runmean {caTools}  R Documentation 
Mean of a Moving Window
Description
Moving (aka running, rolling) Window Mean calculated over a vector
Usage
runmean(x, k, alg=c("C", "R", "fast", "exact"),
endrule=c("mean", "NA", "trim", "keep", "constant", "func"),
align = c("center", "left", "right"))
Arguments
x 
numeric vector of length n or matrix with n rows. If 
k 
width of moving window; must be an integer between 1 and n 
alg 
an option to choose different algorithms

endrule 
character string indicating how the values at the beginning
and the end, of the data, should be treated. Only first and last
Similar to 
align 
specifies whether result should be centered (default),
leftaligned or rightaligned. If 
Details
Apart from the end values, the result of y = runmean(x, k) is the same as
“for(j=(1+k2):(nk2)) y[j]=mean(x[(jk2):(j+k2)])
”.
The main incentive to write this set of functions was relative slowness of
majority of moving window functions available in R and its packages. With the
exception of runmed
, a running window median function, all
functions listed in "see also" section are slower than very inefficient
“apply(embed(x,k),1,FUN)
” approach. Relative
speed of runmean
function is O(n).
Function EndRule
applies one of the five methods (see endrule
argument) to process endpoints of the input array x
. In current
version of the code the default endrule="mean"
option is calculated
within C code. That is done to improve speed in case of large moving windows.
In case of runmean(..., alg="exact")
function a special algorithm is
used (see references section) to ensure that roundoff errors do not
accumulate. As a result runmean
is more accurate than
filter
(x, rep(1/k,k)) and runmean(..., alg="C")
functions.
Value
Returns a numeric vector or matrix of the same size as x
. Only in case of
endrule="trim"
the output vectors will be shorter and output matrices
will have fewer rows.
Note
Function runmean(..., alg="exact")
is based by code by Vadim Ogranovich,
which is based on Python code (see last reference), pointed out by Gabor
Grothendieck.
Author(s)
Jarek Tuszynski (SAIC) jaroslaw.w.tuszynski@saic.com
References
About roundoff error correction used in
runmean
: Shewchuk, Jonathan Adaptive Precision FloatingPoint Arithmetic and Fast Robust Geometric Predicates, http://www2.cs.cmu.edu/afs/cs/project/quake/public/papers/robustarithmetic.ps
See Also
Links related to:
moving mean 
mean
,kernapply
,filter
,decompose
,stl
,rollmean
from zoo library,subsums
from magic library,Other moving window functions from this package:
runmin
,runmax
,runquantile
,runmad
andrunsd
generic running window functions:
apply
(embed(x,k), 1, FUN)
(fastest),running
from gtools package (extremely slow for this purpose),subsums
from magic library can perform running window operations on data with any dimensions.
Examples
# show runmean for different window sizes
n=200;
x = rnorm(n,sd=30) + abs(seq(n)n/4)
x[seq(1,n,10)] = NaN; # add NANs
col = c("black", "red", "green", "blue", "magenta", "cyan")
plot(x, col=col[1], main = "Moving Window Means")
lines(runmean(x, 3), col=col[2])
lines(runmean(x, 8), col=col[3])
lines(runmean(x,15), col=col[4])
lines(runmean(x,24), col=col[5])
lines(runmean(x,50), col=col[6])
lab = c("data", "k=3", "k=8", "k=15", "k=24", "k=50")
legend(0,0.9*n, lab, col=col, lty=1 )
# basic tests against 2 standard R approaches
k=25; n=200;
x = rnorm(n,sd=30) + abs(seq(n)n/4) # create random data
a = runmean(x,k, endrule="trim") # tested function
b = apply(embed(x,k), 1, mean) # approach #1
c = cumsum(c( sum(x[1:k]), diff(x,k) ))/k # approach #2
eps = .Machine$double.eps ^ 0.5
stopifnot(all(abs(ab)<eps));
stopifnot(all(abs(ac)<eps));
# test against loop approach
# this test works fine at the R prompt but fails during package check  need to investigate
k=25;
data(iris)
x = iris[,1]
n = length(x)
x[seq(1,n,11)] = NaN; # add NANs
k2 = k
k1 = kk21
a = runmean(x, k)
b = array(0,n)
for(j in 1:n) {
lo = max(1, jk1)
hi = min(n, j+k2)
b[j] = mean(x[lo:hi], na.rm = TRUE)
}
#stopifnot(all(abs(ab)<eps)); # commented out for time beeing  on to do list
# compare calculation at array ends
a = runmean(x, k, endrule="mean") # fast C code
b = runmean(x, k, endrule="func") # slow R code
stopifnot(all(abs(ab)<eps));
# Testing of different methods to each other for nonfinite data
# Only alg "C" and "exact" can handle not finite numbers
eps = .Machine$double.eps ^ 0.5
n=200; k=51;
x = rnorm(n,sd=30) + abs(seq(n)n/4) # nice behaving data
x[seq(1,n,10)] = NaN; # add NANs
x[seq(1,n, 9)] = Inf; # add infinities
b = runmean( x, k, alg="C")
c = runmean( x, k, alg="exact")
stopifnot(all(abs(bc)<eps));
# Test if moving windows forward and backward gives the same results
# Test also performed on data with nonfinite numbers
a = runmean(x , alg="C", k)
b = runmean(x[n:1], alg="C", k)
stopifnot(all(abs(a[n:1]b)<eps));
a = runmean(x , alg="exact", k)
b = runmean(x[n:1], alg="exact", k)
stopifnot(all(abs(a[n:1]b)<eps));
# test vector vs. matrix inputs, especially for the edge handling
nRow=200; k=25; nCol=10
x = rnorm(nRow,sd=30) + abs(seq(nRow)n/4)
x[seq(1,nRow,10)] = NaN; # add NANs
X = matrix(rep(x, nCol ), nRow, nCol) # replicate x in columns of X
a = runmean(x, k)
b = runmean(X, k)
stopifnot(all(abs(ab[,1])<eps)); # vector vs. 2D array
stopifnot(all(abs(b[,1]b[,nCol])<eps)); # compare rows within 2D array
# Exhaustive testing of different methods to each other for different windows
numeric.test = function (x, k) {
a = runmean( x, k, alg="fast")
b = runmean( x, k, alg="C")
c = runmean( x, k, alg="exact")
d = runmean( x, k, alg="R", endrule="func")
eps = .Machine$double.eps ^ 0.5
stopifnot(all(abs(ab)<eps));
stopifnot(all(abs(bc)<eps));
stopifnot(all(abs(cd)<eps));
}
n=200;
x = rnorm(n,sd=30) + abs(seq(n)n/4) # nice behaving data
for(i in 1:5) numeric.test(x, i) # test small window sizes
for(i in 1:5) numeric.test(x, ni+1) # test large window size
# speed comparison
## Not run:
x=runif(1e7); k=1e4;
system.time(runmean(x,k,alg="fast"))
system.time(runmean(x,k,alg="C"))
system.time(runmean(x,k,alg="exact"))
system.time(runmean(x,k,alg="R")) # R version of the function
x=runif(1e5); k=1e2; # reduce vector and window sizes
system.time(runmean(x,k,alg="R")) # R version of the function
system.time(apply(embed(x,k), 1, mean)) # standard R approach
system.time(filter(x, rep(1/k,k), sides=2)) # the fastest alternative I know
## End(Not run)
# show different runmean algorithms with data spanning many orders of magnitude
n=30; k=5;
x = rep(100/3,n)
d=1e10
x[5] = d;
x[13] = d;
x[14] = d*d;
x[15] = d*d*d;
x[16] = d*d*d*d;
x[17] = d*d*d*d*d;
a = runmean(x, k, alg="fast" )
b = runmean(x, k, alg="C" )
c = runmean(x, k, alg="exact")
y = t(rbind(x,a,b,c))
y