Standard Deviation of Moving Windows
Moving (aka running, rolling) Window's Standard Deviation calculated over a vector
runsd(x, k, center = runmean(x,k),
endrule=c("sd", "NA", "trim", "keep", "constant", "func"),
align = c("center", "left", "right"))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 mean ( |
align |
specifies whether result should be centered (default),
left-aligned or right-aligned. If |
Apart from the end values, the result of y = runmad(x, k) is the same as
“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 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 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.
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.
Jarek Tuszynski (SAIC) jaroslaw.w.tuszynski@saic.com
Links related to:
runsd - sd
Other moving window functions from this package: runmin,
runmax, runquantile, runmad and
runmean
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.
# 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
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
## Not run:
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))
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.