composition_stats.power

composition_stats.power(x, a)

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

xarray_like, float

a matrix of proportions where rows = compositions and columns = components each composition (row) must add up to unity (see closure())

afloat

a scalar float

Returns

numpy.ndarray, np.float64

A matrix of proportions where all of the values are nonzero and each composition (row) adds up to 1

Examples

>>> import numpy as np
>>> from composition_stats import power
>>> x = np.array([.1,.3,.4, .2])
>>> power(x, .1)
array([ 0.23059566,  0.25737316,  0.26488486,  0.24714631])