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authorJohannes Ranke <jranke@uni-bremen.de>2016-09-10 05:21:52 +0200
committerJohannes Ranke <jranke@uni-bremen.de>2016-09-10 05:55:25 +0200
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+ René Lehmann and Johannes Ranke
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+
+ <h1>
+ Function to perform isometric log-ratio transformation
+</h1>
+
+<div class="row">
+ <div class="span8">
+ <h2>Usage</h2>
+ <pre><span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="symbol">x</span><span class="keyword">)</span>
+ <span class="functioncall"><a href='ilr.html'>invilr</a></span><span class="keyword">(</span><span class="symbol">x</span><span class="keyword">)</span></pre>
+
+ <h2>Arguments</h2>
+ <dl>
+ <dt>x</dt>
+ <dd>
+ A numeric vector. Naturally, the forward transformation is only sensible for
+ vectors with all elements being greater than zero.
+ </dd>
+ </dl>
+
+ <div class="Description">
+ <h2>Description</h2>
+
+ <p>This implementation is a special case of the class of isometric log-ratio transformations.</p>
+
+ </div>
+
+ <div class="Value">
+ <h2>Value</h2>
+
+ <p><dl>
+ The result of the forward or backward transformation. The returned components always
+ sum to 1 for the case of the inverse log-ratio transformation.
+</dl></p>
+
+ </div>
+
+ <div class="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>
+
+ <h2 id="examples">Examples</h2>
+ <pre class="examples"><div class='input'><span class="comment"># Order matters</span>
+<span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="number">0.1</span><span class="keyword">,</span> <span class="number">1</span><span class="keyword">,</span> <span class="number">10</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] -1.628174 -2.820079
+</div>
+<div class='input'><span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="number">10</span><span class="keyword">,</span> <span class="number">1</span><span class="keyword">,</span> <span class="number">0.1</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] 1.628174 2.820079
+</div>
+<div class='input'><span class="comment"># Equal entries give ilr transformations with zeros as elements</span>
+<span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="number">3</span><span class="keyword">,</span> <span class="number">3</span><span class="keyword">,</span> <span class="number">3</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] 0 0
+</div>
+<div class='input'><span class="comment"># Almost equal entries give small numbers</span>
+<span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="number">0.3</span><span class="keyword">,</span> <span class="number">0.4</span><span class="keyword">,</span> <span class="number">0.3</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] -0.2034219 0.1174457
+</div>
+<div class='input'><span class="comment"># Only the ratio between the numbers counts, not their sum</span>
+<span class="functioncall"><a href='ilr.html'>invilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="number">0.7</span><span class="keyword">,</span> <span class="number">0.29</span><span class="keyword">,</span> <span class="number">0.01</span><span class="keyword">)</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] 0.70 0.29 0.01
+</div>
+<div class='input'><span class="functioncall"><a href='ilr.html'>invilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="number">2.1</span> <span class="keyword">*</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="number">0.7</span><span class="keyword">,</span> <span class="number">0.29</span><span class="keyword">,</span> <span class="number">0.01</span><span class="keyword">)</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] 0.70 0.29 0.01
+</div>
+<div class='input'><span class="comment"># Inverse transformation of larger numbers gives unequal elements</span>
+<span class="functioncall"><a href='ilr.html'>invilr</a></span><span class="keyword">(</span><span class="keyword">-</span><span class="number">10</span><span class="keyword">)</span></div>
+<div class='output'>[1] 7.213536e-07 9.999993e-01
+</div>
+<div class='input'><span class="functioncall"><a href='ilr.html'>invilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="keyword">-</span><span class="number">10</span><span class="keyword">,</span> <span class="number">0</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] 7.207415e-07 9.991507e-01 8.486044e-04
+</div>
+<div class='input'><span class="comment"># The sum of the elements of the inverse ilr is 1</span>
+<span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/sum'>sum</a></span><span class="keyword">(</span><span class="functioncall"><a href='ilr.html'>invilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="keyword">-</span><span class="number">10</span><span class="keyword">,</span> <span class="number">0</span><span class="keyword">)</span><span class="keyword">)</span><span class="keyword">)</span></div>
+<div class='output'>[1] 1
+</div>
+<div class='input'><span class="comment"># This is why we do not need all elements of the inverse transformation to go back:</span>
+<span class="symbol">a</span> <span class="assignement">&lt;-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="number">0.1</span><span class="keyword">,</span> <span class="number">0.3</span><span class="keyword">,</span> <span class="number">0.5</span><span class="keyword">)</span>
+<span class="symbol">b</span> <span class="assignement">&lt;-</span> <span class="functioncall"><a href='ilr.html'>invilr</a></span><span class="keyword">(</span><span class="symbol">a</span><span class="keyword">)</span>
+<span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/length'>length</a></span><span class="keyword">(</span><span class="symbol">b</span><span class="keyword">)</span> <span class="comment"># Four elements</span></div>
+<div class='output'>[1] 4
+</div>
+<div class='input'><span class="functioncall"><a href='ilr.html'>ilr</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/c'>c</a></span><span class="keyword">(</span><span class="symbol">b</span><span class="keyword">[</span><span class="number">1</span><span class="keyword">:</span><span class="number">3</span><span class="keyword">]</span><span class="keyword">,</span> <span class="number">1</span> <span class="keyword">-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/sum'>sum</a></span><span class="keyword">(</span><span class="symbol">b</span><span class="keyword">[</span><span class="number">1</span><span class="keyword">:</span><span class="number">3</span><span class="keyword">]</span><span class="keyword">)</span><span class="keyword">)</span><span class="keyword">)</span> <span class="comment"># Gives c(0.1, 0.3, 0.5)</span></div>
+<div class='output'>[1] 0.1 0.3 0.5
+</div></pre>
+ </div>
+ <div class="span4 sidebar">
+ <!-- <ul>
+ <li>ilr</li><li>invilr</li>
+ </ul>
+ <ul>
+ <li> manip </li>
+ </ul> -->
+
+ <h2>See also</h2>
+ <p>Another implementation can be found in R package <code>robCompositions</code>.</p>
+
+
+
+ <h2>Author</h2>
+
+ René Lehmann and Johannes Ranke
+
+
+ </div>
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