skbio.stats.composition.power

skbio.stats.composition.power(x, a)[source]

State: Experimental as of 0.4.0. Performs the power operation.

This operation is defined as follows

\[`x \odot a = C[x_1^a, \ldots, x_D^a]\]

\(C[x]\) 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, float) – a matrix of proportions where rows = compositions and columns = components
  • a (float) – a scalar float
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 power
>>> x = np.array([.1,.3,.4, .2])
>>> power(x, .1)
array([ 0.23059566,  0.25737316,  0.26488486,  0.24714631])