## The two functions below are used to set up a matrix and set/get its

## inverse. If the inverse is already calculated, the second function,

## which is suposed to calculate the inverse, gets the already calcu-

## lated inverse, which is cached on memory.

##

## These functions assume that the matrix is already square and inver-

## tible, that is, nonsingular. There are no tests to certify for it.

makeCacheMatrix <- function(x = matrix()) {

## This function creates a special "matrix", which is really a list

## containing a function to:

## 1. set the value of the matrix - makeCacheMatrix$set()

## 2. get the value of the matrix - makeCacheMatrix$get()

## 3. set the value of the inverse - makeCacheMatrix$setinv()

## 4. get the value of the inverse - makeCacheMatrix$setinv()

m <- NULL

set <- function(y) {

x <<- y # x is defined outside; is the argument to the main function

m <<- NULL # m is defined outside

}

get <- function() x

setinv <- function(inv) m <<- inv # m is defined outside this function

getinv <- function() m

list(set = set, get = get,

setinv = setinv,

getinv = getinv)

}

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

## This function calculates the inverse of the special "matrix"

## created with makeCacheMatrix(). However, it first checks to see

## if the inverse has already been calculated. If so, it gets the

## inverse from the cache and skips the computation. Otherwise, it

## calculates the inverse of the data and sets the value of the in-

## verse in the cache via the setinv function.

##

## The matrix is assumed to be square and nonsingular.

m <- x$getinv()

if(!is.null(m)) { # gets the cached inverse; doesn't need to calculate

message("getting cached data")

return(m)

}

data <- x$get()

m <- solve(data) # calculates the inverse

x$setinv(m)

m # returns the calculated inverse

}