text: # Licensed under a 3-clause BSD style license - see LICENSE.rst
  
  import abc
  import functools
  import inspect
  from types import FunctionType, MappingProxyType
  
  import numpy as np
  
  import astropy.units as u
  from astropy.io.registry import UnifiedReadWriteMethod
  from astropy.utils.decorators import classproperty
  from astropy.utils.metadata import MetaData
  
  from .connect import CosmologyFromFormat, CosmologyRead, CosmologyToFormat, CosmologyWrite
  from .parameter import Parameter
  
  # Originally authored by Andrew Becker (becker@astro.washington.edu),
  # and modified by Neil Crighton (neilcrighton@gmail.com), Roban Kramer
  # (robanhk@gmail.com), and Nathaniel Starkman (n.starkman@mail.utoronto.ca).
  
  # Many of these adapted from Hogg 1999, astro-ph/9905116
  # and Linder 2003, PRL 90, 91301
  
  __all__ = ["Cosmology", "CosmologyError", "FlatCosmologyMixin"]
  
  __doctest_requires__ = {}  # needed until __getattr__ removed
  
  # registry of cosmology classes with {key=name : value=class}
  _COSMOLOGY_CLASSES = dict()
  
  
  class CosmologyError(Exception):
      pass
  
  
  class Cosmology(metaclass=abc.ABCMeta):
      """Base-class for all Cosmologies.
  
      Parameters
      ----------
      *args
          Arguments into the cosmology; used by subclasses, not this base class.
      name : str or None (optional, keyword-only)
          The name of the cosmology.
      meta : dict or None (optional, keyword-only)
          Metadata for the cosmology, e.g., a reference.
      **kwargs
          Arguments into the cosmology; used by subclasses, not this base class.
  
      Notes
      -----
      Class instances are static -- you cannot (and should not) change the values
      of the parameters.  That is, all of the above attributes (except meta) are
      read only.
  
      For details on how to create performant custom subclasses, see the
      documentation on :ref:`astropy-cosmology-fast-integrals`.
      """
  
      meta = MetaData()
  
      # Unified I/O object interchange methods
      from_format = UnifiedReadWriteMethod(CosmologyFromFormat)
      to_format = UnifiedReadWriteMethod(CosmologyToFormat)
  
      # Unified I/O read and write methods
      read = UnifiedReadWriteMethod(CosmologyRead)
      write = UnifiedReadWriteMethod(CosmologyWrite)
  
      # Parameters
      __parameters__ = ()
      __all_parameters__ = ()
  
      # ---------------------------------------------------------------
  
      def __init_subclass__(cls):
          super().__init_subclass__()
  
          # -------------------
          # Parameters
  
          # Get parameters that are still Parameters, either in this class or above.
          parameters = []
          derived_parameters = []
          for n in cls.__parameters__:
              p = getattr(cls, n)
              if isinstance(p, Parameter):
                  derived_parameters.append(n) if p.derived else parameters.append(n)
  
          # Add new parameter definitions
          for n, v in cls.__dict__.items():
              if n in parameters or n.startswith("_") or not isinstance(v, Parameter):
                  continue
              derived_parameters.append(n) if v.derived else parameters.append(n)
  
          # reorder to match signature
          ordered = [parameters.pop(parameters.index(n))
                     for n in cls._init_signature.parameters.keys()
                     if n in parameters]
          parameters = ordered + parameters  # place "unordered" at the end
          cls.__parameters__ = tuple(parameters)
          cls.__all_parameters__ = cls.__parameters__ + tuple(derived_parameters)
  
          # -------------------
          # register as a Cosmology subclass
          _COSMOLOGY_CLASSES[cls.__qualname__] = cls
  
      @classproperty(lazy=True)
      def _init_signature(cls):
          """Initialization signature (without 'self')."""
          # get signature, dropping "self" by taking arguments [1:]
          sig = inspect.signature(cls.__init__)
          sig = sig.replace(parameters=list(sig.parameters.values())[1:])
          return sig
  
      # ---------------------------------------------------------------
  
      def __init__(self, name=None, meta=None):
          self._name = name
          self.meta.update(meta or {})
  
      @property
      def name(self):
          """The name of the Cosmology instance."""
          return self._name
  
      def clone(self, *, meta=None, **kwargs):
          """Returns a copy of this object with updated parameters, as specified.
  
          This cannot be used to change the type of the cosmology, so ``clone()``
          cannot be used to change between flat and non-flat cosmologies.
  
          Parameters
          ----------
          meta : mapping or None (optional, keyword-only)
              Metadata that will update the current metadata.
          **kwargs
              Cosmology parameter (and name) modifications.
              If any parameter is changed and a new name is not given, the name
              will be set to "[old name] (modified)".
  
          Returns
          -------
          newcosmo : `~astropy.cosmology.Cosmology` subclass instance
              A new instance of this class with updated parameters as specified.
              If no modifications are requested, then a reference to this object
              is returned instead of copy.
  
          Examples
          --------
          To make a copy of the ``Planck13`` cosmology with a different matter
          density (``Om0``), and a new name:
  
              >>> from astropy.cosmology import Planck13
              >>> newcosmo = Planck13.clone(name="Modified Planck 2013", Om0=0.35)
  
          If no name is specified, the new name will note the modification.
  
              >>> Planck13.clone(Om0=0.35).name
              'Planck13 (modified)'
          """
          # Quick return check, taking advantage of the Cosmology immutability.
          if meta is None and not kwargs:
              return self
  
          # There are changed parameter or metadata values.
          # The name needs to be changed accordingly, if it wasn't already.
          kwargs.setdefault("name", (self.name + " (modified)"
                                     if self.name is not None else None))
  
          # mix new meta into existing, preferring the former.
          new_meta = {**self.meta, **(meta or {})}
          # Mix kwargs into initial arguments, preferring the former.
          new_init = {**self._init_arguments, "meta": new_meta, **kwargs}
          # Create BoundArgument to handle args versus kwargs.
          # This also handles all errors from mismatched arguments
          ba = self._init_signature.bind_partial(**new_init)
          # Return new instance, respecting args vs kwargs
          return self.__class__(*ba.args, **ba.kwargs)
  
      @property
      def _init_arguments(self):
          # parameters
          kw = {n: getattr(self, n) for n in self.__parameters__}
  
          # other info
          kw["name"] = self.name
          kw["meta"] = self.meta
  
          return kw
  
      # ---------------------------------------------------------------
      # comparison methods
  
      def is_equivalent(self, other):
          r"""Check equivalence between Cosmologies.
  
          Two cosmologies may be equivalent even if not the same class.
          For example, an instance of ``LambdaCDM`` might have :math:`\Omega_0=1`
          and :math:`\Omega_k=0` and therefore be flat, like ``FlatLambdaCDM``.
  
          Parameters
          ----------
          other : `~astropy.cosmology.Cosmology` subclass instance
              The object in which to compare.
  
          Returns
          -------
          bool
              True if cosmologies are equivalent, False otherwise.
          """
          # The options are: 1) same class & parameters; 2) same class, different
          # parameters; 3) different classes, equivalent parameters; 4) different
          # classes, different parameters. (1) & (3) => True, (2) & (4) => False.
          equiv = self.__equiv__(other)
          if equiv is NotImplemented and hasattr(other, "__equiv__"):
              equiv = other.__equiv__(self)  # that failed, try from 'other'
  
          return equiv if equiv is not NotImplemented else False
  
      def __equiv__(self, other):
          """Cosmology equivalence. Use ``.is_equivalent()`` for actual check!
  
          Parameters
          ----------
          other : `~astropy.cosmology.Cosmology` subclass instance
              The object in which to compare.
  
          Returns
          -------
          bool or `NotImplemented`
              `NotImplemented` if 'other' is from a different class.
              `True` if 'other' is of the same class and has matching parameters
              and parameter values. `False` otherwise.
          """
          if other.__class__ is not self.__class__:
              return NotImplemented  # allows other.__equiv__
  
          # check all parameters in 'other' match those in 'self' and 'other' has
          # no extra parameters (latter part should never happen b/c same class)
          params_eq = (set(self.__all_parameters__) == set(other.__all_parameters__)
                       and all(np.all(getattr(self, k) == getattr(other, k))
                               for k in self.__all_parameters__))
          return params_eq
  
      def __eq__(self, other):
          """Check equality between Cosmologies.
  
          Checks the Parameters and immutable fields (i.e. not "meta").
  
          Parameters
          ----------
          other : `~astropy.cosmology.Cosmology` subclass instance
              The object in which to compare.
  
          Returns
          -------
          bool
              True if Parameters and names are the same, False otherwise.
          """
          if other.__class__ is not self.__class__:
              return NotImplemented  # allows other.__eq__
  
          # check all parameters in 'other' match those in 'self'
          equivalent = self.__equiv__(other)
          # non-Parameter checks: name
          name_eq = (self.name == other.name)
  
          return equivalent and name_eq
  
      # ---------------------------------------------------------------
  
      def __repr__(self):
          ps = {k: getattr(self, k) for k in self.__parameters__}  # values
          cps = {k: getattr(self.__class__, k) for k in self.__parameters__}  # Parameter objects
  
          namelead = f"{self.__class__.__qualname__}("
          if self.name is not None:
              namelead += f"name=\"{self.name}\", "
          # nicely formatted parameters
          fmtps = (k + '=' + format(v, cps[k].format_spec if v is not None else '')
                   for k, v in ps.items())
  
          return namelead + ", ".join(fmtps) + ")"
  
      def __astropy_table__(self, cls, copy, **kwargs):
          """Return a `~astropy.table.Table` of type ``cls``.
  
          Parameters
          ----------
          cls : type
              Astropy ``Table`` class or subclass.
          copy : bool
              Ignored.
          **kwargs : dict, optional
              Additional keyword arguments. Passed to ``self.to_format()``.
              See ``Cosmology.to_format.help("astropy.table")`` for allowed kwargs.
  
          Returns
          -------
          `astropy.table.Table` or subclass instance
              Instance of type ``cls``.
          """
          return self.to_format("astropy.table", cls=cls, **kwargs)
  
  
  class FlatCosmologyMixin(metaclass=abc.ABCMeta):
      """
      Mixin class for flat cosmologies. Do NOT instantiate directly.
      Note that all instances of ``FlatCosmologyMixin`` are flat, but not all
      flat cosmologies are instances of ``FlatCosmologyMixin``. As example,
      ``LambdaCDM`` **may** be flat (for the a specific set of parameter values),
      but ``FlatLambdaCDM`` **will** be flat.
      """
      pass
  
  
  # -----------------------------------------------------------------------------
  
  
  def __getattr__(attr):
      from . import flrw
  
      if hasattr(flrw, attr):
          import warnings
  
          from astropy.utils.exceptions import AstropyDeprecationWarning
  
          warnings.warn(
              f"`astropy.cosmology.core.{attr}` has been moved (since v5.0) and "
              f"should be imported as ``from astropy.cosmology import {attr}``."
              " In future this will raise an exception.",
              AstropyDeprecationWarning
          )
  
          return getattr(flrw, attr)
  
      raise AttributeError(f"module {__name__!r} has no attribute {attr!r}.")
  