R: Auxiliary functions to compute user-defined ilr and ipt...

gsi.merge2signary {compositions} | R Documentation

## Auxiliary functions to compute user-defined ilr and ipt transforms.

### Description

Compute the basis of a clr-plane, to use with isometric log-ratio or planar transform of a (dataset of) compositions.

### Usage

              gsi.merge2signary( M )
              gsi.ilrBase2signary( V )
              gsi.optimalilrBase( x )
              gsi.buildilrBase( W=c(1,-1) )
              gsi.signary2ilrBase( W=c(1,-1) )
              gsi.OrderIlr( V )

### Arguments

`M` | a merge structure (as explained in `hclust`)
`x` | a compositional data set
`W` | a signary matrix (as explained below) defining a partition
`V` | a matrix of change of basis from clr/cpt to ilr/ipt

### Details

A signary matrix is a matrix with the same shape as an ilr matrix, but containing only +1, 0 or -1 values (thus, it is a kind of "extended binary"). If the value W[i,j]= +1, then part "i" is involved in coordinate "j" in the numerator; if W[i,j]=-1, it is involed in the denominator, and if W[i,j]=0 then part "i" does not take part in coordinate "j".

Functions `gsi.merge2signary` and `gsi.buildilrBase` are intended to compute `ilrBase` matrices associated to user-defined partition structures. Function `gsi.ilrBase2signary` offers the inverse functionality.

Function `gsi.OrderIlr` returns a list with two elements: "ilrBase" and "order". The first one contains the ilr basis with coordinates reordered in decreasing number of involved parts (so, all parts are involved in the first coordinate, and only two in the last). The second one gives a permutation of the parts so that involved parts in each coordinate are always together. Note that ilrBase does not have its parts permuted!

### Value

These functions will not be usually called on themselves, but through their wrappers, mainly `ilrBase`. Functions `gsi.merge2signary` and `gsi.ilrBase2signary` return a signary matrix (as explained in "details"), `gsi.optimalilrBase` returns a merge structure (as epxlained in `hclust`), and `gsi.buildilrBase` (and its alias `gsi.signary2ilrBase`) returns an ilr matrix. These functions are thought to be called sequentially.
Apart, `gsi.OrderIlr` reorders both parts and coordinates to ease dendrogram-like representations (see `CoDaDendrogram`).

### Note

It is better not to use gsi.* functions directly since they are internal functions of the package. Use their wrappers.

### Author(s)

Raimon Tolosana-Delgado, K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C. Barcel'o-Vidal (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300

### See Also

`ilrBase`,`ipt`,`ilr`, http://ima.udg.es/Activitats/CoDaWork03

### Examples

    m <- matrix(data=c(-1,-2,
                      -3,-4,
                       1, 2),ncol=2,nrow=3,byrow=TRUE)
    w <- gsi.merge2signary(m)
    w
    V=gsi.buildilrBase(w)
    V
    gsi.ilrBase2signary(V)
    gsi.OrderIlr(V)

[Package compositions version 2.0-0 Index]