## The pair of makeCacheMatrix and cacheSolve functions

## optimize the calculation of the inverse of a matrix by storing the result

## for later use. This avoids calculating the same result twice, which may be

## time consuming for large matrices.

##

## Example

##

## cm <- makeCacheMatrix(matrix(rnorm(9), 3, 3))

## cacheSolve(cm) # calculation performed

## cacheSolve(cm) # cached value returned

## makeCacheMatrix takes a matrix as its input parameter

## and returns a special matrix object composed of four

## functions in a list:

## get() : returns the underlying matrix

## set(y) : sets or updates the underlying matrix

## getinverse() : returns the inverse of the matrix

## setinverse(inverse) : sets or updates 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)

}

## cacheSolve takes a special matrix created by makeCacheMatrix

## and returns its inverse. If the inverse has been previously

## calculated, the cached value is returned. Otherwise the calculation

## is performed and cached for future use.

## Per the assignment instructions, this assumes a square matrix.

cacheSolve <- function(x, ...) {

i <- x$getinverse()

if(!is.null(i)) {

message("getting cached inverse")

return(i)

}

matrix <- x$get()

inverse <- solve(matrix)

x$setinverse(inverse)

inverse

}