cachematrix.R

## Matrix inversion is usually a costly computation and there may be some benefit to caching the inverse of a matrix
## rather than compute it repeatedly. Below is a pair of functions that cache the inverse of a matrix.

## This function creates a special "matrix" object that can cache its inverse.

makeCacheMatrix <- function(x = matrix()) {
    r <- NULL
    set <- function(y) {
        x <<- y
        r <<- NULL
    }
    get <- function() x
    setreverse <- function(reverse) r <<- reverse
    getreverse <- function() r
    list(set = set, get = get,
         setreverse = setreverse,
         getreverse = getreverse)
}


## This function computes the inverse of the special "matrix" returned by makeCacheMatrix above. If the inverse has 
## already been calculated (and the matrix has not changed), then the cachesolve should retrieve the inverse from the cache.

cacheSolve <- function(x, ...) {
    ## Return a matrix that is the inverse of 'x'
    r <- x$getreverse()
    if(!is.null(r)) {
      message("getting cached reversed matrix")
      return(r)
    }
    data <- x$get()
    r <- solve(data, ...)
    x$setreverse(r)
    r
}