#> [[2]]
#> [1]   NA   NA   NA 1.25 1.75 2.25
#>
# multiple columns and multiple windows at once
frollmean(d, c(3, 4))
#> [[1]]
#> [1]  NA  NA 1.0 1.5 2.0 2.5
#>
#> [[2]]
#> [1]   NA   NA   NA 1.25 1.75 2.25
#>
#> [[3]]
#> [1]   NA   NA 1.00 1.25 1.50 1.75
#>
#> [[4]]
#> [1]    NA    NA    NA 1.125 1.375 1.625
#>
## three calls above will use multiple cores when available

# partial window using adaptive rolling function
an = function(n, len) c(seq.int(n), rep(n, len-n))
n = an(3, nrow(d))
#> [[1]]
#> [1] 0.50 0.75 1.00 1.50 2.00 2.50
#>
#> [[2]]
#> [1] 0.750 0.875 1.000 1.250 1.500 1.750
#>

# frollsum
frollsum(d, 3:4)
#> [[1]]
#> [1]  NA  NA 3.0 4.5 6.0 7.5
#>
#> [[2]]
#> [1] NA NA NA  5  7  9
#>
#> [[3]]
#> [1]   NA   NA 3.00 3.75 4.50 5.25
#>
#> [[4]]
#> [1]  NA  NA  NA 4.5 5.5 6.5
#>

# frollapply
frollapply(d, 3:4, sum)
#> [[1]]
#> [1]  NA  NA 3.0 4.5 6.0 7.5
#>
#> [[2]]
#> [1] NA NA NA  5  7  9
#>
#> [[3]]
#> [1]   NA   NA 3.00 3.75 4.50 5.25
#>
#> [[4]]
#> [1]  NA  NA  NA 4.5 5.5 6.5
#>
f = function(x, ...) if (sum(x, ...)>5) min(x, ...) else max(x, ...)
frollapply(d, 3:4, f, na.rm=TRUE)
#> [[1]]
#> [1]  NA  NA 1.5 2.0 1.5 2.0
#>
#> [[2]]
#> [1]  NA  NA  NA 2.0 1.0 1.5
#>
#> [[3]]
#> [1]   NA   NA 1.25 1.50 1.75 1.50
#>
#> [[4]]
#> [1]   NA   NA   NA 1.50 1.00 1.25
#>

# performance vs exactness
set.seed(108)
x = sample(c(rnorm(1e3, 1e6, 5e5), 5e9, 5e-9))
n = 15
ma = function(x, n, na.rm=FALSE) {
ans = rep(NA_real_, nx<-length(x))
for (i in n:nx) ans[i] = mean(x[(i-n+1):i], na.rm=na.rm)
ans
}
fastma = function(x, n, na.rm) {
if (!missing(na.rm)) stop("NAs are unsupported, wrongly propagated by cumsum")
cs = cumsum(x)
scs = shift(cs, n)
scs[n] = 0
as.double((cs-scs)/n)
}
system.time(ans1<-ma(x, n))
#>    user  system elapsed
#>   0.006   0.000   0.006
system.time(ans2<-fastma(x, n))
#>    user  system elapsed
#>       0       0       0
system.time(ans3<-frollmean(x, n))
#>    user  system elapsed
#>       0       0       0
system.time(ans4<-frollmean(x, n, algo="exact"))
#>    user  system elapsed
#>       0       0       0
system.time(ans5<-frollapply(x, n, mean))
#>    user  system elapsed
#>   0.004   0.000   0.005
anserr = list(
fastma = ans2-ans1,
froll_fast = ans3-ans1,
froll_exact = ans4-ans1,
frollapply = ans5-ans1
)
errs = sapply(lapply(anserr, abs), sum, na.rm=TRUE)
sapply(errs, format, scientific=FALSE) # roundoff
#>             fastma         froll_fast        froll_exact         frollapply
#>    "0.00001287466" "0.00000001833541"                "0"                "0"

# frollapply corner cases
f = function(x) head(x, 2)     ## FUN returns non length 1
try(frollapply(1:5, 3, f))
#> Error in frollapply(1:5, 3, f) :
#>   frollapply: results from provided FUN are not length 1
f = function(x) {              ## FUN sometimes returns non length 1
n = length(x)
# length 1 will be returned only for first iteration where we check length
if (n==x[n]) x[1L] else range(x) # range(x)[2L] is silently ignored!
}
frollapply(1:5, 3, f)
#> [1] NA NA  1  2  3
options(datatable.verbose=TRUE)
x = c(1,2,1,1,1,2,3,2)
frollapply(x, 3, uniqueN)     ## FUN returns integer
#> frollapplyR: allocating memory for results 1x1
#> forder.c received 3 rows and 1 columns
#> frollapply: results from provided FUN are not of type double, coercion from integer or logical will be applied on each iteration
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> frollapply: took 0.000s
#> frollapplyR: processing of 1 column(s) and 1 window(s) took 0.000s
#> [1] NA NA  2  2  1  2  3  2
numUniqueN = function(x) as.numeric(uniqueN(x))
frollapply(x, 3, numUniqueN)
#> frollapplyR: allocating memory for results 1x1
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> forder.c received 3 rows and 1 columns
#> frollapply: took 0.000s
#> frollapplyR: processing of 1 column(s) and 1 window(s) took 0.000s
#> [1] NA NA  2  2  1  2  3  2
x = c(1,2,1,1,NA,2,NA,2)
frollapply(x, 3, anyNA)       ## FUN returns logical
#> frollapplyR: allocating memory for results 1x1
#> frollapply: results from provided FUN are not of type double, coercion from integer or logical will be applied on each iteration
#> frollapply: took 0.000s
#> frollapplyR: processing of 1 column(s) and 1 window(s) took 0.000s
#> [1] NA NA  0  0  1  1  1  1
as.logical(frollapply(x, 3, anyNA))
#> frollapplyR: allocating memory for results 1x1
#> frollapply: results from provided FUN are not of type double, coercion from integer or logical will be applied on each iteration
#> frollapply: took 0.000s
#> frollapplyR: processing of 1 column(s) and 1 window(s) took 0.000s
#> [1]    NA    NA FALSE FALSE  TRUE  TRUE  TRUE  TRUE
options(datatable.verbose=FALSE)
f = function(x) {             ## FUN returns character
if (sum(x)>5) "big" else "small"
}
try(frollapply(1:5, 3, f))
#> Error in frollapply(1:5, 3, f) :
#>   frollapply: results from provided FUN are not of type double
f = function(x) {             ## FUN is not type-stable
n = length(x)
# double type will be returned only for first iteration where we check type
if (n==x[n]) 1 else NA # NA logical turns into garbage without coercion to double
}
try(frollapply(1:5, 3, f))
#> Error in frollapply(1:5, 3, f) :
#>   REAL() can only be applied to a 'numeric', not a 'logical'