mushi.composition.perturb_inv

perturb_inv(x, y)

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
>>> import mushi.composition as cmp
>>> x = np.array([.1,.3,.4, .2])
>>> y = np.array([1./6,1./6,1./3,1./3])
>>> cmp.perturb_inv(x,y)
DeviceArray([0.14285714, 0.42857143, 0.28571429, 0.14285714], dtype=float64)