## This program calculates the inverse of a Matrix. For efficiency' sake, it also leverages

## a cache memory in order to avoid recalculating an inverse matrix previously done.

##

## Usage:

## 1. Assign the makeCacheMatrix' returned Matrix to a variable

## 2. Calculate its inverse Matrix using cacheSolve

## 3. Call cacheSolve one more time to verify it is using a cache

## 4. Clear cache redoing step 1 and repeat step 2 to check the cache is not used

##

## Example:

## 1. matrixTest = makeCacheMatrix( matrix( c(2,0,1,3,0,0,5,1,1), nrow=3, ncol=3, byrow=TRUE ) )

## 2. cacheSolve( matrixTest )

## 3. cacheSolve( matrixTest )

## 4. matrixTest = makeCacheMatrix( matrix( c(2,0,1,3,0,0,5,1,1), nrow=3, ncol=3, byrow=TRUE ) )

## cacheSolve( matrixTest )

##

## makeCacheMatrix sets up an special Matrix object, which contains 2 variables

## getters and setters functions for each one of them.

##

## By default, the Matrix is initialized empty. Another matrix can be passed as parameter.

## The inverse of a Matrix can only be calculated for a squared matrix, which means it has to have the same number of rows and columns.

##

makeCacheMatrix <- function( dataMatrix = matrix() ) {

inverseMatrix <- NULL

## Set the matrix

set <- function( newDataMatrix ) {

dataMatrix <<- newDataMatrix

inverseMatrix <<- NULL

}

## Get the matrix

get <- function() dataMatrix

## Set the inverse of the matrix

setInverse <- function( inverse ) inverseMatrix <<- inverse

## Get the inverse of the matrix

getInverse <- function() inverseMatrix

## Return a list with all setter and getter functions

list(set = set,

get = get,

setInverse = setInverse,

getInverse = getInverse)

}

## cacheSolve returns the inverse of a makeCacheMatrix object passed as parameter.

## In case the inverse is stored in a cache, it returns the value stored there,

## otherwise the inverse is calculated.

##

cacheSolve <- function( matrix, ... ) {

## Verify the inverse matrix is cached

inverse <- matrix$getInverse()

if ( !is.null( inverse ) ) {

message( "Getting cached data..." )

return( inverse )

}

## In case it is not cached, calculate it

data <- matrix$get()

inverse <- solve( data, ... )

matrix$setInverse( inverse )

inverse

}