numeric vector of length n or matrix with n rows. If x is a
matrix than each column will be processed separately.
k
width of moving window; must be an integer between one and n
endrule
character string indicating how the values at the beginning
and the end, of the array, should be treated. Only first and last k2
values at both ends are affected, where k2 is the half-bandwidth
k2 = k %/% 2.
"quantile" - applies the quantile
function to smaller and smaller sections of the array. Equivalent to:
for(i in 1:k2) out[i]=quantile(x[1:(i+k2)]).
"trim" - trim the ends; output array length is equal to
length(x)-2*k2 (out = out[(k2+1):(n-k2)]). This option mimics
output of apply(embed(x,k),1,FUN) and other
related functions.
"keep" - fill the ends with numbers from x vector
(out[1:k2] = x[1:k2])
"constant" - fill the ends with first and last calculated
value in output array (out[1:k2] = out[k2+1])
"NA" - fill the ends with NA's (out[1:k2] = NA)
"func" - same as "quantile" but implimented
in R. This option could be very slow, and is included mostly for testing
Similar to endrule in runmed function which has the
following options: “c("median", "keep", "constant")” .
probs
numeric vector of probabilities with values in [0,1] range
used by runquantile. For example Probs=c(0,0.5,1) would be
equivalent to running runmin, runmed and runmax.
Same as probs in quantile function.
type
an integer between 1 and 9 selecting one of the nine quantile
algorithms, same as type in quantile function.
Another even more readable description of nine ways to calculate quantiles
can be found at http://mathworld.wolfram.com/Quantile.html.
align
specifies whether result should be centered (default),
left-aligned or right-aligned. If endrule="quantile" then setting
align to "left" or "right" will fall back on slower implementation
equivalent to endrule="func".
Details
Apart from the end values, the result of y = runquantile(x, k) is the same as
“for(j=(1+k2):(n-k2)) y[j]=quintile(x[(j-k2):(j+k2)],na.rm = TRUE)”. It can handle
non-finite numbers like NaN's and Inf's (like quantile(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. Relative
speeds of runquantile is O(n*k)
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
If x is a matrix than function runquantile returns a matrix of
size [n xlength(probs)]. If x is vactor
a than function runquantile returns a matrix of size
[dim(x) xlength(probs)].
If endrule="trim" the output will have fewer rows.
About insertion sort used in runmad and runquantile:
R. Sedgewick (1988): Algorithms. Addison-Wesley (page 99)
See Also
Links related to:
Running Quantile - quantile, runmed,
smooth, rollmedian from
zoo library
Other moving window functions from this package: runmin,
runmax, runmean, runmad and
runsd
Running Minimum - min
Running Maximum - max, rollmax from zoo library
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 plot using runquantile
k=31; n=200;
x = rnorm(n,sd=30) + abs(seq(n)-n/4)
y=runquantile(x, k, probs=c(0.05, 0.25, 0.5, 0.75, 0.95))
col = c("black", "red", "green", "blue", "magenta", "cyan")
plot(x, col=col[1], main = "Moving Window Quantiles")
lines(y[,1], col=col[2])
lines(y[,2], col=col[3])
lines(y[,3], col=col[4])
lines(y[,4], col=col[5])
lines(y[,5], col=col[6])
lab = c("data", "runquantile(.05)", "runquantile(.25)", "runquantile(0.5)",
"runquantile(.75)", "runquantile(.95)")
legend(0,230, lab, col=col, lty=1 )
# show plot using runquantile
k=15; n=200;
x = rnorm(n,sd=30) + abs(seq(n)-n/4)
y=runquantile(x, k, probs=c(0.05, 0.25, 0.5, 0.75, 0.95))
col = c("black", "red", "green", "blue", "magenta", "cyan")
plot(x, col=col[1], main = "Moving Window Quantiles (smoothed)")
lines(runmean(y[,1],k), col=col[2])
lines(runmean(y[,2],k), col=col[3])
lines(runmean(y[,3],k), col=col[4])
lines(runmean(y[,4],k), col=col[5])
lines(runmean(y[,5],k), col=col[6])
lab = c("data", "runquantile(.05)", "runquantile(.25)", "runquantile(0.5)",
"runquantile(.75)", "runquantile(.95)")
legend(0,230, lab, col=col, lty=1 )
# basic tests against runmin & runmax
y = runquantile(x, k, probs=c(0, 1))
a = runmin(x,k) # test only the inner part
stopifnot(all(a==y[,1], na.rm=TRUE));
a = runmax(x,k) # test only the inner part
stopifnot(all(a==y[,2], na.rm=TRUE));
# basic tests against runmed, including testing endrules
a = runquantile(x, k, probs=0.5, endrule="keep")
b = runmed(x, k, endrule="keep")
stopifnot(all(a==b, na.rm=TRUE));
a = runquantile(x, k, probs=0.5, endrule="constant")
b = runmed(x, k, endrule="constant")
stopifnot(all(a==b, na.rm=TRUE));
# basic tests against apply/embed
a = runquantile(x,k, c(0.3, 0.7), endrule="trim")
b = t(apply(embed(x,k), 1, quantile, probs = c(0.3, 0.7)))
eps = .Machine$double.eps ^ 0.5
stopifnot(all(abs(a-b)<eps));
# test against loop approach
# this test works fine at the R prompt but fails during package check - need to investigate
k=25; n=200;
x = rnorm(n,sd=30) + abs(seq(n)-n/4) # create random data
x[seq(1,n,11)] = NaN; # add NANs
k2 = k
k1 = k-k2-1
a = runquantile(x, k, probs=c(0.3, 0.8) )
b = matrix(0,n,2);
for(j in 1:n) {
lo = max(1, j-k1)
hi = min(n, j+k2)
b[j,] = quantile(x[lo:hi], probs=c(0.3, 0.8), na.rm = TRUE)
}
#stopifnot(all(abs(a-b)<eps));
# compare calculation of array ends
a = runquantile(x, k, probs=0.4, endrule="quantile") # fast C code
b = runquantile(x, k, probs=0.4, endrule="func") # slow R code
stopifnot(all(abs(a-b)<eps));
# test if moving windows forward and backward gives the same results
k=51;
a = runquantile(x , k, probs=0.4)
b = runquantile(x[n:1], k, probs=0.4)
stopifnot(all(a[n:1]==b, na.rm=TRUE));
# test vector vs. matrix inputs, especially for the edge handling
nRow=200; k=25; nCol=10
x = rnorm(nRow,sd=30) + abs(seq(nRow)-n/4)
x[seq(1,nRow,10)] = NaN; # add NANs
X = matrix(rep(x, nCol ), nRow, nCol) # replicate x in columns of X
a = runquantile(x, k, probs=0.6)
b = runquantile(X, k, probs=0.6)
stopifnot(all(abs(a-b[,1])<eps)); # vector vs. 2D array
stopifnot(all(abs(b[,1]-b[,nCol])<eps)); # compare rows within 2D array
# Exhaustive testing of runquantile to standard R approach
numeric.test = function (x, k) {
probs=c(1, 25, 50, 75, 99)/100
a = runquantile(x,k, c(0.3, 0.7), endrule="trim")
b = t(apply(embed(x,k), 1, quantile, probs = c(0.3, 0.7), na.rm=TRUE))
eps = .Machine$double.eps ^ 0.5
stopifnot(all(abs(a-b)<eps));
}
n=50;
x = rnorm(n,sd=30) + abs(seq(n)-n/4) # nice behaving data
for(i in 2:5) numeric.test(x, i) # test small window sizes
for(i in 1:5) numeric.test(x, n-i+1) # test large window size
x[seq(1,50,10)] = NaN; # add NANs and repet the test
for(i in 2:5) 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
## Not run:
x=runif(1e6); k=1e3+1;
system.time(runquantile(x,k,0.5)) # Speed O(n*k)
system.time(runmed(x,k)) # Speed O(n * log(k))
## End(Not run)