From fc80302d2a4071995a63cd4991caa21c9b5dc8a3 Mon Sep 17 00:00:00 2001
From: githubsahuja <sumeetahuja@hotmail.com>
Date: Sat, 1 Oct 2016 16:46:52 -0700
Subject: [PATCH] Programming assignment 2 - required functions implemented

---
 cachematrix.R | 119 +++++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 114 insertions(+), 5 deletions(-)

diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..37bf0f6774b 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,124 @@
-## Put comments here that give an overall description of what your
-## functions do
+## Programming Assignment 2: Lexical Scoping
+## Requires to write a R function that is able to cache potentially time-consuming 
+## computation - Matrix Inversion. This is usually a costly computation and there
+## may be benefit to cache the inverse of a matrix rather than compute it repeatedly.
 
-## Write a short comment describing this function
+## Assignment is to write 2 functions
+## Function 1: makeCacheMatrix 
+## This function creates a special "matrix" object that can cache its inverse.
+## Function 2: cacheSolve
+## This function computes the inverse of the special "matrix" returned by
+## makeCacheMatrix above. If the inverse has already been calculated (and the matrix 
+## has not changed), then the cacheSolve should retrieve the inverse from the cache.
+
+## makeCacheMatrix: 
+## This function creates a special "matrix" object that can cache its inverse
+##
+## Details of creating a makeCacheMatrix object will consist of 
+## Four functions encapsulated in a list 
+## 	1. set the matrix 
+## 	2. get the matrix 
+## 	3. set the inverse of the matrix 
+## 	4. get the inverse of the matrix 
+
+## Arguments: 
+## x    A square invertible matrix; 
+##      For this assignment - matrix is assumed to be always invertible
+##
+## Usage: 
+## makeCacheMatrix(x)
+##
+## Example:
+## sq_matrix <- matrix(rnorm(9), nrow=3, ncol=3) 
+## cachedM <- makeCacheMatrix(sq_matrix) 
+##
+## if you give this function a non-invertible matrix then you should see a error message
+##
+## nonInvertibleMatrix <- (1:9, nrow=3, ncol=3) 
+## cachedM <- makeCacheMatrix(sq_matrix) 
+## This should error and following message should be printed on console 
+## "Error: Matrix is not invertible, cannot convert to special matrix"
 
 makeCacheMatrix <- function(x = matrix()) {
+	## Confirm whether the matrix is invertible
+	if (det(x) == 0) {
+		print("Error: Matrix is not invertible, cannot convert to special matrix")
+		return;
+	}
+
+	inverseM <- NULL
+
+	## Set the matrix, does not calculate the inverse
+	setMatrix <- function(y) {
+		# Assign variables to parent environment
+		x <<- y
+		inverseM <<- NULL
+	}
+
+	## Get the matrix only
+	getMatrix <- function() x
+
+	## Set the inverse matrix
+	setInverse <- function(invM) inverseM <<- invM
 
+	## Get the inverse matrix
+	getInverse <- function() inverseM 
+
+	## Collate the get and set functions in the list
+	list(set = setMatrix, get = getMatrix,
+			setInverseM = setInverse, getInverseM = getInverse)
 }
 
 
-## Write a short comment describing this function
+## cacheSolve: 
+## This function computes the inverse of the special "matrix" returned by
+## makeCacheMatrix above. If the inverse has already been calculated (and the matrix 
+## has not changed), then the cacheSolve should retrieve the inverse from the cache.
+##
+## Arguments: 
+## x    special matrix - returned by makeCacheMatrix; 
+##
+## Usage: 
+## cacheSolve(x)
+##
+## Example:
+## >sq_matrix <- matrix(rnorm(9), nrow=3, ncol=3) 
+## >cachedM <- makeCacheMatrix(sq_matrix) 
+## >solveM <- cacheSolve(cachedM) 
+## >solveM
+##         [,1]  [,2]  [,3]
+## [1,] -7.049 3.413 4.234
+## [2,] -3.927 1.597 2.916
+## [3,] -5.509 2.048 3.008
+## 
+## >solveM_2<- cacheSolve(m) 
+## [1] "Cached data retrieved" 
+## >solveM_2
+## you should see same output as the one previously printed for print(solveM)
 
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+	## Retrieve the inverse matrix
+	inverseMatrix <- x$getInverseM ()
+
+	## Check if value exists - this would imply that cached value is returned
+	## Print a message for user and return the value
+      if(!is.null(inverseMatrix )) {
+		print("Cached data retrieved")
+		## Return a matrix that is the inverse of 'x'
+		return(inverseMatrix )
+	}
+
+	## if value does not exist, retrieve the matrix
+	data <- x$get()
+
+	## inverse the matrix. 
+	## No need to check "data" for square invertible matrix as that has been taken care
+	## within makeCacheMatrix function
+	inverseMatrix <- solve(data, ...)
+
+	## cache the inverse matrix for later retrieval
+	x$setInverseM (inverseMatrix )
+
+	## Return a matrix that is the inverse of 'x'
+	inverseMatrix 
 }