From 119c52cf8a99245997c609b6d8a9ef90062aba3a Mon Sep 17 00:00:00 2001
From: Xiaodan Zhang <zhang349@illinois.edu>
Date: Sun, 20 Apr 2014 00:46:11 -0500
Subject: [PATCH 1/2] First submission of ProgrammingAssignment2

---
 cachematrix.R | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..a9a02941612 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,4 +1,4 @@
-## Put comments here that give an overall description of what your
+# Put comments here that give an overall description of what your
 ## functions do
 
 ## Write a short comment describing this function

From 3a7408235074ee4ee0322ac3e395e314aef5dc2a Mon Sep 17 00:00:00 2001
From: Xiaodan Zhang <zhang349@illinois.edu>
Date: Sun, 20 Apr 2014 17:16:45 -0500
Subject: [PATCH 2/2] modified cachematrix function

---
 cachematrix.R | 58 ++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 50 insertions(+), 8 deletions(-)

diff --git a/cachematrix.R b/cachematrix.R
index a9a02941612..595f4ec6742 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,57 @@
-# Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
+# The first function, makeCacheMatrix creates a special "matrix", 
+# which is really a list containing a function to
+# set the value of the matrix
+# get the value of the matrix
+# set the value of the inverse
+# get the value of the inverse
 
 makeCacheMatrix <- function(x = matrix()) {
-
+    # initialize the inverse matrix value
+    inv <- NULL
+    
+    # set the value of the matrix
+    set <- function(y) {
+        x <<- y
+        inv <<- NULL
+    }
+    
+    # get the value of the matrix
+    get <- function() x
+    
+    # set the value of the inverse
+    set_inverse <- function(inv_input) inv <<- inv_input
+    # get the value of the inverse
+    get_inverse <- function() inv
+    
+    # return a list of all the above functions
+    list(set = set, get = get,
+         set_inverse = set_inverse,
+         get_inverse = get_inverse)
+    
 }
 
-
-## Write a short comment describing this function
+## The following function calculates the inverse of the special 
+## "matrix" created with the above function. 
+## It first checks to see if the inverse has already been calculated. 
+## If so, it gets the inverse from the cache and skips the 
+## computation. Otherwise, it calculates the inverse of the 
+## matrix and sets the value of the inverse in the cache via 
+## the setinv function.
 
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+    # check if the inverse is already cached,
+    # if so, we get the inverse from the cache directly
+    inv <- x$get_inverse()
+    if(!is.null(inv)) {
+        message("getting cached inverse")
+        return(inv)
+    }
+    # else, we first get the matrix
+    data <- x$get()
+    # and calculate the inverse
+    inv <- solve(data, ...)
+    # next, cache the inverse of the matrix
+    x$set_inverse(inv)
+    # and finally, return the result
+    inv
 }