graded.R

makeCacheMatrix <- function(x = numeric()) {
    
    
    i<-NULL
    set<-function(y) { x<<-y #sets the matrix value which future input to cacheSolve will be compared against
    }
    get<-function() x # returns the matrix when called
    setinverse<-function(inverse) i<<-inverse # stores the matrix inverse provided as its input
    getinverse<-function() i #returns the inverse when called
    invisible(list(set=set, get= get, setinverse= setinverse, getinverse = getinverse)) #creates a list of the four functions    
}

a<<-makeCacheMatrix() #allows for the four functions within makeCacheMatrix to be called more conveniently.
#For example, a$set()..

## function designed to calculate the inverse of an inputted matrix. If the matrix has not changed, then the
##function returns the cache'd inverse of the matrix rather than computing it again

cacheSolve <- function(x, ...) {
    
    f<-a$get() #return the matrix value stored in makeCacheMatrix
    i<-a$getinverse() # Return the inverse matrix stored in makeCacheMatrix
    
    if(is.null(i)) {       #if the function has not been called before, and therefore does not have a matrix value stored,
        # compute and store a matrix
        i<-solve(x)     # compute the inverse of matrix x
        a$setinverse(i) # store this value in makeCacheMatrix 
        a$set(x)
        i
    }
    else if(identical(x, f)) {        ##if the value of the last matrix "f" equals the new matrix input to cacheSolve "x",
        # then return the cached inverse 
        print("getting cached data")        
        i
    }
    else {                 # if the matrix "x" is different to that currently stored in makeCacheMatrix, 
        #then calculate a new inverse for the matrix and store the inverse in makeCacheMatrix
        
        i<-solve(x)
        a$setinverse(i)
        a$set(x)
        i
        ## Return a matrix that is the inverse of 'x'
    }
}