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.
## The following pair of functions is used to cache the inverse of a matrix.

## The first function makeCacheMatrix creates a a special "matrix" object, 
## which is really a list containing a function to:
## 1. set the matrix
## 2. get the matrix
## 3. set the inverse of the matrix
## 4. get the inverse of the matrix

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)
}


## The function cacheSolve 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. Otherwise, it computes the inverse of the matrix
## and sets the inverse of the matrix in the cache via the  setinverse  function.

## This function assumes that the matrix supplied is always invertible.

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