mushi.composition.inner
- inner(x, y)[source]
Calculates 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
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
inner product result
- Return type
Examples
>>> import numpy as np >>> import mushi.composition as cmp >>> x = np.array([.1, .3, .4, .2]) >>> y = np.array([.2, .4, .2, .2]) >>> cmp.inner(x, y) DeviceArray(0.21078525, dtype=float64)