cachematrix.R

## a pair of functions that cache the inverse of a matrix 

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

makeCacheMatrix <- function(x = matrix()) {
    i <- NULL
    set <- function(y){
        x <<- y
        i <<- NULL
    }
    get <- function() x
    setinverse <- function(inverse) i <<- inverse
    getinverse <- function() i
    list(set = set, get = get,
        setinverse = setinverse,
        getinverse = getinverse)

}


## 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'
    i <- x$getinverse()
    if(!is.null(i)){
        message("getting cached data")
        return(i)
    }
    data <- x$get()
    i <- solve(data,...)
    x$setinverse(i)
    i
}