From f3cfe5b7b522db941d52f64ba37f563eb7dd2a8f Mon Sep 17 00:00:00 2001
From: coursera-datascience <heom.duq@gmail.com>
Date: Thu, 10 Apr 2014 15:26:07 -0400
Subject: [PATCH] Completed functions that cache the inverse of a matrix.

1. The makeCacheMatrix function creates a special "matrix" object that
can cache its inverse. 2. The cacheSolve function computes the inverse
of the special "matrix". If the inverse has already been calculated and
the matrix has not changed, the cacheSolve function retrieves the
inverse from the cache.
---
 cachematrix.R | 70 +++++++++++++++++++++++++++++++++++++++++++++------
 1 file changed, 62 insertions(+), 8 deletions(-)

diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..89a1d823fea 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,69 @@
-## Put comments here that give an overall description of what your
-## functions do
+## Description--------------
+## Two customized functions that cache the inverse of a matrix.
 
-## Write a short comment describing this function
+# 1. makeCacheMatrix
 
-makeCacheMatrix <- function(x = matrix()) {
+# Description --------------
+# The function creates a special "matrix" object that can cache its inverse.
 
-}
+# Usage--------------------
+# makeCacheMatrix(a)
 
+# Arguments----------------
+# a    a square numeric or complex matrix. Logical matrices are coerced to numeric.
 
-## Write a short comment describing this function
+# Examples-----------------
+# mx <- rbind(c(1,3), c(5, 6))
+# makeCacheMatrix(mx)
+#
+# mx <- rbind(c(1,3), c(5, 6))
+# cashed <- makeCacheMatrix(mx)
 
-cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+makeCacheMatrix <- function(x = matrix()) {        
+        inv <- NULL               # Object to hold the value of an inversed matrix
+        set <- function(y) {      
+                x <<- y           # Assign the value of the matrix to the object x in the parent environment
+                m <<- NULL        # Assign NULL to an object in the parent environment
+        }
+        get <- function() {       # Get the value of the matrix
+                x
+        }
+        setinverse <- function(solve){ # Set the value of the inversed matrix
+                inv <<- solve     # Assign the inversed to an object in the parent environment
+        }                             
+        getinverse <- function(){ # Get the value of the inversed matrix
+                inv
+        }
+        list(set = set, get = get, setinverse = setinverse, getinverse = getinverse)
 }
+
+# 2. cacheSolve
+
+# Description --------------
+# The function computes the inverse of the special "matrix".
+# If the inverse has already been calculated and the matrix has not changed, 
+# the cacheSolve function retrieves the inverse from the cache.
+
+# Usage--------------------
+# cacheSolve(a, ...)
+
+# Argument----------------
+# a    a cashed object in the environment which calls the cacheSolve function
+#...   further arguments passed to or from other methods
+
+# Examples-----------------
+# cacheSolve(cashed)
+
+cacheSolve <- function(x, ...) {  # A cashed object in the parent frame is passed to the function
+        inv <- x$getinverse()     # Retrieve the inversed matrix from the object passed from the parent frame
+        if (!is.null(inv)){       # If the object contains an inversed matrix
+                message("getting cached data")
+                return (inv)      # retrieve the inversed matrix and exit the function
+        }                       
+        
+        # Lines below will be reached ONLY when no inversed matrix exists
+        data <- x$get()           # Get the matrix from the object passed from the parent frame 
+        inv <- solve(data, ...)   # Inverse the data matrix
+        x$setinverse(inv)         # Set the inversed matrix to the object passed from the parent frame
+        inv                       # Return an inversed matrix
+}
\ No newline at end of file