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# skbio.stats.composition.perturb_inv

`skbio.stats.composition.``perturb_inv`(x, y)

  State: Experimental as of 0.4.0. Performs the inverse perturbation operation.

  This operation is defined as

  \[x \ominus y = C[x_1 y_1^{-1}, \ldots, x_D y_D^{-1}]\]

  \(C[x]\) is the closure operation defined as

  \[C[x] = \left[\frac{x_1}{\sum_{i=1}^{D} x_i},\ldots, \frac{x_D}{\sum_{i=1}^{D} x_i} \right]\]

  for some \(D\) dimensional real vector \(x\) and \(D\) is the number of components for every composition.

  Parameters:

  - x (array_like) – a matrix of proportions where rows = compositions and columns = components
  - y (array_like) – a matrix of proportions where rows = compositions and columns = components

  Returns: | A matrix of proportions where all of the values are nonzero and each composition (row) adds up to 1
  Return type: | numpy.ndarray, np.float64

  Examples

      >>> import numpy as np
      >>> from skbio.stats.composition import perturb_inv
      >>> x = np.array([.1,.3,.4, .2])
      >>> y = np.array([1./6,1./6,1./3,1./3])
      >>> perturb_inv(x,y)
      array([ 0.14285714,  0.42857143,  0.28571429,  0.14285714])