cachematrix.R

###################################################################
##
## Assignment: Caching the Inverse of a Matrix
## 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 (there are also alternatives to matrix inversion that
## we will not discuss here). Your assignment is to write a pair of 
## functions that cache the inverse of a matrix.
##
###################################################################

###################################################################
##
## makeCacheMatrix: creates a special matrix object that can cache
##                  its inverse.
##
###################################################################

makeCacheMatrix <- function(x = matrix()) {
        ## intialisation
        mtx <- x
        inv <- NULL
        
        set <- function(y) {
                mtx <<- y
                inv <<- NULL
        }
        get <- function() mtx
        setinv <- function( inverse ) inv <<- inverse
        getinv <- function() inv
        
        list( set = set, 
              get = get,
              setinv = setinv,
              getinv = getinv )
}

###################################################################
##
## 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.
##
###################################################################

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