toqito.matrix_props.is_stochastic
=================================

.. py:module:: toqito.matrix_props.is_stochastic

.. autoapi-nested-parse::

   Checks if the matrix is stochastic.





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

.. py:function:: is_stochastic(mat, mat_type)

   Verify matrix is doubly, right or left stochastic.

   When the nonnegative elements in a row of a square matrix sum up to 1, the matrix is right stochastic and if the
   columns sum up to 1, the matrix is left stochastic [@WikiStochasticMatrix].

   When a matrix is right and left stochastic, it is a doubly stochastic matrix [@WikiDoublyStochasticMatrix]
   .

   !!! See Also
       [`is_doubly_stochastic()`][toqito.matrix_props.is_doubly_stochastic]

   .. rubric:: Examples

   The elements of an identity matrix and a Pauli-X matrix are nonnegative such that the rows and columns
   sum up to 1.
   We expect these matrices to be left and right stochastic. The same cannot be said about a Pauli-Z or a Pauli-Y
   matrix.

   ```python exec="1" source="above"
   import numpy as np
   from toqito.matrix_props import is_stochastic

   print(is_stochastic(np.eye(5), "right"))
   print(is_stochastic(np.eye(5), "left"))
   print(is_stochastic(np.eye(5), "doubly"))
   ```

   ```python exec="1" source="above"
   from toqito.matrices import pauli
   from toqito.matrix_props import is_stochastic

   print(is_stochastic(pauli("X"), "left"))
   print(is_stochastic(pauli("X"), "right"))
   print(is_stochastic(pauli("X"), "doubly"))
   ```

   ```python exec="1" source="above"
   from toqito.matrices import pauli
   from toqito.matrix_props import is_stochastic

   print(is_stochastic(pauli("Z"), "right"))
   print(is_stochastic(pauli("Z"), "left"))
   print(is_stochastic(pauli("Z"), "doubly"))
   ```
                     `mat_type`

   :raises TypeError: If something other than `"doubly"`, `"left"` or `"right"` is used for

   :param mat: Matrix of interest
   :param mat_type: Type of stochastic matrix. `"left"` for left stochastic matrix and `"right"` for right stochastic
   :param matrix and `"doubly"` for a doubly stochastic matrix.:

   :returns: Returns `True` if the matrix is doubly, right or left stochastic, `False` otherwise.