uvbeam.py

# -*- mode: python; coding: utf-8 -*
# Copyright (c) 2018 Radio Astronomy Software Group
# Licensed under the 2-clause BSD License

"""Primary container for radio telescope antenna beams.

"""
from __future__ import absolute_import, division, print_function

import numpy as np
import warnings
import copy
from scipy import interpolate

from .uvbase import UVBase
from . import parameter as uvp
from . import utils as uvutils


class UVBeam(UVBase):
    """
    A class for defining a radio telescope antenna beam.

    Attributes:
        UVParameter objects: For full list see UVBeam Parameters
            (http://pyuvdata.readthedocs.io/en/latest/uvbeam_parameters.html).
            Some are always required, some are required for certain beam_types,
            antenna_types and pixel_coordinate_systems and others are always optional.
    """

    coordinate_system_dict = {
        'az_za': {'axes': ['azimuth', 'zen_angle'],
                  'description': 'uniformly gridded azimuth, zenith angle coordinate system, '
                  'where az runs from East to North in radians'},
        'orthoslant_zenith': {'axes': ['zenorth_x', 'zenorth_y'],
                              'description': 'orthoslant projection at zenith where y points North, '
                              'x point East'},
        'healpix': {'axes': ['hpx_inds'],
                    'description': 'HEALPix map with zenith at the north pole and '
                                   'az, za coordinate axes (for the basis_vector_array) '
                                   'where az runs from East to North'}}

    interpolation_function_dict = {'az_za_simple': '_interp_az_za_rect_spline'}

    def __init__(self):
        """Create a new UVBeam object."""
        # add the UVParameters to the class
        self._Nfreqs = uvp.UVParameter('Nfreqs', description='Number of frequency channels',
                                       expected_type=int)

        self._Nspws = uvp.UVParameter('Nspws', description='Number of spectral windows '
                                      '(ie non-contiguous spectral chunks). '
                                      'More than one spectral window is not '
                                      'currently supported.', expected_type=int)

        desc = ('Number of basis vectors specified at each pixel, options '
                'are 2 or 3 (or 1 if beam_type is "power")')
        self._Naxes_vec = uvp.UVParameter('Naxes_vec', description=desc,
                                          expected_type=int, acceptable_vals=[2, 3])

        desc = ('Number of basis vectors components specified at each pixel, options '
                'are 2 or 3.  Only required for E-field beams.')
        self._Ncomponents_vec = uvp.UVParameter('Ncomponents_vec', description=desc,
                                                expected_type=int, acceptable_vals=[2, 3], required=False)

        desc = ('Pixel coordinate system, options are: "'
                + '", "'.join(list(self.coordinate_system_dict.keys())) + '".')
        for key in self.coordinate_system_dict:
            desc = desc + (' "' + key + '" is a ' + self.coordinate_system_dict[key]['description']
                           + '. It has axes [' + ', '.join(self.coordinate_system_dict[key]['axes']) + '].')
        self._pixel_coordinate_system = uvp.UVParameter('pixel_coordinate_system',
                                                        description=desc, form='str',
                                                        expected_type=str,
                                                        acceptable_vals=list(self.coordinate_system_dict.keys()))

        desc = ('Number of elements along the first pixel axis. '
                'Not required if pixel_coordinate_system is "healpix".')
        self._Naxes1 = uvp.UVParameter('Naxes1', description=desc, expected_type=int,
                                       required=False)

        desc = ('Coordinates along first pixel axis. '
                'Not required if pixel_coordinate_system is "healpix".')
        self._axis1_array = uvp.UVParameter('axis1_array', description=desc,
                                            expected_type=np.float,
                                            required=False, form=('Naxes1',))

        desc = ('Number of elements along the second pixel axis. '
                'Not required if pixel_coordinate_system is "healpix".')
        self._Naxes2 = uvp.UVParameter('Naxes2', description=desc, expected_type=int,
                                       required=False)

        desc = ('Coordinates along second pixel axis. '
                'Not required if pixel_coordinate_system is "healpix".')
        self._axis2_array = uvp.UVParameter('axis2_array', description=desc,
                                            expected_type=np.float,
                                            required=False, form=('Naxes2',))

        desc = ('Healpix nside parameter. Only required if pixel_coordinate_system is "healpix".')
        self._nside = uvp.UVParameter('nside', description=desc, expected_type=int,
                                      required=False)

        desc = ('Healpix ordering parameter, allowed values are "ring" and "nested". '
                'Only required if pixel_coordinate_system is "healpix".')
        self._ordering = uvp.UVParameter('ordering', description=desc, expected_type=str,
                                         required=False, acceptable_vals=['ring', 'nested'])

        desc = ('Number of healpix pixels. Only required if pixel_coordinate_system is "healpix".')
        self._Npixels = uvp.UVParameter('Npixels', description=desc, expected_type=int,
                                        required=False)

        desc = ('Healpix pixel numbers. Only required if pixel_coordinate_system is "healpix".')
        self._pixel_array = uvp.UVParameter('pixel_array', description=desc, expected_type=int,
                                            required=False, form=('Npixels',))

        desc = 'String indicating beam type. Allowed values are "efield", and "power".'
        self._beam_type = uvp.UVParameter('beam_type', description=desc, form='str',
                                          expected_type=str,
                                          acceptable_vals=['efield', 'power'])

        desc = ('Beam basis vector components -- directions for which the '
                'electric field values are recorded in the pixel coordinate system. '
                'Not required if beam_type is "power". The shape depends on the '
                'pixel_coordinate_system, if it is "healpix", the shape is: '
                '(Naxes_vec, Ncomponents_vec, Npixels), otherwise it is '
                '(Naxes_vec, Ncomponents_vec, Naxes2, Naxes1)')
        self._basis_vector_array = uvp.UVParameter('basis_vector_array',
                                                   description=desc, required=False,
                                                   expected_type=np.float,
                                                   form=('Naxes_vec', 'Ncomponents_vec', 'Naxes2', 'Naxes1'),
                                                   acceptable_range=(0, 1),
                                                   tols=1e-3)

        self._Nfeeds = uvp.UVParameter('Nfeeds', description='Number of feeds. '
                                       'Not required if beam_type is "power".',
                                       expected_type=int, acceptable_vals=[1, 2],
                                       required=False)

        desc = ('Array of feed orientations. shape (Nfeeds). '
                'options are: N/E or x/y or R/L. Not required if beam_type is "power".')
        self._feed_array = uvp.UVParameter('feed_array', description=desc, required=False,
                                           expected_type=str, form=('Nfeeds',),
                                           acceptable_vals=['N', 'E', 'x', 'y',
                                                            'R', 'L'])

        self._Npols = uvp.UVParameter('Npols', description='Number of polarizations. '
                                      'Only required if beam_type is "power".',
                                      expected_type=int, required=False)

        desc = ('Array of polarization integers, shape (Npols). '
                'Uses the same convention as UVData: pseudo-stokes 1:4 (pI, pQ, pU, pV);  '
                'circular -1:-4 (RR, LL, RL, LR); linear -5:-8 (XX, YY, XY, YX). '
                'Only required if beam_type is "power".')
        self._polarization_array = uvp.UVParameter('polarization_array',
                                                   description=desc, required=False,
                                                   expected_type=int, form=('Npols',),
                                                   acceptable_vals=list(np.arange(-8, 0)) + list(np.arange(1, 5)))

        desc = 'Array of frequencies, shape (Nspws, Nfreqs), units Hz'
        self._freq_array = uvp.UVParameter('freq_array', description=desc,
                                           form=('Nspws', 'Nfreqs'),
                                           expected_type=np.float,
                                           tols=1e-3)  # mHz

        self._spw_array = uvp.UVParameter('spw_array',
                                          description='Array of spectral window '
                                          'Numbers, shape (Nspws)', form=('Nspws',),
                                          expected_type=int)

        desc = ('Normalization standard of data_array, options are: '
                '"physical", "peak" or "solid_angle". Physical normalization '
                'means that the frequency dependence of the antenna sensitivity '
                'is included in the data_array while the frequency dependence '
                'of the receiving chain is included in the bandpass_array. '
                'Peak normalized means that for each frequency the data_array'
                'is separately normalized such that the peak is 1 (so the beam '
                'is dimensionless) and all direction-independent frequency '
                'dependence is moved to the bandpass_array (if the beam_type is "efield", '
                'then peak normalized means that the absolute value of the peak is 1). '
                'Solid angle normalized means the peak normalized '
                'beam is divided by the integral of the beam over the sphere, '
                'so the beam has dimensions of 1/stradian.')
        self._data_normalization = uvp.UVParameter('data_normalization', description=desc,
                                                   form='str', expected_type=str,
                                                   acceptable_vals=["physical", "peak", "solid_angle"])

        desc = ('Depending on beam type, either complex E-field values ("efield" beam type) '
                'or power values ("power" beam type) for beam model. units are linear '
                'normalized to either peak or solid angle as given by data_normalization. '
                'The shape depends on the beam_type and pixel_coordinate_system, if it is '
                '"healpix", the shape is: (Naxes_vec, Nspws, Nfeeds or Npols, Nfreqs, Npixels), '
                'otherwise it is (Naxes_vec, Nspws, Nfeeds or Npols, Nfreqs, Naxes2, Naxes1)')
        self._data_array = uvp.UVParameter('data_array', description=desc,
                                           expected_type=np.complex,
                                           form=('Naxes_vec', 'Nspws', 'Nfeeds',
                                                 'Nfreqs', 'Naxes2', 'Naxes1'),
                                           tols=1e-3)

        desc = ('Frequency dependence of the beam. Depending on the data_normalization, '
                'this may contain only the frequency dependence of the receiving '
                'chain ("physical" normalization) or all the frequency dependence '
                '("peak" normalization).')
        self._bandpass_array = uvp.UVParameter('bandpass_array', description=desc,
                                               expected_type=np.float,
                                               form=('Nspws', 'Nfreqs'),
                                               tols=1e-3)

        # --------- metadata -------------
        self._telescope_name = uvp.UVParameter('telescope_name',
                                               description='Name of telescope '
                                               '(string)', form='str',
                                               expected_type=str)

        self._feed_name = uvp.UVParameter('feed_name',
                                          description='Name of physical feed '
                                          '(string)', form='str',
                                          expected_type=str)

        self._feed_version = uvp.UVParameter('feed_version',
                                             description='Version of physical feed '
                                             '(string)', form='str',
                                             expected_type=str)

        self._model_name = uvp.UVParameter('model_name',
                                           description='Name of beam model '
                                           '(string)', form='str',
                                           expected_type=str)

        self._model_version = uvp.UVParameter('model_version',
                                              description='Version of beam model '
                                              '(string)', form='str',
                                              expected_type=str)

        self._history = uvp.UVParameter('history', description='String of history, units English',
                                        form='str', expected_type=str)

        # ---------- phased_array stuff -------------
        desc = ('String indicating antenna type. Allowed values are "simple", and '
                '"phased_array"')
        self._antenna_type = uvp.UVParameter('antenna_type', form='str', expected_type=str,
                                             description=desc,
                                             acceptable_vals=['simple', 'phased_array'])

        desc = ('Required if antenna_type = "phased_array". Number of elements '
                'in phased array')
        self._Nelements = uvp.UVParameter('Nelements', required=False,
                                          description=desc, expected_type=int)

        desc = ('Required if antenna_type = "phased_array". Element coordinate '
                'system, options are: N-E or x-y')
        self._element_coordinate_system = \
            uvp.UVParameter('element_coordinate_system', required=False,
                            description=desc, expected_type=str,
                            acceptable_vals=['N-E', 'x-y'])

        desc = ('Required if antenna_type = "phased_array". Array of element '
                'locations in element coordinate system,  shape: (2, Nelements)')
        self._element_location_array = uvp.UVParameter('element_location_array',
                                                       required=False,
                                                       description=desc,
                                                       form=('2', 'Nelements'),
                                                       expected_type=np.float)

        desc = ('Required if antenna_type = "phased_array". Array of element '
                'delays, units: seconds, shape: (Nelements)')
        self._delay_array = uvp.UVParameter('delay_array', required=False,
                                            description=desc,
                                            form=('Nelements',),
                                            expected_type=np.float)

        desc = ('Required if antenna_type = "phased_array". Array of element '
                'gains, units: dB, shape: (Nelements)')
        self._gain_array = uvp.UVParameter('gain_array', required=False,
                                           description=desc,
                                           form=('Nelements',),
                                           expected_type=np.float)

        desc = ('Required if antenna_type = "phased_array". Matrix of complex '
                'element couplings, units: dB, '
                'shape: (Nelements, Nelements, Nfeed, Nfeed, Nspws, Nfreqs)')
        self._coupling_matrix = uvp.UVParameter('coupling_matrix', required=False,
                                                description=desc,
                                                form=('Nelements', 'Nelements',
                                                      'Nfeed', 'Nfeed', 'Nspws', 'Nfreqs'),
                                                expected_type=np.complex)

        # -------- extra, non-required parameters ----------
        desc = ('String indicating interpolation function. Must be set to use '
                'the interp_* methods. Allowed values are : "'
                + '", "'.join(list(self.interpolation_function_dict.keys())) + '".')
        self._interpolation_function = uvp.UVParameter('interpolation_function',
                                                       required=False,
                                                       form='str', expected_type=str,
                                                       description=desc,
                                                       acceptable_vals=list(self.interpolation_function_dict.keys()))

        desc = ('Any user supplied extra keywords, type=dict. Keys should be '
                '8 character or less strings if writing to beam fits files. '
                'Use the special key "comment" for long multi-line string comments.')
        self._extra_keywords = uvp.UVParameter('extra_keywords', required=False,
                                               description=desc, value={},
                                               spoof_val={}, expected_type=dict)

        desc = ('Reference input impedance of the receiving chain (sets the reference '
                'for the S parameters), units: Ohms')
        self._reference_input_impedance = uvp.UVParameter('reference_input_impedance', required=False,
                                                          description=desc,
                                                          expected_type=np.float, tols=1e-3)

        desc = ('Reference output impedance of the receiving chain (sets the reference '
                'for the S parameters), units: Ohms')
        self._reference_output_impedance = uvp.UVParameter('reference_output_impedance', required=False,
                                                           description=desc,
                                                           expected_type=np.float, tols=1e-3)

        desc = 'Array of receiver temperatures, shape (Nspws, Nfreqs), units K'
        self._receiver_temperature_array = \
            uvp.UVParameter('receiver_temperature_array', required=False,
                            description=desc, form=('Nspws', 'Nfreqs'),
                            expected_type=np.float, tols=1e-3)

        desc = 'Array of antenna losses, shape (Nspws, Nfreqs), units dB?'
        self._loss_array = uvp.UVParameter('loss_array', required=False,
                                           description=desc, form=('Nspws', 'Nfreqs'),
                                           expected_type=np.float,
                                           tols=1e-3)

        desc = 'Array of antenna-amplifier mismatches, shape (Nspws, Nfreqs), units ?'
        self._mismatch_array = uvp.UVParameter('mismatch_array', required=False,
                                               description=desc,
                                               form=('Nspws', 'Nfreqs'),
                                               expected_type=np.float,
                                               tols=1e-3)

        desc = ('S parameters of receiving chain, shape (4, Nspws, Nfreqs), '
                'ordering: s11, s12, s21, s22. see '
                'https://en.wikipedia.org/wiki/Scattering_parameters#Two-Port_S-Parameters')
        self._s_parameters = uvp.UVParameter('s_parameters', required=False,
                                             description=desc,
                                             form=(4, 'Nspws', 'Nfreqs'),
                                             expected_type=np.float,
                                             tols=1e-3)

        super(UVBeam, self).__init__()

    def check(self, check_extra=True, run_check_acceptability=True):
        """
        Check that all required parameters are set reasonably.

        Check that required parameters exist and have appropriate shapes.
        Optionally check if the values are acceptable.

        Args:
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check if values in required parameters
                are acceptable. Default is True.
        """
        # first make sure the required parameters and forms are set properly
        # for the pixel_coordinate_system
        self.set_cs_params()

        # first run the basic check from UVBase
        super(UVBeam, self).check(check_extra=check_extra,
                                  run_check_acceptability=run_check_acceptability)

        # check that basis_vector_array are basis vectors
        if self.basis_vector_array is not None:
            if np.max(np.linalg.norm(self.basis_vector_array, axis=1)) > (1 + 1e-15):
                raise ValueError('basis vectors must have lengths of 1 or less.')

        # issue warning if extra_keywords keys are longer than 8 characters
        for key in list(self.extra_keywords.keys()):
            if len(key) > 8:
                warnings.warn('key {key} in extra_keywords is longer than 8 '
                              'characters. It will be truncated to 8 if written '
                              'to a fits file format.'.format(key=key))

        # issue warning if extra_keywords values are lists, arrays or dicts
        for key, value in self.extra_keywords.items():
            if isinstance(value, (list, dict, np.ndarray)):
                warnings.warn('{key} in extra_keywords is a list, array or dict, '
                              'which will raise an error when writing fits '
                              'files'.format(key=key))

        return True

    def set_cs_params(self):
        """
        Set various forms and required parameters depending on pixel_coordinate_system.
        """
        if self.pixel_coordinate_system == 'healpix':
            self._Naxes1.required = False
            self._axis1_array.required = False
            self._Naxes2.required = False
            self._axis2_array.required = False
            self._nside.required = True
            self._ordering.required = True
            self._Npixels.required = True
            self._pixel_array.required = True
            self._basis_vector_array.form = ('Naxes_vec', 'Ncomponents_vec', 'Npixels')
            if self.beam_type == "power":
                self._data_array.form = ('Naxes_vec', 'Nspws', 'Npols', 'Nfreqs',
                                         'Npixels')
            else:
                self._data_array.form = ('Naxes_vec', 'Nspws', 'Nfeeds', 'Nfreqs',
                                         'Npixels')
        else:
            self._Naxes1.required = True
            self._axis1_array.required = True
            self._Naxes2.required = True
            self._axis2_array.required = True
            if self.pixel_coordinate_system == 'az_za':
                self._axis1_array.acceptable_range = [0, 2. * np.pi]
                self._axis2_array.acceptable_range = [0, np.pi]
            self._nside.required = False
            self._ordering.required = False
            self._Npixels.required = False
            self._pixel_array.required = False
            self._basis_vector_array.form = ('Naxes_vec', 'Ncomponents_vec', 'Naxes2', 'Naxes1')
            if self.beam_type == "power":
                self._data_array.form = ('Naxes_vec', 'Nspws', 'Npols', 'Nfreqs',
                                         'Naxes2', 'Naxes1')
            else:
                self._data_array.form = ('Naxes_vec', 'Nspws', 'Nfeeds', 'Nfreqs',
                                         'Naxes2', 'Naxes1')

    def set_efield(self):
        """Set beam_type to 'efield' and adjust required parameters."""
        self.beam_type = 'efield'
        self._Naxes_vec.acceptable_vals = [2, 3]
        self._Ncomponents_vec.required = True
        self._basis_vector_array.required = True
        self._Nfeeds.required = True
        self._feed_array.required = True
        self._Npols.required = False
        self._polarization_array.required = False
        self._data_array.expected_type = np.complex
        # call set_cs_params to fix data_array form
        self.set_cs_params()

    def set_power(self):
        """Set beam_type to 'power' and adjust required parameters."""
        self.beam_type = 'power'
        self._Naxes_vec.acceptable_vals = [1, 2, 3]
        self._basis_vector_array.required = False
        self._Ncomponents_vec.required = False
        self._Nfeeds.required = False
        self._feed_array.required = False
        self._Npols.required = True
        self._polarization_array.required = True

        # If cross pols are included, the power beam is complex. Otherwise it's real
        self._data_array.expected_type = np.float
        for pol in self.polarization_array:
            if pol in [3, 4, -3, -4, -7, -8]:
                self._data_array.expected_type = np.complex

        # call set_cs_params to fix data_array form
        self.set_cs_params()

    def set_simple(self):
        """Set antenna_type to 'simple' and adjust required parameters."""
        self.antenna_type = 'simple'
        self._Nelements.required = False
        self._element_coordinate_system.required = False
        self._element_location_array.required = False
        self._delay_array.required = False
        self._gain_array.required = False
        self._coupling_matrix.required = False

    def set_phased_array(self):
        """Set antenna_type to 'phased_array' and adjust required parameters."""
        self.antenna_type = 'phased_array'
        self._Nelements.required = True
        self._element_coordinate_system.required = True
        self._element_location_array.required = True
        self._delay_array.required = True
        self._gain_array.required = True
        self._coupling_matrix.required = True

    def peak_normalize(self):
        """
        Convert to peak normalization.
        """
        if self.data_normalization == 'solid_angle':
            raise NotImplementedError('Conversion from solid_angle to peak '
                                      'normalization is not yet implemented')
        for i in range(self.Nfreqs):
            max_val = abs(self.data_array[:, :, :, i, :]).max()
            self.data_array[:, :, :, i, :] /= max_val
            self.bandpass_array[:, i] *= max_val
        self.data_normalization = 'peak'

    def _stokes_matrix(self, pol_index):
        """
        Calculate Pauli matrices (where indices are reordered from the quantum mechanical
        convention to an order which gives the ordering of the pseudo-Stokes vector
        ['pI', 'pQ', 'pU, 'pV']) according to https://arxiv.org/pdf/1401.2095.pdf.

        Args:
            pol_index : Polarization index for which the Pauli matrix is generated, the index
            must lie between 0 and 3 ('pI': 0, 'pQ': 1, 'pU': 2, 'pV':3).
        """

        if pol_index < 0:
            raise ValueError('n must be positive integer.')
        if pol_index > 4:
            raise ValueError('n should lie between 0 and 3.')
        if pol_index == 0:
            pauli_mat = np.array([[1., 0.], [0., 1.]])
        if pol_index == 1:
            pauli_mat = np.array([[1., 0.], [0., -1.]])
        if pol_index == 2:
            pauli_mat = np.array([[0., 1.], [1., 0.]])
        if pol_index == 3:
            pauli_mat = np.array([[0., -1.j], [1.j, 0.]])

        return pauli_mat

    def _construct_mueller(self, jones, pol_index1, pol_index2):
        """
        Generate Mueller component as done in https://arxiv.org/pdf/1802.04151.pdf

                Mij = Tr(J sigma_i J^* sigma_j)

        where sigma_i and sigma_j are Pauli matrices

        Args:
            jones : Jones matrices containing the electric field for the dipole arms
                or linear polarizations.
            pol_index1 : Polarization index referring to the first index of Mij (i).
            pol_index2 : Polarization index referring to the second index of Mij (j).

        Returns:
            npix numpy array containing the Mij values.
        """
        pauli_mat1 = self._stokes_matrix(pol_index1)
        pauli_mat2 = self._stokes_matrix(pol_index2)

        Mij = 0.5 * np.einsum('...ab,...bc,...cd,...ad', pauli_mat1, jones, pauli_mat2, np.conj(jones))
        Mij = np.abs(Mij)

        return Mij

    def efield_to_pstokes(self, run_check=True, check_extra=True, run_check_acceptability=True, inplace=True):
        """
        Convert E-field to pseudo-stokes power as done in https://arxiv.org/pdf/1802.04151.pdf.

                M_ij = Tr(sigma_i J sigma_j J^*)

        where sigma_i and sigma_j are Pauli matrices.

        Args:
            run_check : Option to check for the existence and proper shapes of the required parameters
                after converting to power. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of required parameters
                after combining objects. Default is True.
            check_extra : Option to check optional parameters as well as required ones. Default is True.
            inplace : Option to perform the select directly on self (True, default) or return a new UVBeam
                object, which is a subselection of self (False).
        """
        if inplace:
            beam_object = self
        else:
            beam_object = copy.deepcopy(self)

        if beam_object.beam_type != 'efield':
            raise ValueError('beam_type must be efield.')

        if self.pixel_coordinate_system != 'healpix':
            raise ValueError('Currently only healpix format is supported')

        # construct jones matrix containing the electric field
        _sh = beam_object.data_array.shape
        efield_data = beam_object.data_array
        Nfreqs = beam_object.Nfreqs

        pol_strings = ['pI', 'pQ', 'pU', 'pV']
        power_data = np.zeros((1, 1, len(pol_strings), _sh[-2], _sh[-1]), dtype=np.complex)
        beam_object.polarization_array = np.array([uvutils.polstr2num(ps.upper()) for ps in pol_strings])

        for fq_i in range(Nfreqs):
            jones = np.zeros((_sh[-1], 2, 2), dtype=np.complex)
            pol_strings = ['pI', 'pQ', 'pU', 'pV']
            jones[:, 0, 0] = efield_data[0, 0, 0, fq_i, :]
            jones[:, 0, 1] = efield_data[0, 0, 1, fq_i, :]
            jones[:, 1, 0] = efield_data[1, 0, 0, fq_i, :]
            jones[:, 1, 1] = efield_data[1, 0, 1, fq_i, :]

            for pol_i in range(len(pol_strings)):
                power_data[:, :, pol_i, fq_i, :] = self._construct_mueller(jones, pol_i, pol_i)

        beam_object.data_array = power_data
        beam_object.polarization_array = np.array([uvutils.polstr2num(ps.upper()) for ps in pol_strings])
        beam_object.Naxes_vec = 1
        beam_object.set_power()

        history_update_string = (' Converted from efield to pseudo-stokes power using pyuvdata.')
        beam_object.Npols = beam_object.Nfeeds ** 2
        beam_object.history = beam_object.history + history_update_string
        beam_object.Nfeeds = None
        beam_object.feed_array = None
        beam_object.basis_vector_array = None
        beam_object.Ncomponents_vec = None

        if run_check:
            beam_object.check(check_extra=check_extra,
                              run_check_acceptability=run_check_acceptability)
        if not inplace:
            return beam_object

    def efield_to_power(self, calc_cross_pols=True, keep_basis_vector=False,
                        run_check=True, check_extra=True, run_check_acceptability=True,
                        inplace=True):
        """
        Convert E-field beam to power beam.

        Args:
            calc_cross_pols: If True, calculate the crossed polarization beams
                (e.g. 'xy' and 'yx'), otherwise only calculate the same
                polarization beams (e.g. 'xx' and 'yy'). Default is True.
            keep_basis_vector: If True, keep the directionality information and
                just multiply the efields for each basis vector separately
                (caution: this is not what is standardly meant by the power beam).
                Default is False.
            run_check: Option to check for the existence and proper shapes of
                required parameters after converting to power. Default is True.
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of
                required parameters after combining objects. Default is True.
            inplace: Option to perform the select directly on self (True, default) or return
                a new UVBeam object, which is a subselection of self (False)
        """
        if inplace:
            beam_object = self
        else:
            beam_object = copy.deepcopy(self)

        if beam_object.beam_type != 'efield':
            raise ValueError('beam_type must be efield')

        efield_data = beam_object.data_array
        efield_naxes_vec = beam_object.Naxes_vec

        feed_pol_order = [(0, 0)]
        if beam_object.Nfeeds > 1:
            feed_pol_order.append((1, 1))

        if calc_cross_pols:
            beam_object.Npols = beam_object.Nfeeds ** 2
            if beam_object.Nfeeds > 1:
                feed_pol_order.extend([(0, 1), (1, 0)])
        else:
            beam_object.Npols = beam_object.Nfeeds

        pol_strings = []
        for pair in feed_pol_order:
            pol_strings.append(beam_object.feed_array[pair[0]] + beam_object.feed_array[pair[1]])
        beam_object.polarization_array = np.array([uvutils.polstr2num(ps.upper()) for ps in pol_strings])

        if not keep_basis_vector:
            beam_object.Naxes_vec = 1

        # adjust requirements, fix data_array form
        beam_object.set_power()
        power_data = np.zeros(beam_object._data_array.expected_shape(beam_object), dtype=np.complex)

        if keep_basis_vector:
            for pol_i, pair in enumerate(feed_pol_order):
                power_data[:, :, pol_i] = (efield_data[:, :, pair[0]]
                                           * np.conj(efield_data[:, :, pair[1]]))

        else:
            for pol_i, pair in enumerate(feed_pol_order):
                if efield_naxes_vec == 2:
                    for comp_i in range(2):
                        power_data[0, :, pol_i] += \
                            ((efield_data[0, :, pair[0]]
                              * np.conj(efield_data[0, :, pair[1]]))
                             * beam_object.basis_vector_array[0, comp_i]**2
                             + (efield_data[1, :, pair[0]]
                                * np.conj(efield_data[1, :, pair[1]]))
                             * beam_object.basis_vector_array[1, comp_i]**2
                             + (efield_data[0, :, pair[0]]
                                * np.conj(efield_data[1, :, pair[1]])
                                + efield_data[1, :, pair[0]]
                                * np.conj(efield_data[0, :, pair[1]]))
                             * (beam_object.basis_vector_array[0, comp_i]
                                * beam_object.basis_vector_array[1, comp_i]))
                else:
                    raise ValueError('Conversion to power with 3-vector efields '
                                     'is not currently supported because we have '
                                     'no examples to work with.')

        power_data = np.real_if_close(power_data, tol=10)

        beam_object.data_array = power_data
        beam_object.Nfeeds = None
        beam_object.feed_array = None
        if not keep_basis_vector:
            beam_object.basis_vector_array = None
            beam_object.Ncomponents_vec = None

        history_update_string = (' Converted from efield to power using pyuvdata.')

        beam_object.history = beam_object.history + history_update_string

        if run_check:
            beam_object.check(check_extra=check_extra,
                              run_check_acceptability=run_check_acceptability)
        if not inplace:
            return beam_object

    def _interp_freq(self, freq_array):
        """
        Simple interpolation function for frequency axis.

        Args:
            freq_array: frequency values to interpolate to

        Returns:
            an array of interpolated values, shape: (Naxes_vec, Nspws, Nfeeds or Npols, freq_array.size, Npixels or (Naxis2, Naxis1))
            an array of distances from nearest frequency, shape: (freq_array.size)
        """
        assert(isinstance(freq_array, np.ndarray))
        assert(freq_array.ndim == 1)

        nfreqs = freq_array.size

        for f_i in range(nfreqs):
            freq_dists = self.freq_array[0, :] - freq_array[f_i]

        if self.Nfreqs == 1:
            raise ValueError('Only one frequency in UVBeam so cannot interpolate.')

        if np.iscomplexobj(self.data_array):
            data_type = np.complex
        else:
            data_type = np.float
        interp_data_shape = np.array(self.data_array.shape)
        interp_data_shape[3] = nfreqs
        interp_data = np.zeros(interp_data_shape, dtype=data_type)

        if (np.min(freq_array) < np.min(self.freq_array) or np.max(freq_array) > np.max(self.freq_array)):
            raise ValueError('at least one interpolation frequency is outside of '
                             'the UVBeam freq_array range.')

        def get_lambda(real_lut, imag_lut=None):
                # Returns function objects for interpolation reuse
            if imag_lut is None:
                return lambda freqs: real_lut(freqs)
            else:
                return lambda freqs: (real_lut(freqs) + 1j * imag_lut(freqs))

        if np.iscomplexobj(self.data_array):
            # interpolate real and imaginary parts separately
            real_lut = interpolate.interp1d(self.freq_array[0, :], self.data_array.real, axis=3)
            imag_lut = interpolate.interp1d(self.freq_array[0, :], self.data_array.imag, axis=3)
            lut = get_lambda(real_lut, imag_lut)
        else:
            lut = interpolate.interp1d(self.freq_array[0, :], self.data_array, axis=3)
            lut = get_lambda(lut)

        interp_data = lut(freq_array)

        return interp_data

    def _interp_az_za_rect_spline(self, az_array, za_array, freq_array, reuse_spline=False):
        """
        Simple interpolation function for az_za coordinate system.

        Args:
            az_array: az values to interpolate to (same length as za_array)
            za_array: za values to interpolate to (same length as az_array)
            freq_array: frequency values to interpolate to
            reuse_spline: Save the interpolation functions for reuse.

        Returns:
            an array of interpolated values, shape: (Naxes_vec, Nspws, Nfeeds or Npols, Nfreqs, az_array.size)
            an array of interpolated basis vectors, shape: (Naxes_vec, Ncomponents_vec, az_array.size)
        """
        if self.pixel_coordinate_system != 'az_za':
            raise ValueError('pixel_coordinate_system must be "az_za"')

        if reuse_spline and not hasattr(self, 'saved_interp_functions'):
            self.saved_interp_functions = {}

        if freq_array is not None:
            assert(isinstance(freq_array, np.ndarray))
            input_data_array = self._interp_freq(freq_array)
            input_nfreqs = freq_array.size
        else:
            input_data_array = self.data_array
            input_nfreqs = self.Nfreqs
            freq_array = self.freq_array[0]
        if az_array is None:
            return input_data_array, self.basis_vector_array

        assert(isinstance(az_array, np.ndarray))
        assert(isinstance(za_array, np.ndarray))
        assert(az_array.ndim == 1)
        assert(az_array.shape == za_array.shape)

        npoints = az_array.size

        axis1_diff = np.diff(self.axis1_array)[0]
        axis2_diff = np.diff(self.axis2_array)[0]
        max_axis_diff = np.max([axis1_diff, axis2_diff])

        phi_vals, theta_vals = np.meshgrid(self.axis1_array, self.axis2_array)

        assert(input_data_array.shape[3] == input_nfreqs)

        if np.iscomplexobj(input_data_array):
            data_type = np.complex
        else:
            data_type = np.float

        if self.beam_type == 'efield':
            data_shape = (self.Naxes_vec, self.Nspws, self.Nfeeds, input_nfreqs, npoints)
        else:
            data_shape = (self.Naxes_vec, self.Nspws, self.Npols, input_nfreqs, npoints)
        interp_data = np.zeros(data_shape, dtype=data_type)

        if self.basis_vector_array is not None:
            if (np.any(self.basis_vector_array[0, 1, :] > 0)
                    or np.any(self.basis_vector_array[1, 0, :] > 0)):
                """ Input basis vectors are not aligned to the native theta/phi
                coordinate system """
                raise NotImplementedError('interpolation for input basis '
                                          'vectors that are not aligned to the '
                                          'native theta/phi coordinate system '
                                          'is not yet supported')
            else:
                """ The basis vector array comes in defined at the rectangular grid.
                Redefine it for the interpolation points """
                interp_basis_vector = np.zeros([self.Naxes_vec,
                                                self.Ncomponents_vec,
                                                npoints])
                interp_basis_vector[0, 0, :] = np.ones(npoints)  # theta hat
                interp_basis_vector[1, 1, :] = np.ones(npoints)  # phi hat
        else:
            interp_basis_vector = None

        def get_lambda(real_lut, imag_lut=None):
                # Returns function objects for interpolation reuse
            if imag_lut is None:
                return lambda za, az: real_lut(za, az, grid=False)
            else:
                return lambda za, az: (real_lut(za, az, grid=False) + 1j * imag_lut(za, az, grid=False))

        # Npols is only defined for power beams.  For E-field beams need Nfeeds.
        if self.beam_type == 'power':
            Npol_feeds = self.Npols
        else:
            Npol_feeds = self.Nfeeds

        for index1 in range(self.Nspws):
            for index3 in range(input_nfreqs):
                freq = freq_array[index3]
                if reuse_spline:
                    luts = np.empty((self.Naxes_vec, self.Nspws, Npol_feeds), dtype=object)
                for index0 in range(self.Naxes_vec):
                    for index2 in range(Npol_feeds):
                        if reuse_spline and freq in self.saved_interp_functions.keys():
                            lut = self.saved_interp_functions[freq][index0, index1, index2]
                        else:
                            if np.iscomplexobj(input_data_array):
                                # interpolate real and imaginary parts separately
                                real_lut = interpolate.RectBivariateSpline(self.axis2_array,
                                                                           self.axis1_array,
                                                                           input_data_array[index0, index1, index2, index3, :].real)
                                imag_lut = interpolate.RectBivariateSpline(self.axis2_array,
                                                                           self.axis1_array,
                                                                           input_data_array[index0, index1, index2, index3, :].imag)
                                lut = get_lambda(real_lut, imag_lut)
                            else:
                                lut = interpolate.RectBivariateSpline(self.axis2_array,
                                                                      self.axis1_array,
                                                                      input_data_array[index0, index1, index2, index3, :])
                                lut = get_lambda(lut)
                        if reuse_spline:
                            luts[index0, index1, index2] = lut
                        if index0 == 0 and index1 == 0 and index2 == 0 and index3 == 0:
                            for point_i in range(npoints):
                                pix_dists = np.sqrt((theta_vals - za_array[point_i])**2.
                                                    + (phi_vals - az_array[point_i])**2.)
                                if np.min(pix_dists) > (max_axis_diff * 2.0):
                                    raise ValueError('at least one interpolation location is outside of '
                                                     'the UVBeam pixel coverage.')
                        interp_data[index0, index1, index2, index3, :] = lut(za_array, az_array)

            if reuse_spline:
                self.saved_interp_functions[freq] = luts

        return interp_data, interp_basis_vector

    def interp(self, az_array=None, za_array=None, freq_array=None, reuse_spline=False):
        """
        Interpolate beam to given az, za locations (in radians).

        Args:
            az_array: az values to interpolate to (same length as za_array)
            za_array: za values to interpolate to (same length as az_array)
            freq_array: frequency values to interpolate to

        Returns:
            an array of interpolated values, shape: (Naxes_vec, Nspws, Nfeeds or Npols,
                Nfreqs or freq_array.size if freq_array is passed,
                Npixels/(Naxis1, Naxis2) or az_array.size if az/za_arrays are passed)
            an array of interpolated basis vectors (or self.basis_vector_array
                if az/za_arrays are not passed), shape: (Naxes_vec, Ncomponents_vec,
                Npixels/(Naxis1, Naxis2) or az_array.size if az/za_arrays are passed)
        """
        if self.interpolation_function is None:
            raise ValueError('interpolation_function must be set on object first')

        interp_func = self.interpolation_function_dict[self.interpolation_function]
        return getattr(self, interp_func)(az_array, za_array, freq_array, reuse_spline)

    def to_healpix(self, nside=None, run_check=True, check_extra=True,
                   run_check_acceptability=True,
                   inplace=True):
        """
        Convert beam in to healpix coordinates.
        The interpolation is done using the interpolation method specified in
        self.interpolation_function.

        Note that this interpolation isn't perfect. Interpolating an Efield beam
        and then converting to power gives a different result than converting
        to power and then interpolating at about a 5% level.

        Args:
            nside: The nside to use for the Healpix map. If not specified, use
                the nside that gives the closest resolution that is higher than the
                input resolution.
            run_check: Option to check for the existence and proper shapes of
                required parameters after converting to healpix. Default is True.
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of
                required parameters after combining objects. Default is True.
            inplace: Option to perform the select directly on self (True, default) or return
                a new UVBeam object, which is a subselection of self (False)
        """
        try:
            import healpy as hp
        except ImportError:  # pragma: no cover
            uvutils._reraise_context('healpy is not installed but is required for '
                                     'healpix functionality')

        if inplace:
            beam_object = self
        else:
            beam_object = copy.deepcopy(self)

        if nside is None:
            min_res = np.min(np.array([np.diff(beam_object.axis1_array)[0], np.diff(beam_object.axis2_array)[0]]))
            nside_min_res = np.sqrt(3 / np.pi) * np.radians(60.) / min_res
            nside = int(2**np.ceil(np.log2(nside_min_res)))
            assert(hp.pixelfunc.nside2resol(nside) < min_res)

        npix = hp.nside2npix(nside)
        hpx_res = hp.pixelfunc.nside2resol(nside)

        if np.iscomplexobj(beam_object.data_array):
            data_type = np.complex
        else:
            data_type = np.float
        pixels = np.arange(hp.nside2npix(nside))
        hpx_theta, hpx_phi = hp.pix2ang(nside, pixels)

        phi_vals, theta_vals = np.meshgrid(self.axis1_array, self.axis2_array)

        # Don't ask for interpolation to pixels that aren't inside the beam area
        inds_to_use = []
        for index in range(pixels.size):
            pix_dists = np.sqrt((theta_vals - hpx_theta[index])**2.
                                + (phi_vals - hpx_phi[index])**2.)
            if np.min(pix_dists) < hpx_res * 2:
                inds_to_use.append(index)

        inds_to_use = np.array(inds_to_use)

        if inds_to_use.size < npix:
            pixels = pixels[inds_to_use]
            hpx_theta = hpx_theta[inds_to_use]
            hpx_phi = hpx_phi[inds_to_use]

        interp_data, interp_basis_vector = \
            self.interp(az_array=hpx_phi, za_array=hpx_theta)

        beam_object.pixel_coordinate_system = 'healpix'
        beam_object.nside = nside
        beam_object.Npixels = npix
        beam_object.ordering = 'ring'
        beam_object.set_cs_params()

        if beam_object.basis_vector_array is not None:
            beam_object.basis_vector_array = interp_basis_vector

        beam_object.pixel_array = pixels
        beam_object.Npixels = beam_object.pixel_array.size
        beam_object.data_array = interp_data

        beam_object.Naxes1 = None
        beam_object.Naxes2 = None
        beam_object.axis1_array = None
        beam_object.axis2_array = None

        history_update_string = (' Interpolated from regularly gridded '
                                 'azimuth/zenith_angle to HEALPix using pyuvdata '
                                 'with interpolation_function = '
                                 + self.interpolation_function + '.')

        beam_object.history = beam_object.history + history_update_string

        if run_check:
            beam_object.check(check_extra=check_extra,
                              run_check_acceptability=run_check_acceptability)
        if not inplace:
            return beam_object

    def __add__(self, other, run_check=True, check_extra=True,
                run_check_acceptability=True, inplace=False):
        """
        Combine two UVBeam objects. Objects can be added along frequency,
        feed or polarization (for efield or power beams), and/or pixel axes.

        Args:
            other: Another UVBeam object which will be added to self.
            run_check: Option to check for the existence and proper shapes of
                required parameters after combining objects. Default is True.
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of
                required parameters after combining objects. Default is True.
            inplace: Overwrite self as we go, otherwise create a third object
                as the sum of the two (default).
        """
        if inplace:
            this = self
        else:
            this = copy.deepcopy(self)
        # Check that both objects are UVBeam and valid
        this.check(check_extra=check_extra, run_check_acceptability=False)
        if not issubclass(other.__class__, this.__class__):
            if not issubclass(this.__class__, other.__class__):
                raise ValueError('Only UVBeam (or subclass) objects can be added '
                                 'to a UVBeam (or subclass) object')
        other.check(check_extra=check_extra, run_check_acceptability=False)

        # Check objects are compatible
        compatibility_params = ['_beam_type', '_data_normalization', '_telescope_name',
                                '_feed_name', '_feed_version', '_model_name',
                                '_model_version', '_pixel_coordinate_system',
                                '_Naxes_vec', '_nside', '_ordering']
        for a in compatibility_params:
            if getattr(this, a) != getattr(other, a):
                msg = 'UVParameter ' + \
                    a[1:] + ' does not match. Cannot combine objects.'
                raise ValueError(msg)

        # check for presence of optional parameters with a frequency axis in both objects
        optional_freq_params = ['_receiver_temperature_array', '_loss_array',
                                '_mismatch_array', '_s_parameters']
        for attr in optional_freq_params:
            this_attr = getattr(this, attr)
            other_attr = getattr(other, attr)
            if (this_attr.value is None or other_attr.value is None) and this_attr != other_attr:
                warnings.warn('Only one of the UVBeam objects being combined '
                              'has optional parameter {attr}. After the sum the '
                              'final object will not have {attr}'.format(attr=attr))
                if this_attr.value is not None:
                    this_attr.value = None
                    setattr(this, attr, this_attr)

        # Build up history string
        history_update_string = ' Combined data along '
        n_axes = 0

        # Check we don't have overlapping data
        if this.beam_type == 'power':
            both_pol = np.intersect1d(this.polarization_array,
                                      other.polarization_array)
        else:
            both_pol = np.intersect1d(this.feed_array, other.feed_array)

        both_freq = np.intersect1d(this.freq_array[0, :], other.freq_array[0, :])

        if this.pixel_coordinate_system == 'healpix':
            both_pixels = np.intersect1d(this.pixel_array, other.pixel_array)
        else:
            both_axis1 = np.intersect1d(this.axis1_array, other.axis1_array)
            both_axis2 = np.intersect1d(this.axis2_array, other.axis2_array)

        if len(both_pol) > 0:
            if len(both_freq) > 0:
                if self.pixel_coordinate_system == 'healpix':
                    if len(both_pixels) > 0:
                        raise ValueError('These objects have overlapping data and'
                                         ' cannot be combined.')
                else:
                    if len(both_axis1) > 0:
                        if len(both_axis2) > 0:
                            raise ValueError('These objects have overlapping data and'
                                             ' cannot be combined.')

        if this.pixel_coordinate_system == 'healpix':
            temp = np.nonzero(~np.in1d(other.pixel_array, this.pixel_array))[0]
            if len(temp) > 0:
                pix_new_inds = temp
                new_pixels = other.pixel_array[temp]
                history_update_string += 'healpix pixel'
                n_axes += 1
            else:
                pix_new_inds, new_pixels = ([], [])
        else:
            temp = np.nonzero(~np.in1d(other.axis1_array, this.axis1_array))[0]
            if len(temp) > 0:
                ax1_new_inds = temp
                new_ax1 = other.axis1_array[temp]
                history_update_string += 'first image'
                n_axes += 1
            else:
                ax1_new_inds, new_ax1 = ([], [])

            temp = np.nonzero(~np.in1d(other.axis2_array, this.axis2_array))[0]
            if len(temp) > 0:
                ax2_new_inds = temp
                new_ax2 = other.axis2_array[temp]
                if n_axes > 0:
                    history_update_string += ', second image'
                else:
                    history_update_string += 'second image'
                n_axes += 1
            else:
                ax2_new_inds, new_ax2 = ([], [])

        temp = np.nonzero(~np.in1d(other.freq_array[0, :],
                                   this.freq_array[0, :]))[0]
        if len(temp) > 0:
            fnew_inds = temp
            new_freqs = other.freq_array[0, temp]
            if n_axes > 0:
                history_update_string += ', frequency'
            else:
                history_update_string += 'frequency'
            n_axes += 1
        else:
            fnew_inds, new_freqs = ([], [])

        if this.beam_type == 'power':
            temp = np.nonzero(~np.in1d(other.polarization_array,
                                       this.polarization_array))[0]
            if len(temp) > 0:
                pnew_inds = temp
                new_pols = other.polarization_array[temp]
                if n_axes > 0:
                    history_update_string += ', polarization'
                else:
                    history_update_string += 'polarization'
                n_axes += 1
            else:
                pnew_inds, new_pols = ([], [])
        else:
            temp = np.nonzero(~np.in1d(other.feed_array,
                                       this.feed_array))[0]
            if len(temp) > 0:
                pnew_inds = temp
                new_pols = other.feed_array[temp]
                if n_axes > 0:
                    history_update_string += ', feed'
                else:
                    history_update_string += 'feed'
                n_axes += 1
            else:
                pnew_inds, new_pols = ([], [])

        # Pad out self to accommodate new data
        if this.pixel_coordinate_system == 'healpix':
            if len(pix_new_inds) > 0:
                data_pix_axis = 4
                data_pad_dims = tuple(list(this.data_array.shape[0:data_pix_axis])
                                      + [len(pix_new_inds)]
                                      + list(this.data_array.shape[data_pix_axis + 1:]))
                data_zero_pad = np.zeros(data_pad_dims)

                this.pixel_array = np.concatenate([this.pixel_array,
                                                   other.pixel_array[pix_new_inds]])
                order = np.argsort(this.pixel_array)
                this.pixel_array = this.pixel_array[order]

                this.data_array = np.concatenate([this.data_array, data_zero_pad],
                                                 axis=data_pix_axis)[:, :, :, :, order]

                if this.beam_type == 'efield':
                    basisvec_pix_axis = 2
                    basisvec_pad_dims = tuple(list(this.basis_vector_array.shape[0:basisvec_pix_axis])
                                              + [len(pix_new_inds)]
                                              + list(this.basis_vector_array.shape[basisvec_pix_axis + 1:]))
                    basisvec_zero_pad = np.zeros(basisvec_pad_dims)

                    this.basis_vector_array = np.concatenate([this.basis_vector_array,
                                                              basisvec_zero_pad],
                                                             axis=basisvec_pix_axis)[:, :, order]
        else:
            if len(ax1_new_inds) > 0:
                data_ax1_axis = 5
                data_pad_dims = tuple(list(this.data_array.shape[0:data_ax1_axis])
                                      + [len(ax1_new_inds)]
                                      + list(this.data_array.shape[data_ax1_axis + 1:]))
                data_zero_pad = np.zeros(data_pad_dims)

                this.axis1_array = np.concatenate([this.axis1_array,
                                                   other.axis1_array[ax1_new_inds]])
                order = np.argsort(this.axis1_array)
                this.axis1_array = this.axis1_array[order]
                this.data_array = np.concatenate([this.data_array, data_zero_pad],
                                                 axis=data_ax1_axis)[:, :, :, :, :, order]

                if this.beam_type == 'efield':
                    basisvec_ax1_axis = 3
                    basisvec_pad_dims = tuple(list(this.basis_vector_array.shape[0:basisvec_ax1_axis])
                                              + [len(ax1_new_inds)]
                                              + list(this.basis_vector_array.shape[basisvec_ax1_axis + 1:]))
                    basisvec_zero_pad = np.zeros(basisvec_pad_dims)

                    this.basis_vector_array = np.concatenate([this.basis_vector_array, basisvec_zero_pad],
                                                             axis=basisvec_ax1_axis)[:, :, :, order]

            if len(ax2_new_inds) > 0:
                data_ax2_axis = 4
                data_pad_dims = tuple(list(this.data_array.shape[0:data_ax2_axis])
                                      + [len(ax2_new_inds)]
                                      + list(this.data_array.shape[data_ax2_axis + 1:]))
                data_zero_pad = np.zeros(data_pad_dims)

                this.axis2_array = np.concatenate([this.axis2_array,
                                                   other.axis2_array[ax2_new_inds]])
                order = np.argsort(this.axis2_array)
                this.axis2_array = this.axis2_array[order]

                this.data_array = np.concatenate([this.data_array, data_zero_pad],
                                                 axis=data_ax2_axis)[:, :, :, :, order, ...]

                if this.beam_type == 'efield':
                    basisvec_ax2_axis = 2
                    basisvec_pad_dims = tuple(list(this.basis_vector_array.shape[0:basisvec_ax2_axis])
                                              + [len(ax2_new_inds)]
                                              + list(this.basis_vector_array.shape[basisvec_ax2_axis + 1:]))
                    basisvec_zero_pad = np.zeros(basisvec_pad_dims)

                    this.basis_vector_array = np.concatenate([this.basis_vector_array, basisvec_zero_pad],
                                                             axis=basisvec_ax2_axis)[:, :, order, ...]

        if len(fnew_inds) > 0:
            faxis = 3
            data_pad_dims = tuple(list(this.data_array.shape[0:faxis])
                                  + [len(fnew_inds)]
                                  + list(this.data_array.shape[faxis + 1:]))
            data_zero_pad = np.zeros(data_pad_dims)

            this.freq_array = np.concatenate([this.freq_array,
                                              other.freq_array[:, fnew_inds]], axis=1)
            order = np.argsort(this.freq_array[0, :])
            this.freq_array = this.freq_array[:, order]

            this.bandpass_array = np.concatenate([this.bandpass_array,
                                                  np.zeros((1, len(fnew_inds)))],
                                                 axis=1)[:, order]

            this.data_array = np.concatenate([this.data_array, data_zero_pad],
                                             axis=faxis)[:, :, :, order, ...]
            if this.receiver_temperature_array is not None:
                this.receiver_temperature_array = np.concatenate([this.receiver_temperature_array,
                                                                  np.zeros((1, len(fnew_inds)))],
                                                                 axis=1)[:, order]
            if this.loss_array is not None:
                this.loss_array = np.concatenate([this.loss_array,
                                                  np.zeros((1, len(fnew_inds)))],
                                                 axis=1)[:, order]
            if this.mismatch_array is not None:
                this.mismatch_array = np.concatenate([this.mismatch_array,
                                                      np.zeros((1, len(fnew_inds)))],
                                                     axis=1)[:, order]
            if this.s_parameters is not None:
                this.s_parameters = np.concatenate([this.s_parameters,
                                                    np.zeros((4, 1, len(fnew_inds)))],
                                                   axis=2)[:, :, order]

        if len(pnew_inds) > 0:
            paxis = 2
            data_pad_dims = tuple(list(this.data_array.shape[0:paxis])
                                  + [len(pnew_inds)]
                                  + list(this.data_array.shape[paxis + 1:]))
            data_zero_pad = np.zeros(data_pad_dims)

            if this.beam_type == 'power':
                this.polarization_array = np.concatenate([this.polarization_array,
                                                          other.polarization_array[pnew_inds]])
                order = np.argsort(np.abs(this.polarization_array))
                this.polarization_array = this.polarization_array[order]
            else:
                this.feed_array = np.concatenate([this.feed_array,
                                                  other.feed_array[pnew_inds]])
                order = np.argsort(this.feed_array)
                this.feed_array = this.feed_array[order]

            this.data_array = np.concatenate([this.data_array, data_zero_pad], axis=paxis)[
                :, :, order, ...]

        # Now populate the data
        if this.beam_type == 'power':
            this.Npols = this.polarization_array.shape[0]
            pol_t2o = np.nonzero(np.in1d(this.polarization_array,
                                         other.polarization_array))[0]
        else:
            this.Nfeeds = this.feed_array.shape[0]
            pol_t2o = np.nonzero(np.in1d(this.feed_array, other.feed_array))[0]

        freq_t2o = np.nonzero(np.in1d(this.freq_array[0, :],
                                      other.freq_array[0, :]))[0]

        if this.pixel_coordinate_system == 'healpix':
            this.Npixels = this.pixel_array.shape[0]
            pix_t2o = np.nonzero(np.in1d(this.pixel_array, other.pixel_array))[0]
            this.data_array[np.ix_(np.arange(this.Naxes_vec), [0], pol_t2o, freq_t2o,
                                   pix_t2o)] = other.data_array
            if this.beam_type == 'efield':
                this.basis_vector_array[np.ix_(np.arange(this.Naxes_vec), np.arange(2),
                                               pix_t2o)] = other.basis_vector_array
        else:
            this.Naxes1 = this.axis1_array.shape[0]
            this.Naxes2 = this.axis2_array.shape[0]
            ax1_t2o = np.nonzero(np.in1d(this.axis1_array, other.axis1_array))[0]
            ax2_t2o = np.nonzero(np.in1d(this.axis2_array, other.axis2_array))[0]
            this.data_array[np.ix_(np.arange(this.Naxes_vec), [0], pol_t2o, freq_t2o,
                                   ax2_t2o, ax1_t2o)] = other.data_array
            if this.beam_type == 'efield':
                this.basis_vector_array[np.ix_(np.arange(this.Naxes_vec), np.arange(2),
                                               ax2_t2o, ax1_t2o)] = other.basis_vector_array

        this.bandpass_array[np.ix_([0], freq_t2o)] = other.bandpass_array

        if this.receiver_temperature_array is not None:
            this.receiver_temperature_array[np.ix_([0], freq_t2o)] = other.receiver_temperature_array
        if this.loss_array is not None:
            this.loss_array[np.ix_([0], freq_t2o)] = other.loss_array
        if this.mismatch_array is not None:
            this.mismatch_array[np.ix_([0], freq_t2o)] = other.mismatch_array
        if this.s_parameters is not None:
            this.s_parameters[np.ix_(np.arange(4), [0], freq_t2o)] = other.s_parameters

        this.Nfreqs = this.freq_array.shape[1]

        # Check specific requirements
        if this.Nfreqs > 1:
            freq_separation = np.diff(this.freq_array[0, :])
            if not np.isclose(np.min(freq_separation), np.max(freq_separation),
                              rtol=this._freq_array.tols[0], atol=this._freq_array.tols[1]):
                warnings.warn('Combined frequencies are not evenly spaced. This will '
                              'make it impossible to write this data out to some file types.')

        if self.beam_type == 'power' and this.Npols > 2:
            pol_separation = np.diff(this.polarization_array)
            if np.min(pol_separation) < np.max(pol_separation):
                warnings.warn('Combined polarizations are not evenly spaced. This will '
                              'make it impossible to write this data out to some file types.')

        if n_axes > 0:
            history_update_string += ' axis using pyuvdata.'
            this.history += history_update_string

        this.history = uvutils._combine_histories(this.history, other.history)

        # Check final object is self-consistent
        if run_check:
            this.check(check_extra=check_extra,
                       run_check_acceptability=run_check_acceptability)

        if not inplace:
            return this

    def __iadd__(self, other):
        """
        In place add.

        Args:
            other: Another UVBeam object which will be added to self.
        """
        self.__add__(other, inplace=True)
        return self

    def _get_beam(self, pol):
        """
        Get the healpix beam map corresponding to the specififed polarization,
        pseudo-stokes I: 'pI', Q: 'pQ', U: 'pU' and V: 'pV' or linear dipole polarization: 'XX', 'YY', etc.

        Args:
          pol : polarization string or integer, Ex. a pseudo-stokes pol 'pI', or a linear pol 'XX'

        Return:
          beam : healpix beam
        """
        # assert map is in healpix coords
        assert self.pixel_coordinate_system == 'healpix', "pixel_coordinate_system must be healpix"
        # assert type is int, not string
        if isinstance(pol, (str, np.str)):
            pol = uvutils.polstr2num(pol)
        pol_array = self.polarization_array
        if pol in pol_array:
            stokes_p_ind = np.where(np.isin(pol_array, pol))[0][0]
            beam = self.data_array[0, 0, stokes_p_ind]
        else:
            raise ValueError('Do not have the right polarization information')

        return beam

    def get_beam_area(self, pol='pI'):
        """
        Computes the integral of the beam, which has units of steradians

        Pseudo-Stokes 'pI' (I), 'pQ'(Q), 'pU'(U), 'pV'(V) beam and linear dipole 'XX', 'XY', 'YX' and 'YY' are
        supported. See Equations 4 and 5 of Moore et al. (2017) ApJ 836, 154
        or arxiv:1502.05072 and Kohn et al. (2018) or https://arxiv.org/pdf/1802.04151.pdf for details.

        Args:
          pol : polarization string, Ex. a pseudo-stokes pol 'pI', or a linear pol 'XX'

        Returns:
          omega : float, integral of the beam across the sky [steradians]
        """
        if isinstance(pol, (str, np.str)):
            pol = uvutils.polstr2num(pol)
        if self.beam_type != 'power':
            raise ValueError('beam_type must be power')
        if self.Naxes_vec > 1:
            raise ValueError('Expect scalar for power beam, found vector')
        if self._data_normalization.value != 'peak':
            raise ValueError('beam must be peak normalized')
        if self.pixel_coordinate_system != 'healpix':
            raise ValueError('Currently only healpix format supported')

        nside = self.nside

        # get beam
        beam = self._get_beam(pol)

        # get integral
        omega = np.sum(beam, axis=-1) * np.pi / (3. * nside**2)

        return omega

    def get_beam_sq_area(self, pol='pI'):
        """
        Computes the integral of the beam^2, which has units of steradians

        Pseudo-Stokes 'pI' (I), 'pQ'(Q), 'pU'(U), 'pV'(V) beam and linear dipole 'XX', 'XY', 'YX' and 'YY' are
        supported. See Equations 4 and 5 of Moore et al. (2017) ApJ 836, 154
        or arxiv:1502.05072 for details.

        Args:
          pol : polarization string, Ex. a pseudo-stokes pol 'pI', or a linear pol 'XX'

        Returns:
          omega : float, integral of the beam^2 across the sky [steradians]
        """
        if isinstance(pol, (str, np.str)):
            pol = uvutils.polstr2num(pol)
        if self.beam_type != 'power':
            raise ValueError('beam_type must be power')
        if self.Naxes_vec > 1:
            raise ValueError('Expect scalar for power beam, found vector')
        if self._data_normalization.value != 'peak':
            raise ValueError('beam must be peak normalized')
        if self.pixel_coordinate_system != 'healpix':
            raise ValueError('Currently only healpix format supported')

        nside = self.nside

        # get beam
        beam = self._get_beam(pol)

        # get integral
        omega = np.sum(beam**2, axis=-1) * np.pi / (3. * nside**2)

        return omega

    def select(self, axis1_inds=None, axis2_inds=None, pixels=None,
               frequencies=None, freq_chans=None,
               feeds=None, polarizations=None, run_check=True, check_extra=True,
               run_check_acceptability=True, inplace=True):
        """
        Select specific image axis indices or pixels (if healpix), frequencies and
        feeds or polarizations (if power) to keep in the object while discarding others.

        The history attribute on the object will be updated to identify the
        operations performed.

        Args:
            axis1_inds: The indices along the first image axis to keep in the object.
                Cannot be set if pixel_coordinate_system is "healpix".
            axis2_inds: The indices along the second image axis to keep in the object.
                Cannot be set if pixel_coordinate_system is "healpix".
            pixels: The healpix pixels to keep in the object.
                Cannot be set if pixel_coordinate_system is not "healpix".
            frequencies: The frequencies to keep in the object.
            freq_chans: The frequency channel numbers to keep in the object.
            feeds: The feeds to keep in the object. Cannot be set if the beam_type is "power".
            polarizations: The polarizations to keep in the object.
                Cannot be set if the beam_type is "efield".
            run_check: Option to check for the existence and proper shapes of
                required parameters after downselecting data on this object. Default is True.
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of
                required parameters after  downselecting data on this object. Default is True.
            inplace: Option to perform the select directly on self (True, default) or return
                a new UVBeam object, which is a subselection of self (False)
        """
        if inplace:
            beam_object = self
        else:
            beam_object = copy.deepcopy(self)

        # build up history string as we go
        history_update_string = '  Downselected to specific '
        n_selects = 0

        if axis1_inds is not None:
            if beam_object.pixel_coordinate_system == 'healpix':
                raise ValueError('axis1_inds cannot be used with healpix coordinate system')

            history_update_string += 'parts of first image axis'
            n_selects += 1

            axis1_inds = list(sorted(set(list(axis1_inds))))
            if min(axis1_inds) < 0 or max(axis1_inds) > beam_object.Naxes1 - 1:
                raise ValueError('axis1_inds must be > 0 and < Naxes1')
            beam_object.Naxes1 = len(axis1_inds)
            beam_object.axis1_array = beam_object.axis1_array[axis1_inds]

            if beam_object.Naxes1 > 1:
                axis1_spacing = np.diff(beam_object.axis1_array)
                if not np.isclose(np.min(axis1_spacing), np.max(axis1_spacing),
                                  rtol=beam_object._axis1_array.tols[0],
                                  atol=beam_object._axis1_array.tols[1]):
                    warnings.warn('Selected values along first image axis are '
                                  'not evenly spaced. This is not supported by '
                                  'the regularly gridded beam fits format')

            beam_object.data_array = beam_object.data_array[:, :, :, :, :, axis1_inds]
            if beam_object.beam_type == 'efield':
                beam_object.basis_vector_array = beam_object.basis_vector_array[:, :, :, axis1_inds]

        if axis2_inds is not None:
            if beam_object.pixel_coordinate_system == 'healpix':
                raise ValueError('axis2_inds cannot be used with healpix coordinate system')

            if n_selects > 0:
                history_update_string += ', parts of second image axis'
            else:
                history_update_string += 'parts of second image axis'
            n_selects += 1

            axis2_inds = list(sorted(set(list(axis2_inds))))
            if min(axis2_inds) < 0 or max(axis2_inds) > beam_object.Naxes2 - 1:
                raise ValueError('axis2_inds must be > 0 and < Naxes2')
            beam_object.Naxes2 = len(axis2_inds)
            beam_object.axis2_array = beam_object.axis2_array[axis2_inds]

            if beam_object.Naxes2 > 1:
                axis2_spacing = np.diff(beam_object.axis2_array)
                if not np.isclose(np.min(axis2_spacing), np.max(axis2_spacing),
                                  rtol=beam_object._axis2_array.tols[0],
                                  atol=beam_object._axis2_array.tols[1]):
                    warnings.warn('Selected values along second image axis are '
                                  'not evenly spaced. This is not supported by '
                                  'the regularly gridded beam fits format')

            beam_object.data_array = beam_object.data_array[:, :, :, :, axis2_inds, :]
            if beam_object.beam_type == 'efield':
                beam_object.basis_vector_array = beam_object.basis_vector_array[:, :, axis2_inds, :]

        if pixels is not None:
            if beam_object.pixel_coordinate_system != 'healpix':
                raise ValueError('pixels can only be used with healpix coordinate system')

            history_update_string += 'healpix pixels'
            n_selects += 1

            pix_inds = np.zeros(0, dtype=np.int)
            for p in pixels:
                if p in beam_object.pixel_array:
                    pix_inds = np.append(pix_inds, np.where(beam_object.pixel_array == p)[0])
                else:
                    raise ValueError('Pixel {p} is not present in the pixel_array'.format(p=p))

            pix_inds = list(sorted(set(list(pix_inds))))
            beam_object.Npixels = len(pix_inds)
            beam_object.pixel_array = beam_object.pixel_array[pix_inds]

            beam_object.data_array = beam_object.data_array[:, :, :, :, pix_inds]
            if beam_object.beam_type == 'efield':
                beam_object.basis_vector_array = beam_object.basis_vector_array[:, :, pix_inds]

        if freq_chans is not None:
            freq_chans = uvutils._get_iterable(freq_chans)
            if frequencies is None:
                frequencies = beam_object.freq_array[0, freq_chans]
            else:
                frequencies = uvutils._get_iterable(frequencies)
                frequencies = np.sort(list(set(frequencies)
                                           | set(beam_object.freq_array[0, freq_chans])))

        if frequencies is not None:
            frequencies = uvutils._get_iterable(frequencies)
            if n_selects > 0:
                history_update_string += ', frequencies'
            else:
                history_update_string += 'frequencies'
            n_selects += 1

            freq_inds = np.zeros(0, dtype=np.int)
            # this works because we only allow one SPW. This will have to be reworked when we support more.
            freq_arr_use = beam_object.freq_array[0, :]
            for f in frequencies:
                if f in freq_arr_use:
                    freq_inds = np.append(freq_inds, np.where(freq_arr_use == f)[0])
                else:
                    raise ValueError('Frequency {f} is not present in the freq_array'.format(f=f))

            freq_inds = list(sorted(set(list(freq_inds))))
            beam_object.Nfreqs = len(freq_inds)
            beam_object.freq_array = beam_object.freq_array[:, freq_inds]
            beam_object.bandpass_array = beam_object.bandpass_array[:, freq_inds]

            if beam_object.Nfreqs > 1:
                freq_separation = beam_object.freq_array[0, 1:] - beam_object.freq_array[0, :-1]
                if not np.isclose(np.min(freq_separation), np.max(freq_separation),
                                  rtol=beam_object._freq_array.tols[0],
                                  atol=beam_object._freq_array.tols[1]):
                    warnings.warn('Selected frequencies are not evenly spaced. This '
                                  'is not supported by the regularly gridded beam fits format')

            if beam_object.pixel_coordinate_system == 'healpix':
                beam_object.data_array = beam_object.data_array[:, :, :, freq_inds, :]
            else:
                beam_object.data_array = beam_object.data_array[:, :, :, freq_inds, :, :]

            if beam_object.antenna_type == 'phased_array':
                beam_object.coupling_matrix = beam_object.coupling_matrix[:, :, :, :, :, freq_inds]

            if beam_object.receiver_temperature_array is not None:
                beam_object.receiver_temperature_array = beam_object.receiver_temperature_array[:, freq_inds]

            if beam_object.loss_array is not None:
                beam_object.loss_array = beam_object.loss_array[:, freq_inds]

            if beam_object.mismatch_array is not None:
                beam_object.mismatch_array = beam_object.mismatch_array[:, freq_inds]

            if beam_object.s_parameters is not None:
                beam_object.s_parameters = beam_object.s_parameters[:, :, freq_inds]

        if feeds is not None:
            if beam_object.beam_type == 'power':
                raise ValueError('feeds cannot be used with power beams')

            feeds = uvutils._get_iterable(feeds)
            if n_selects > 0:
                history_update_string += ', feeds'
            else:
                history_update_string += 'feeds'
            n_selects += 1

            feed_inds = np.zeros(0, dtype=np.int)
            for f in feeds:
                if f in beam_object.feed_array:
                    feed_inds = np.append(feed_inds, np.where(beam_object.feed_array == f)[0])
                else:
                    raise ValueError('Feed {f} is not present in the feed_array'.format(f=f))

            feed_inds = list(sorted(set(list(feed_inds))))
            beam_object.Nfeeds = len(feed_inds)
            beam_object.feed_array = beam_object.feed_array[feed_inds]

            if beam_object.pixel_coordinate_system == 'healpix':
                beam_object.data_array = beam_object.data_array[:, :, feed_inds, :, :]
            else:
                beam_object.data_array = beam_object.data_array[:, :, feed_inds, :, :, :]

        if polarizations is not None:
            if beam_object.beam_type == 'efield':
                raise ValueError('polarizations cannot be used with efield beams')

            polarizations = uvutils._get_iterable(polarizations)
            if n_selects > 0:
                history_update_string += ', polarizations'
            else:
                history_update_string += 'polarizations'
            n_selects += 1

            pol_inds = np.zeros(0, dtype=np.int)
            for p in polarizations:
                if p in beam_object.polarization_array:
                    pol_inds = np.append(pol_inds, np.where(beam_object.polarization_array == p)[0])
                else:
                    raise ValueError('polarization {p} is not present in the polarization_array'.format(p=p))

            pol_inds = list(sorted(set(list(pol_inds))))
            beam_object.Npols = len(pol_inds)
            beam_object.polarization_array = beam_object.polarization_array[pol_inds]

            if len(pol_inds) > 2:
                pol_separation = (beam_object.polarization_array[1:]
                                  - beam_object.polarization_array[:-1])
                if np.min(pol_separation) < np.max(pol_separation):
                    warnings.warn('Selected polarizations are not evenly spaced. This '
                                  'is not supported by the regularly gridded beam fits format')

            if beam_object.pixel_coordinate_system == 'healpix':
                beam_object.data_array = beam_object.data_array[:, :, pol_inds, :, :]
            else:
                beam_object.data_array = beam_object.data_array[:, :, pol_inds, :, :, :]

        history_update_string += ' using pyuvdata.'
        beam_object.history = beam_object.history + history_update_string

        # check if object is self-consistent
        if run_check:
            beam_object.check(check_extra=check_extra,
                              run_check_acceptability=run_check_acceptability)

        if not inplace:
            return beam_object

    def _convert_from_filetype(self, other):
        for p in other:
            param = getattr(other, p)
            setattr(self, p, param)

    def _convert_to_filetype(self, filetype):
        if filetype is 'beamfits':
            from . import beamfits
            other_obj = beamfits.BeamFITS()
        else:
            raise ValueError('filetype must be beamfits')
        for p in self:
            param = getattr(self, p)
            setattr(other_obj, p, param)
        return other_obj

    def read_beamfits(self, filename, run_check=True, check_extra=True,
                      run_check_acceptability=True):
        """
        Read in data from a beamfits file.

        Args:
            filename: The beamfits file or list of files to read from.
            run_check: Option to check for the existence and proper shapes of
                required parameters after reading in the file. Default is True.
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of
                required parameters after reading in the file. Default is True.
        """
        from . import beamfits
        if isinstance(filename, (list, tuple)):
            self.read_beamfits(filename[0], run_check=run_check,
                               check_extra=check_extra,
                               run_check_acceptability=run_check_acceptability)
            if len(filename) > 1:
                for f in filename[1:]:
                    beam2 = UVBeam()
                    beam2.read_beamfits(f, run_check=run_check,
                                        check_extra=check_extra,
                                        run_check_acceptability=run_check_acceptability)
                    self += beam2
                del(beam2)
        else:
            beamfits_obj = beamfits.BeamFITS()
            beamfits_obj.read_beamfits(filename, run_check=run_check,
                                       check_extra=check_extra,
                                       run_check_acceptability=run_check_acceptability)
            self._convert_from_filetype(beamfits_obj)
            del(beamfits_obj)

    def write_beamfits(self, filename, run_check=True, check_extra=True,
                       run_check_acceptability=True, clobber=False):
        """
        Write the data to a beamfits file.

        Args:
            filename: The beamfits file to write to.
            run_check: Option to check for the existence and proper shapes of
                required parameters before writing the file. Default is True.
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of
                required parameters before writing the file. Default is True.
            clobber: Option to overwrite the filename if the file already exists.
                Default is False.
        """
        beamfits_obj = self._convert_to_filetype('beamfits')
        beamfits_obj.write_beamfits(filename, run_check=run_check,
                                    check_extra=check_extra,
                                    run_check_acceptability=run_check_acceptability,
                                    clobber=clobber)
        del(beamfits_obj)

    def read_cst_beam(self, filename, beam_type='power', feed_pol='x', rotate_pol=None,
                      frequency=None, telescope_name=None, feed_name=None,
                      feed_version=None, model_name=None, model_version=None,
                      history='', run_check=True, check_extra=True,
                      run_check_acceptability=True):
        """
        Read in data from a cst file.

        Args:
            filename: The cst file or list of files to read from. If a list is passed,
                the files are combined along the appropriate axes.
            beam_type: what beam_type to read in ('power' or 'efield'). Defaults to 'power'.
            feed_pol: the feed or polarization or list of feeds or polarizations the files correspond to.
                Defaults to 'x' (meaning x for efield or xx for power beams).
            rotate_pol: If True, assume the structure in the simulation is symmetric under
                90 degree rotations about the z-axis (so that the y polarization can be
                constructed by rotating the x polarization or vice versa).
                Default: True if feed_pol is a single value, False if it is a list.
            frequency: the frequency or list of frequencies corresponding to the filename(s).
                This is assumed to be in the same order as the files, so if it's used,
                make sure the files are an ordered datatype.
                If not passed, the code attempts to parse it from the filenames.
            telescope_name: the name of the telescope corresponding to the filename(s).
            feed_name: the name of the feed corresponding to the filename(s).
            feed_version: the version of the feed corresponding to the filename(s).
            model_name: the name of the model corresponding to the filename(s).
            model_version: the version of the model corresponding to the filename(s).
            history: A string detailing the history of the filename(s).
            run_check: Option to check for the existence and proper shapes of
                required parameters after reading in the file. Default is True.
            check_extra: Option to check optional parameters as well as
                required ones. Default is True.
            run_check_acceptability: Option to check acceptable range of the values of
                required parameters after reading in the file. Default is True.
        """
        from . import cst_beam
        if isinstance(filename, np.ndarray):
            if len(filename.shape) > 1:
                raise ValueError('filename can not be a multi-dimensional array')
            filename = filename.tolist()
        if isinstance(filename, (list, tuple)):
            if len(filename) == 1:
                filename = filename[0]

        if isinstance(frequency, np.ndarray):
            if len(frequency.shape) > 1:
                raise ValueError('frequency can not be a multi-dimensional array')
            frequency = frequency.tolist()
        if isinstance(frequency, (list, tuple)):
            if len(frequency) == 1:
                frequency = frequency[0]

        if isinstance(feed_pol, np.ndarray):
            if len(feed_pol.shape) > 1:
                raise ValueError('frequency can not be a multi-dimensional array')
            feed_pol = feed_pol.tolist()
        if isinstance(feed_pol, (list, tuple)):
            if len(feed_pol) == 1:
                feed_pol = feed_pol[0]

        if isinstance(filename, (list, tuple)):
            if frequency is not None:
                if isinstance(frequency, (list, tuple)):
                    if not len(frequency) == len(filename):
                        raise ValueError('If frequency and filename are both '
                                         'lists they need to be the same length')
                    freq = frequency[0]
                else:
                    freq = frequency
            else:
                freq = None

            if isinstance(feed_pol, (list, tuple)):
                if not len(feed_pol) == len(filename):
                    raise ValueError('If feed_pol and filename are both '
                                     'lists they need to be the same length')
                pol = feed_pol[0]
                if rotate_pol is None:
                    rotate_pol = False
            else:
                pol = feed_pol
                if rotate_pol is None:
                    rotate_pol = True
            if isinstance(freq, (list, tuple)):
                raise ValueError('frequency can not be a nested list')
            if isinstance(pol, (list, tuple)):
                raise ValueError('feed_pol can not be a nested list')
            self.read_cst_beam(filename[0], beam_type=beam_type,
                               feed_pol=pol, rotate_pol=rotate_pol,
                               frequency=freq,
                               telescope_name=telescope_name,
                               feed_name=feed_name,
                               feed_version=feed_version,
                               model_name=model_name,
                               model_version=model_version,
                               history=history, run_check=run_check,
                               check_extra=check_extra,
                               run_check_acceptability=run_check_acceptability)
            for file_i, f in enumerate(filename[1:]):
                if isinstance(f, (list, tuple)):
                    raise ValueError('filename can not be a nested list')

                if isinstance(frequency, (list, tuple)):
                    freq = frequency[file_i + 1]
                elif frequency is not None:
                    freq = frequency
                else:
                    freq = None
                if isinstance(feed_pol, (list, tuple)):
                    pol = feed_pol[file_i + 1]
                else:
                    pol = feed_pol
                beam2 = UVBeam()
                beam2.read_cst_beam(f, beam_type=beam_type,
                                    feed_pol=pol, rotate_pol=rotate_pol,
                                    frequency=freq,
                                    telescope_name=telescope_name,
                                    feed_name=feed_name,
                                    feed_version=feed_version,
                                    model_name=model_name,
                                    model_version=model_version,
                                    history=history, run_check=run_check,
                                    check_extra=check_extra,
                                    run_check_acceptability=run_check_acceptability)
                self += beam2
            del(beam2)
        else:
            if isinstance(frequency, (list, tuple)):
                raise ValueError('Too many frequencies specified')
            if isinstance(feed_pol, (list, tuple)):
                raise ValueError('Too many feed_pols specified')
            if rotate_pol is None:
                rotate_pol = True
            cst_beam_obj = cst_beam.CSTBeam()
            cst_beam_obj.read_cst_beam(filename, beam_type=beam_type,
                                       feed_pol=feed_pol, rotate_pol=rotate_pol,
                                       frequency=frequency,
                                       telescope_name=telescope_name,
                                       feed_name=feed_name,
                                       feed_version=feed_version,
                                       model_name=model_name,
                                       model_version=model_version,
                                       history=history, run_check=run_check,
                                       check_extra=check_extra,
                                       run_check_acceptability=run_check_acceptability)
            self._convert_from_filetype(cst_beam_obj)
            del(cst_beam_obj)