toqito.rand.random_psd_operator
===============================

.. py:module:: toqito.rand.random_psd_operator

.. autoapi-nested-parse::

   Generates a random positive semidefinite operator.





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

.. py:function:: random_psd_operator(dim, is_real = False, seed = None)

   Generate a random positive semidefinite operator.

   A positive semidefinite operator is a Hermitian operator that has only real and non-negative eigenvalues.
   This function generates a random positive semidefinite operator by constructing a Hermitian matrix,
   based on the fact that a Hermitian matrix can have real eigenvalues.

   .. rubric:: Examples

   Using `|toqito⟩`, we may generate a random positive semidefinite matrix.
   For \(\text{dim}=2\), this can be accomplished as follows.

   ```python exec="1" source="above" session="psd_operator"
   from toqito.rand import random_psd_operator

   complex_psd_mat = random_psd_operator(2)

   print(complex_psd_mat)
   ```

   We can confirm that this matrix indeed represents a valid positive semidefinite matrix by utilizing
   the `is_positive_semidefinite` function from the `|toqito⟩` library, as demonstrated below:

   ```python exec="1" source="above" session="psd_operator"
   from toqito.matrix_props import is_positive_semidefinite

   print(is_positive_semidefinite(complex_psd_mat))
   ```


   We can also generate random positive semidefinite matrices that are real-valued as follows.

   ```python exec="1" source="above" session="psd_operator"
   from toqito.rand import random_psd_operator

   real_psd_mat = random_psd_operator(2, is_real=True)

   print(real_psd_mat)
   ```


   Again, verifying that this is a valid positive semidefinite matrix can be done as follows.

   ```python exec="1" source="above" session="psd_operator"
   from toqito.matrix_props import is_positive_semidefinite
   print(is_positive_semidefinite(real_psd_mat))
   ```


   It is also possible to add a seed for reproducibility.

   ```python exec="1" source="above" session="psd_operator"
   from toqito.rand import random_psd_operator

   seeded = random_psd_operator(2, is_real=True, seed=42)

   print(seeded)
   ```

   :param dim: The dimension of the operator.
   :param is_real: Boolean denoting whether the returned matrix will have all real entries or not. Default is `False`.
   :param seed: A seed used to instantiate numpy's random number generator.

   :returns: A `dim` x `dim` random positive semidefinite matrix.