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\name{runsd}
\alias{runsd}
\title{Standard Deviation of Moving Windows}
\description{ Moving (aka running, rolling) Window's Standard Deviation
calculated over a vector}
\usage{
runsd(x, k, center = runmean(x,k),
endrule=c("sd", "NA", "trim", "keep", "constant", "func"),
align = c("center", "left", "right"))
}
\arguments{
\item{x}{numeric vector of length n or matrix with n rows. If \code{x} is a
matrix than each column will be processed separately.}
\item{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 \code{center} function, since
\code{\link{runmed}} does not take even k's.}
\item{endrule}{character string indicating how the values at the beginning
and the end, of the data, should be treated. Only first and last \code{k2}
values at both ends are affected, where \code{k2} is the half-bandwidth
\code{k2 = k \%/\% 2}.
\itemize{
\item \code{"sd"} - applies the \code{sd} function to
smaller and smaller sections of the array. Equivalent to:
\code{for(i in 1:k2) out[i]=mad(x[1:(i+k2)])}.
\item \code{"trim"} - trim the ends; output array length is equal to
\code{length(x)-2*k2 (out = out[(k2+1):(n-k2)])}. This option mimics
output of \code{\link{apply}} \code{(\link{embed}(x,k),1,FUN)} and other
related functions.
\item \code{"keep"} - fill the ends with numbers from \code{x} vector
\code{(out[1:k2] = x[1:k2])}. This option makes more sense in case of
smoothing functions, kept here for consistency.
\item \code{"constant"} - fill the ends with first and last calculated
value in output array \code{(out[1:k2] = out[k2+1])}
\item \code{"NA"} - fill the ends with NA's \code{(out[1:k2] = NA)}
\item \code{"func"} - same as \code{"mad"} option except that implemented
in R for testing purposes. Avoid since it can be very slow for large windows.
}
Similar to \code{endrule} in \code{\link{runmed}} function which has the
following options: \dQuote{\code{c("median", "keep", "constant")}} .
}
\item{center}{moving window center. Defaults
to running mean (\code{\link{runmean}} function). Similar to \code{center}
in \code{\link{mad}} function. }
\item{align}{specifies whether result should be centered (default),
left-aligned or right-aligned. If \code{endrule}="sd" then setting
\code{align} to "left" or "right" will fall back on slower implementation
equivalent to \code{endrule}="func". }
}
\details{
Apart from the end values, the result of y = runmad(x, k) is the same as
\dQuote{\code{for(j=(1+k2):(n-k2)) y[j]=sd(x[(j-k2):(j+k2)], na.rm = TRUE)}}. It can handle
non-finite numbers like NaN's and Inf's (like \code{\link{mean}(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 \code{\link{runmed}}, a running window median function, all
functions listed in "see also" section are slower than very inefficient
\dQuote{\code{\link{apply}(\link{embed}(x,k),1,FUN)}} approach.
}
\value{
Returns a numeric vector or matrix of the same size as \code{x}. Only in case of
\code{endrule="trim"} the output vectors will be shorter and output matrices
will have fewer rows.
}
\author{Jarek Tuszynski (SAIC) \email{jaroslaw.w.tuszynski@saic.com}}
\seealso{
Links related to:
\itemize{
\item \code{runsd} - \code{\link{sd}}, \code{\link[fSeries]{rollVar}} from
\pkg{fSeries} library
\item Other moving window functions from this package: \code{\link{runmin}},
\code{\link{runmax}}, \code{\link{runquantile}}, \code{\link{runmad}} and
\code{\link{runmean}}
\item generic running window functions: \code{\link{apply}}\code{
(\link{embed}(x,k), 1, FUN)} (fastest), \code{\link[fSeries]{rollFun}}
from \pkg{fSeries} (slow), \code{\link[gtools]{running}} from \pkg{gtools}
package (extremely slow for this purpose), \code{\link[zoo]{rapply}} from
\pkg{zoo} library, \code{\link[magic]{subsums}} from
\pkg{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=runmean(x, k)
y=runsd(x, k, center=m)
plot(x, col=col[1], main = "Moving Window Analysis Functions")
lines(m , col=col[2])
lines(m-y/2, col=col[3])
lines(m+y/2, col=col[3])
lab = c("data", "runmean", "runmean-runsd/2", "runmean+runsd/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 = runsd(x,k, endrule="trim")
b = apply(embed(x,k), 1, sd)
stopifnot(all(abs(a-b)<eps));
k=24 # even size window
a = runsd(x,k, endrule="trim")
b = apply(embed(x,k), 1, sd)
stopifnot(all(abs(a-b)<eps));
# test against loop approach
# this test works fine at the R prompt but fails during package check - need to investigate
k=25; n=200;
x = rnorm(n,sd=30) + abs(seq(n)-n/4) # create random data
x[seq(1,n,11)] = NaN; # add NANs
k2 = k%/%2
k1 = k-k2-1
a = runsd(x, k)
b = array(0,n)
for(j in 1:n) {
lo = max(1, j-k1)
hi = min(n, j+k2)
b[j] = sd(x[lo:hi], na.rm = TRUE)
}
#stopifnot(all(abs(a-b)<eps));
# compare calculation at array ends
k=25; n=100;
x = rnorm(n,sd=30) + abs(seq(n)-n/4)
a = runsd(x, k, endrule="sd" ) # fast C code
b = runsd(x, k, endrule="func") # slow R code
stopifnot(all(abs(a-b)<eps));
# test if moving windows forward and backward gives the same results
k=51;
a = runsd(x , k)
b = runsd(x[n:1], 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 = runsd(x, k)
b = runsd(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
# speed comparison
\dontrun{
x=runif(1e5); k=51; # reduce vector and window sizes
system.time(runsd( x,k,endrule="trim"))
system.time(apply(embed(x,k), 1, sd))
}
}
\keyword{ts}
\keyword{array}
\keyword{utilities}
\concept{moving mad}
\concept{rolling mad}
\concept{running mad}
\concept{running window}
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