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diff --git a/docs/ilr.html b/docs/ilr.html new file mode 100644 index 00000000..c5fea9cb --- /dev/null +++ b/docs/ilr.html @@ -0,0 +1,168 @@ +<!DOCTYPE html> +<html lang="en"> + <head> + <meta charset="utf-8"> +<title>ilr. mkin 0.9.44.9000</title> +<meta name="viewport" content="width=device-width, initial-scale=1.0"> +<meta name="author" content=" + René Lehmann and Johannes Ranke +"> + +<link href="css/bootstrap.css" rel="stylesheet"> +<link href="css/bootstrap-responsive.css" rel="stylesheet"> +<link href="css/highlight.css" rel="stylesheet"> +<link href="css/staticdocs.css" rel="stylesheet"> + +<!--[if lt IE 9]> + <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script> +<![endif]--> + +<script type="text/x-mathjax-config"> + MathJax.Hub.Config({ + tex2jax: { + inlineMath: [ ['$','$'], ["\\(","\\)"] ], + processEscapes: true + } + }); +</script> +<script type="text/javascript" + src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> +</script> + </head> + + <body> + <div class="navbar"> + <div class="navbar-inner"> + <div class="container"> + <a class="brand" href="index.html">mkin 0.9.44.9000</a> + <div class="nav"> + <ul class="nav"> + <li><a href="index.html">Home</a></li> + <li><a href="reference.html">Reference</a></li> + </ul> + </div> + </div> + </div> +</div> + + + <div class="container"> + <header> + + </header> + + <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"><-</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"><-</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> +</div> + + <footer> + <p class="pull-right"><a href="#">Back to top</a></p> +<p>Built by <a href="https://github.com/hadley/staticdocs">staticdocs</a>. Styled with <a href="https://getbootstrap.com/2.0.4/">bootstrap</a>.</p> + </footer> + </div> + </body> +</html>
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