# runminmax: Minimum and Maximum of Moving Windows In caTools: Tools: Moving Window Statistics, GIF, Base64, ROC AUC, etc

## Description

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

## Usage

 ```1 2 3 4 5 6``` ``` 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113``` ``` # 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) ```

caTools documentation built on March 28, 2021, 9:07 a.m.