cachematrix.R

## This function creates four separate functions that are stored in a list that when accessed
## will create a matrix, solve for it's inverse, and then cache both in the global environment
## the four functions in the list are as follows:
## 1. set: assigns the provided matrix as a cached global variable
## 2. get: returns the cached matrix of the set function
## 3. setinv: creates an inverse matrix and stores it as a cached global variable
## 4. getinv: returns the cached inverse matrix

makeCacheMatrix <- function(x = matrix()) {
  
  ## define "inv" as NULL within the scope of the function, this variable will later be used
  ## to store the inverse matrix
  inv <- NULL 
  
  ## create a function to assign the matrix provided to the variable "x" 
  ## in the parent environment of the makeCacheMatrix() function
  ## as opposed to the current environment of the set() function
  set <- function(y) {
    x <<- y 
    inv <<- NULL
  }
  
  ## create a function that will return the matrix stored in "x"
  get <- function() x 
  
  ## assign the inverse matrix "z" to the inv variable within the parent environment
  setinv <- function(z) inv <<- z 
  
  ## return the invese matrix object stored in the variable "inv"
  getinv <- function() inv
  
  ##create a list of all the functions for setting and getting matrix and inverse matrix
  list(set = set, get = get,
       setinv = setinv,
       getinv = getinv)
}


## This function first tests for the existance of a cached inverse matrix which is returned if
## it exists, otherwise it creates an inverse matrix and caches it using 
# the four functions created by makeCacheMatrix

cacheSolve <- function(x, ...) {
  
  ## use the getinv() function from makeCacheMatrix function to retrieve the 
  ## inverse generated by the setinv() function
  inv <- x$getinv() 
  
  ## if the variable "inv" already contains a cached inverse matrix, return the inverse matrix
  if(!is.null(inv)) {
    message("getting cached data")
    return(inv)
  }
  
  ## otherwise create an inverse matrix by first retrieving the cached matrix with get()
  ## then solving for the inverse with the solve() function
  ## store the solution inverse matrix in the "inv" variable using the function setinv()
  ## then return the inverse matrix stored in the "inv" variable
  
  data <- x$get()
  inv <- solve(data, ...)
  x$setinv(inv)
  inv
}