+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
## Programming assignment 2
+## Put comments here that give an overall description of what your
+## functions do
+
+## This function will create a new matrix obj which can cache inverse that can be used later
+
+ makeCacheMatrix <- function(x = matrix()) {
+ ## @x: a square invertible matrix
+ ## return: a list containing functions to
+ ## 1. set the matrix
+ ## 2. get the matrix
+ ## 3. set the inverse
+ ## 4. get the inverse
+ ## this list is used as the input to cacheSolve()
+ m <- NULL
+ set <- function(y) {
+ x <<- y
+ m <<- NULL
+ }
+ ##print (x)
+ get <- function() x
+ setinverse <- function(inverse) m <<- inverse
+ ##print (m)
+ getinverse <- function() m
+ list(set = set, get = get,
+ setinverse = setinverse,
+ getinverse = getinverse)
+
+ }
+ ## End of makecachematrix()
+
+ ## 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.
+
+
+cacheSolve <- function(x, ...) {
+ inverse<- x$getinverse()
+ # if the inverse has already been calculated
+ if(!is.null(inverse)) {
+ # get it from the cache and skips the computation.
+ message("getting cached data")
+ return(inverse)
+ }
+ # otherwise, calculates the inverse
+ data<-x$get()
+ inverse = solve(data)
+ # sets the value of the inverse in the cache via the setinv function.
+ x$setinverse(inverse)
+
+ return(inverse)
+}
+## end of cacheSolve
+
+## test function
+testInverseCache <- function(mat){
+ ## Pass a matrix filled with random numbers
+ cachematdata <- makeCacheMatrix(mat)
+ # Lets do some profiling .. first run
+ start.time <-Sys.time()
+ # Pass matrix object to cacheSolve
+ cacheSolve(cachematdata)
+ timeTaken <- Sys.time() - start.time
+ print ("Time taken without caching")
+ print(timeTaken)
+ # Now call again same with same matix .. this time it should pick from cache so
+ ## shall take less time
+ start.time <- Sys.time()
+ cacheSolve(cachematdata)
+ timeTaken <- Sys.time() - start.time
+ print ("Time taken after caching")
+ print(timeTaken)
+}
+## End of testInverseCache
+
+## Sample Test data
+set.seed(1)
+r = rnorm(4000000)
+mat = matrix(r, nrow=2000, ncol=2000)
+testInverseCache(mat)
+
## [1] "Time taken without caching"
+## Time difference of 28.1537 secs
+
## getting cached data
+
## [1] "Time taken after caching"
+## Time difference of 0.002998114 secs
+
+
+
+
+