From 38f9e15f0c972c1516ae737a2bca8d7789581bbd Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 6 Oct 2016 09:19:21 +0200 Subject: Static documentation rebuilt by pkgdown::build_site() --- docs/reference/ilr.html | 152 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 152 insertions(+) create mode 100644 docs/reference/ilr.html (limited to 'docs/reference/ilr.html') diff --git a/docs/reference/ilr.html b/docs/reference/ilr.html new file mode 100644 index 00000000..355cbb78 --- /dev/null +++ b/docs/reference/ilr.html @@ -0,0 +1,152 @@ + + + + + + + + +ilr. mkin + + + + + + + + + + + + + + + + + + + + + + + + +
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+

+

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+ +
+
+ +

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

+ + + 
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.

+
+ +
+

References

+ +

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

+
+ +
+

See also

+ +

Another implementation can be found in R package robCompositions.

+
+ +

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
+#>
+
+
+

Author

+ + René Lehmann and Johannes Ranke + +
+
+ + +
+ + + -- cgit v1.2.1