skbio.stats.composition.inner

skbio.stats.composition.inner(x, y)

Calculate the Aitchson inner product.

This inner product is defined as follows:

\[\langle x, y \rangle_a = \frac{1}{2D} \sum\limits_{i=1}^{D} \sum\limits_{j=1}^{D} \ln\left(\frac{x_i}{x_j}\right) \ln\left(\frac{y_i}{y_j}\right)\]

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 or scalar of shape (n_compositions, n_compositions)

Inner product result.

Examples

>>> import numpy as np
>>> from skbio.stats.composition import inner
>>> x = np.array([.1, .3, .4, .2])
>>> y = np.array([.2, .4, .2, .2])
>>> inner(x, y)  
0.2107852473...