idt {compositions} | R Documentation |

## Isometric default transform

### Description

Compute the isometric default transform of a vector (or dataset) of compositions or amounts in the selected class.

### Usage

```
idt(x,...)
## Default S3 method:
idt( x,... )
## S3 method for class 'acomp'
idt( x ,...)
## S3 method for class 'rcomp'
idt( x ,...)
## S3 method for class 'aplus'
idt( x ,...)
## S3 method for class 'rplus'
idt( x ,...)
## S3 method for class 'rmult'
idt( x ,...)
## S3 method for class 'ccomp'
idt( x ,...)
## S3 method for class 'factor'
idt( x ,...)
## S3 method for class 'data.frame'
idt( x ,...)
idtInv(x,orig=gsi.orig(x),...)
## Default S3 method:
idtInv( x ,orig=gsi.orig(x),...)
## S3 method for class 'acomp'
idtInv( x ,orig=gsi.orig(x), V=gsi.getV(x),...)
## S3 method for class 'rcomp'
idtInv( x ,orig=gsi.orig(x), V=gsi.getV(x),...)
## S3 method for class 'aplus'
idtInv( x ,orig=gsi.orig(x),...)
## S3 method for class 'rplus'
idtInv( x ,orig=gsi.orig(x),...)
## S3 method for class 'ccomp'
idtInv( x ,orig=gsi.orig(x),...)
## S3 method for class 'rmult'
idtInv( x ,orig=gsi.orig(x),...)
## S3 method for class 'factor'
idtInv( x ,orig=gsi.orig(x), V=gsi.getV(x),...)
## S3 method for class 'data.frame'
idtInv( x , orig=gsi.orig(x), ...)
```

### Arguments

`x` |
a classed amount or composition, to be transformed with its
isometric default transform, or its inverse; in case of the method for |

`...` |
generic arguments past to underlying functions |

`orig` |
a compositional object which should be mimicked
by the inverse transformation. It is the generic
argument. Typically the |

`V` |
matrix of ( |

### Details

The general idea of this package is to analyse the same data with
different geometric concepts, in a fashion as similar as possible. For each of the
four concepts there exists an isometric transform expressing the geometry
in a full-rank euclidean vector space. Such a transformation is computed
by `idt`

. For `acomp`

the transform is `ilr`

, for
`rcomp`

it is `ipt`

, for
`aplus`

it is `ilt`

, and for
`rplus`

it is `iit`

. Keep in mind that the
transform does not keep the variable names, since there is no guaranteed
one-to-one relation between the original parts and each transformed
variable.

The inverse `idtInv`

is intended to allow for an "easy" and automatic
back-transformation, without intervention of the user. The argument `orig`

(the one determining the behaviour of `idtInv`

as a generic function)
tells the function which back-transformation should be applied, and
gives the column names of `orig`

to the back-transformed
values of `x`

. Therefore, it is very conventient to give the original classed
data set used in the analysis as `orig`

.

### Value

A corresponding matrix of row-vectors containing the transforms. (Exception: idt.data.frame can return a data.frame if the input has no "origClass"-attribute)

### Author(s)

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

### References

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified
R package to analyze Compositional Data, *Computers &
Geosciences*, 34 (4), pages 320-338, doi: 10.1016/j.cageo.2006.11.017.

### See Also

`backtransform`

, `cdt`

, `ilr`

, `ipt`

,
`ilt`

, `cdtInv`

, `ilrInv`

, `iptInv`

,
`iltInv`

, `iitInv`

### Examples

```
## Not run:
# the idt is defined by
idt <- function(x) UseMethod("idt",x)
idt.default <- function(x) x
idt.acomp <- function(x) ilr(x)
idt.rcomp <- function(x) ipt(x)
idt.aplus <- ilt
idt.rplus <- iit
## End(Not run)
idt(acomp(1:5))
idt(rcomp(1:5))
data(Hydrochem)
x = Hydrochem[,c("Na","K","Mg","Ca")]
y = acomp(x)
z = idt(y)
y2 = idtInv(z,y)
par(mfrow=c(2,2))
for(i in 1:4){plot(y[,i],y2[,i])}
```

*compositions*version 2.0-8 Index]