mean_product

mean_product(a, b)

Average of the elements for an element-wise product of two matrices.

If the matrices are square it is

\[\frac{1}{n^2} \sum_{i,j=1}^n a_{i, j} b_{i, j}.\]

Parameters

• a (Array) – First input array to be multiplied.

• b (Array) – Second input array to be multiplied.

Returns

Average of the product.

Return type

Array

See also

u_product

Examples

>>> import numpy as np
>>> import dcor
>>> a = np.array([[1, 2, 4], [1, 2, 4], [1, 2, 4]])
>>> b = np.array([[1, .5, .25], [1, .5, .25], [1, .5, .25]])
>>> dcor.mean_product(a, b)
1.0
>>> dcor.mean_product(a, a)
7.0

If the matrices involved are not square, but have the same dimensions, the average of the product is still well defined

>>> c = np.array([[1, 2], [1, 2], [1, 2]])
>>> dcor.mean_product(c, c)
2.5