# The canonical basis in the clr plane used for 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

1 2 3 |

### Arguments

`x` |
optional dataset or vector of compositions |

`z` |
optional dataset or vector containing ilr or ipt coordinates |

`D` |
number of parts of the simplex |

`method` |
method to build the basis, one of "basic", "balanced", "optimal" "PBhclust", "PBmaxvar" or "PBangprox" |

### Details

Method "basic" computes a triangular Helmert matrix (corresponding to
the original ilr transformation defined by Egozcue et al, 2003).
In this case, `ilrBase`

is a wrapper catching
the answers of `gsi.ilrBase`

and is to be
used as the more convenient function.

Method "balanced" returns an ilr matrix associated with a balanced partition,
splitting the parts in groups as equal as possible. Transforms `ilr`

and `ipt`

computed
with this basis are less affected by any component (as happens with "basic").

The following methods are all data-driven and will fail if `x`

is not given.
Some of these methods are extended to non-acomp datasets via the `cpt`

general functionality. Use with care with non-acomp objects!

Method "optimal" is a wrapper to `gsi.optimalilrBase`

, providing the ilr basis
with less influence of missing values. It is computed as a hierarchical
cluster of variables, with parts previously transformed to
1 (if the value is lost) or 0 (if it is recorded).

Methods "PBhclust", "PBmaxvar" and "PBangprox" are principal balance methods (i.e.
balances approximating principal components in different ways). These are all
resolved by calls to `gsi.PrinBal`

. Principal balances functionality should be
considered beta!

### Value

All methods give a matrix containing by columns the basis elements for the
canonical basis of the clr-plane used for the ilr and ipt transform. Only one of the
arguments `x`

, `z`

or `D`

is needed
to determine the dimension of the simplex.

### 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

http://ima.udg.es/Activitats/CoDaWork03

### See Also

`clr`

,`ilr`

,`ipt`

### Examples

1 2 3 4 5 6 7 |