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<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script> <!--[if lt IE 9]> <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script> <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script> <![endif]--> </head> <body> <div class="container template-reference-topic"> <header> <div class="navbar navbar-default navbar-fixed-top" role="navigation"> <div class="container"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.9.48.1</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"> <li> <a href="../reference/index.html">Functions and data</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false"> Articles <span class="caret"></span> </a> <ul class="dropdown-menu" role="menu"> <li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> <li> <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> </li> <li> <a 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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'>#> [1] -1.628174 -2.820079</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'>#> [1] 1.628174 2.820079</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'>#> [1] 0 0</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'>#> [1] -0.2034219 0.1174457</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'>#> [1] 0.70 0.29 0.01</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'>#> [1] 0.70 0.29 0.01</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'>#> [1] 7.213536e-07 9.999993e-01</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'>#> [1] 7.207415e-07 9.991507e-01 8.486044e-04</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'>#> [1] 1</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>) <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'>#> [1] 4</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'>#> [1] 0.1 0.3 0.5</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> </div> </div> <footer> <div class="copyright"> <p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.3.0.9000.</p> </div> </footer> </div> </body> </html>