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<h1>Caching the Mean: A Speed Test</h1>
<p><strong>Gauden Galea</strong><br/>
<a href="https://github.com/ggData/ProgrammingAssignment2">https://github.com/ggData/ProgrammingAssignment2</a><br/>
<em>15 April 2014</em></p>
<p>The first code chunk defines the two example functions provided for the assignment. This is based on the example provided by Roger Peng <a href="https://class.coursera.org/rprog-002/human_grading/view/courses/972078/assessments/3/submissions">here</a></p>
<ul>
<li><code>makeVector()</code> receives a <code>numeric</code> vector and returns a modified form of that vector that is able to store the mean if once it is calculated. This version of the function is modified using the <a href="https://class.coursera.org/rprog-002/forum/thread?thread_id=370#comment-953">proposed changes by Patrick Gillen and modified by Lenka Vyslouzilova</a>.</li>
<li><code>cachemean()</code> takes a modified vector created as above and returns the cached mean if it is already stored. The mean will thus need to be only calculated once.</li>
</ul>
<pre><code class="r">makeVector <- function(x = numeric()) {
m <- NULL
x <- x
set <- function(y) {
x <<- y
m <<- NULL
}
get <- function() x
setmean <- function(mean) m <<- mean
getmean <- function() m
list(set = set, get = get, setmean = setmean, getmean = getmean)
}
cachemean <- function(x, ...) {
m <- x$getmean()
if (!is.null(m)) {
# message('getting cached data')
return(m)
}
data <- x$get()
m <- mean(data, ...)
x$setmean(m)
m
}
</code></pre>
<p>Two test functions are now set up:</p>
<ul>
<li><code>test_mean(x, r)</code> takes a numeric vector, <code>x</code>, and calculates its mean <code>r</code> times. It finally prints out the value of the mean as a check on proper functioning.</li>
<li><code>test_cache_mean(x,r)</code> takes the same two arguments. It first converts the <code>x</code> vector into a caching object using the <code>makeVector()</code> function. Then it runs <code>cachemean()</code> on that object <code>r</code> times. Finally it prints out the value of <code>cachemean()</code> as a check on proper functioning.</li>
</ul>
<p>These two functions should return similar results but the second should run much faster.</p>
<pre><code class="r">test_mean = function(x, r) {
for (i in 1:r) {
mean(x)
}
message(mean(x))
}
test_cache_mean = function(x, r) {
y = makeVector(x)
for (i in 1:r) {
cachemean(y)
}
message(cachemean(y))
}
</code></pre>
<p>The final chunk runs both tests a large number of times and checks:</p>
<ol>
<li>the total time taken for each run</li>
<li>whether the results of the two functions are identical</li>
</ol>
<pre><code class="r">test_vec = 1:1000 * 1.35
r = 1e+06 # number of repetitions of the test
system.time(test_mean(test_vec, r))
</code></pre>
<pre><code>## 675.675
</code></pre>
<pre><code>## user system elapsed
## 16.18 0.05 16.28
</code></pre>
<pre><code class="r">system.time(test_cache_mean(test_vec, r))
</code></pre>
<pre><code>## 675.675
</code></pre>
<pre><code>## user system elapsed
## 2.633 0.009 2.678
</code></pre>
<pre><code class="r">
identical(mean(test_vec), cachemean(makeVector(test_vec)))
</code></pre>
<pre><code>## [1] TRUE
</code></pre>
<h2>Results</h2>
<p>Here are the results of one such run of these tests with one million iterations (they will differ to some degree from the results produced by the actual run above):</p>
<pre><code>> system.time(test_mean(test_vec, r))
675.675
user system elapsed
16.470 0.042 16.573
> system.time(test_cache_mean(test_vec, r))
675.675
user system elapsed
2.624 0.011 2.645
> identical(mean(test_vec), cachemean(makeVector(test_vec)))
[1] TRUE
</code></pre>
<p>For the given vector,</p>
<ol>
<li>Both functions returned the correct, identical, value of 675.675 for the mean</li>
<li>One million iterations of the <code>cachemean()</code> functions took a total of 2.645 seconds as compared to 16.573 seconds for the normal function, less than one-fifth of the time.</li>
</ol>
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