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

.. py:module:: rand.random_psd_operator

.. autoapi-nested-parse::

   Generates a random positive semidefinite operator.



Functions
---------

.. autoapisummary::

   rand.random_psd_operator.random_psd_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 :code:`|toqito⟩`, we may generate a random positive semidefinite matrix.
   For :math:`\text{dim}=2`, this can be accomplished as follows.

   .. jupyter-execute::

    from toqito.rand import random_psd_operator

    complex_psd_mat = random_psd_operator(2)

    complex_psd_mat

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

   .. jupyter-execute::

    from toqito.matrix_props import is_positive_semidefinite

    is_positive_semidefinite(complex_psd_mat)

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

   .. jupyter-execute::

    from toqito.rand import random_psd_operator

    real_psd_mat = random_psd_operator(2, is_real=True)

    real_psd_mat


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

   .. jupyter-execute::

    from toqito.matrix_props import is_positive_semidefinite
    is_positive_semidefinite(real_psd_mat)


   It is also possible to add a seed for reproducibility.

   .. jupyter-execute::

    from toqito.rand import random_psd_operator

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

    seeded


   .. rubric:: References

   .. footbibliography::

   :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 :code:`False`.
   :param seed: A seed used to instantiate numpy's random number generator.
   :return: A :code:`dim` x :code:`dim` random positive semidefinite matrix.