# Licensed under a 3-clause BSD style license - see LICENSE.rst
import sys
import warnings
from math import sqrt, pi, exp, log
from abc import ABCMeta, abstractmethod

import numpy as np

from .. import constants as const
from ..config import ConfigurationItem
from ..utils.misc import isiterable
from .. import units as u

from . import parameters

# Originally authored by Andrew Becker (becker@astro.washington.edu),
# and modified by Neil Crighton (neilcrighton@gmail.com) and Roban
# Kramer (robanhk@gmail.com).

# Many of these adapted from Hogg 1999, astro-ph/9905116
# and Linder 2003, PRL 90, 91301

__all__ = ["FLRW", "LambdaCDM", "FlatLambdaCDM", "wCDM", "FlatwCDM",
           "Flatw0waCDM", "w0waCDM", "wpwaCDM", "w0wzCDM","get_current",
           "set_current", "WMAP5", "WMAP7", "WMAP9", "Planck13"]

# Constants

# speed of light in km/s
c_kms = const.c.to('km/s').value

# Mpc in km
Mpc_km = u.Mpc.to(u.km)

# Gyr in seconds; note these are Julian years, which are defined
# to be exactly 365.25 days of 86400 seconds each. If we used the units
# framework, the days would be 365.242... days.
Gyr = 1e9 * 365.25 * 24 * 60 * 60

arcsec_in_radians = 1 / 3600. * pi / 180
arcmin_in_radians = 1 / 60. * pi / 180


#Radiation parameter over c^2
a_B_c2 = 4 * const.sigma_sb.cgs.value / const.c.cgs.value**3

DEFAULT_COSMOLOGY = ConfigurationItem(
    'default_cosmology', 'no_default',
    'The default cosmology to use. Note this is only read on import, '
    'changing this value at runtime has no effect.')


class CosmologyError(Exception):
    pass

class Cosmology(object):
    """ Placeholder for when a more general Cosmology class is
    implemented. """
    pass

class FLRW(Cosmology):
    """ A class describing an isotropic and homogeneous
    (Friedmann-Lemaitre-Robertson-Walker) cosmology.

    This is an abstract base class -- you can't instantiate
    examples of this class, but must work with one of its
    subclasses such as `LambdaCDM` or `wCDM`.

    Notes
    -----
    Class instances are static -- you can't change the values
    of the parameters.  That is, all of the attributes above are
    read only.

    The neutrino treatment assumes all neutrino species are massless.
    """
    __metaclass__ = ABCMeta

    def __init__(self, H0, Om0, Ode0, Tcmb0=2.725, Neff=3.04, name='FLRW'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        Ode0 : float
          Omega dark energy: density of dark energy in units
          of the critical density at z=0.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """

        # all densities are in units of the critical density
        self._Om0 = float(Om0)
        self._Ode0 = float(Ode0)
        self._Tcmb0 = float(Tcmb0)
        self._Neff = float(Neff)
        self.name = name

        # Hubble parameter at z=0, km/s/Mpc
        self._H0 = float(H0)
        # H0 in s^-1
        H0_s = self._H0 / Mpc_km
        # 100 km/s/Mpc * h = H0 (so h is dimensionless)
        self._h = self._H0 / 100.
        # Hubble time in Gyr
        self._hubble_time = 1. / H0_s / Gyr
        # Hubble distance in Mpc
        self._hubble_distance = c_kms / self._H0

        # critical density at z=0 (grams per cubic cm)
        self._critical_density0 = 3. * H0_s**2 / (8. * pi * const.G.cgs.value)

        # Compute photon density, Tcmb, neutrino parameters
        # Tcmb0=0 removes both photons and neutrinos, is handled
        # as a special case for efficiency
        if self._Tcmb0 > 0:
            # Compute photon density from Tcmb
            self._Ogamma0 = a_B_c2 * self._Tcmb0**4 / self._critical_density0

            #Compute Neutrino Omega
            # The constant in front is 7/8 (4/11)^4/3 -- see any
            #  cosmology book for an explanation; the 7/8 is FD vs. BE
            #  statistics, the 4/11 is the temperature effect
            self._Onu0 = 0.2271073 * self._Neff * self._Ogamma0
        else:
            self._Ogamma0 = 0.0
            self._Onu0 = 0.0

        #Compute curvature density
        self._Ok0 = 1.0 - self._Om0 - self._Ode0 - self._Ogamma0 - self._Onu0

    def __repr__(self):
        return "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g, Ok0=%.3g)" % \
            (self.name, self._H0, self._Om0, self._Ode0, self._Ok0)

    #Set up a set of properties for H0, Om0, Ode0, Ok0, etc. for user access.
    #Note that we don't let these be set (so, obj.Om0 = value fails)

    @property
    def H0(self):
        """ Return the Hubble constant in [km/sec/Mpc] at z=0"""
        return self._H0

    @property
    def Om0(self):
        """ Omega matter; matter density/critical density at z=0"""
        return self._Om0

    @property
    def Ode0(self):
        """ Omega dark energy; dark energy density/critical density at z=0"""
        return self._Ode0

    @property
    def Ok0(self):
        """ Omega curvature; the effective curvature density/critical density
        at z=0"""
        return self._Ok0

    @property
    def Tcmb0(self):
        """ Temperature of the CMB in Kelvin at z=0"""
        return self._Tcmb0

    @property
    def Neff(self):
        """ Number of effective neutrino species"""
        return self._Neff

    @property
    def h(self):
        """ Dimensionless Hubble constant: h = H_0 / 100 [km/sec/Mpc]"""
        return self._h

    @property
    def hubble_time(self):
        """ Hubble time in [Gyr]"""
        return self._hubble_time

    @property
    def hubble_distance(self):
        """ Hubble distance in [Mpc]"""
        return self._hubble_distance

    @property
    def critical_density0(self):
        """ Critical density in [g cm^-3] at z=0"""
        return self._critical_density0

    @property
    def Ogamma0(self):
        """ Omega gamma; the density/critical density of photons at z=0"""
        return self._Ogamma0

    @property
    def Onu0(self):
        """ Omega nu; the density/critical density of neutrinos at z=0"""
        return self._Onu0

    @abstractmethod
    def w(self, z):
        """ The dark energy equation of state.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        w : ndarray, or float if input scalar
          The dark energy equation of state

        Notes
        ------
        The dark energy equation of state is defined as
        :math:`w(z) = P(z)/\\rho(z)`, where :math:`P(z)` is the
        pressure at redshift z and :math:`\\rho(z)` is the density
        at redshift z, both in units where c=1.

        This must be overridden by subclasses.
        """
        raise NotImplementedError("w(z) is not implemented")

    def Om(self, z):
        """ Return the density parameter for non-relativistic matter
        at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        Om : ndarray, or float if input scalar
          The density of non-relativistic matter relative to the critical
          density at each redshift.
        """

        if isiterable(z):
            z = np.asarray(z)
        return self._Om0 * (1. + z)**3 * self.inv_efunc(z)**2

    def Ok(self, z):
        """ Return the equivalent density parameter for curvature
        at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        Ok : ndarray, or float if input scalar
          The equivalent density parameter for curvature at each redshift.
        """

        if self._Ok0 == 0:
            #Common enough case to be worth checking
            return np.zeros_like(z)

        if isiterable(z):
            z = np.asarray(z)
        return self._Ok0 * (1. + z)**2 * self.inv_efunc(z)**2

    def Ode(self, z):
        """ Return the density parameter for dark energy at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        Ode : ndarray, or float if input scalar
          The density of non-relativistic matter relative to the critical
          density at each redshift.
        """

        if self._Ode0 == 0:
            return np.zeros_like(z)

        return self._Ode0 * self.de_density_scale(z) * self.inv_efunc(z)**2

    def Ogamma(self, z):
        """ Return the density parameter for photons at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        Ogamma : ndarray, or float if input scalar
          The energy density of photons relative to the critical
          density at each redshift.
        """

        if self._Ogamma0 == 0:
            #Common enough case to be worth checking (although it clearly
            # doesn't represent any real universe)
            return np.zeros_like(z)

        if isiterable(z):
            z = np.asarray(z)
        return self._Ogamma0 * (1. + z)**4 * self.inv_efunc(z)**2

    def Onu(self, z):
        """ Return the density parameter for massless neutrinos at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        Onu : ndarray, or float if input scalar
          The energy density of photons relative to the critical
          density at each redshift.  Note that this includes only
          their relativistic energy, since they are assumed massless.
        """

        if self._Onu0 == 0:
            #Common enough case to be worth checking (although it clearly
            # doesn't represent any real universe)
            return np.zeros_like(z)

        if isiterable(z):
            z = np.asarray(z)
        return self._Onu0 * (1. + z)**4 * self.inv_efunc(z)**2

    def Tcmb(self, z):
        """ Return the CMB temperature at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        Tcmb : ndarray, or float if z is scalar
          The temperature of the CMB in K.
        """

        if isiterable(z):
            z = np.asarray(z)
        return self._Tcmb0 * (1.0 + z)

    def _w_integrand(self, ln1pz):
        """ Internal convenience function for w(z) integral."""

        #See Linder 2003, PRL 90, 91301 eq (5)
        #Assumes scalar input, since this should only be called
        # inside an integral

        z = exp(ln1pz)-1.0
        return 1.0 + self.w(z)

    def de_density_scale(self, z):
        """ Evaluates the redshift dependence of the dark energy density.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        I : ndarray, or float if input scalar
          The scaling of the energy density of dark energy with redshift.

        Notes
        -----
        The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`,
        and is given by

        .. math::

            I = \\exp \\left( 3 \int_{a}^1 \\frac{ da^{\\prime} }{ a^{\\prime} }
            \\left[ 1 + w\\left( a^{\\prime} \\right) \\right] \\right)

        It will generally helpful for subclasses to overload this method if
        the integral can be done analytically for the particular dark
        energy equation of state that they implement.
        """

        # This allows for an arbitrary w(z) following eq (5) of
        # Linder 2003, PRL 90, 91301.  The code here evaluates
        # the integral numerically.  However, most popular
        # forms of w(z) are designed to make this integral analytic,
        # so it is probably a good idea for subclasses to overload this
        # method if an analytic form is available.
        #
        # The integral we actually use (the one given in Linder)
        # is rewritten in terms of z, so looks slightly different than the
        # one in the documentation string, but it's the same thing.

        from scipy.integrate import quad

        if isiterable(z):
            z = np.asarray(z)
            ival = np.array([quad(self._w_integrand,0,log(1+redshift))[0]
                             for redshift in z])
            return np.exp(3 * ival)
        else:
            ival = quad(self._w_integrand,0,log(1+z))[0]
            return exp(3 * ival)

    def efunc(self, z):
        """ Function used to calculate H(z), the Hubble parameter.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The redshift scaling of the Hubble constant.

        Notes
        -----
        The return value, E, is defined such that :math:`H(z) = H_0 E`.

        It is not necessary to override this method, but if de_density_scale
        takes a particularly simple form, it may be advantageous to.
        """

        if isiterable(z):
            z = np.asarray(z)

        Om0, Ode0, Ok0 = self._Om0, self._Ode0, self._Ok0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return np.sqrt(zp1**2 * ((Or0 * zp1 + Om0) * zp1 + Ok0) +
                       Ode0 * self.de_density_scale(z))

    def inv_efunc(self, z):
        """Inverse of efunc.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The redshift scaling of the inverse Hubble constant.
        """

        #Avoid the function overhead by repeating code
        if isiterable(z):
            z = np.asarray(z)
        Om0, Ode0, Ok0 = self._Om0, self._Ode0, self._Ok0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return 1.0/np.sqrt(zp1**2 * ((Or0 * zp1 + Om0) * zp1 + Ok0) +
                           Ode0 * self.de_density_scale(z))

    def _tfunc(self, z):
        """ Integrand of the lookback time.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        I : ndarray, or float if input scalar
          The integrand for the lookback time

        References
        ----------
        Eqn 30 from Hogg 1999.
        """

        if isiterable(z):
            zp1 = 1.0 + np.asarray(z)
        else:
            zp1 = 1. + z

        return 1.0 / (zp1 * self.efunc(z))

    def _xfunc(self, z):
        """ Integrand of the absorption distance.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        X : ndarray, or float if input scalar
          The integrand for the absorption distance

        References
        ----------
        See Hogg 1999 section 11.
        """

        if isiterable(z):
            zp1 = 1.0 + np.asarray(z)
        else:
            zp1 = 1. + z
        return zp1**2 / self.efunc(z)

    def H(self, z):
        """ Hubble parameter (km/s/Mpc) at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        H : ndarray, or float if input scalar
          Hubble parameter in km/s/Mpc at each input redshift.
        """

        return self._H0 * self.efunc(z)

    def scale_factor(self, z):
        """ Scale factor at redshift `z`.

        The scale factor is defined as :math:`a = 1 / (1 + z)`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        a : ndarray, or float if input scalar
          Scale factor at each input redshift.
        """

        if isiterable(z):
            z = np.asarray(z)

        return 1. / (1. + z)


    def lookback_time(self, z):
        """ Lookback time in Gyr to redshift `z`.

        The lookback time is the difference between the age of the
        Universe now and the age at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        t : ndarray, or float if input scalar
          Lookback time in Gyr to each input redshift.
        """

        from scipy.integrate import quad
        if not isiterable(z):
            return self._hubble_time * quad(self._tfunc, 0, z)[0]

        out = np.array([quad(self._tfunc, 0, redshift)[0] for redshift in z])
        return self._hubble_time * np.array(out)

    def age(self, z):
        """ Age of the universe in Gyr at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        t : ndarray, or float if input scalar
          The age of the universe in Gyr at each input redshift.
        """

        from scipy.integrate import quad
        if not isiterable(z):
            return self._hubble_time * quad(self._tfunc, z, np.inf)[0]

        out = [quad(self._tfunc, redshift, np.inf)[0] for redshift in z]
        return self._hubble_time * np.array(out)

    def critical_density(self, z):
        """ Critical density in grams per cubic cm at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        rho : ndarray, or float if input scalar
          Critical density in g/cm^3 at each input redshift.
        """

        return self._critical_density0 * (self.efunc(z))**2

    def comoving_distance(self, z):
        """ Comoving line-of-sight distance in Mpc at a given
        redshift.

        The comoving distance along the line-of-sight between two
        objects remains constant with time for objects in the Hubble
        flow.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        d : ndarray, or float if input scalar
          Comoving distance in Mpc to each input redshift.
        """

        from scipy.integrate import quad
        if not isiterable(z):
            return self._hubble_distance * quad(self.inv_efunc, 0, z)[0]

        out = [quad(self.inv_efunc, 0, redshift)[0] for redshift in z]
        return self._hubble_distance * np.array(out)

    def comoving_transverse_distance(self, z):
        """ Comoving transverse distance in Mpc at a given redshift.

        This value is the transverse comoving distance at redshift `z`
        corresponding to an angular separation of 1 radian. This is
        the same as the comoving distance if omega_k is zero (as in
        the current concordance lambda CDM model).

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        d : ndarray, or float if input scalar
          Comoving transverse distance in Mpc at each input redshift.

        Notes
        -----
        This quantity also called the 'proper motion distance' in some
        texts.
        """

        Ok0 = self._Ok0
        dc = self.comoving_distance(z)
        if Ok0 == 0:
            return dc
        sqrtOk0 = sqrt(abs(Ok0))
        dh = self._hubble_distance
        if Ok0 > 0:
            return dh / sqrtOk0 * np.sinh(sqrtOk0 * dc / dh)
        else:
            return dh / sqrtOk0 * np.sin(sqrtOk0 * dc / dh)

    def angular_diameter_distance(self, z):
        """ Angular diameter distance in Mpc at a given redshift.

        This gives the proper (sometimes called 'physical') transverse
        distance corresponding to an angle of 1 radian for an object
        at redshift `z`.

        Weinberg, 1972, pp 421-424; Weedman, 1986, pp 65-67; Peebles,
        1993, pp 325-327.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        d : ndarray, or float if input scalar
          Angular diameter distance in Mpc at each input redshift.
        """

        if isiterable(z):
            z = np.asarray(z)

        return self.comoving_transverse_distance(z) / (1. + z)

    def luminosity_distance(self, z):
        """ Luminosity distance in Mpc at redshift `z`.

        This is the distance to use when converting between the
        bolometric flux from an object at redshift `z` and its
        bolometric luminosity.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        d : ndarray, or float if input scalar
          Luminosity distance in Mpc at each input redshift.

        References
        ----------
        Weinberg, 1972, pp 420-424; Weedman, 1986, pp 60-62.
        """

        if isiterable(z):
            z = np.asarray(z)

        return (1. + z) * self.comoving_transverse_distance(z)

    def angular_diameter_distance_z1z2(self, z1, z2):
        """ Angular diameter distance between objects at 2 redshifts.
        Useful for gravitational lensing.

        Parameters
        ----------
        z1, z2 : array_like, shape (N,)
          Input redshifts. z2 must be large than z1.

        Returns
        -------
        d : ndarray, shape (N,) or float if input scalar
          The angular diameter distance between each input redshift
          pair.

        Raises
        ------
        CosmologyError
          If omega_k is < 0.

        Notes
        -----
        This method only works for flat or open curvature
        (omega_k >= 0).
        """

        # does not work for negative curvature
        Ok0 = self._Ok0
        if Ok0 < 0:
            raise CosmologyError('Ok0 must be >= 0 to use this method.')

        outscalar = False
        if not isiterable(z1) and not isiterable(z2):
            outscalar = True

        z1 = np.atleast_1d(z1)
        z2 = np.atleast_1d(z2)

        if z1.size != z2.size:
            raise ValueError('z1 and z2 must be the same size.')

        if (z1 > z2).any():
            raise ValueError('z2 must greater than z1')

        # z1 < z2
        if (z2 < z1).any():
            z1, z2 = z2, z1

        dm1 = self.comoving_transverse_distance(z1)
        dm2 = self.comoving_transverse_distance(z2)
        dh_2 = self._hubble_distance**2

        out = 1. / (1. + z2) * (dm2*np.sqrt(1. + Ok0*dm1**2 / dh_2) -
                                dm1*np.sqrt(1. + Ok0*dm2**2 / dh_2))

        if outscalar:
            return out[0]

        return out

    def absorption_distance(self, z):
        """ Absorption distance at redshift `z`.

        This is used to calculate the number of objects with some
        cross section of absorption and number density intersecting a
        sightline per unit redshift path.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        d : ndarray, or float if input scalar
          Absorption distance (dimensionless) at each input redshift.

        References
        ----------
        Hogg 1999 Section 11. (astro-ph/9905116)
        Bahcall, John N. and Peebles, P.J.E. 1969, ApJ, 156L, 7B
        """

        from scipy.integrate import quad
        if not isiterable(z):
            return quad(self._xfunc, 0, z)[0]

        out = [quad(self._xfunc, 0, redshift)[0] for redshift in z]
        return np.array(out)

    def distmod(self, z):
        """ Distance modulus at redshift `z`.

        The distance modulus is defined as the (apparent magnitude -
        absolute magnitude) for an object at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        distmod : ndarray, or float if input scalar
          Distance modulus at each input redshift.
        """

        # Remember that the luminosity distance is in Mpc
        return 5. * np.log10(self.luminosity_distance(z) * 1.e5)

    def comoving_volume(self, z):
        """ Comoving volume in cubic Mpc at redshift `z`.

        This is the volume of the universe encompassed by redshifts
        less than `z`. For the case of omega_k = 0 it is a sphere of
        radius `comoving_distance(z)` but it is less intuitive if
        omega_k is not 0.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        V : ndarray, or float if input scalar
          Comoving volume in Mpc^3 at each input redshift.
        """

        Ok0 = self._Ok0
        if Ok0 == 0:
            return 4. / 3. * pi * self.comoving_distance(z)**3

        dh = self._hubble_distance
        dm = self.comoving_transverse_distance(z)
        term1 = 4. * pi * dh ** 3 / (2. * Ok0)
        term2 = dm / dh * np.sqrt(1 + Ok0 * (dm / dh) ** 2)
        term3 = sqrt(abs(Ok0)) * dm / dh

        if Ok0 > 0:
            return term1 * (term2 - 1. / sqrt(abs(Ok0)) * np.arcsinh(term3))
        else:
            return term1 * (term2 - 1. / sqrt(abs(Ok0)) * np.arcsin(term3))

    def kpc_comoving_per_arcmin(self, z):
        """ Separation in transverse comoving kpc corresponding to an
        arcminute at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        d : ndarray, or float if input scalar
          The distance in comoving kpc corresponding to an arcmin at each
          input redshift.
        """
        return self.comoving_transverse_distance(z) * 1.e3 * arcmin_in_radians


    def kpc_proper_per_arcmin(self, z):
        """ Separation in transverse proper kpc corresponding to an
        arcminute at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        d : ndarray, or float if input scalar
          The distance in proper kpc corresponding to an arcmin at each
          input redshift.
        """
        return self.angular_diameter_distance(z) * 1.e3 * arcmin_in_radians


    def arcsec_per_kpc_comoving(self, z):
        """ Angular separation in arcsec corresponding to a comoving kpc
        at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        theta : ndarray, or float if input scalar
          The angular separation in arcsec corresponding to a comoving kpc
          at each input redshift.
        """
        return 1 / (self.comoving_transverse_distance(z) *
                    1.e3 * arcsec_in_radians)


    def arcsec_per_kpc_proper(self, z):
        """ Angular separation in arcsec corresponding to a proper kpc at
        redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        theta : ndarray, or float if input scalar
          The angular separation in arcsec corresponding to a proper kpc
          at each input redshift.
        """
        return 1 / (self.angular_diameter_distance(z) * 1.e3 *
                    arcsec_in_radians)


class LambdaCDM(FLRW):
    """FLRW cosmology with a cosmological constant and curvature.

    This has no additional attributes beyond those of FLRW.

    Examples
    --------
    >>> from astro.cosmology import LambdaCDM
    >>> cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """

    def __init__(self, H0, Om0, Ode0, Tcmb0=2.725, Neff=3.04,
                 name='LambdaCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        Ode0 : float
          Omega dark energy: density of the cosmological constant in units
          of the critical density at z=0.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, Ode0, Tcmb0, Neff, name=name)

    def w(self, z):
        """Returns dark energy equation of state at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        w : ndarray, or float if input scalar
          The dark energy equation of state

        Notes
        ------
        The dark energy equation of state is defined as
        :math:`w(z) = P(z)/\\rho(z)`, where :math:`P(z)` is the
        pressure at redshift z and :math:`\\rho(z)` is the density
        at redshift z, both in units where c=1.  Here this is
        :math:`w(z) = -1`.
        """

        return -1.0*np.ones_like(z)

    def de_density_scale(self, z):
        """ Evaluates the redshift dependence of the dark energy density.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        I : ndarray, or float if input scalar
          The scaling of the energy density of dark energy with redshift.

        Notes
        -----
        The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`,
        and in this case is given by :math:`I = 1`.
        """

        return np.ones_like(z)

    def efunc(self, z):
        """ Function used to calculate H(z), the Hubble parameter.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The redshift scaling of the Hubble consant.

        Notes
        -----
        The return value, E, is defined such that :math:`H(z) = H_0 E`.
        """

        if isiterable(z):
            z = np.asarray(z)

        #We override this because it takes a particularly simple
        # form for a cosmological constant
        Om0, Ode0, Ok0 = self._Om0, self._Ode0, self._Ok0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return np.sqrt(zp1**2 * ((Or0 * zp1 + Om0) * zp1 + Ok0) + Ode0)

    def inv_efunc(self, z):
        r""" Function used to calculate :math:`\frac{1}{H_z}`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The inverse redshift scaling of the Hubble constant.

        Notes
        -----
        The return value, E, is defined such that :math:`H_z = H_0 /
        E`.
        """

        if isiterable(z):
            z = np.asarray(z)
        Om0, Ode0, Ok0 = self._Om0, self._Ode0, self._Ok0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return 1.0 / np.sqrt(zp1**2 * ((Or0 * zp1 + Om0) * zp1 + Ok0) + Ode0)

class FlatLambdaCDM(LambdaCDM):
    """FLRW cosmology with a cosmological constant and no curvature.

    This has no additional attributes beyond those of FLRW.

    Examples
    --------
    >>> from astro.cosmology import FlatLambdaCDM
    >>> cosmo = FlatLambdaCDM(H0=70, Om0=0.3)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """
    def __init__(self, H0, Om0, Tcmb0=2.725, Neff=3.04, name='FlatLambdaCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, 0.0, Tcmb0, Neff, name=name)
        #Do some twiddling after the fact to get flatness
        self._Ode0 = 1.0 - self._Om0 - self._Ogamma0 - self._Onu0
        self._Ok0 = 0.0

    def __repr__(self):
        return "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g)" % \
            (self.name, self._H0, self._Om0, self._Ode0)


    def efunc(self, z):
        """ Function used to calculate H(z), the Hubble parameter.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The redshift scaling of the Hubble consant.

        Notes
        -----
        The return value, E, is defined such that :math:`H(z) = H_0 E`.
        """

        if isiterable(z):
            z = np.asarray(z)

        #We override this because it takes a particularly simple
        # form for a cosmological constant
        Om0, Ode0 = self._Om0, self._Ode0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return np.sqrt(zp1**3 * (Or0 * zp1 + Om0) + Ode0)

    def inv_efunc(self, z):
        r"""Function used to calculate :math:`\frac{1}{H_z}`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The inverse redshift scaling of the Hubble constant.

        Notes
        -----
        The return value, E, is defined such that :math:`H_z = H_0 / E`.
        """

        if isiterable(z):
            z = np.asarray(z)
        Om0, Ode0 = self._Om0, self._Ode0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return 1.0 / np.sqrt(zp1**3 * (Or0 * zp1 + Om0) + Ode0)

class wCDM(FLRW):
    """FLRW cosmology with a constant dark energy equation of state
    and curvature.

    This has one additional attribute beyond those of FLRW.

    Examples
    --------
    >>> from astro.cosmology import wCDM
    >>> cosmo = wCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """

    def __init__(self, H0, Om0, Ode0, w0=-1., Tcmb0=2.725,
                 Neff=3.04, name='wCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        Ode0 : float
          Omega dark energy: density of dark energy in units
          of the critical density at z=0.

        w0 : float
          Dark energy equation of state at all redshifts.
          This is pressure/density for dark energy in units where c=1.
          A cosmological constant has w0=-1.0.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, Ode0, Tcmb0, Neff, name=name)
        self._w0 = float(w0)

    def __repr__(self):
        return "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g, Ok0=%.3g, w0=%.3g)" % \
            (self.name, self._H0, self._Om0,
             self._Ode0, self._Ok0, self._w0)

    @property
    def w0(self):
        """ Dark energy equation of state"""
        return self._w0

    def w(self, z):
        """Returns dark energy equation of state at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        w : ndarray, or float if input scalar
          The dark energy equation of state

        Notes
        ------
        The dark energy equation of state is defined as
        :math:`w(z) = P(z)/\\rho(z)`, where :math:`P(z)` is the
        pressure at redshift z and :math:`\\rho(z)` is the density
        at redshift z, both in units where c=1.  Here this is
        :math:`w(z) = w_0`.
        """

        return self._w0*np.ones_like(z)

    def de_density_scale(self, z):
        """ Evaluates the redshift dependence of the dark energy density.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        I : ndarray, or float if input scalar
          The scaling of the energy density of dark energy with redshift.

        Notes
        -----
        The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`,
        and in this case is given by
        :math:`I = \\left(1 + z\\right)^{3\\left(1 + w_0\\right)}`
        """

        if isiterable(z):
            z = np.asarray(z)
        return (1.0 + z)**(3 * (1 + self._w0))

    def efunc(self, z):
        """ Function used to calculate H(z), the Hubble parameter.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The redshift scaling of the Hubble consant.

        Notes
        -----
        The return value, E, is defined such that :math:`H(z) = H_0 E`.
        """

        if isiterable(z):
            z = np.asarray(z)
        Om0, Ode0, Ok0, w0 = self._Om0, self._Ode, self._Ok0, self._w0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return np.sqrt(zp1**2 * ((Or0 * zp1 + Om0) * zp1 + Ok0) +
                       Ode0 * zp1**(3.0 * (1 + w0)))

    def inv_efunc(self, z):
        r""" Function used to calculate :math:`\frac{1}{H_z}`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The inverse redshift scaling of the Hubble constant.

        Notes
        -----
        The return value, E, is defined such that :math:`H_z = H_0 / E`.
        """

        if isiterable(z):
            z = np.asarray(z)
        Om0, Ode0, Ok0, w0 = self._Om0, self._Ode0, self._Ok0, self._w0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return 1.0 / np.sqrt(zp1**2 * ((Or0 * zp1 + Om0) * zp1 + Ok0) +
                             Ode0 * zp1**(3 * (1 + w0)))


class FlatwCDM(wCDM):
    """FLRW cosmology with a constant dark energy equation of state
    and no spatial curvature.

    This has one additional attribute beyond those of FLRW.

    Examples
    --------
    >>> from astro.cosmology import FlatwCDM
    >>> cosmo = FlatwCDM(H0=70, Om0=0.3, w0=-0.9)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """

    def __init__(self, H0, Om0, w0=-1., Tcmb0=2.725,
                 Neff=3.04, name='FlatwCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        w0 : float
          Dark energy equation of state at all redshifts.
          This is pressure/density for dark energy in units where c=1.
          A cosmological constant has w0=-1.0.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name: string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, 0.0, Tcmb0, Neff, name=name)
        self._w0 = float(w0)
        #Do some twiddling after the fact to get flatness
        self._Ode0 = 1.0 - self._Om0 - self._Ogamma0 - self._Onu0
        self._Ok0 = 0.0

    def __repr__(self):
        return "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g, w0=%.3g)" % \
            (self.name, self._H0, self._Om0,
             self._Ode0, self._w0)

    def efunc(self, z):
        """ Function used to calculate H(z), the Hubble parameter.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The redshift scaling of the Hubble consant.

        Notes
        -----
        The return value, E, is defined such that :math:`H(z) = H_0 E`.
        """

        if isiterable(z):
            z = np.asarray(z)
        Om0, Ode0, w0 = self._Om0, self._Ode, self._w0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return np.sqrt(zp1**3 * (Or0 * zp1 + Om0) +
                       Ode0 * zp1**(3.0 * (1 + w0)))

    def inv_efunc(self, z):
        r""" Function used to calculate :math:`\frac{1}{H_z}`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        E : ndarray, or float if input scalar
          The inverse redshift scaling of the Hubble constant.

        Notes
        -----
        The return value, E, is defined such that :math:`H_z = H_0 / E`.
        """

        if isiterable(z):
            z = np.asarray(z)
        Om0, Ode0, Ok0, w0 = self._Om0, self._Ode0, self._Ok0, self._w0
        Or0 = self._Ogamma0 + self._Onu0
        zp1 = 1.0 + z

        return 1.0 / np.sqrt(zp1**3 * (Or0 * zp1 + Om0) +
                             Ode0 * zp1**(3 * (1 + w0)))

class w0waCDM(FLRW):
    """FLRW cosmology with a CPL dark energy equation of state and curvature.

    The equation for the dark energy equation of state uses the
    CPL form as described in Chevallier & Polarski Int. J. Mod. Phys.
    D10, 213 (2001) and Linder PRL 90, 91301 (2003):
    :math:`w(z) = w_0 + w_a (1-a) = w_0 + w_a z / (1+z)`.

    Examples
    --------
    >>> from astro.cosmology import w0waCDM
    >>> cosmo = w0waCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9, wa=0.2)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """

    def __init__(self, H0, Om0, Ode0, w0=-1., wa=0., Tcmb0=2.725,
                 Neff=3.04, name='w0waCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        Ode0 : float
          Omega dark energy: density of dark energy in units
          of the critical density at z=0.

        w0 : float
          Dark energy equation of state at z=0 (a=1).
          This is pressure/density for dark energy in units where c=1.

        wa : float
          Negative derivative of the dark energy equation of state
          with respect to the scale factor.  A cosmological constant has
          w0=-1.0 and wa=0.0.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, Ode0, Tcmb0, Neff, name=name)
        self._w0 = float(w0)
        self._wa = float(wa)

    def __repr__(self):
        return "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g, Ok0=%.3g, w0=%.3g, wa=%.3g)" %\
            (self.name, self._H0, self._Om0, self._Ode0, self._Ok0,
             self._w0, self._wa)

    @property
    def w0(self):
        """ Dark energy equation of state at z=0"""
        return self._w0

    @property
    def wa(self):
        """ Negative derivative of dark energy equation of state w.r.t. a"""
        return self._wa

    def w(self, z):
        """Returns dark energy equation of state at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        w : ndarray, or float if input scalar
          The dark energy equation of state

        Notes
        ------
        The dark energy equation of state is defined as
        :math:`w(z) = P(z)/\\rho(z)`, where :math:`P(z)` is the
        pressure at redshift z and :math:`\\rho(z)` is the density
        at redshift z, both in units where c=1.  Here this is
        :math:`w(z) = w_0 + w_a (1 - a) = w_0 + w_a \\frac{z}{1+z}`.
        """

        if isiterable(z):
            z = np.asarray(z)

        return self._w0 + self._wa * z / (1.0 + z)

    def de_density_scale(self, z):
        """ Evaluates the redshift dependence of the dark energy density.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        I : ndarray, or float if input scalar
          The scaling of the energy density of dark energy with redshift.

        Notes
        -----
        The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`,
        and in this case is given by

        .. math::

          I = \\left(1 + z\\right)^{3 \\left(1 + w_0 + w_a\\right)}
          \exp \\left(-3 w_a \\frac{z}{1+z}\\right)

        """
        if isiterable(z):
            z = np.asarray(z)
        zp1 = 1.0 + z
        return zp1**(3 * (1 + self._w0 + self._wa)) * \
            exp(-3 * self._wa * z / zp1)

class Flatw0waCDM(w0waCDM):
    """FLRW cosmology with a CPL dark energy equation of state and no curvature.

    The equation for the dark energy equation of state uses the
    CPL form as described in Chevallier & Polarski Int. J. Mod. Phys.
    D10, 213 (2001) and Linder PRL 90, 91301 (2003):
    :math:`w(z) = w_0 + w_a (1-a) = w_0 + w_a z / (1+z)`.

    Examples
    --------
    >>> from astro.cosmology import Flatw0waCDM
    >>> cosmo = Flatw0waCDM(H0=70, Om0=0.3, w0=-0.9, wa=0.2)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """
    def __init__(self, H0, Om0, w0=-1., wa=0., Tcmb0=2.725,
                 Neff=3.04, name='Flatw0waCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        w0 : float
          Dark energy equation of state at z=0 (a=1).
          This is pressure/density for dark energy in units where c=1.

        wa : float
          Negative derivative of the dark energy equation of state
          with respect to the scale factor.  A cosmological constant has
          w0=-1.0 and wa=0.0.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, 0.0, Tcmb0, Neff, name=name)
        #Do some twiddling after the fact to get flatness
        self._Ode0 = 1.0 - self._Om0 - self._Ogamma0 - self._Onu0
        self._Ok0 = 0.0
        self._w0 = float(w0)
        self._wa = float(wa)

    def __repr__(self):
        return "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g, w0=%.3g, wa=%.3g)" %\
            (self.name, self._H0, self._Om0, self._Ode0, self._w0, self._wa)


class wpwaCDM(FLRW):
    """FLRW cosmology with a CPL dark energy equation of state, a pivot
    redshift, and curvature.

    The equation for the dark energy equation of state uses the
    CPL form as described in Chevallier & Polarski Int. J. Mod. Phys.
    D10, 213 (2001) and Linder PRL 90, 91301 (2003), but modified
    to have a pivot redshift as in the findings of the Dark Energy
    Task Force (Albrecht et al. arXiv:0901.0721 (2009)):
    :math:`w(a) = w_p + w_a (a_p - a) = w_p + w_a( 1/(1+zp) - 1/(1+z) )`.

    Examples
    --------
    >>> from astro.cosmology import wpwaCDM
    >>> cosmo = wpwaCDM(H0=70,Om0=0.3,Ode0=0.7,wp=-0.9,wa=0.2,zp=0.4)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """

    def __init__(self, H0, Om0, Ode0, wp=-1., wa=0., zp=0,
                 Tcmb0=2.725, Neff=3.04, name='wpwaCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        Ode0 : float
          Omega dark energy: density of dark energy in units
          of the critical density at z=0.

        wp : float
          Dark energy equation of state at the pivot redshift zp.
          This is pressure/density for dark energy in units where c=1.

        wa : float
          Negative derivative of the dark energy equation of state
          with respect to the scale factor.  A cosmological constant
          has w0=-1.0 and wa=0.0.

        zp : float
          Pivot redshift -- the redshift where w(z) = wp

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, Ode0, Tcmb0, Neff, name=name)
        self._wp = float(wp)
        self._wa = float(wa)
        self._zp = float(zp)

    def __repr__(self):
        str = "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g, Ok0=%.3g, wp=%.3g, "+\
            "wa=%.3g, zp=%.3g)"
        return str % (self.name, self._H0, self._Om0, self._Ode0,
                      self._Ok0, self._wp, self._wa, self._zp)

    @property
    def wp(self):
        """ Dark energy equation of state at the pivot redshift zp"""
        return self._wp

    @property
    def wa(self):
        """ Negative derivative of dark energy equation of state w.r.t. a"""
        return self._wa

    @property
    def zp(self):
        """ The pivot redshift, where w(z) = wp"""
        return self._zp

    def w(self, z):
        """Returns dark energy equation of state at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        w : ndarray, or float if input scalar
          The dark energy equation of state

        Notes
        ------
        The dark energy equation of state is defined as
        :math:`w(z) = P(z)/\\rho(z)`, where :math:`P(z)` is the
        pressure at redshift z and :math:`\\rho(z)` is the density
        at redshift z, both in units where c=1.  Here this is
        :math:`w(z) = w_p + w_a (a_p - a)` where :math:`a = 1/1+z`
        and :math:`a_p = 1 / 1 + z_p`.
        """

        if isiterable(z):
            z = np.asarray(z)

        apiv = 1.0 / (1.0 + self._zp)
        return self._wp + self._wa * (apiv - 1.0 / (1. + z))

    def de_density_scale(self, z):
        """ Evaluates the redshift dependence of the dark energy density.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        I : ndarray, or float if input scalar
          The scaling of the energy density of dark energy with redshift.

        Notes
        -----
        The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`,
        and in this case is given by

        .. math::

          a_p = \\frac{1}{1 + z_p}

          I = \\left(1 + z\\right)^{3 \\left(1 + w_p + a_p w_a\\right)}
          \exp \\left(-3 w_a \\frac{z}{1+z}\\right)
        """

        if isiterable(z):
            z = np.asarray(z)
        zp1 = 1.0 + z
        apiv = 1.0 / (1.0 + self._zp)
        return zp1**(3 * (1 + self._wp + apiv * self._wa)) * \
            exp(-3 * self._wa * z / zp1)

class w0wzCDM(FLRW):
    """FLRW cosmology with a variable dark energy equation of state
    and curvature.

    The equation for the dark energy equation of state uses the
    simple form: :math:`w(z) = w_0 + w_z z`.

    This form is not recommended for z > 1.

    Examples
    --------
    >>> from astro.cosmology import wawzCDM
    >>> cosmo = wawzCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9, wz=0.2)

    The comoving distance in Mpc at redshift z:

    >>> dc = cosmo.comoving_distance(z)
    """

    def __init__(self, H0, Om0, Ode0, w0=-1., wz=0., Tcmb0=2.725,
                 Neff=3.04, name='w0wzCDM'):
        """ Initializer.

        Parameters
        ----------
        H0 : float
          Hubble constant in [km/sec/Mpc] at z=0

        Om0 : float
          Omega matter: density of non-relativistic matter in units
          of the critical density at z=0.

        Ode0 : float
          Omega dark energy: density of dark energy in units
          of the critical density at z=0.

        Ok0 : float
          Omega curvature: equivalent curvature density in units
          of the critical density at z=0.

        w0 : float
          Dark energy equation of state at z=0.
          This is pressure/density for dark energy in units where c=1.
          A cosmological constant has w0=-1.0.

        wz : float
          Derivative of the dark energy equation of state with respect to z.

        Tcmb0 : float
          Temperature of the CMB in Kelvin at z=0 (def: 2.725)

        Neff : float
          Effective number of Neutrino species (def: 3.04)

        name : string
          Optional name for this cosmological object.
        """
        FLRW.__init__(self, H0, Om0, Ode0, Tcmb0, Neff, name=name)
        self._w0 = float(w0)
        self._wz = float(wz)

    def __repr__(self):
        return "%s(H0=%.3g, Om0=%.3g, Ode0=%.3g, w0=%.3g, wz=%.3g)" % \
            (self.name, self._H0, self._Om0, self._Ode0, self._w0, self._wz)

    @property
    def w0(self):
        """ Dark energy equation of state at z=0"""
        return self._w0

    @property
    def wz(self):
        """ Derivative of the dark energy equation of state w.r.t. z"""
        return self._wz

    def w(self, z):
        """Returns dark energy equation of state at redshift `z`.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        w : ndarray, or float if input scalar
          The dark energy equation of state

        Notes
        ------
        The dark energy equation of state is defined as
        :math:`w(z) = P(z)/\\rho(z)`, where :math:`P(z)` is the
        pressure at redshift z and :math:`\\rho(z)` is the density
        at redshift z, both in units where c=1.  Here this is given by
        :math:`w(z) = w_0 + w_z z`.
        """

        if isiterable(z):
            z = np.asarray(z)

        return self._w0 + self._wz * z

    def de_density_scale(self, z):
        """ Evaluates the redshift dependence of the dark energy density.

        Parameters
        ----------
        z : array_like
          Input redshifts.

        Returns
        -------
        I : ndarray, or float if input scalar
          The scaling of the energy density of dark energy with redshift.

        Notes
        -----
        The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`,
        and in this case is given by

        .. math::

          I = \\left(1 + z\\right)^{3 \\left(1 + w_0 - w_z\\right)}
          \exp \\left(-3 w_z z\\right)
        """

        if isiterable(z):
            z = np.asarray(z)
        zp1 = 1.0 + z
        return zp1**(3 * (1 + self._w0 - self._wz)) * exp(-3 * self._wz * z)

# Pre-defined cosmologies. This loops over the parameter sets in the
# parameters module and creates a LambdaCDM or FlatLambdaCDM instance
# with the same name as the parameter set in the current module's namespace.
# Note this assumes all the cosmologies in parameters are LambdaCDM,
# which is true at least as of this writing.

for key in parameters.available:
    par = getattr(parameters, key)
    if par['flat']:
        cosmo = FlatLambdaCDM(par['H0'], par['Om0'], Tcmb0=par['Tcmb0'],
                              Neff=par['Neff'], name=key)
    else:
        cosmo = LambdaCDM(par['H0'], par['Om0'], par['Ode0'],
                          Tcmb0=par['Tcmb0'], Neff=par['Neff'],
                          m_nu=par['m_nu'], name=key)
    cosmo.__doc__ = "%s cosmology\n\n(from %s)" % (key, par['reference'])
    setattr(sys.modules[__name__], key, cosmo)

# don't leave these variables floating around in the namespace
del key, par, cosmo

#########################################################################
# The variable below contains the current cosmology used by the
# convenience functions below and by other astropy functions if no
# cosmology is explicitly given. It can be set with set_current() and
# should be accessed using get_current().
#########################################################################


def get_cosmology_from_string(arg):
    """ Return a cosmology instance from a string.
    """
    if arg == 'no_default':
        cosmo = None
    else:
        try:
            cosmo = getattr(sys.modules[__name__], arg)
        except AttributeError:
            s = "Unknown cosmology '%s'. Valid cosmologies:\n%s" % (
                    arg, parameters.available)
            raise ValueError(s)
    return cosmo

_current = get_cosmology_from_string(DEFAULT_COSMOLOGY())


def get_current():
    """ Get the current cosmology.

    If no current has been set, the WMAP7 comology is returned and a
    warning is given.

    Returns
    -------
    cosmo : `Cosmology` instance

    See Also
    --------
    set_current : sets the current cosmology
    """
    if _current is None:
        warnings.warn('No default cosmology has been specified, '
                      'using 7-year WMAP.')
        return WMAP7

    return _current


def set_current(cosmo):
    """ Set the current cosmology.

    Call this with an empty string ('') to get a list of the strings
    that map to available pre-defined cosmologies.

    .. warning::
        `set_current` is the only way to change the current cosmology at
        runtime! The current cosmology can also be read from an option
        in the astropy configuration file when astropy.cosmology is first
        imported. However, any subsequent changes to the cosmology
        configuration option using `ConfigurationItem.set
        <astropy.config.configuration.ConfigurationItem.set>` at run-time
        will not update the current cosmology.

    Parameters
    ----------
    cosmo : str or `Cosmology` instance
      The cosmology to use.



    See Also
    --------
    get_current : returns the currently-set cosmology
    """
    global _current
    if isinstance(cosmo, basestring):
        _current = get_cosmology_from_string(cosmo)
    elif isinstance(cosmo, Cosmology):
        _current = cosmo
    else:
        raise ValueError(
            "Argument must be a string or cosmology instance. Valid strings:"
            "\n%s" % parameters.available)
