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# skbio.stats.composition.clr_inv

`skbio.stats.composition.``clr_inv`(mat)

  State: Experimental as of 0.4.0. Performs inverse centre log ratio 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

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

  Parameters: | mat (array_like, float) – a matrix of real values where rows = transformed compositions and columns = components
  Returns: | inverse clr transformed matrix
  Return type: | numpy.ndarray

  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])