cachematrix.R

## 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.
## Below are a pair of functions that are used to create a special object that 
## stores a matrix and caches its inverse.

## This function creates a special "matrix" object that can cache its inverse.


makeCacheMatrix <- function(x = matrix()) {
    m <- NULL
    set <- function(y) {
        x <<- y
        m <<- NULL
    }
    get <- function() x
    set_inverse <- function(inverse) {
        m <<- inverse
    } 
    get_inverse <- function() m
    list(set = set, get = get,
         set_inverse = set_inverse,
         get_inverse = get_inverse)
}


## This function computes the inverse of the special "matrix" created by 
## makeCacheMatrix above. If the inverse has already been calculated (and the 
## matrix has not changed), then it should retrieve the inverse from the cache.


cacheSolve <- function(x, ...) {
    m <- x$get_inverse()
    if(!is.null(m)){
        message("getting cached data")
        return(m)
    }
    data <- x$get()
    m <- solve(data, ...)
    x$set_inverse(m)
    m
}