skbio.stats.composition.clr_inv#

skbio.stats.composition.clr_inv(mat, axis=-1, validate=True)[source]#

Perform inverse centre log ratio (CLR) transformation.

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

\[clr^{-1}: U \rightarrow S^D\]

where \(U= \{x :\sum\limits_{i=1}^D x = 0 \; \forall x \in \mathbb{R}^D\}\)

This transformation is defined as follows:

\[clr^{-1}(x) = C[\exp( x_1, \ldots, x_D)]\]

Changed in version 0.7.0: The function now works on any dimension in arrays of any number of dimensions.

Parameters:
matarray_like of shape (…, n_components, …)

A matrix of CLR-transformed data.

axisint, optional

Axis along which inverse CLR transformation will be performed. Each vector on this axis is considered as a CLR-transformed composition. Default is the last axis (-1).

Added in version 0.7.0.

validate: bool, optional

Check if the matrix has been centered at 0. Violation will result in a warning rather than an error, for backward compatibility. Defaults to True.

Added in version 0.7.0.

Returns:
ndarray of shape (…, n_components, …)

Inverse CLR-transformed matrix.

See also

clr

Notes

The output of clr_inv is guaranteed to have each composition sum to 1. But this property isn’t required for the input for clr. Therefore, clr_inv does not completely invert clr. Instead, clr_inv(clr(mat)) and closure(mat) are equal.

Examples

>>> import numpy as np
>>> from skbio.stats.composition import clr_inv
>>> x = np.array([.1, .3, .4, .2])
>>> clr_inv(x)
array([ 0.21383822,  0.26118259,  0.28865141,  0.23632778])
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