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
        setinv <- function(inv) i <<- inv
        getinv <- function() i
        list(set = set, get = get, setinv = setinv, getinv = getinv)
}


##  computes the inverse of the special "matrix" returned by makeCacheMatrix above

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