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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> </div> </div> <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2> </nav></div> </div> <footer><div class="copyright"> <p></p><p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> </div> </footer></div> </body></html>