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# Source code for astropy.units.equivalencies

    # Licensed under a 3-clause BSD style license - see LICENSE.rst

    """
    A set of standard astronomical equivalencies.
    """

    from __future__ import (absolute_import, division, print_function,
                            unicode_literals)

    from ..constants import si as _si
    from . import si
    from . import cgs
    from . import astrophys

    __all__ = ['parallax', 'spectral', 'spectral_density', 'doppler_radio',
               'doppler_optical', 'doppler_relativistic', 'mass_energy',
               'brightness_temperature', 'dimensionless_angles']

    def dimensionless_angles():
        """Allow angles to be equivalent to dimensionless (with 1 rad = 1 m/m = 1).

        It is special compared to other equivalency pairs in that it
        allows this independent of the power to which the angle is raised,
        and indepedent of whether it is part of a more complicated unit.
        """
        return [(si.radian, None)]

    def parallax():
        """
        Returns a list of equivalence pairs that handle the conversion
        between parallax angle and distance.
        """
        return [
            (si.arcsecond, astrophys.parsec, lambda x: 1. / x)
        ]

    def spectral():
        """
        Returns a list of equivalence pairs that handle spectral
        wavelength, wave number, frequency, and energy equivalences.

        Allows conversions between wavelength units, wave number units,
        frequency units, and energy units as they relate to light.

        """
        hc = _si.h.value * _si.c.value
        inv_m = si.m ** -1
        return [
            (si.m, si.Hz, lambda x: _si.c.value / x),
            (si.m, si.J, lambda x: hc / x),
            (si.m, inv_m, lambda x: 1.0 / x),
            (si.Hz, si.J, lambda x: _si.h.value * x, lambda x: x / _si.h.value),
            (si.Hz, inv_m, lambda x: x / _si.c.value, lambda x: _si.c.value * x),
            (si.J, inv_m, lambda x: x / hc, lambda x: hc * x)
        ]

    def spectral_density(wav, factor=None):
        """
        Returns a list of equivalence pairs that handle spectral density
        with regard to wavelength and frequency.

        Parameters
        ----------
        wav : Quantity
            Quantity associated with values being converted
            (e.g., wavelength or frequency).

        Notes
        -----
        The ``factor`` argument is left for backward-compatibility with the syntax
        ``spectral_density(unit, factor)`` but users are encouraged to use
        ``spectral_density(factor * unit)`` instead.

        """
        from .core import UnitBase

        if isinstance(wav, UnitBase):
            if factor is None:
                raise ValueError(
                    'If ``wav`` is specified as a unit, ``factor`` should be set')
            wav = factor * wav   # Convert to Quantity

        c_Aps = _si.c.to(si.AA / si.s).value  # Angstrom/s
        h_cgs = _si.h.cgs.value  # erg * s
        hc = c_Aps * h_cgs

        fla = cgs.erg / si.angstrom / si.cm ** 2 / si.s
        fnu = cgs.erg / si.Hz / si.cm ** 2 / si.s
        nufnu = cgs.erg / si.cm ** 2 / si.s
        lafla = nufnu
        photlam = astrophys.photon / (si.cm ** 2 * si.s * si.AA)
        photnu = astrophys.photon / (si.cm ** 2 * si.s * si.Hz)

        def converter(x):
            return x * (wav.to(si.AA, spectral()).value ** 2 / c_Aps)

        def iconverter(x):
            return x / (wav.to(si.AA, spectral()).value ** 2 / c_Aps)

        def converter_fnu_nufnu(x):
            return x * wav.to(si.Hz, spectral()).value

        def iconverter_fnu_nufnu(x):
            return x / wav.to(si.Hz, spectral()).value

        def converter_fla_lafla(x):
            return x * wav.to(si.AA, spectral()).value

        def iconverter_fla_lafla(x):
            return x / wav.to(si.AA, spectral()).value

        def converter_photlam_fla(x):
            return hc * x / wav.to(si.AA, spectral()).value

        def iconverter_photlam_fla(x):
            return x * wav.to(si.AA, spectral()).value / hc

        def converter_photlam_fnu(x):
            return h_cgs * x * wav.to(si.AA, spectral()).value

        def iconverter_photlam_fnu(x):
            return x / (wav.to(si.AA, spectral()).value * h_cgs)

        def converter_photlam_photnu(x):
            return x * wav.to(si.AA, spectral()).value ** 2 / c_Aps

        def iconverter_photlam_photnu(x):
            return c_Aps * x / wav.to(si.AA, spectral()).value ** 2

        converter_photnu_fnu = converter_photlam_fla

        iconverter_photnu_fnu = iconverter_photlam_fla

        def converter_photnu_fla(x):
            return x * hc * c_Aps / wav.to(si.AA, spectral()).value ** 3

        def iconverter_photnu_fla(x):
            return x * wav.to(si.AA, spectral()).value ** 3 / (hc * c_Aps)

        return [
            (si.AA, fnu, converter, iconverter),
            (fla, fnu, converter, iconverter),
            (si.AA, si.Hz, converter, iconverter),
            (fla, si.Hz, converter, iconverter),
            (fnu, nufnu, converter_fnu_nufnu, iconverter_fnu_nufnu),
            (fla, lafla, converter_fla_lafla, iconverter_fla_lafla),
            (photlam, fla, converter_photlam_fla, iconverter_photlam_fla),
            (photlam, fnu, converter_photlam_fnu, iconverter_photlam_fnu),
            (photlam, photnu, converter_photlam_photnu, iconverter_photlam_photnu),
            (photnu, fnu, converter_photnu_fnu, iconverter_photnu_fnu),
            (photnu, fla, converter_photnu_fla, iconverter_photnu_fla)
        ]

    def doppler_radio(rest):
        r"""
        Return the equivalency pairs for the radio convention for velocity.

        The radio convention for the relation between velocity and frequency is:

        :math:`V = c \frac{f_0 - f}{f_0}  ;  f(V) = f_0 ( 1 - V/c )`

        Parameters
        ----------
        rest : Quantity
            Any quantity supported by the standard spectral equivalencies
            (wavelength, energy, frequency, wave number).

        References
        ----------
        `NRAO site defining the conventions <http://www.gb.nrao.edu/~fghigo/gbtdoc/doppler.html>`_

        Examples
        --------
        >>> import astropy.units as u
        >>> CO_restfreq = 115.27120*u.GHz  # rest frequency of 12 CO 1-0 in GHz
        >>> radio_CO_equiv = u.doppler_radio(CO_restfreq)
        >>> measured_freq = 115.2832*u.GHz
        >>> radio_velocity = measured_freq.to(u.km/u.s, equivalencies=radio_CO_equiv)
        >>> radio_velocity
        <Quantity -31.2090920889... km / s>
        """

        ckms = _si.c.to('km/s').value

        def to_vel_freq(x):
            restfreq = rest.to(si.Hz, equivalencies=spectral()).value
            return (restfreq-x) / (restfreq) * ckms

        def from_vel_freq(x):
            restfreq = rest.to(si.Hz, equivalencies=spectral()).value
            voverc = x/ckms
            return restfreq * (1-voverc)

        def to_vel_wav(x):
            restwav = rest.to(si.AA, spectral()).value
            return (x-restwav) / (x) * ckms

        def from_vel_wav(x):
            restwav = rest.to(si.AA, spectral()).value
            return restwav * ckms / (ckms-x)

        def to_vel_en(x):
            resten = rest.to(si.eV, equivalencies=spectral()).value
            return (resten-x) / (resten) * ckms

        def from_vel_en(x):
            resten = rest.to(si.eV, equivalencies=spectral()).value
            voverc = x/ckms
            return resten * (1-voverc)

        return [(si.Hz, si.km/si.s, to_vel_freq, from_vel_freq),
                (si.AA, si.km/si.s, to_vel_wav, from_vel_wav),
                (si.eV, si.km/si.s, to_vel_en, from_vel_en),
                ]

    def doppler_optical(rest):
        r"""
        Return the equivalency pairs for the optical convention for velocity.

        The optical convention for the relation between velocity and frequency is:

        :math:`V = c \frac{f_0 - f}{f  }  ;  f(V) = f_0 ( 1 + V/c )^{-1}`

        Parameters
        ----------
        rest : Quantity
            Any quantity supported by the standard spectral equivalencies
            (wavelength, energy, frequency, wave number).

        References
        ----------
        `NRAO site defining the conventions <http://www.gb.nrao.edu/~fghigo/gbtdoc/doppler.html>`_

        Examples
        --------
        >>> import astropy.units as u
        >>> CO_restfreq = 115.27120*u.GHz  # rest frequency of 12 CO 1-0 in GHz
        >>> optical_CO_equiv = u.doppler_optical(CO_restfreq)
        >>> measured_freq = 115.2832*u.GHz
        >>> optical_velocity = measured_freq.to(u.km/u.s, equivalencies=optical_CO_equiv)
        >>> optical_velocity
        <Quantity -31.205843488... km / s>
        """

        ckms = _si.c.to('km/s').value

        def to_vel_freq(x):
            restfreq = rest.to(si.Hz, equivalencies=spectral()).value
            return ckms * (restfreq-x) / x

        def from_vel_freq(x):
            restfreq = rest.to(si.Hz, equivalencies=spectral()).value
            voverc = x/ckms
            return restfreq / (1+voverc)

        def to_vel_wav(x):
            restwav = rest.to(si.AA, spectral()).value
            return ckms * (x/restwav-1)

        def from_vel_wav(x):
            restwav = rest.to(si.AA, spectral()).value
            voverc = x/ckms
            return restwav * (1+voverc)

        def to_vel_en(x):
            resten = rest.to(si.eV, equivalencies=spectral()).value
            return ckms * (resten-x) / x

        def from_vel_en(x):
            resten = rest.to(si.eV, equivalencies=spectral()).value
            voverc = x/ckms
            return resten / (1+voverc)

        return [(si.Hz, si.km/si.s, to_vel_freq, from_vel_freq),
                (si.AA, si.km/si.s, to_vel_wav, from_vel_wav),
                (si.eV, si.km/si.s, to_vel_en, from_vel_en),
                ]

    def doppler_relativistic(rest):
        r"""
        Return the equivalency pairs for the relativistic convention for velocity.

        The full relativistic convention for the relation between velocity and frequency is:

        :math:`V = c \frac{f_0^2 - f^2}{f_0^2 + f^2} ;  f(V) = f_0 \frac{\left(1 - (V/c)^2\right)^{1/2}}{(1+V/c)}`

        Parameters
        ----------
        rest : Quantity
            Any quantity supported by the standard spectral equivalencies
            (wavelength, energy, frequency, wave number).

        References
        ----------
        `NRAO site defining the conventions <http://www.gb.nrao.edu/~fghigo/gbtdoc/doppler.html>`_

        Examples
        --------
        >>> import astropy.units as u
        >>> CO_restfreq = 115.27120*u.GHz  # rest frequency of 12 CO 1-0 in GHz
        >>> relativistic_CO_equiv = u.doppler_relativistic(CO_restfreq)
        >>> measured_freq = 115.2832*u.GHz
        >>> relativistic_velocity = measured_freq.to(u.km/u.s, equivalencies=relativistic_CO_equiv)
        >>> relativistic_velocity
        <Quantity -31.207467619...
        >>> measured_velocity = 1250 * u.km/u.s
        >>> relativistic_frequency = measured_velocity.to(u.GHz, equivalencies=relativistic_CO_equiv)
        >>> relativistic_frequency
        <Quantity 114.7915686...
        >>> relativistic_wavelength = measured_velocity.to(u.mm, equivalencies=relativistic_CO_equiv)
        >>> relativistic_wavelength
        <Quantity 2.6116243681...
        """

        ckms = _si.c.to('km/s').value

        def to_vel_freq(x):
            restfreq = rest.to(si.Hz, equivalencies=spectral()).value
            return (restfreq**2-x**2) / (restfreq**2+x**2) * ckms

        def from_vel_freq(x):
            restfreq = rest.to(si.Hz, equivalencies=spectral()).value
            voverc = x/ckms
            return restfreq * ((1-voverc) / (1+(voverc)))**0.5

        def to_vel_wav(x):
            restwav = rest.to(si.AA, spectral()).value
            return (x**2-restwav**2) / (restwav**2+x**2) * ckms

        def from_vel_wav(x):
            restwav = rest.to(si.AA, spectral()).value
            voverc = x/ckms
            return restwav * ((1+voverc) / (1-voverc))**0.5

        def to_vel_en(x):
            resten = rest.to(si.eV, spectral()).value
            return (resten**2-x**2) / (resten**2+x**2) * ckms

        def from_vel_en(x):
            resten = rest.to(si.eV, spectral()).value
            voverc = x/ckms
            return resten * ((1-voverc) / (1+(voverc)))**0.5

        return [(si.Hz, si.km/si.s, to_vel_freq, from_vel_freq),
                (si.AA, si.km/si.s, to_vel_wav, from_vel_wav),
                (si.eV, si.km/si.s, to_vel_en, from_vel_en),
                ]

    def mass_energy():
        """
        Returns a list of equivalence pairs that handle the conversion
        between mass and energy.
        """

        return [(si.kg, si.J, lambda x: x * _si.c.value ** 2,
                 lambda x: x / _si.c.value ** 2),
                (si.kg / si.m ** 2, si.J / si.m ** 2 ,
                 lambda x: x * _si.c.value ** 2,
                 lambda x: x / _si.c.value ** 2),
                (si.kg / si.m ** 3, si.J / si.m ** 3 ,
                 lambda x: x * _si.c.value ** 2,
                 lambda x: x / _si.c.value ** 2),
                (si.kg / si.s, si.J / si.s , lambda x: x * _si.c.value ** 2,
                 lambda x: x / _si.c.value ** 2),
        ]

    def brightness_temperature(beam_area, disp):
        """
        "Antenna Gain" or "sensitivity" equivalency: Defines the conversion between
        Jy/beam and "brightness temperature", :math:`T_B`, in Kelvins.  This is a
        unit very commonly used in radio astronomy.  Typically, the gain refers to
        the conversion between corrected antenna temperature :math:`T_A^*` and flux
        density.  See, e.g., "Tools of Radio Astronomy" (Wilson 2009) eqn 8.16 and
        eqn 8.19 (these pages are available on `google books
        <http://books.google.com/books?id=9KHw6R8rQEMC&pg=PA179&source=gbs_toc_r&cad=4#v=onepage&q&f=false>`__).

        :math:`T_B \equiv S_\\nu / \left(2 k \\nu^2 / c^2 \\right)`

        However, the beam area is essential for this computation: the brighntess
        temperature is inversely proportional to the beam area

        Parameters
        ----------
        beam_area : Beam Area equivalent
            Beam area in angular units, i.e. steradian equivalent
        disp : `Quantity` with spectral units
            The observed `spectral` equivalent `Unit` (e.g., frequency or
            wavelength)

        Examples
        --------
        Arecibo C-band beam gain ~ 7 K/Jy::

            >>> import numpy as np
            >>> from astropy import units as u
            >>> beam_area = np.pi*(50*u.arcsec)**2
            >>> freq = 5*u.GHz
            >>> u.Jy.to(u.K, equivalencies=u.brightness_temperature(beam_area,freq))
            7.052588858...
            >>> (1*u.Jy).to(u.K, equivalencies=u.brightness_temperature(beam_area,freq))
            <Quantity 7.05258...

        VLA synthetic beam::

            >>> beam_area = np.pi*(15*u.arcsec)**2
            >>> freq = 5*u.GHz
            >>> u.Jy.to(u.K, equivalencies=u.brightness_temperature(beam_area,freq))
            78.36209843...
        """
        beam = beam_area.to(si.sr).value
        nu = disp.to(si.GHz, spectral())

        def convert_Jy_to_K(x_jybm):
            factor = (2 * _si.k_B * si.K * nu**2 / _si.c**2).to(astrophys.Jy).value
            return (x_jybm / beam / factor)

        def convert_K_to_Jy(x_K):
            factor = (astrophys.Jy / (2 * _si.k_B * nu**2 / _si.c**2)).to(si.K).value
            return (x_K * beam / factor)

        return [(astrophys.Jy, si.K, convert_Jy_to_K, convert_K_to_Jy)]