runmad {caTools}  R Documentation 
Median Absolute Deviation of Moving Windows
Description
Moving (aka running, rolling) Window MAD (Median Absolute Deviation) calculated over a vector
Usage
runmad(x, k, center = runmed(x,k), constant = 1.4826,
endrule=c("mad", "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 one and n. In case
of even k's one will have to provide different 
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 
center 
moving window center. Defaults
to running median ( 
constant 
scale factor such that for Gaussian
distribution X, 
align 
specifies whether result should be centered (default),
leftaligned or rightaligned. If 
Details
Apart from the end values, the result of y = runmad(x, k) is the same as
“for(j=(1+k2):(nk2)) y[j]=mad(x[(jk2):(j+k2)], na.rm = TRUE)
”.
It can handle nonfinite numbers like NaN's and Inf's
(like “mad(x, na.rm = TRUE)
”).
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.
Functions runquantile
and runmad
are using insertion sort to
sort the moving window, but gain speed by remembering results of the previous
sort. Since each time the window is moved, only one point changes, all but one
points in the window are already sorted. Insertion sort can fix that in O(k)
time.
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.
Author(s)
Jarek Tuszynski (SAIC) jaroslaw.w.tuszynski@saic.com
References
About insertion sort used in runmad
function see:
R. Sedgewick (1988): Algorithms. AddisonWesley (page 99)
See Also
Links related to:

runmad
mad
Other moving window functions from this package:
runmin
,runmax
,runquantile
,runmean
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 runmed function
k=25; n=200;
x = rnorm(n,sd=30) + abs(seq(n)n/4)
col = c("black", "red", "green")
m=runmed(x, k)
y=runmad(x, k, center=m)
plot(x, col=col[1], main = "Moving Window Analysis Functions")
lines(m , col=col[2])
lines(my/2, col=col[3])
lines(m+y/2, col=col[3])
lab = c("data", "runmed", "runmedrunmad/2", "runmed+runmad/2")
legend(0,0.9*n, lab, col=col, lty=1 )
# basic tests against apply/embed
eps = .Machine$double.eps ^ 0.5
k=25 # odd size window
a = runmad(x,k, center=runmed(x,k), endrule="trim")
b = apply(embed(x,k), 1, mad)
stopifnot(all(abs(ab)<eps));
k=24 # even size window
a = runmad(x,k, center=runquantile(x,k,0.5,type=2), endrule="trim")
b = apply(embed(x,k), 1, mad)
stopifnot(all(abs(ab)<eps));
# test against loop approach
# this test works fine at the R prompt but fails during package check  need to investigate
k=24; n=200;
x = rnorm(n,sd=30) + abs(seq(n)n/4) # create random data
x = rep(1:5,40)
#x[seq(1,n,11)] = NaN; # commented out for time beeing  on to do list
#x[5] = NaN; # commented out for time beeing  on to do list
k2 = k
k1 = kk21
ac = array(runquantile(x,k,0.5))
a = runmad(x, k, center=ac)
bc = array(0,n)
b = array(0,n)
for(j in 1:n) {
lo = max(1, jk1)
hi = min(n, j+k2)
bc[j] = median(x[lo:hi], na.rm = TRUE)
b [j] = mad (x[lo:hi], na.rm = TRUE, center=bc[j])
}
eps = .Machine$double.eps ^ 0.5
#stopifnot(all(abs(acbc)<eps)); # commented out for time beeing  on to do list
#stopifnot(all(abs(ab)<eps)); # commented out for time beeing  on to do list
# compare calculation at array ends
k=25; n=200;
x = rnorm(n,sd=30) + abs(seq(n)n/4)
c = runquantile(x,k,0.5,type=2) # find the center
a = runmad(x, k, center=c, endrule="mad" ) # fast C code
b = runmad(x, k, center=c, endrule="func") # slow R code
stopifnot(all(abs(ab)<eps));
# test if moving windows forward and backward gives the same results
k=51;
a = runmad(x , k)
b = runmad(x[n:1], k)
stopifnot(all(a[n:1]==b, na.rm=TRUE));
# 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 = matrix(rep(x, nCol ), nRow, nCol) # replicate x in columns of X
a = runmad(x, k, center = runquantile(x,k,0.5,type=2))
b = runmad(X, k, center = runquantile(X,k,0.5,type=2))
stopifnot(all(abs(ab[,1])<eps)); # vector vs. 2D array
stopifnot(all(abs(b[,1]b[,nCol])<eps)); # compare rows within 2D array
# speed comparison
## Not run:
x=runif(1e5); k=51; # reduce vector and window sizes
system.time(runmad( x,k,endrule="trim"))
system.time(apply(embed(x,k), 1, mad))
## End(Not run)