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diff --git a/docs/reference/ilr.html b/docs/reference/ilr.html new file mode 100644 index 00000000..355cbb78 --- /dev/null +++ b/docs/reference/ilr.html @@ -0,0 +1,152 @@ +<!-- Generated by pkgdown: do not edit by hand --> +<!DOCTYPE html> +<html> + <head> + <meta charset="utf-8"> +<meta http-equiv="X-UA-Compatible" content="IE=edge"> +<meta name="viewport" content="width=device-width, initial-scale=1.0"> + +<title>ilr. mkin</title> + +<!-- jquery --> +<script src="https://code.jquery.com/jquery-3.1.0.min.js" integrity="sha384-nrOSfDHtoPMzJHjVTdCopGqIqeYETSXhZDFyniQ8ZHcVy08QesyHcnOUpMpqnmWq" crossorigin="anonymous"></script> + +<!-- Bootstrap --> +<link href="https://maxcdn.bootstrapcdn.com/bootswatch/3.3.7/cerulean/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"> + +<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script> + +<!-- Font Awesome icons --> +<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" integrity="sha384-T8Gy5hrqNKT+hzMclPo118YTQO6cYprQmhrYwIiQ/3axmI1hQomh7Ud2hPOy8SP1" crossorigin="anonymous"> + + +<!-- pkgdown --> +<link href="../pkgdown.css" rel="stylesheet"> +<script src="../pkgdown.js"></script> + +<!-- mathjax --> +<script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></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"> + <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"> + <span class="icon-bar"></span> + <span class="icon-bar"></span> + <span class="icon-bar"></span> + </button> + <a class="navbar-brand" href="../index.html">mkin</a> + </div> + <div id="navbar" class="navbar-collapse collapse"> + <ul class="nav navbar-nav"> + <li> + <a href="../index.html">Home</a> +</li> +<li> + <a href="../reference/index.html">Reference</a> +</li> + </ul> + <ul class="nav navbar-nav navbar-right"> + <li> + <a href="https://github.com/jranke/mkin"> + <span class="fa fa-github fa-lg"></span> + + </a> +</li> + </ul> + </div><!--/.nav-collapse --> + </div><!--/.container --> +</div><!--/.navbar --> + + </header> + + <div class="page-header"> + <h1> +</h1> +</div> + +<div class="row"> + <div class="col-md-9"> + + <p>This implementation is a special case of the class of isometric log-ratio transformations.</p> + + + <pre><span class='fu'>ilr</span>(<span class='no'>x</span>) + <span class='fu'>invilr</span>(<span class='no'>x</span>)</pre> + + <h2>Arguments</h2> + <dl class="dl-horizontal"> + <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="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 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> + + <div class="See also"> + <h2>See also</h2> + + <p>Another implementation can be found in R package <code>robCompositions</code>.</p> + </div> + + <h2 id="examples">Examples</h2> + <pre class="examples"><div class='input'><span class='co'># Order matters</span> +<span class='fu'>ilr</span>(<span class='fu'>c</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'>c</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'>c</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'>c</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'>c</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'>c</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'>c</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'>sum</span>(<span class='fu'>invilr</span>(<span class='fu'>c</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'>c</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'>length</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'>c</span>(<span class='no'>b</span>[<span class='fl'>1</span>:<span class='fl'>3</span>], <span class='fl'>1</span> - <span class='fu'>sum</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"> + <h2>Author</h2> + + René Lehmann and Johannes Ranke + + </div> +</div> + + <footer> + <p>Built by <a href="http://hadley.github.io/pkgdown/">pkgdown</a>. Styled with <a href="http://getbootstrap.com">Bootstrap 3</a>.</p> + </footer> + </div> + + </body> +</html> |