runmin & runmax {caTools} R Documentation

Minimum and Maximum of Moving Windows

Description

Moving (aka running, rolling) Window Minimum and Maximum calculated over a vector

Usage

runmin(x, k, alg=c("C", "R"),
endrule=c("min", "NA", "trim", "keep", "constant", "func"),
align = c("center", "left", "right"))
runmax(x, k, alg=c("C", "R"),
endrule=c("max", "NA", "trim", "keep", "constant", "func"),
align = c("center", "left", "right"))

Arguments

 x 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.

Author(s)

Jarek Tuszynski (SAIC) jaroslaw.w.tuszynski@saic.com

• 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, main = "Moving Window Analysis Functions")
lines(runmin(x,k), col=col)
lines(runmean(x,k), col=col)
lines(runmax(x,k), col=col)
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)

[Package caTools version 1.18.2 Index]