toqito.matrices.comparison
==========================

.. py:module:: toqito.matrices.comparison

.. autoapi-nested-parse::

   Computes comparison matrix.





Module Contents
---------------

.. py:function:: 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
   [@WikiComparisonMatrix]. 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,

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

   .. rubric:: Examples

   ```python exec="1" source="above"
   import numpy as np
   from toqito.matrices import comparison
   A = np.array([[2, -1],
               [3, 4]])
   print(comparison(A))
   ```

   :raises ValueError: If the input matrix is not square.

   :param mat: The input square matrix.

   :returns: The comparison matrix of the input matrix.