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<h1>Function to perform isometric log-ratio transformation</h1>
<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>
<pre class="usage"><span class='fu'>ilr</span>(<span class='no'>x</span>)
<span class='fu'>invilr</span>(<span class='no'>x</span>)</pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>x</th>
<td><p>A numeric vector. Naturally, the forward transformation is only sensible for
vectors with all elements being greater than zero.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>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>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Peter Filzmoser, Karel Hron (2008) Outlier Detection for Compositional Data Using Robust Methods. Math Geosci 40 233-248</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p>Another implementation can be found in R package <code>robCompositions</code>.</p></div>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'># Order matters</span>
<span class='fu'>ilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.1</span>, <span class='fl'>1</span>, <span class='fl'>10</span>))</div><div class='output co'>#> <span class='error'>Error in ilr(c(0.1, 1, 10)): konnte Funktion "ilr" nicht finden</span></div><div class='input'><span class='fu'>ilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>10</span>, <span class='fl'>1</span>, <span class='fl'>0.1</span>))</div><div class='output co'>#> <span class='error'>Error in ilr(c(10, 1, 0.1)): konnte Funktion "ilr" nicht finden</span></div><div class='input'><span class='co'># Equal entries give ilr transformations with zeros as elements</span>
<span class='fu'>ilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>3</span>, <span class='fl'>3</span>, <span class='fl'>3</span>))</div><div class='output co'>#> <span class='error'>Error in ilr(c(3, 3, 3)): konnte Funktion "ilr" nicht finden</span></div><div class='input'><span class='co'># Almost equal entries give small numbers</span>
<span class='fu'>ilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.3</span>, <span class='fl'>0.4</span>, <span class='fl'>0.3</span>))</div><div class='output co'>#> <span class='error'>Error in ilr(c(0.3, 0.4, 0.3)): konnte Funktion "ilr" nicht finden</span></div><div class='input'><span class='co'># Only the ratio between the numbers counts, not their sum</span>
<span class='fu'>invilr</span>(<span class='fu'>ilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span>)))</div><div class='output co'>#> <span class='error'>Error in invilr(ilr(c(0.7, 0.29, 0.01))): konnte Funktion "invilr" nicht finden</span></div><div class='input'><span class='fu'>invilr</span>(<span class='fu'>ilr</span>(<span class='fl'>2.1</span> * <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span>)))</div><div class='output co'>#> <span class='error'>Error in invilr(ilr(2.1 * c(0.7, 0.29, 0.01))): konnte Funktion "invilr" nicht finden</span></div><div class='input'><span class='co'># Inverse transformation of larger numbers gives unequal elements</span>
<span class='fu'>invilr</span>(-<span class='fl'>10</span>)</div><div class='output co'>#> <span class='error'>Error in invilr(-10): konnte Funktion "invilr" nicht finden</span></div><div class='input'><span class='fu'>invilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(-<span class='fl'>10</span>, <span class='fl'>0</span>))</div><div class='output co'>#> <span class='error'>Error in invilr(c(-10, 0)): konnte Funktion "invilr" nicht finden</span></div><div class='input'><span class='co'># The sum of the elements of the inverse ilr is 1</span>
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/sum'>sum</a></span>(<span class='fu'>invilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(-<span class='fl'>10</span>, <span class='fl'>0</span>)))</div><div class='output co'>#> <span class='error'>Error in invilr(c(-10, 0)): konnte Funktion "invilr" nicht finden</span></div><div class='input'><span class='co'># This is why we do not need all elements of the inverse transformation to go back:</span>
<span class='no'>a</span> <span class='kw'><-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.1</span>, <span class='fl'>0.3</span>, <span class='fl'>0.5</span>)
<span class='no'>b</span> <span class='kw'><-</span> <span class='fu'>invilr</span>(<span class='no'>a</span>)</div><div class='output co'>#> <span class='error'>Error in invilr(a): konnte Funktion "invilr" nicht finden</span></div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/length'>length</a></span>(<span class='no'>b</span>) <span class='co'># Four elements</span></div><div class='output co'>#> <span class='error'>Error in eval(expr, envir, enclos): Objekt 'b' nicht gefunden</span></div><div class='input'><span class='fu'>ilr</span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='no'>b</span>[<span class='fl'>1</span>:<span class='fl'>3</span>], <span class='fl'>1</span> - <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/sum'>sum</a></span>(<span class='no'>b</span>[<span class='fl'>1</span>:<span class='fl'>3</span>]))) <span class='co'># Gives c(0.1, 0.3, 0.5)</span></div><div class='output co'>#> <span class='error'>Error in ilr(c(b[1:3], 1 - sum(b[1:3]))): konnte Funktion "ilr" nicht finden</span></div></pre>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#arguments">Arguments</a></li>
<li><a href="#value">Value</a></li>
<li><a href="#references">References</a></li>
<li><a href="#see-also">See also</a></li>
<li><a href="#examples">Examples</a></li>
</ul>
<h2>Author</h2>
<p>René Lehmann and Johannes Ranke</p>
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