cachematrix.R

##  A pair of functions that cache the inverse of a matrix.
    
## makeCacheMatrix: This function creates a special "matrix" object that can cache its inverse.
##
## cacheSolve: 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.




## This function creates a special "matrix", which is really a list containing a function to
## 1. set the value of the matrix
## 2. get the value of the matrix
## 3. set the value of the inverse 
## 4. get the value of the inverse

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


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