matrices.comparison¶

Computes comparison matrix.

Functions¶

comparison(mat)

Compute comparison matrix of a given square matrix.

Module Contents¶

matrices.comparison.comparison(mat)¶

Compute comparison matrix of a given square matrix.

This function computes the comparison matrix \(M(A)\) for a square matrix \(A\) as defined in [1]. For each entry, the diagonal entries are given by the absolute value of the original diagonal entries of \(A\), while the off-diagonal entries are given by minus the absolute value of the corresponding entries. In other words,

\[\begin{split}m_{ij} = \begin{cases} |a_{ij}|, & \text{if } i = j, \\ -|a_{ij}|, & \text{if } i \neq j. \end{cases}\end{split}\]

Examples

import numpy as np
from toqito.matrices import comparison
A = np.array([[2, -1],
            [3, 4]])
print(comparison(A))

[[ 2. -1.]
 [-3.  4.]]

References

Parameters:: mat (numpy.ndarray) – The input square matrix.
Raises:: ValueError – If the input matrix is not square.
Returns:: The comparison matrix of the input matrix.
Return type:: numpy.ndarray