toqito.matrix_props.mutual_coherence

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

Module Contents

toqito.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 [@WikiMutualCoh]. It provides a measure of how similar the vectors are to each other.

Examples

`python exec="1" source="above" 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)) `

Raises:

• ValueError – If arrays in list are not 1D.

• TypeError – If input is not a list.

Parameters:

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

Returns:

The mutual coherence of the collection of input vectors.

Return type:

float | numpy.floating