#

# Functions `makeCacheMatrix` and `cacheSolve`.

#

# These are so close to the examples `makeVector` and `cachemean` that it almost

# feels like cheating...

# The `makeCacheMatrix` function creates a list of closures, which access a

# stored matrix and an alternative representation of the matrix.

#

# Returns a list of functions which encapsulate the matrix object:

# * getter & setter for the matrix

# * getter & setter for the alternative representation

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

# Initialize the matrix alternative

altx <- NULL

# setter, which sets the `x` and `altx` in the parent scope

set <- function(y) {

x <<- y

# If altx is already set (non-NULL), then we're invalidating the cache;

# otherwise we're just initializing it.

if (!is.null(altx)) message("invalidating cache")

set_alt(NULL)

}

# getter for `x` in the parent scope

get <- function() x

# setter for `altx` in the parent scope

set_alt <- function(alt) {

altx <<- alt

}

# getter for `altx` in the parent scope

get_alt <- function() altx

list(set=set, get=get, set_alt=set_alt, get_alt=get_alt)

}

# The `cacheSolve` function returns the cached inverse of the matrix inside the

# scope accessed by the functions in `x`, solving and caching the inverse if it

# does not already exist.

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

# `m` is NULL if the cache is empty

m <- x$get_alt()

if (is.null(m)) {

data <- x$get()

m <- solve(data, ...)

x$set_alt(m)

}

else {

message("getting cached data")

}

m

}