cachematrix.R

## Matrix inversion is usually a costly computation and their may 
## be some benefit to caching the inverse of a matrix rather than compute it repeatedly.
## This is a pair of functions that cache the inverse of a matrix.

##Example:
# x=matrix(runif(9,1,10),3,3)
# a<-makeCacheMatrix(x)
 
# returning the matrix
# a$get()

# solve the matrix, cache the inverse, return the inverse
# cacheSolve(a)

# get the cached inverse (returns NULL if not cached yet)
# a$getsolve()

## makeCacheMatrix: creates a special "matrix" object that can cache its inverse
## defines public functions a$get(), a$getsolve()
makeCacheMatrix <- function(x = matrix()) {
  xs <- NULL
  set <- function(y) {
    x <<- y
    xs <<- NULL
  }
  get <- function() x
  setsolve <- function(solve) xs <<- solve
  getsolve <- function() xs
  list(set = set, get = get,
       setsolve = setsolve,
       getsolve = getsolve)
}

## cacheSolve: computes the inverse of the special "matrix" returned by
## makeCacheMatrix above, if the inverse has already been calculated, then it
## retrieves the inverse from the cache
cacheSolve <- function(x, ...) {
  xs <- x$getsolve()
  if(!is.null(xs)) {
    message("getting cached data")
    return(xs)
  }
  data <- x$get()
  xs <- solve(data, ...)
  x$setsolve(xs)
  xs
}