skbio.stats.composition.ilr_inv

skbio.stats.composition.ilr_inv(mat, basis=None, check=True)[source]

State: Experimental as of 0.4.0. Performs inverse isometric log ratio transform.

This function transforms compositions from the real space to Aitchison geometry. The \(ilr^{-1}\) transform is both an isometry, and an isomorphism defined on the following spaces

\(ilr^{-1}: \mathbb{R}^{D-1} \rightarrow S^D\)

The inverse ilr transformation is defined as follows

\[ilr^{-1}(x) = \bigoplus\limits_{i=1}^{D-1} x \odot e_i\]

where \([e_1,\ldots, e_{D-1}]\) is an orthonormal basis in the simplex.

If an orthonormal basis isn’t specified, the J. J. Egozcue orthonormal basis derived from Gram-Schmidt orthogonalization will be used by default.

Parameters:
  • mat (numpy.ndarray, float) – a matrix of transformed proportions where rows = compositions and columns = components
  • basis (numpy.ndarray, float, optional) – orthonormal basis for Aitchison simplex defaults to J.J.Egozcue orthonormal basis
  • check (bool) – Specifies if the basis is orthonormal.

Examples

>>> import numpy as np
>>> from skbio.stats.composition import ilr
>>> x = np.array([.1, .3, .6,])
>>> ilr_inv(x)
array([ 0.34180297,  0.29672718,  0.22054469,  0.14092516])

Notes

If the basis parameter is specified, it is expected to be a basis in the Aitchison simplex. If there are D-1 elements specified in mat, then the dimensions of the basis needs be D-1 x D, where rows represent basis vectors, and the columns represent proportions.