Description Usage Arguments Details Value Author(s) References See Also Examples

Compute the centered log ratio transform of a (dataset of) from isometric log-ratio transform(s) and its inverse. Equivalently, compute centered and isometric planar transforms from each other. Acts in vectors and in bilinear forms. For bilinear forms, transform between variation-form from clr-form.

1 2 3 4 5 6 7 8 9 | ```
clr2ilr( x , V=ilrBase(x=x) )
ilr2clr( z , V=ilrBase(z=z), x=gsi.orig(z) )
clrvar2ilr( varx , V=ilrBase(D=ncol(varx)) )
ilrvar2clr( varz , V=ilrBase(D=ncol(varz)+1) ,x=NULL)
clrvar2variation(Sigma)
variation2clrvar(TT)
is.clrvar(M, tol=1e-10)
is.ilrvar(M, tol=1e-10)
``` |

`x` |
the clr/cpt-transform of composition(s) (in the ilr2-routines provided only to give column names.) |

`z` |
the ilr/ipt-transform of composition(s) |

`varx, Sigma` |
variance or covariance matrix of clr/cpt-transformed compositions |

`varz` |
variance or covariance matrix of ilr/ipt-transformed compositions |

`V` |
a matrix with columns giving the chosen basis of the clr-plane |

`TT` |
variation matrix |

`M` |
a matrix, to check if it is a valid variance |

`tol` |
tolerance for the check |

These functions perform a matrix multiplication with `V`

in an
appropriate way.

`clr2ilr`

gives the ilr/ipt transform of the same composition(s),

`ilr2clr`

gives the clr/cpt transform of the same
composition(s),

`clrvar2ilr`

gives the variance-/covariance-matrix of the ilr/ipt transform of the same compositional data set,

`ilrvar2clr`

and `clrvar2variation`

give the variance-/covariance-matrix of the clr/cpt
transform of the same compositional data set.

`variation2clrvar`

gives the variation matrix from the clr-covariance matrix

`is.*var`

check if the given matrix satisfies the conditions to be an ilr-variance
resp. a clr-variance

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

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

Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn
(2002) A consise guide to the algebraic geometric structure of the
simplex, the sample space for compositional data analysis, *Terra
Nostra*, Schriften der Alfred Wegener-Stiftung, 03/2003

1 2 3 4 5 6 7 | ```
data(SimulatedAmounts)
ilrInv(clr2ilr(clr(sa.lognormals)))-clo(sa.lognormals)
clrInv(ilr2clr(ilr(sa.lognormals)))-clo(sa.lognormals)
ilrvar2clr(var(ilr(sa.lognormals)))-var(clr(sa.lognormals))
clrvar2ilr(var(cpt(sa.lognormals)))-var(ipt(sa.lognormals))
variation(acomp(sa.lognormals))
clrvar2variation(var(acomp(sa.lognormals)))
``` |

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