:py:mod:`MomentGauge.Utility`
=============================

.. py:module:: MomentGauge.Utility


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


Functions
~~~~~~~~~

.. autoapisummary::

   MomentGauge.Utility.generalized_eigh_cholesky
   MomentGauge.Utility.generalized_eigh



.. py:function:: generalized_eigh_cholesky(A, B)

   Compute the generalilzed eignvalue problem :math:`A \mathbf{x} = \lambda B \mathbf{x}` in which A and B are Hermite matrix


   :param A: a Hermite matrix of the shape (M, M)
   :type A: array of shape (M,M)
   :param B: a Hermite matrix of the shape (M, M)
   :type B: array of shape (M,M)

   :returns:

             A tuple containing

                 **w**: *array of shape (M)* - The eigenvalues in ascending order, each repeated according to its multiplicity.

                 **V**: *array of shape (M,M)* - The matrix whose ith column V[:, i] is the normalized eigenvector corresponding to the ith eigenvalue.
   :rtype: Tuple


.. py:function:: generalized_eigh(A, B)

   Compute the generalilzed eignvalue problem :math:`A \mathbf{x} = \lambda B \mathbf{x}` in which A and B are Hermite matrix


   :param A: a Hermite matrix of the shape (M, M)
   :type A: array of shape (M,M)
   :param B: a Hermite matrix of the shape (M, M)
   :type B: array of shape (M,M)

   :returns:

             A tuple containing

                 **w**: *array of shape (M)* - The eigenvalues in ascending order, each repeated according to its multiplicity.

                 **V**: *array of shape (M,M)* - The matrix whose ith column V[:, i] is the normalized eigenvector corresponding to the ith eigenvalue.
   :rtype: Tuple