## This script executes a simple performance comparison between computing

## several times in a row the inverse of a (relatively) large matrix using

## the default R function 'solve' versus the same computation using the

## cached matrix inverse functions 'makeCacheMatrix' and 'cacheSolve'

## We start by sourcing the cachematrix.R script

if (file.exists("cachematrix.R")) {

source("cachematrix.R")

}

## Compute the inverse using solve

inverse_compute <- function(m, it) {

for (i in 1:it) im <- solve(m)

im

}

## Compute the inverse using solveCache

cache_inverse_compute <- function(m, it) {

for (i in 1:it) im <- cacheSolve(m)

im

}

## The perfTest() function reports the difference betwee the running time

## of a large matrix inversion a number of times using the solve() function and

## the running time of the same matrix inversion using the cacheSolve() function

## developed for the programming assignment. The function has 2 arguments:

## - m_size = number of rows and columns of the matrix to be inverted

## - iterations = number of times the matrix will be inverted

deltaTime <- function(m_size = 100, iterations = 10) {

## Check if the functions required by cached inverse are available

if (!exists("cacheSolve") | !exists("makeCacheMatrix")) {

message(paste("Can not find cache matrix inversion functions.",

"Please source the 'cachematrix.R' file and try again."))

return(NA)

}

## Generate the matrix to be inverted

mat <- matrix(runif(m_size ^ 2, -3, 3), nrow = m_size, ncol = m_size)

## Create the cache matrix object using makeCacheMatrix

cache_mat <- makeCacheMatrix()

cache_mat$set(mat)

## Measure the time it takes to do the inversion using solve()

time1 <- as.vector(system.time(

inverse_mat <- inverse_compute(mat, iterations)))

## Measure the time it takes to do the inversion using cacheSolve()

time2 <- as.vector(system.time(

cache_inverse_mat <- cache_inverse_compute(cache_mat, iterations)))

## Report on the computing time and speedup

speedup <- time1[1] / time2[1]

## Report the results

message(paste(" Number of iterations:",iterations,"\n",

"Matrix size:",m_size,"x",m_size,"\n",

"Running time for 'solve()':",time1[1],"sec.\n",

"Running time for 'cacheSolve()':",time2[1],"sec.\n",

"Speed-up:",speedup,"times"))

## Cleanup the environment

rm(inverse_mat)

rm(cache_inverse_mat)

rm(time1)

rm(time2)

rm(speedup)

}