skbio.stats.composition.perturb_inv#

skbio.stats.composition.perturb_inv(x, y)[source]#

Perform 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:

xarray_like of shape (n_compositions, n_components): A matrix of proportions.
yarray_like of shape (n_compositions, n_components): A matrix of proportions.

Returns:

ndarray of shape (n_compositions, n_components): A matrix of proportions where all of the values are non-zero and each composition (row) adds up to 1.

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])