Wrote the cache matrix functions

Author: Ludovic Claude

cachematrix.R

@@ -1,15 +1,48 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
+## Matrix inversion is usually a costly computation and there may be some benefit to caching the inverse of
+## a matrix rather than compute it repeatedly.
+## makeCacheMatrix and cacheSolve can be used to create a matrix that is able to cache its inverse.
+## Typical usage:
+##     ````
+##     m <- makeCacheMatrix(matrix(1:4,2,2))
+##     cacheSolve(m)
+##     m$get()
+##     cacheSolve(m)
+##     ````
 
+## makeCacheMatrix creates a special "matrix", which is really a list containing a function to
+## 1. set the value of the matrix
+## 2. get the value of the matrix
+## 3. set the value of the inverse matrix
+## 4. get the value of the inverse metrix
 makeCacheMatrix <- function(x = matrix()) {
+  
+  i <- NULL
+  set <- function(y) {
+    x <<- y
+    i <<- NULL
+  }
+  get <- function() x
+  setinverse <- function(inverse) i <<- inverse
+  getinverse <- function() i
+  list(set = set, get = get,
+       setinverse = setinverse,
+       getinverse = getinverse)  
 
 }
 
 
-## Write a short comment describing this function
+## cacheSolve takes a cached matrix as argument and returns the inverse of the matrix.
+## The inverse is stored inside the cached matrix on first call, then retrived from the cache on subsequent calls.
 
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+  ## Return a matrix that is the inverse of 'x'
+  i <- x$getinverse()
+  if(!is.null(i)) {
+    message("getting cached data")
+    return(i)
+  }
+  data <- x$get()
+  i <- solve(data, ...)
+  x$setinverse(i)
+  i
 }