From 91a5834dd701211f929fd25419dc34561ce3b4e7 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 14 Feb 2025 09:15:20 +0100 Subject: Initialize dev docs --- docs/dev/reference/ilr.html | 163 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 163 insertions(+) create mode 100644 docs/dev/reference/ilr.html (limited to 'docs/dev/reference/ilr.html') diff --git a/docs/dev/reference/ilr.html b/docs/dev/reference/ilr.html new file mode 100644 index 00000000..c6efae2d --- /dev/null +++ b/docs/dev/reference/ilr.html @@ -0,0 +1,163 @@ + +Function to perform isometric log-ratio transformation — ilr • mkin + Skip to contents + + +
+
+
+ +

Function to perform isometric log-ratio transformation

+ Source: R/ilr.R +
ilr.Rd
+
+ +
+

This implementation is a special case of the class of isometric log-ratio +transformations.

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+ +
+

Usage

+ 
ilr(x)
+
+invilr(x)
+
+ +
+

Arguments

+ + +
x
+

A numeric vector. Naturally, the forward transformation is only +sensible for vectors with all elements being greater than zero.

+ +
+
+

Value

+

The result of the forward or backward transformation. The returned +components always sum to 1 for the case of the inverse log-ratio +transformation.

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+
+

References

+

Peter Filzmoser, Karel Hron (2008) Outlier Detection for +Compositional Data Using Robust Methods. Math Geosci 40 233-248

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+

See also

+

Another implementation can be found in R package +robCompositions.

+
+
+

Author

+

René Lehmann and Johannes Ranke

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+ +
+

Examples

+ 

+# Order matters
+ilr(c(0.1, 1, 10))
+#> [1] -1.628174 -2.820079
+ilr(c(10, 1, 0.1))
+#> [1] 1.628174 2.820079
+# Equal entries give ilr transformations with zeros as elements
+ilr(c(3, 3, 3))
+#> [1] 0 0
+# Almost equal entries give small numbers
+ilr(c(0.3, 0.4, 0.3))
+#> [1] -0.2034219  0.1174457
+# Only the ratio between the numbers counts, not their sum
+invilr(ilr(c(0.7, 0.29, 0.01)))
+#> [1] 0.70 0.29 0.01
+invilr(ilr(2.1 * c(0.7, 0.29, 0.01)))
+#> [1] 0.70 0.29 0.01
+# Inverse transformation of larger numbers gives unequal elements
+invilr(-10)
+#> [1] 7.213536e-07 9.999993e-01
+invilr(c(-10, 0))
+#> [1] 7.207415e-07 9.991507e-01 8.486044e-04
+# The sum of the elements of the inverse ilr is 1
+sum(invilr(c(-10, 0)))
+#> [1] 1
+# This is why we do not need all elements of the inverse transformation to go back:
+a <- c(0.1, 0.3, 0.5)
+b <- invilr(a)
+length(b) # Four elements
+#> [1] 4
+ilr(c(b[1:3], 1 - sum(b[1:3]))) # Gives c(0.1, 0.3, 0.5)
+#> [1] 0.1 0.3 0.5
+
+
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+ + + + + + + -- cgit v1.2.1