Assignment: Caching the Inverse of a Matrix

Ashok Kumar T.

Introduction

Caching is a technology based on the memory subsystem of your computer. The main purpose of a cache is to accelerate your computer tasks more rapidly.

The aim of this programming assignment is to write an R function that is able to cache potentially time-consuming computations. For example, taking the mean of a numeric vector in R is typically a fast operation. However, for a very long vector, it may take too long to compute the mean, especially if it has to be computed repeatedly (e.g. in a loop). If the contents of a vector are not changed, it may make sense to cache the value of the mean so that when we need it again, it can be looked up in the cache rather than recomputed.

Program Disscussion

Matrix inversion is usually a costly computation and there may be some benefit to caching the inverse of a matrix rather than computing it repeatedly (there are also alternatives to matrix inversion that is not discussed here). In this assignment, a pair of functions makeCacheMatrix and cacheSolve are written to cache the inverse of a matrix.

makeCacheMatrix is a function which creates a special "matrix" object that can cache its inverse, and cacheSolve is a function which computes the inverse of the special "matrix" returned by makeCacheMatrix. If the inverse has already been calculated (and the matrix has not changed), then cacheSolve will retrieve the inverse from the cache.

Computing the inverse of a square matrix can be done with the solve function in R. For example, if X is a square invertible matrix, then solve(X) returns its inverse.

The first function makeCacheMatrix creates a special "matrix", which is really a list containing a function to

1. get - To get the value of the matrix
2. set - To set the value of the matrix
3. getInverse - To get the inverse of the matrix
4. setInverse - To set the inverse of the matrix

makeCacheMatrix <- function(x = matrix())
{
	m <- NULL
	set <- function(y)
	{
		x <<- y
		m <<- NULL
	}
	get <- function() x
	setInverse <- function(i) m <<- solve(x)
	getInverse <- function() m
	list(set = set, get = get, setInverse = setInverse, getInverse = getInverse)
}

The other function cacheSolve calculates the inverse of the special "matrix" created with the above function. It first checks to see if the inverse of the matrix has already been calculated. If so, it gets the inverse from the cache and skips the computation. Otherwise, it calculates the inverse of the data and sets the inverse matrix in the cache via the setInverse function.

cacheSolve <- function(x, ...)
{
	m <- x$getInverse()
	if(!is.null(m))
	{
		return(m)
	}
	m <- solve(x$get())
	x$setInverse(m)
	m
}

Program Implementation

The complete program cachematrix.R can be publicly accessed via GitHub repositorycachematrix.R.

> source("cachematrix.R")
> a <- makeCacheMatrix(matrix(1:4,2))
> a$get()
     [,1] [,2]
[1,]    1    3
[2,]    2    4
> a$getInverse()
NULL
> a$setInverse()
> a$getInverse()
     [,1] [,2]
[1,]   -2  1.5
[2,]    1 -0.5
> cacheSolve(a)
     [,1] [,2]
[1,]   -2  1.5
[2,]    1 -0.5
> a$set(matrix(5:8,2))
> a$getInverse()
NULL
> a$get()
     [,1] [,2]
[1,]    5    7
[2,]    6    8
> cacheSolve(a)
     [,1] [,2]
[1,]   -4  3.5
[2,]    3 -2.5
> a$getInverse()
     [,1] [,2]
[1,]   -4  3.5
[2,]    3 -2.5