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
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: |
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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.