# Rle Tips and Tricks

    rollmeanRle <- function (x, k)
    {
        n <- length(x)
        cumsum(c(Rle(sum(window(x, 1, k))), window(x, k + 1, n) - window(x, 1, n - k))) / k
    }

    rollvarRle <- function(x, k)
    {
        n <- length(x)
        means <- rollmeanRle(x, k)
        nextMean <- window(means, 2, n - k + 1)
        cumsum(c(Rle(sum((window(x, 1, k) - means[1])^2)),
        k * diff(means)^2 - (window(x, 1, n - k) - nextMean)^2 + (window(x, k + 1, n) - nextMean)^2)) / (k - 1)
    }

    rollcovRle <- function(x, y, k)
    {
        n <- length(x)
        meanX <- rollmeanRle(x, k)
        meanY <- rollmeanRle(y, k)
        nextMeanX <- window(meanX, 2, n - k + 1)
        nextMeanY <- window(meanY, 2, n - k + 1)
        cumsum(c(Rle(sum((window(x, 1, k) - meanX[1]) * (window(y, 1, k) - meanY[1]))),
        k * diff(meanX) * diff(meanY) - (window(x, 1, n - k) - nextMeanX) * (window(y, 1, n - k) - nextMeanY) + (window(x, k + 1, n) - nextMeanX) * (window(y, k + 1, n) - nextMeanY))) / (k - 1)
    }

    rollsdRle <- function(x, k)
    {
       sqrt(rollvarRle(x, k))
    }

    rollcorRle <- function(x, y, k)
    {
       rollcovRle(x, y, k) / (rollsdRle(x, k) * rollsdRle(y, k))
    }