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.
"min" & "max" - applies the underlying function to
smaller and smaller sections of the array. In case of min equivalent to:
for(i in 1:k2) out[i]=min(x[1:(i+k2)]). Default.
"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 "min" & "max" 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")” .
alg
an option allowing to choose different algorithms or
implementations. Default is to use of code written in C (option alg="C").
Option alg="R" will use slower code written in R. Useful for
debugging and studying the algorithm.
align
specifies whether result should be centered (default),
left-aligned or right-aligned. If endrule="min" or "max" 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 = runFUN(x, k) is the same as
“for(j=(1+k2):(n-k2)) y[j]=FUN(x[(j-k2):(j+k2)], na.rm = TRUE)”, where FUN
stands for min or max functions. Both functions can handle non-finite
numbers like NaN's and Inf's the same way as min(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 runmin and runmax functions is O(n) in best and average
case and O(n*k) in worst case.
Both functions work with infinite numbers (NA,NaN,Inf,
-Inf). Also default endrule is hardwired in C for speed.
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.
Other moving window functions from this package: runmean,
runquantile, runmad and runsd
R functions: runmed, min, max
Similar functions in other packages: 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 runmin, runmax and runmed
k=25; n=200;
x = rnorm(n,sd=30) + abs(seq(n)-n/4)
col = c("black", "red", "green", "blue", "magenta", "cyan")
plot(x, col=col[1], main = "Moving Window Analysis Functions")
lines(runmin(x,k), col=col[2])
lines(runmean(x,k), col=col[3])
lines(runmax(x,k), col=col[4])
legend(0,.9*n, c("data", "runmin", "runmean", "runmax"), col=col, lty=1 )
# basic tests against standard R approach
a = runmin(x,k, endrule="trim") # test only the inner part
b = apply(embed(x,k), 1, min) # Standard R running min
stopifnot(all(a==b));
a = runmax(x,k, endrule="trim") # test only the inner part
b = apply(embed(x,k), 1, max) # Standard R running min
stopifnot(all(a==b));
# test against loop approach
k=25;
data(iris)
x = iris[,1]
n = length(x)
x[seq(1,n,11)] = NaN; # add NANs
k2 = k
k1 = k-k2-1
a1 = runmin(x, k)
a2 = runmax(x, k)
b1 = array(0,n)
b2 = array(0,n)
for(j in 1:n) {
lo = max(1, j-k1)
hi = min(n, j+k2)
b1[j] = min(x[lo:hi], na.rm = TRUE)
b2[j] = max(x[lo:hi], na.rm = TRUE)
}
# this test works fine at the R prompt but fails during package check - need to investigate
## Not run:
stopifnot(all(a1==b1, na.rm=TRUE));
stopifnot(all(a2==b2, na.rm=TRUE));
## End(Not run)
# Test if moving windows forward and backward gives the same results
# Two data sets also corespond to best and worst-case scenatio data-sets
k=51; n=200;
a = runmin(n:1, k)
b = runmin(1:n, k)
stopifnot(all(a[n:1]==b, na.rm=TRUE));
a = runmax(n:1, k)
b = runmax(1:n, 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[seq(1,nRow,10)] = NaN; # add NANs
X = matrix(rep(x, nCol ), nRow, nCol) # replicate x in columns of X
a = runmax(x, k)
b = runmax(X, k)
stopifnot(all(a==b[,1], na.rm=TRUE)); # vector vs. 2D array
stopifnot(all(b[,1]==b[,nCol], na.rm=TRUE)); # compare rows within 2D array
a = runmin(x, k)
b = runmin(X, k)
stopifnot(all(a==b[,1], na.rm=TRUE)); # vector vs. 2D array
stopifnot(all(b[,1]==b[,nCol], na.rm=TRUE)); # compare rows within 2D array
# Compare C and R algorithms to each other for extreme window sizes
numeric.test = function (x, k) {
a = runmin( x, k, alg="C")
b = runmin( x, k, alg="R")
c =-runmax(-x, k, alg="C")
d =-runmax(-x, k, alg="R")
stopifnot(all(a==b, na.rm=TRUE));
#stopifnot(all(c==d, na.rm=TRUE));
#stopifnot(all(a==c, na.rm=TRUE));
stopifnot(all(b==d, na.rm=TRUE));
}
n=200; # n is an even number
x = rnorm(n,sd=30) + abs(seq(n)-n/4) # random data
for(i in 1:5) numeric.test(x, i) # test for small window size
for(i in 1:5) numeric.test(x, n-i+1) # test for large window size
n=201; # n is an odd number
x = rnorm(n,sd=30) + abs(seq(n)-n/4) # random data
for(i in 1:5) numeric.test(x, i) # test for small window size
for(i in 1:5) numeric.test(x, n-i+1) # test for large window size
n=200; # n is an even number
x = rnorm(n,sd=30) + abs(seq(n)-n/4) # random data
x[seq(1,200,10)] = NaN; # with some NaNs
for(i in 1:5) numeric.test(x, i) # test for small window size
for(i in 1:5) numeric.test(x, n-i+1) # test for large window size
n=201; # n is an odd number
x = rnorm(n,sd=30) + abs(seq(n)-n/4) # random data
x[seq(1,200,2)] = NaN; # with some NaNs
for(i in 1:5) numeric.test(x, i) # test for small window size
for(i in 1:5) numeric.test(x, n-i+1) # test for large window size
# speed comparison
## Not run:
n = 1e7; k=991;
x1 = runif(n); # random data - average case scenario
x2 = 1:n; # best-case scenario data for runmax
x3 = n:1; # worst-case scenario data for runmax
system.time( runmax( x1,k,alg="C")) # C alg on average data O(n)
system.time( runmax( x2,k,alg="C")) # C alg on best-case data O(n)
system.time( runmax( x3,k,alg="C")) # C alg on worst-case data O(n*k)
system.time(-runmin(-x1,k,alg="C")) # use runmin to do runmax work
system.time( runmax( x1,k,alg="R")) # R version of the function
x=runif(1e5); k=1e2; # reduce vector and window sizes
system.time(runmax(x,k,alg="R")) # R version of the function
system.time(apply(embed(x,k), 1, max)) # standard R approach
## End(Not run)