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runmean(x, k, alg=c("C", "R", "fast", "exact"),
endrule=c("mean", "NA", "trim", "keep", "constant", "func"),
align = c("center", "left", "right"))x is a
matrix than each column will be processed separately."C"- a version is written in C. It can handle non-finite
numbers like NaN's and Inf's (likemean(x, na.rm = TRUE)).
It workk2
values at both ends are affected, where k2 is the half-bandwidth
k2 = k %/% 2endrule="mean" then setting
align to "left" or "right" will fall back on slower implementation
equivalent to endrulex. Only in case of
endrule="trim" the output vectors will be shorter and output matrices
will have fewer rows.for(j=(1+k2):(n-k2)) y[j]=mean(x[(j-k2):(j+k2)])runmed, a running window median function, all
functions listed in "see also" section are slower than very inefficient
apply(embed(x,k),1,FUN)runmean function is O(n).
Function EndRule applies one of the five methods (see endrule
argument) to process end-points 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 round-off errors do not
accumulate. As a result runmean is more accurate than
filter(x, rep(1/k,k)) and runmean(..., alg="C")
functions.runmean:
Shewchuk, JonathanAdaptive Precision Floating-Point Arithmetic and Fast
Robust Geometric Predicates,mean,kernapply,filter,runsum.exact,decompose,stl,rollMeanfromrollmeanfromsubsumsfromrunmin,runmax,runquantile,runmadandrunsdrunmedapply(embed(x,k), 1, FUN)(fastest),rollFunfromrunningfromrapplyfromsubsumsfrom# 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$double.eps ^ 0.5
stopifnot(all(abs(a-b)<eps));
stopifnot(all(abs(a-c)<eps));
# test against loop approach
# this test works fine at the R prompt but fails during package check - need to investigate
k=25;
data(iris)
x = iris[,1]
n = length(x)
x[seq(1,n,11)] = NaN; # add NANs
k2 = k k1 = k-k2-1
a = runmean(x, k)
b = array(0,n)
for(j in 1:n) {
lo = max(1, j-k1)
hi = min(n, j+k2)
b[j] = mean(x[lo:hi], na.rm = TRUE)
}
#stopifnot(all(abs(a-b)<eps)); # commented out for time beeing - on to do list
# compare calculation at array ends
a = runmean(x, k, endrule="mean") # fast C code
b = runmean(x, k, endrule="func") # slow R code
stopifnot(all(abs(a-b)<eps));
# Testing of different methods to each other for non-finite data
# Only alg "C" and "exact" can handle not finite numbers
eps = .Machine$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(b-c)<eps));
# Test if moving windows forward and backward gives the same results
# Test also performed on data with non-finite 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(a-b[,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(a-b)<eps));
stopifnot(all(abs(b-c)<eps));
stopifnot(all(abs(c-d)<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, n-i+1) # test large window size
# speed comparison
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
# 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))
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