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authorJohannes Ranke <jranke@uni-bremen.de>2023-02-13 05:19:08 +0100
committerJohannes Ranke <jranke@uni-bremen.de>2023-02-13 05:19:08 +0100
commit8d1a84ac2190538ed3bac53a303064e281595868 (patch)
treeacb894d85ab7ec87c4911c355a5264a77e08e34b /docs/dev/reference/ilr.html
parent51d63256a7b3020ee11931d61b4db97b9ded02c0 (diff)
parent4200e566ad2600f56bc3987669aeab88582139eb (diff)
Merge branch 'main' into custom_lsoda_call
Diffstat (limited to 'docs/dev/reference/ilr.html')
-rw-r--r--docs/dev/reference/ilr.html235
1 files changed, 97 insertions, 138 deletions
diff --git a/docs/dev/reference/ilr.html b/docs/dev/reference/ilr.html
index 452647d6..c1396303 100644
--- a/docs/dev/reference/ilr.html
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+transformations."><meta name="robots" content="noindex"><!-- mathjax --><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]>
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@@ -99,48 +42,50 @@ transformations." />
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+ </li>
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<div class="col-md-9 contents">
<div class="page-header">
<h1>Function to perform isometric log-ratio transformation</h1>
- <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/ilr.R'><code>R/ilr.R</code></a></small>
+ <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/ilr.R" class="external-link"><code>R/ilr.R</code></a></small>
<div class="hidden name"><code>ilr.Rd</code></div>
</div>
@@ -149,86 +94,100 @@ transformations." />
transformations.</p>
</div>
- <pre class="usage"><span class='fu'>ilr</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span>
-
-<span class='fu'>invilr</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span></pre>
+ <div id="ref-usage">
+ <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">ilr</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">invilr</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
+ </div>
- <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>
+ <div id="arguments">
+ <h2>Arguments</h2>
+ <dl><dt>x</dt>
+<dd><p>A numeric vector. Naturally, the forward transformation is only
+sensible for vectors with all elements being greater than zero.</p></dd>
- <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
+</dl></div>
+ <div id="value">
+ <h2>Value</h2>
+
- <p>The result of the forward or backward transformation. The returned
+<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>
-
+ </div>
+ <div id="references">
+ <h2>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
+ </div>
+ <div id="see-also">
+ <h2>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="author"><a class="anchor" href="#author"></a>Author</h2>
-
+ </div>
+ <div id="author">
+ <h2>Author</h2>
<p>René Lehmann and Johannes Ranke</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='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.1</span>, <span class='fl'>1</span>, <span class='fl'>10</span><span class='op'>)</span><span class='op'>)</span>
-</div><div class='output co'>#&gt; [1] -1.628174 -2.820079</div><div class='input'><span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>10</span>, <span class='fl'>1</span>, <span class='fl'>0.1</span><span class='op'>)</span><span class='op'>)</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='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fl'>3</span>, <span class='fl'>3</span><span class='op'>)</span><span class='op'>)</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='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.3</span>, <span class='fl'>0.4</span>, <span class='fl'>0.3</span><span class='op'>)</span><span class='op'>)</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='op'>(</span><span class='fu'>ilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</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='op'>(</span><span class='fu'>ilr</span><span class='op'>(</span><span class='fl'>2.1</span> <span class='op'>*</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.7</span>, <span class='fl'>0.29</span>, <span class='fl'>0.01</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</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='op'>(</span><span class='op'>-</span><span class='fl'>10</span><span class='op'>)</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='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>10</span>, <span class='fl'>0</span><span class='op'>)</span><span class='op'>)</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'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span><span class='op'>(</span><span class='fu'>invilr</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='op'>-</span><span class='fl'>10</span>, <span class='fl'>0</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</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='va'>a</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0.1</span>, <span class='fl'>0.3</span>, <span class='fl'>0.5</span><span class='op'>)</span>
-<span class='va'>b</span> <span class='op'>&lt;-</span> <span class='fu'>invilr</span><span class='op'>(</span><span class='va'>a</span><span class='op'>)</span>
-<span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>b</span><span class='op'>)</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='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='va'>b</span><span class='op'>[</span><span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span>, <span class='fl'>1</span> <span class='op'>-</span> <span class='fu'><a href='https://rdrr.io/r/base/sum.html'>sum</a></span><span class='op'>(</span><span class='va'>b</span><span class='op'>[</span><span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>]</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</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 id="ref-examples">
+ <h2>Examples</h2>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Order matters</span></span></span>
+<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.1</span>, <span class="fl">1</span>, <span class="fl">10</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] -1.628174 -2.820079</span>
+<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">10</span>, <span class="fl">1</span>, <span class="fl">0.1</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1.628174 2.820079</span>
+<span class="r-in"><span><span class="co"># Equal entries give ilr transformations with zeros as elements</span></span></span>
+<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">3</span>, <span class="fl">3</span>, <span class="fl">3</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0 0</span>
+<span class="r-in"><span><span class="co"># Almost equal entries give small numbers</span></span></span>
+<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.3</span>, <span class="fl">0.4</span>, <span class="fl">0.3</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] -0.2034219 0.1174457</span>
+<span class="r-in"><span><span class="co"># Only the ratio between the numbers counts, not their sum</span></span></span>
+<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.7</span>, <span class="fl">0.29</span>, <span class="fl">0.01</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.70 0.29 0.01</span>
+<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="fu">ilr</span><span class="op">(</span><span class="fl">2.1</span> <span class="op">*</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.7</span>, <span class="fl">0.29</span>, <span class="fl">0.01</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.70 0.29 0.01</span>
+<span class="r-in"><span><span class="co"># Inverse transformation of larger numbers gives unequal elements</span></span></span>
+<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="op">-</span><span class="fl">10</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 7.213536e-07 9.999993e-01</span>
+<span class="r-in"><span><span class="fu">invilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">10</span>, <span class="fl">0</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 7.207415e-07 9.991507e-01 8.486044e-04</span>
+<span class="r-in"><span><span class="co"># The sum of the elements of the inverse ilr is 1</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu">invilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">10</span>, <span class="fl">0</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 1</span>
+<span class="r-in"><span><span class="co"># This is why we do not need all elements of the inverse transformation to go back:</span></span></span>
+<span class="r-in"><span><span class="va">a</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.1</span>, <span class="fl">0.3</span>, <span class="fl">0.5</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">b</span> <span class="op">&lt;-</span> <span class="fu">invilr</span><span class="op">(</span><span class="va">a</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/length.html" class="external-link">length</a></span><span class="op">(</span><span class="va">b</span><span class="op">)</span> <span class="co"># Four elements</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 4</span>
+<span class="r-in"><span><span class="fu">ilr</span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="va">b</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span>, <span class="fl">1</span> <span class="op">-</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">b</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">3</span><span class="op">]</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="co"># Gives c(0.1, 0.3, 0.5)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> [1] 0.1 0.3 0.5</span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+ </div>
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