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- René Lehmann and Johannes Ranke
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-
- <h1>
- Function to perform isometric log-ratio transformation
-</h1>
-
-<div class="row">
- <div class="span8">
- <h2>Usage</h2>
- <pre><div>ilr(x) invilr(x)</div></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'># Order matters
-ilr(c(0.1, 1, 10))
-</div>
-<div class='output'>[1] -1.628174 -2.820079
-</div>
-<div class='input'>ilr(c(10, 1, 0.1))
-</div>
-<div class='output'>[1] 1.628174 2.820079
-</div>
-<div class='input'># Equal entries give ilr transformations with zeros as elements
-ilr(c(3, 3, 3))
-</div>
-<div class='output'>[1] 0 0
-</div>
-<div class='input'># Almost equal entries give small numbers
-ilr(c(0.3, 0.4, 0.3))
-</div>
-<div class='output'>[1] -0.2034219 0.1174457
-</div>
-<div class='input'># Only the ratio between the numbers counts, not their sum
-invilr(ilr(c(0.7, 0.29, 0.01)))
-</div>
-<div class='output'>[1] 0.70 0.29 0.01
-</div>
-<div class='input'>invilr(ilr(2.1 * c(0.7, 0.29, 0.01)))
-</div>
-<div class='output'>[1] 0.70 0.29 0.01
-</div>
-<div class='input'># Inverse transformation of larger numbers gives unequal elements
-invilr(-10)
-</div>
-<div class='output'>[1] 7.213536e-07 9.999993e-01
-</div>
-<div class='input'>invilr(c(-10, 0))
-</div>
-<div class='output'>[1] 7.207415e-07 9.991507e-01 8.486044e-04
-</div>
-<div class='input'># The sum of the elements of the inverse ilr is 1
-sum(invilr(c(-10, 0)))
-</div>
-<div class='output'>[1] 1
-</div>
-<div class='input'># This is why we do not need all elements of the inverse transformation to go back:
-a &lt;- c(0.1, 0.3, 0.5)
-b &lt;- invilr(a)
-length(b) # Four elements
-</div>
-<div class='output'>[1] 4
-</div>
-<div class='input'>ilr(c(b[1:3], 1 - sum(b[1:3]))) # Gives c(0.1, 0.3, 0.5)
-</div>
-<div class='output'>[1] 0.1 0.3 0.5
-</div></pre>
- </div>
- <div class="span4">
- <!-- <ul>
- <li>ilr</li><li>invilr</li>
- </ul>
- <ul>
- <li> manip </li>
- </ul> -->
-
- <h2>See also</h2>
-
- Another implementation can be found in R package <code>robCompositions</code>.
-
-
- <h2>Author</h2>
-
- René Lehmann and Johannes Ranke
-
-
- </div>
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