Update cachematrix.R

Programming Assignment2 Submission coursera.

Author: qd

cachematrix.R

@@ -1,15 +1,61 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
-
+### makeCacheMatrix(x) sets up a placeholder list for
+## the matrix variable x and the inverse matrix INV
+##
+## cacheSolve(x) returns the inverse INV or the cached INV
+## if it already exists in the placeholder list
+## see example, below:
+##
+## Caution: if the values of the matrix 'x' change
+## makeCacheMatrix(x) needs to be called with the updated values
+##
+## ----  START of sample input/output of actual run----
+## > A <- matrix(c(1,5,2,-5),2,2)  
+## > A
+## [,1] [,2]
+## [1,]    1    2
+## [2,]    5   -5
+## > Acache <- makeCacheMatrix(A)
+## > cacheSolve(Acache) 
+## [,1]        [,2]              # the first time
+## [1,] 0.3333333  0.13333333    # the inverse is calculated
+## [2,] 0.3333333 -0.06666667
+## > cacheSolve(Acache)
+## getting cached data           # subsequent calls
+## [,1]        [,2]              # return cached data
+## [1,] 0.3333333  0.13333333
+## [2,] 0.3333333 -0.06666667
+## > 
+## ----  END of sample input/output of actual run----
+##
+## makeCacheMatrix(x) sets up a placeholder list for
+## the matrix variable x and the inverse matrix INV
 makeCacheMatrix <- function(x = matrix()) {
-
+  INV <- NULL
+  set <- function(y) {
+    x <<- y
+    INV <<- NULL
+  }
+  get <- function() x
+  setinverse <- function(inverse) INV <<- inverse
+  getinverse <- function() INV
+  list(set = set, get = get,
+       setinverse = setinverse,
+       getinverse = getinverse)
 }
-
-
-## Write a short comment describing this function
-
+##
+##  cacheSolve(x) computes the inverse of the special
+## "matrix" list returned by `makeCacheMatrix` above. If the inverse has
+##  already been calculated, then
+## `cacheSolve` retrieves the inverse from the cache
 cacheSolve <- function(x, ...) {
         ## Return a matrix that is the inverse of 'x'
+  INV <- x$getinverse()
+  if(!is.null(INV)) {
+    message("getting cached data")
+    return(INV)
+  }
+  data <- x$get()
+  INV <- solve(data, ...)
+  x$setinverse(INV)
+  INV
 }