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<h1 data-toc-skip>Benchmarks</h1>
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<small class="dont-index">Source: <a href="https://github.com/msberends/AMR/blob/HEAD/vignettes/benchmarks.Rmd" class="external-link"><code>vignettes/benchmarks.Rmd</code></a></small>
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<p>One of the most important features of this package is the complete
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microbial taxonomic database, supplied by the <a href="http://www.catalogueoflife.org" class="external-link">Catalogue of Life</a> (CoL) and
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the <a href="https://lpsn.dsmz.de" class="external-link">List of Prokaryotic names with
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Standing in Nomenclature</a> (LPSN). We created a function
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<code><a href="../reference/as.mo.html">as.mo()</a></code> that transforms any user input value to a valid
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microbial ID by using intelligent rules combined with the microbial
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taxonomy.</p>
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<p>Using the <code>microbenchmark</code> package, we can review the
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calculation performance of this function. Its function
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<code><a href="https://rdrr.io/pkg/microbenchmark/man/microbenchmark.html" class="external-link">microbenchmark()</a></code> runs different input expressions
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independently of each other and measures their time-to-result.</p>
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<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
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<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/joshuaulrich/microbenchmark/" class="external-link">microbenchmark</a></span><span class="op">)</span>
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<span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://msberends.github.io/AMR/">AMR</a></span><span class="op">)</span>
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<span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://dplyr.tidyverse.org" class="external-link">dplyr</a></span><span class="op">)</span></code></pre></div>
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<p>In the next test, we try to ‘coerce’ different input values into the
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microbial code of <em>Staphylococcus aureus</em>. Coercion is a
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computational process of forcing output based on an input. For
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microorganism names, coercing user input to taxonomically valid
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microorganism names is crucial to ensure correct interpretation and to
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enable grouping based on taxonomic properties.</p>
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<p>The actual result is the same every time: it returns its
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microorganism code <code>B_STPHY_AURS</code> (<em>B</em> stands for
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<em>Bacteria</em>, its taxonomic kingdom).</p>
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<p>But the calculation time differs a lot:</p>
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<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
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<code class="sourceCode R"><span class="va">S.aureus</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/microbenchmark/man/microbenchmark.html" class="external-link">microbenchmark</a></span><span class="op">(</span>
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"sau"</span><span class="op">)</span>, <span class="co"># WHONET code</span>
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"stau"</span><span class="op">)</span>,
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"STAU"</span><span class="op">)</span>,
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"staaur"</span><span class="op">)</span>,
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"STAAUR"</span><span class="op">)</span>,
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"S. aureus"</span><span class="op">)</span>,
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"S aureus"</span><span class="op">)</span>,
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"Staphylococcus aureus"</span><span class="op">)</span>, <span class="co"># official taxonomic name</span>
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"Staphylococcus aureus (MRSA)"</span><span class="op">)</span>, <span class="co"># additional text</span>
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"Sthafilokkockus aaureuz"</span><span class="op">)</span>, <span class="co"># incorrect spelling</span>
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"MRSA"</span><span class="op">)</span>, <span class="co"># Methicillin Resistant S. aureus</span>
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<span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"VISA"</span><span class="op">)</span>, <span class="co"># Vancomycin Intermediate S. aureus</span>
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times <span class="op">=</span> <span class="fl">25</span><span class="op">)</span>
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<span class="fu"><a href="https://docs.ropensci.org/skimr/reference/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">S.aureus</span>, unit <span class="op">=</span> <span class="st">"ms"</span>, signif <span class="op">=</span> <span class="fl">2</span><span class="op">)</span>
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<span class="co"># Unit: milliseconds</span>
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<span class="co"># expr min lq mean median uq max neval</span>
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<span class="co"># as.mo("sau") 12.0 13.0 17.0 14.0 15 53 25</span>
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<span class="co"># as.mo("stau") 51.0 59.0 74.0 71.0 90 97 25</span>
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<span class="co"># as.mo("STAU") 53.0 60.0 77.0 87.0 91 96 25</span>
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<span class="co"># as.mo("staaur") 11.0 13.0 16.0 14.0 15 48 25</span>
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<span class="co"># as.mo("STAAUR") 13.0 14.0 19.0 15.0 16 48 25</span>
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<span class="co"># as.mo("S. aureus") 28.0 31.0 48.0 59.0 63 70 25</span>
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<span class="co"># as.mo("S aureus") 28.0 29.0 42.0 33.0 58 83 25</span>
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<span class="co"># as.mo("Staphylococcus aureus") 3.9 4.1 6.1 4.4 5 43 25</span>
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<span class="co"># as.mo("Staphylococcus aureus (MRSA)") 250.0 260.0 270.0 270.0 270 390 25</span>
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<span class="co"># as.mo("Sthafilokkockus aaureuz") 160.0 190.0 200.0 200.0 220 240 25</span>
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<span class="co"># as.mo("MRSA") 13.0 13.0 19.0 14.0 15 50 25</span>
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<span class="co"># as.mo("VISA") 21.0 22.0 29.0 24.0 27 61 25</span></code></pre></div>
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<p><img src="benchmarks_files/figure-html/unnamed-chunk-4-1.png" width="750"></p>
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<p>In the table above, all measurements are shown in milliseconds
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(thousands of seconds). A value of 5 milliseconds means it can determine
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200 input values per second. It case of 200 milliseconds, this is only 5
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input values per second. It is clear that accepted taxonomic names are
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extremely fast, but some variations are up to 61 times slower to
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determine.</p>
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<p>To improve performance, we implemented two important algorithms to
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save unnecessary calculations: <strong>repetitive results</strong> and
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<strong>already precalculated results</strong>.</p>
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<div class="section level3">
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<h3 id="repetitive-results">Repetitive results<a class="anchor" aria-label="anchor" href="#repetitive-results"></a>
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</h3>
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<p>Repetitive results are values that are present more than once in a
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vector. Unique values will only be calculated once by
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<code><a href="../reference/as.mo.html">as.mo()</a></code>. So running
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<code>as.mo(c("E. coli", "E. coli"))</code> will check the value
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<code>"E. coli"</code> only once.</p>
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<p>To prove this, we will use <code><a href="../reference/mo_property.html">mo_name()</a></code> for testing - a
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helper function that returns the full microbial name (genus, species and
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possibly subspecies) which uses <code><a href="../reference/as.mo.html">as.mo()</a></code> internally.</p>
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<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
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<code class="sourceCode R"><span class="co"># start with the example_isolates data set</span>
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<span class="va">x</span> <span class="op"><-</span> <span class="va">example_isolates</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%>%</a></span>
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<span class="co"># take all MO codes from the 'mo' column</span>
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<span class="fu"><a href="https://dplyr.tidyverse.org/reference/pull.html" class="external-link">pull</a></span><span class="op">(</span><span class="va">mo</span><span class="op">)</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%>%</a></span>
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<span class="co"># and copy them a thousand times</span>
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<span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">1000</span><span class="op">)</span> <span class="op"><a href="https://magrittr.tidyverse.org/reference/pipe.html" class="external-link">%>%</a></span>
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<span class="co"># then scramble them</span>
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<span class="fu"><a href="https://rdrr.io/r/base/sample.html" class="external-link">sample</a></span><span class="op">(</span><span class="op">)</span>
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<span class="co"># what do these values look like? They are of class <mo>:</span>
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<span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>
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<span class="co"># Class <mo></span>
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<span class="co"># [1] B_ACNTB B_ESCHR_COLI B_STRPT_GRPC B_STPHY_HMNS B_STPHY_CONS</span>
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<span class="co"># [6] B_ESCHR_COLI</span>
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<span class="co"># as the example_isolates data set has 2,000 rows, we should have 2 million items</span>
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<span class="fu"><a href="https://rdrr.io/r/base/length.html" class="external-link">length</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>
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<span class="co"># [1] 2000000</span>
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<span class="co"># and how many unique values do we have?</span>
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<span class="fu"><a href="https://dplyr.tidyverse.org/reference/n_distinct.html" class="external-link">n_distinct</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>
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<span class="co"># [1] 90</span>
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<span class="co"># now let's see:</span>
|
||
<span class="va">run_it</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/microbenchmark/man/microbenchmark.html" class="external-link">microbenchmark</a></span><span class="op">(</span><span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>,
|
||
times <span class="op">=</span> <span class="fl">10</span><span class="op">)</span>
|
||
<span class="fu"><a href="https://docs.ropensci.org/skimr/reference/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">run_it</span>, unit <span class="op">=</span> <span class="st">"ms"</span>, signif <span class="op">=</span> <span class="fl">3</span><span class="op">)</span>
|
||
<span class="co"># Unit: milliseconds</span>
|
||
<span class="co"># expr min lq mean median uq max neval</span>
|
||
<span class="co"># mo_name(x) 200 204 265 225 320 392 10</span></code></pre></div>
|
||
<p>So getting official taxonomic names of 2,000,000 (!!) items
|
||
consisting of 90 unique values only takes 0.225 seconds. That is 112
|
||
nanoseconds on average. You only lose time on your unique input
|
||
values.</p>
|
||
</div>
|
||
<div class="section level3">
|
||
<h3 id="precalculated-results">Precalculated results<a class="anchor" aria-label="anchor" href="#precalculated-results"></a>
|
||
</h3>
|
||
<p>What about precalculated results? If the input is an already
|
||
precalculated result of a helper function such as
|
||
<code><a href="../reference/mo_property.html">mo_name()</a></code>, it almost doesn’t take any time at all. In other
|
||
words, if you run <code><a href="../reference/mo_property.html">mo_name()</a></code> on a valid taxonomic name, it
|
||
will return the results immediately (see ‘C’ below):</p>
|
||
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
|
||
<code class="sourceCode R"><span class="va">run_it</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/microbenchmark/man/microbenchmark.html" class="external-link">microbenchmark</a></span><span class="op">(</span>A <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="st">"STAAUR"</span><span class="op">)</span>,
|
||
B <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="st">"S. aureus"</span><span class="op">)</span>,
|
||
C <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="st">"Staphylococcus aureus"</span><span class="op">)</span>,
|
||
times <span class="op">=</span> <span class="fl">10</span><span class="op">)</span>
|
||
<span class="fu"><a href="https://docs.ropensci.org/skimr/reference/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">run_it</span>, unit <span class="op">=</span> <span class="st">"ms"</span>, signif <span class="op">=</span> <span class="fl">3</span><span class="op">)</span>
|
||
<span class="co"># Unit: milliseconds</span>
|
||
<span class="co"># expr min lq mean median uq max neval</span>
|
||
<span class="co"># A 8.35 8.84 9.10 9.01 9.32 10.20 10</span>
|
||
<span class="co"># B 23.00 24.70 30.30 25.00 26.90 72.70 10</span>
|
||
<span class="co"># C 2.05 2.07 2.44 2.41 2.83 3.05 10</span></code></pre></div>
|
||
<p>So going from <code>mo_name("Staphylococcus aureus")</code> to
|
||
<code>"Staphylococcus aureus"</code> takes 0.0024 seconds - it doesn’t
|
||
even start calculating <em>if the result would be the same as the
|
||
expected resulting value</em>. That goes for all helper functions:</p>
|
||
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
|
||
<code class="sourceCode R"><span class="va">run_it</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/microbenchmark/man/microbenchmark.html" class="external-link">microbenchmark</a></span><span class="op">(</span>A <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_species</a></span><span class="op">(</span><span class="st">"aureus"</span><span class="op">)</span>,
|
||
B <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_genus</a></span><span class="op">(</span><span class="st">"Staphylococcus"</span><span class="op">)</span>,
|
||
C <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="st">"Staphylococcus aureus"</span><span class="op">)</span>,
|
||
D <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_family</a></span><span class="op">(</span><span class="st">"Staphylococcaceae"</span><span class="op">)</span>,
|
||
E <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_order</a></span><span class="op">(</span><span class="st">"Bacillales"</span><span class="op">)</span>,
|
||
F <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_class</a></span><span class="op">(</span><span class="st">"Bacilli"</span><span class="op">)</span>,
|
||
G <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_phylum</a></span><span class="op">(</span><span class="st">"Firmicutes"</span><span class="op">)</span>,
|
||
H <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_kingdom</a></span><span class="op">(</span><span class="st">"Bacteria"</span><span class="op">)</span>,
|
||
times <span class="op">=</span> <span class="fl">10</span><span class="op">)</span>
|
||
<span class="fu"><a href="https://docs.ropensci.org/skimr/reference/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">run_it</span>, unit <span class="op">=</span> <span class="st">"ms"</span>, signif <span class="op">=</span> <span class="fl">3</span><span class="op">)</span>
|
||
<span class="co"># Unit: milliseconds</span>
|
||
<span class="co"># expr min lq mean median uq max neval</span>
|
||
<span class="co"># A 1.89 1.93 2.09 2.05 2.17 2.40 10</span>
|
||
<span class="co"># B 1.89 1.93 2.08 2.00 2.19 2.63 10</span>
|
||
<span class="co"># C 1.91 1.92 2.10 1.97 2.30 2.43 10</span>
|
||
<span class="co"># D 1.90 1.94 2.21 2.02 2.53 2.88 10</span>
|
||
<span class="co"># E 1.87 1.95 2.09 2.04 2.22 2.33 10</span>
|
||
<span class="co"># F 1.84 1.91 1.97 1.92 2.04 2.14 10</span>
|
||
<span class="co"># G 1.87 1.92 2.10 1.96 2.12 2.96 10</span>
|
||
<span class="co"># H 1.90 1.96 2.12 2.06 2.21 2.47 10</span></code></pre></div>
|
||
<p>Of course, when running <code>mo_phylum("Firmicutes")</code> the
|
||
function has zero knowledge about the actual microorganism, namely
|
||
<em>S. aureus</em>. But since the result would be
|
||
<code>"Firmicutes"</code> anyway, there is no point in calculating the
|
||
result. And because this package contains all phyla of all known
|
||
bacteria, it can just return the initial value immediately.</p>
|
||
</div>
|
||
<div class="section level3">
|
||
<h3 id="results-in-other-languages">Results in other languages<a class="anchor" aria-label="anchor" href="#results-in-other-languages"></a>
|
||
</h3>
|
||
<p>When the system language is non-English and supported by this
|
||
<code>AMR</code> package, some functions will have a translated result.
|
||
This almost does’t take extra time (compare “en” from the table below
|
||
with the other languages):</p>
|
||
<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
|
||
<code class="sourceCode R"><span class="va">CoNS</span> <span class="op"><-</span> <span class="fu"><a href="../reference/as.mo.html">as.mo</a></span><span class="op">(</span><span class="st">"CoNS"</span><span class="op">)</span>
|
||
<span class="va">CoNS</span>
|
||
<span class="co"># Class <mo></span>
|
||
<span class="co"># [1] B_STPHY_CONS</span>
|
||
|
||
<span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"en"</span><span class="op">)</span> <span class="co"># or just mo_name(CoNS) on an English system</span>
|
||
<span class="co"># [1] "Coagulase-negative Staphylococcus (CoNS)"</span>
|
||
|
||
<span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"es"</span><span class="op">)</span> <span class="co"># or just mo_name(CoNS) on a Spanish system</span>
|
||
<span class="co"># [1] "Staphylococcus coagulasa negativo (SCN)"</span>
|
||
|
||
<span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"nl"</span><span class="op">)</span> <span class="co"># or just mo_name(CoNS) on a Dutch system</span>
|
||
<span class="co"># [1] "Coagulase-negatieve Staphylococcus (CNS)"</span>
|
||
|
||
<span class="va">run_it</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/microbenchmark/man/microbenchmark.html" class="external-link">microbenchmark</a></span><span class="op">(</span>da <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"da"</span><span class="op">)</span>,
|
||
de <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"de"</span><span class="op">)</span>,
|
||
en <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"en"</span><span class="op">)</span>,
|
||
es <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"es"</span><span class="op">)</span>,
|
||
fr <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"fr"</span><span class="op">)</span>,
|
||
it <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"it"</span><span class="op">)</span>,
|
||
nl <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"nl"</span><span class="op">)</span>,
|
||
pt <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"pt"</span><span class="op">)</span>,
|
||
ru <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"ru"</span><span class="op">)</span>,
|
||
sv <span class="op">=</span> <span class="fu"><a href="../reference/mo_property.html">mo_name</a></span><span class="op">(</span><span class="va">CoNS</span>, language <span class="op">=</span> <span class="st">"sv"</span><span class="op">)</span>,
|
||
times <span class="op">=</span> <span class="fl">100</span><span class="op">)</span>
|
||
<span class="fu"><a href="https://docs.ropensci.org/skimr/reference/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">run_it</span>, unit <span class="op">=</span> <span class="st">"ms"</span>, signif <span class="op">=</span> <span class="fl">4</span><span class="op">)</span>
|
||
<span class="co"># Unit: milliseconds</span>
|
||
<span class="co"># expr min lq mean median uq max neval</span>
|
||
<span class="co"># da 2.133 2.304 3.442 2.494 2.816 46.020 100</span>
|
||
<span class="co"># de 2.128 2.312 3.068 2.520 2.699 53.220 100</span>
|
||
<span class="co"># en 1.014 1.115 1.262 1.227 1.362 2.424 100</span>
|
||
<span class="co"># es 2.133 2.338 2.981 2.570 2.737 43.770 100</span>
|
||
<span class="co"># fr 1.986 2.149 3.139 2.377 2.567 41.610 100</span>
|
||
<span class="co"># it 2.072 2.268 2.911 2.468 2.656 44.560 100</span>
|
||
<span class="co"># nl 2.115 2.286 2.962 2.521 2.723 43.240 100</span>
|
||
<span class="co"># pt 2.055 2.205 2.912 2.520 2.687 39.520 100</span>
|
||
<span class="co"># ru 1.998 2.210 2.866 2.474 2.631 39.820 100</span>
|
||
<span class="co"># sv 2.022 2.187 2.759 2.357 2.536 38.560 100</span></code></pre></div>
|
||
<p>Currently supported languages are Danish, Dutch, English, French,
|
||
German, Italian, Portuguese, Russian, Spanish and Swedish.</p>
|
||
</div>
|
||
</div>
|
||
|
||
<div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
<footer><div class="copyright">
|
||
<p></p>
|
||
<p>Developed by Matthijs S. Berends, Christian F. Luz, Dennis Souverein,
|
||
Erwin E. A. Hassing.</p>
|
||
</div>
|
||
|
||
<div class="pkgdown">
|
||
<p></p>
|
||
<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a>
|
||
2.0.2.</p>
|
||
</div>
|
||
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</footer>
|
||
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||
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|
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