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<h1>Function to perform isometric log-ratio transformation</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/ilr.R" class="external-link"><code>R/ilr.R</code></a></small>
<div class="hidden name"><code>ilr.Rd</code></div>
</div>
<div class="ref-description">
<p>This implementation is a special case of the class of isometric log-ratio
transformations.</p>
</div>
<div id="ref-usage">
<div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">ilr</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span>
<span></span>
<span><span class="fu">invilr</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>x</dt>
<dd><p>A numeric vector. Naturally, the forward transformation is only
sensible for vectors with all elements being greater than zero.</p></dd>
</dl></div>
<div id="value">
<h2>Value</h2>
<p>The result of the forward or backward transformation. The returned
components always sum to 1 for the case of the inverse log-ratio
transformation.</p>
</div>
<div id="references">
<h2>References</h2>
<p>Peter Filzmoser, Karel Hron (2008) Outlier Detection for
Compositional Data Using Robust Methods. Math Geosci 40 233-248</p>
</div>
<div id="see-also">
<h2>See also</h2>
<div class="dont-index"><p>Another implementation can be found in R package
<code>robCompositions</code>.</p></div>
</div>
<div id="author">
<h2>Author</h2>
<p>René Lehmann and Johannes Ranke</p>
</div>
<div id="ref-examples">
<h2>Examples</h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># Order matters</span></span></span>
<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.1</span>, <span class="fl">1</span>, <span class="fl">10</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] -1.628174 -2.820079</span>
<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">10</span>, <span class="fl">1</span>, <span class="fl">0.1</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 1.628174 2.820079</span>
<span class="r-in"><span><span class="co"># Equal entries give ilr transformations with zeros as elements</span></span></span>
<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">3</span>, <span class="fl">3</span>, <span class="fl">3</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 0 0</span>
<span class="r-in"><span><span class="co"># Almost equal entries give small numbers</span></span></span>
<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.3</span>, <span class="fl">0.4</span>, <span class="fl">0.3</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] -0.2034219 0.1174457</span>
<span class="r-in"><span><span class="co"># Only the ratio between the numbers counts, not their sum</span></span></span>
<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.7</span>, <span class="fl">0.29</span>, <span class="fl">0.01</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 0.70 0.29 0.01</span>
<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="fu">ilr</span><span class="op">(</span><span class="fl">2.1</span> <span class="op">*</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.7</span>, <span class="fl">0.29</span>, <span class="fl">0.01</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 0.70 0.29 0.01</span>
<span class="r-in"><span><span class="co"># Inverse transformation of larger numbers gives unequal elements</span></span></span>
<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="op">-</span><span class="fl">10</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 7.213536e-07 9.999993e-01</span>
<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">10</span>, <span class="fl">0</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 7.207415e-07 9.991507e-01 8.486044e-04</span>
<span class="r-in"><span><span class="co"># The sum of the elements of the inverse ilr is 1</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu">invilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">10</span>, <span class="fl">0</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 1</span>
<span class="r-in"><span><span class="co"># This is why we do not need all elements of the inverse transformation to go back:</span></span></span>
<span class="r-in"><span><span class="va">a</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.1</span>, <span class="fl">0.3</span>, <span class="fl">0.5</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">b</span> <span class="op"><-</span> <span class="fu">invilr</span><span class="op">(</span><span class="va">a</span><span class="op">)</span></span></span>
<span class="r-in"><span><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">b</span><span class="op">)</span> <span class="co"># Four elements</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 4</span>
<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">b</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span>, <span class="fl">1</span> <span class="op">-</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">b</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="co"># Gives c(0.1, 0.3, 0.5)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> [1] 0.1 0.3 0.5</span>
<span class="r-in"><span></span></span>
</code></pre></div>
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