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@@ -8,11 +8,13 @@
 
 <title>Function to perform isometric log-ratio transformation — ilr • mkin</title>
 
+
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@@ -32,13 +34,15 @@
 
 
 
-<meta property="og:title" content="Function to perform isometric log-ratio transformation — ilr" />
 
-<meta property="og:description" content="This implementation is a special case of the class of isometric log-ratio transformations." />
+<meta property="og:title" content="Function to perform isometric log-ratio transformation — ilr" />
+<meta property="og:description" content="This implementation is a special case of the class of isometric log-ratio
+transformations." />
 <meta name="twitter:card" content="summary" />
 
 
 
+
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@@ -109,7 +113,6 @@
   <a href="../news/index.html">News</a>
 </li>
       </ul>
-      
       <ul class="nav navbar-nav navbar-right">
         
       </ul>
@@ -131,40 +134,41 @@
     </div>
 
     <div class="ref-description">
-    
-    <p>This implementation is a special case of the class of isometric log-ratio transformations.</p>
-    
+    <p>This implementation is a special case of the class of isometric log-ratio
+transformations.</p>
     </div>
 
     <pre class="usage"><span class='fu'>ilr</span>(<span class='no'>x</span>)
-  <span class='fu'>invilr</span>(<span class='no'>x</span>)</pre>
-    
+
+<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>
+      <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>
-    
+    <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>
-    
+    <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>
-    
+    <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>
+    <pre class="examples"><div class='input'>
+<span class='co'># Order matters</span>
 <span class='fu'>ilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></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'><a href='https://rdrr.io/r/base/c.html'>c</a></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'><a href='https://rdrr.io/r/base/c.html'>c</a></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'><a href='https://rdrr.io/r/base/c.html'>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'>#&gt; [1] -0.2034219  0.1174457</div><div class='input'><span class='co'># Only the ratio between the numbers counts, not their sum</span>
@@ -173,19 +177,16 @@
 <span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span>(<span class='fu'>invilr</span>(<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></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'><a href='https://rdrr.io/r/base/c.html'>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'>&lt;-</span> <span class='fu'>invilr</span>(<span class='no'>a</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></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'><a href='https://rdrr.io/r/base/c.html'>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://rdrr.io/r/base/sum.html'>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'>#&gt; [1] 0.1 0.3 0.5</div></pre>
+<span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></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'><a href='https://rdrr.io/r/base/c.html'>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://rdrr.io/r/base/sum.html'>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'>#&gt; [1] 0.1 0.3 0.5</div><div class='input'>
+</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>