:py:mod:`momentGW.tda`
======================

.. py:module:: momentGW.tda

.. autoapi-nested-parse::

   Construct TDA moments.



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

.. py:class:: dTDA(gw, nmom_max, integrals, mo_energy=None, mo_occ=None)


   Compute the self-energy moments using dTDA.

   :param gw: GW object.
   :type gw: BaseGW
   :param nmom_max: Maximum moment number to calculate.
   :type nmom_max: int
   :param integrals: Integrals object.
   :type integrals: Integrals
   :param mo_energy: Molecular orbital energies. Keys are "g" and "w" for the Green's
                     function and screened Coulomb interaction, respectively.
                     If `None`, use `gw.mo_energy` for both. Default value is `None`.
   :type mo_energy: dict, optional
   :param mo_occ: Molecular orbital occupancies. Keys are "g" and "w" for the
                  Green's function and screened Coulomb interaction, respectively.
                  If `None`, use `gw.mo_occ` for both. Default value is `None`.
   :type mo_occ: dict, optional

   .. py:property:: nmo

      Get the number of MOs.

   .. py:property:: naux

      Get the number of auxiliaries.

   .. py:property:: nov

      Get the number of ov states in the screened Coulomb interaction.

   .. py:method:: build_dd_moments(m0=None)

      Build the moments of the density-density response.

      :param m0: The zeroth moment of the density-density response. If
                 `None`, use `self.integrals.Lia`. This argument allows for
                 custom starting points in the recursion i.e. in optical
                 spectra calculations. Default value is `None`.
      :type m0: numpy.ndarray, optional

      :returns: **moments** -- Moments of the density-density response.
      :rtype: numpy.ndarray


   .. py:method:: kernel(exact=False)

      Run the polarizability calculation to compute moments of the
      self-energy.

      :param exact: Has no effect and is only present for compatibility with
                    `dRPA`. Default value is `False`.
      :type exact: bool, optional

      :returns: * **moments_occ** (*numpy.ndarray*) -- Moments of the occupied self-energy.
                * **moments_vir** (*numpy.ndarray*) -- Moments of the virtual self-energy.


   .. py:method:: convolve(eta, eta_orders=None, mo_energy_g=None, mo_occ_g=None)

      Handle the convolution of the moments of the Green's function
      and screened Coulomb interaction.

      :param eta: Moments of the density-density response partly transformed
                  into moments of the screened Coulomb interaction.
      :type eta: numpy.ndarray
      :param mo_energy_g: Energies of the Green's function. If `None`, use
                          `self.mo_energy_g`. Default value is `None`.
      :type mo_energy_g: numpy.ndarray, optional
      :param eta_orders: List of orders for the rotated density-density moments in
                         `eta`. If `None`, assume it spans all required orders.
                         Default value is `None`.
      :type eta_orders: list, optional
      :param mo_occ_g: Occupancies of the Green's function. If `None`, use
                       `self.mo_occ_g`. Default value is `None`.
      :type mo_occ_g: numpy.ndarray, optional

      :returns: * **moments_occ** (*numpy.ndarray*) -- Moments of the occupied self-energy.
                * **moments_vir** (*numpy.ndarray*) -- Moments of the virtual self-energy.


   .. py:method:: build_se_moments(moments_dd)

      Build the moments of the self-energy via convolution.

      :param moments_dd: Moments of the density-density response.
      :type moments_dd: numpy.ndarray

      :returns: * **moments_occ** (*numpy.ndarray*) -- Moments of the occupied self-energy.
                * **moments_vir** (*numpy.ndarray*) -- Moments of the virtual self-energy.


   .. py:method:: build_dp_moments()

      Build the moments of the dynamic polarizability for optical
      spectra calculations.

      :returns: **moments** -- Moments of the dynamic polarizability.
      :rtype: numpy.ndarray


   .. py:method:: build_dd_moment_inv()

      Build the first inverse (`n=-1`) moment of the density-density
      response.

      :returns: **moment** -- First inverse (`n=-1`) moment of the density-density
                response.
      :rtype: numpy.ndarray

      .. rubric:: Notes

      This is not the full `n=-1` moment, which is

      .. math::
          D^{-1} - D^{-1} V^\dagger (I + V D^{-1} V^\dagger)^{-1} \\
                  V D^{-1}

      but rather

      .. math:: (I + V D^{-1} V^\dagger)^{-1} V D^{-1}

      which ensures that the function scales properly. The final
      contractions are done when constructing the matrix-vector
      product.


   .. py:method:: mpi_slice(n)

      Return the start and end index for the current process for total
      size `n`.

      :param n: Total size.
      :type n: int

      :returns: * **p0** (*int*) -- Start index for current process.
                * **p1** (*int*) -- End index for current process.


   .. py:method:: mpi_size(n)

      Return the number of states in the current process for total size
      `n`.

      :param n: Total size.
      :type n: int

      :returns: **size** -- Number of states in current process.
      :rtype: int