matrix_props.mutual_coherence¶

Computes the mutual coherence for a list of 1D numpy arrays.

Functions¶

mutual_coherence(vectors)

Calculate the mutual coherence of a collection of input vectors.

Module Contents¶

matrix_props.mutual_coherence.mutual_coherence(vectors)¶

Calculate the mutual coherence of a collection of input vectors.

The mutual coherence of a collection of input vectors is defined as the maximum absolute value of the inner product between any two distinct vectors, divided by the product of their norms [1]. It provides a measure of how similar the vectors are to each other.

Examples

import numpy as np
from toqito.matrix_props.mutual_coherence import mutual_coherence
example_A = [np.array([1, 0]), np.array([0, 1])]
print("Result for example_A = ",mutual_coherence(example_A))
# An example with a larger set of vectors
example_B = [np.array([1, 0, 1]), np.array([0, 1, 1]), np.array([1, 1, 0])]
print("Result for example_B = ",mutual_coherence(example_B))

Result for example_A =  0.0
Result for example_B =  0.4999999999999999

References

Parameters:

vectors (list[numpy.ndarray]) – A list of 1D numpy arrays.

Raises:

ValueError – If arrays in list are not 1D.
TypeError – If input is not a list.

Returns:

The mutual coherence of the collection of input vectors.

Return type:

float