aboutsummaryrefslogblamecommitdiff
path: root/docs/reference/ilr.html
blob: 808bcdb7bfa4531db90e63f5c748db85a7d38233 (plain) (tree)
1
2
3
4
5
6
7
8
9






                                                                      
                                                                                      

                                                                                                                                                                               
                  
 
                                                                                                                                                                                                                






                                                                                                                                                                                                                      
                                                   

                                     
                                                                                                  



                                                                               
 

         
                                                    
              
                                                                            










                                                                                                         
                                                          
     

















                                                                                                                    

                                                                                                      
       
     

                                       
           
      
                                              




                                            


                                
 

               

                                 
                                                                   
          
 


                                                                                                     
                                                                             
                                                                 
                                                                                                






                                                                                         
    
                                                                                   
 
                                                                                           
                                                                    
                                                                                                  
 

                                                                                                                                   
 
                                                                                         
    
 
                                                                                            
                                                                                    




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 
                                                                                                                                                                        
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
        












                                                         






                                  
                             
                                     




                                                                                



               
<!-- 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>Function to perform isometric log-ratio transformation — 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/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-BVYiiSIFeK1dGmJRAkycuHAHRg32OmUcww7on3RYdg4Va+PmSTsz/K68vbdEjh4u" 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="../jquery.sticky-kit.min.js"></script>
<script src="../pkgdown.js"></script>

<!-- mathjax -->
<script src='https://mathjax.rstudio.com/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 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">
        <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="../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/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
    </li>
    <li>
      <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
    </li>
  </ul>
</li>
<li>
  <a href="../news/index.html">News</a>
</li>
      </ul>
      
      <ul class="nav navbar-nav navbar-right">
        <li>
  <a href="http://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="row">
  <div class="col-md-9 contents">
    <div class="page-header">
    <h1>Function to perform isometric log-ratio transformation</h1>
    </div>

    
    <p>This implementation is a special case of the class of isometric log-ratio transformations.</p>
    

    <pre class="usage"><span class='fu'>ilr</span>(<span class='no'>x</span>)
  <span class='fu'>invilr</span>(<span 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>

    <p>Another implementation can be found in R package <code>robCompositions</code>.</p>
    

    <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'>c</span>(<span class='fl'>0.1</span>, <span class='fl'>1</span>, <span class='fl'>10</span>))</div><div class='output co'>#&gt; [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'>#&gt; [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'>#&gt; [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'>#&gt; [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'>#&gt; [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'>#&gt; [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'>#&gt; [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'>#&gt; [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'>#&gt; [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'>&lt;-</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'>&lt;-</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'>#&gt; [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'>#&gt; [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>
    
  René Lehmann and Johannes Ranke

  </div>
</div>

      <footer>
      <div class="copyright">
  <p>Developed by Johannes Ranke.</p>
</div>

<div class="pkgdown">
  <p>Site built with <a href="http://hadley.github.io/pkgdown/">pkgdown</a>.</p>
</div>

      </footer>
   </div>

  </body>
</html>

Contact - Imprint