# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals

import numpy as np
from .. import units as u
from ..extern.six.moves import range

__doctest_skip__ = ['wcs_to_celestial_frame']

__all__ = ['add_stokes_axis_to_wcs',
           'custom_frame_mappings',
           'wcs_to_celestial_frame', 'proj_plane_pixel_scales',
           'proj_plane_pixel_area', 'is_proj_plane_distorted',
           'non_celestial_pixel_scales', 'skycoord_to_pixel',
           'pixel_to_skycoord']


def add_stokes_axis_to_wcs(wcs, add_before_ind):
    """
    Add a new Stokes axis that is uncorrelated with any other axes.

    Parameters
    ----------
    wcs : `~astropy.wcs.WCS`
        The WCS to add to
    add_before_ind : int
        Index of the WCS to insert the new Stokes axis in front of.
        To add at the end, do add_before_ind = wcs.wcs.naxis
        The beginning is at position 0.

    Returns
    -------
    A new `~astropy.wcs.WCS` instance with an additional axis
    """

    inds = [i + 1 for i in range(wcs.wcs.naxis)]
    inds.insert(add_before_ind, 0)
    newwcs = wcs.sub(inds)
    newwcs.wcs.ctype[add_before_ind] = 'STOKES'
    newwcs.wcs.cname[add_before_ind] = 'STOKES'
    return newwcs


def _wcs_to_celestial_frame_builtin(wcs):

    from ..coordinates import FK4, FK4NoETerms, FK5, ICRS, Galactic
    from ..time import Time
    from . import WCSSUB_CELESTIAL

    # Keep only the celestial part of the axes
    wcs = wcs.sub([WCSSUB_CELESTIAL])

    if wcs.wcs.lng == -1 or wcs.wcs.lat == -1:
        return None

    radesys = wcs.wcs.radesys

    if np.isnan(wcs.wcs.equinox):
        equinox = None
    else:
        equinox = wcs.wcs.equinox

    xcoord = wcs.wcs.ctype[0][:4]
    ycoord = wcs.wcs.ctype[1][:4]

    # Apply logic from FITS standard to determine the default radesys
    if radesys == '' and xcoord == 'RA--' and ycoord == 'DEC-':
        if equinox is None:
            radesys = "ICRS"
        elif equinox < 1984.:
            radesys = "FK4"
        else:
            radesys = "FK5"

    if radesys == 'FK4':
        if equinox is not None:
            equinox = Time(equinox, format='byear')
        frame = FK4(equinox=equinox)
    elif radesys == 'FK4-NO-E':
        if equinox is not None:
            equinox = Time(equinox, format='byear')
        frame = FK4NoETerms(equinox=equinox)
    elif radesys == 'FK5':
        if equinox is not None:
            equinox = Time(equinox, format='jyear')
        frame = FK5(equinox=equinox)
    elif radesys == 'ICRS':
        frame = ICRS()
    else:
        if xcoord == 'GLON' and ycoord == 'GLAT':
            frame = Galactic()
        else:
            frame = None

    return frame


WCS_FRAME_MAPPINGS = [[_wcs_to_celestial_frame_builtin]]


class custom_frame_mappings(object):
    def __init__(self, mappings=[]):
        if hasattr(mappings, '__call__'):
            mappings = [mappings]
        WCS_FRAME_MAPPINGS.append(mappings)

    def __enter__(self):
        pass

    def __exit__(self, type, value, tb):
        WCS_FRAME_MAPPINGS.pop()


def wcs_to_celestial_frame(wcs):
    """
    For a given WCS, return the coordinate frame that matches the celestial
    component of the WCS.

    Parameters
    ----------
    wcs : :class:`~astropy.wcs.WCS` instance
        The WCS to find the frame for

    Returns
    -------
    frame : :class:`~astropy.coordinates.baseframe.BaseCoordinateFrame` subclass instance
        An instance of a :class:`~astropy.coordinates.baseframe.BaseCoordinateFrame`
        subclass instance that best matches the specified WCS.

    Notes
    -----

    To extend this function to frames not defined in astropy.coordinates, you
    can write your own function which should take a :class:`~astropy.wcs.WCS`
    instance and should return either an instance of a frame, or `None` if no
    matching frame was found. You can register this function temporarily with::

        >>> from astropy.wcs.utils import wcs_to_celestial_frame, custom_frame_mappings
        >>> with custom_frame_mappings(my_function):
        ...     wcs_to_celestial_frame(...)

    """
    for mapping_set in WCS_FRAME_MAPPINGS:
        for func in mapping_set:
            frame = func(wcs)
            if frame is not None:
                return frame
    raise ValueError("Could not determine celestial frame corresponding to "
                     "the specified WCS object")


def proj_plane_pixel_scales(wcs):
    """
    For a WCS returns pixel scales along each axis of the image pixel at
    the ``CRPIX`` location once it is projected onto the
    "plane of intermediate world coordinates" as defined in
    `Greisen & Calabretta 2002, A&A, 395, 1061 <http://adsabs.harvard.edu/abs/2002A%26A...395.1061G>`_.

    .. note::
        This function is concerned **only** about the transformation
        "image plane"->"projection plane" and **not** about the
        transformation "celestial sphere"->"projection plane"->"image plane".
        Therefore, this function ignores distortions arising due to
        non-linear nature of most projections.

    .. note::
        In order to compute the scales corresponding to celestial axes only,
        make sure that the input `~astropy.wcs.WCS` object contains
        celestial axes only, e.g., by passing in the
        `~astropy.wcs.WCS.celestial` WCS object.

    Parameters
    ----------
    wcs : `~astropy.wcs.WCS`
        A world coordinate system object.

    Returns
    -------
    scale : `~numpy.ndarray`
        A vector (`~numpy.ndarray`) of projection plane increments
        corresponding to each pixel side (axis). The units of the returned
        results are the same as the units of `~astropy.wcs.Wcsprm.cdelt`,
        `~astropy.wcs.Wcsprm.crval`, and `~astropy.wcs.Wcsprm.cd` for
        the celestial WCS and can be obtained by inquiring the value
        of `~astropy.wcs.Wcsprm.cunit` property of the input
        `~astropy.wcs.WCS` WCS object.

    See Also
    --------
    astropy.wcs.utils.proj_plane_pixel_area

    """
    return np.sqrt((wcs.pixel_scale_matrix**2).sum(axis=0, dtype=np.float))


def proj_plane_pixel_area(wcs):
    """
    For a **celestial** WCS (see `astropy.wcs.WCS.celestial`) returns pixel
    area of the image pixel at the ``CRPIX`` location once it is projected
    onto the "plane of intermediate world coordinates" as defined in
    `Greisen & Calabretta 2002, A&A, 395, 1061 <http://adsabs.harvard.edu/abs/2002A%26A...395.1061G>`_.

    .. note::
        This function is concerned **only** about the transformation
        "image plane"->"projection plane" and **not** about the
        transformation "celestial sphere"->"projection plane"->"image plane".
        Therefore, this function ignores distortions arising due to
        non-linear nature of most projections.

    .. note::
        In order to compute the area of pixels corresponding to celestial
        axes only, this function uses the `~astropy.wcs.WCS.celestial` WCS
        object of the input ``wcs``.  This is different from the
        `~astropy.wcs.utils.proj_plane_pixel_scales` function
        that computes the scales for the axes of the input WCS itself.

    Parameters
    ----------
    wcs : `~astropy.wcs.WCS`
        A world coordinate system object.

    Returns
    -------
    area : float
        Area (in the projection plane) of the pixel at ``CRPIX`` location.
        The units of the returned result are the same as the units of
        the `~astropy.wcs.Wcsprm.cdelt`, `~astropy.wcs.Wcsprm.crval`,
        and `~astropy.wcs.Wcsprm.cd` for the celestial WCS and can be
        obtained by inquiring the value of `~astropy.wcs.Wcsprm.cunit`
        property of the `~astropy.wcs.WCS.celestial` WCS object.

    Raises
    ------
    ValueError
        Pixel area is defined only for 2D pixels. Most likely the
        `~astropy.wcs.Wcsprm.cd` matrix of the `~astropy.wcs.WCS.celestial`
        WCS is not a square matrix of second order.

    Notes
    -----

    Depending on the application, square root of the pixel area can be used to
    represent a single pixel scale of an equivalent square pixel
    whose area is equal to the area of a generally non-square pixel.

    See Also
    --------
    astropy.wcs.utils.proj_plane_pixel_scales

    """
    psm = wcs.celestial.pixel_scale_matrix
    if psm.shape != (2, 2):
        raise ValueError("Pixel area is defined only for 2D pixels.")
    return np.abs(np.linalg.det(psm))


def is_proj_plane_distorted(wcs, maxerr=1.0e-5):
    r"""
    For a WCS returns `False` if square image (detector) pixels stay square
    when projected onto the "plane of intermediate world coordinates"
    as defined in
    `Greisen & Calabretta 2002, A&A, 395, 1061 <http://adsabs.harvard.edu/abs/2002A%26A...395.1061G>`_.
    It will return `True` if transformation from image (detector) coordinates
    to the focal plane coordinates is non-orthogonal or if WCS contains
    non-linear (e.g., SIP) distortions.

    .. note::
        Since this function is concerned **only** about the transformation
        "image plane"->"focal plane" and **not** about the transformation
        "celestial sphere"->"focal plane"->"image plane",
        this function ignores distortions arising due to non-linear nature
        of most projections.

    Let's denote by *C* either the original or the reconstructed
    (from ``PC`` and ``CDELT``) CD matrix. `is_proj_plane_distorted`
    verifies that the transformation from image (detector) coordinates
    to the focal plane coordinates is orthogonal using the following
    check:

    .. math::
        \left \| \frac{C \cdot C^{\mathrm{T}}}
        {| det(C)|} - I \right \|_{\mathrm{max}} < \epsilon .

    Parameters
    ----------
    wcs : `~astropy.wcs.WCS`
        World coordinate system object

    maxerr : float, optional
        Accuracy to which the CD matrix, **normalized** such
        that :math:`|det(CD)|=1`, should be close to being an
        orthogonal matrix as described in the above equation
        (see :math:`\epsilon`).

    Returns
    -------
    distorted : bool
        Returns `True` if focal (projection) plane is distorted and `False`
        otherwise.

    """
    cwcs = wcs.celestial
    return (not _is_cd_orthogonal(cwcs.pixel_scale_matrix, maxerr) or
            _has_distortion(cwcs))


def _is_cd_orthogonal(cd, maxerr):
    shape = cd.shape
    if not (len(shape) == 2 and shape[0] == shape[1]):
        raise ValueError("CD (or PC) matrix must be a 2D square matrix.")

    pixarea = np.abs(np.linalg.det(cd))
    if (pixarea == 0.0):
        raise ValueError("CD (or PC) matrix is singular.")

    # NOTE: Technically, below we should use np.dot(cd, np.conjugate(cd.T))
    # However, I am not aware of complex CD/PC matrices...
    I = np.dot(cd, cd.T) / pixarea
    cd_unitary_err = np.amax(np.abs(I - np.eye(shape[0])))

    return (cd_unitary_err < maxerr)


def non_celestial_pixel_scales(inwcs):
    """
    Calculate the pixel scale along each axis of a non-celestial WCS,
    for example one with mixed spectral and spatial axes.

    Parameters
    ----------
    inwcs : `~astropy.wcs.WCS`
        The world coordinate system object.

    Returns
    -------
    scale : `numpy.ndarray`
        The pixel scale along each axis.
    """

    if inwcs.is_celestial:
        raise ValueError("WCS is celestial, use celestial_pixel_scales instead")

    pccd = inwcs.pixel_scale_matrix

    if np.allclose(np.extract(1-np.eye(*pccd.shape), pccd), 0):
        return np.abs(np.diagonal(pccd))*u.deg
    else:
        raise ValueError("WCS is rotated, cannot determine consistent pixel scales")


def _has_distortion(wcs):
    """
    `True` if contains any SIP or image distortion components.
    """
    return any(getattr(wcs, dist_attr) is not None
               for dist_attr in ['cpdis1', 'cpdis2', 'det2im1', 'det2im2', 'sip'])


# TODO: in future, we should think about how the following two functions can be
# integrated better into the WCS class.

def skycoord_to_pixel(coords, wcs, origin=0, mode='all'):
    """
    Convert a set of SkyCoord coordinates into pixels.

    Parameters
    ----------
    coords : `~astropy.coordinates.SkyCoord`
        The coordinates to convert.
    wcs : `~astropy.wcs.WCS`
        The WCS transformation to use.
    origin : int
        Whether to return 0 or 1-based pixel coordinates.
    mode : 'all' or 'wcs'
        Whether to do the transformation including distortions (``'all'``) or
        only including only the core WCS transformation (``'wcs'``).

    Returns
    -------
    xp, yp : `numpy.ndarray`
        The pixel coordinates

    See Also
    --------
    astropy.coordinates.SkyCoord.from_pixel
    """

    from .. import units as u
    from . import WCSSUB_CELESTIAL

    if _has_distortion(wcs) and wcs.naxis != 2:
        raise ValueError("Can only handle WCS with distortions for 2-dimensional WCS")

    # Keep only the celestial part of the axes, also re-orders lon/lat
    wcs = wcs.sub([WCSSUB_CELESTIAL])

    if wcs.naxis != 2:
        raise ValueError("WCS should contain celestial component")

    # Check which frame the WCS uses
    frame = wcs_to_celestial_frame(wcs)

    # Check what unit the WCS needs
    xw_unit = u.Unit(wcs.wcs.cunit[0])
    yw_unit = u.Unit(wcs.wcs.cunit[1])

    # Convert positions to frame
    coords = coords.transform_to(frame)

    # Extract longitude and latitude. We first try and use lon/lat directly,
    # but if the representation is not spherical or unit spherical this will
    # fail. We should then force the use of the unit spherical
    # representation. We don't do that directly to make sure that we preserve
    # custom lon/lat representations if available.
    try:
        lon = coords.data.lon.to(xw_unit)
        lat = coords.data.lat.to(yw_unit)
    except AttributeError:
        lon = coords.spherical.lon.to(xw_unit)
        lat = coords.spherical.lat.to(yw_unit)

    # Convert to pixel coordinates
    if mode == 'all':
        xp, yp = wcs.all_world2pix(lon.value, lat.value, origin)
    elif mode == 'wcs':
        xp, yp = wcs.wcs_world2pix(lon.value, lat.value, origin)
    else:
        raise ValueError("mode should be either 'all' or 'wcs'")

    return xp, yp


def pixel_to_skycoord(xp, yp, wcs, origin=0, mode='all', cls=None):
    """
    Convert a set of pixel coordinates into a `~astropy.coordinates.SkyCoord`
    coordinate.

    Parameters
    ----------
    xp, yp : float or `numpy.ndarray`
        The coordinates to convert.
    wcs : `~astropy.wcs.WCS`
        The WCS transformation to use.
    origin : int
        Whether to return 0 or 1-based pixel coordinates.
    mode : 'all' or 'wcs'
        Whether to do the transformation including distortions (``'all'``) or
        only including only the core WCS transformation (``'wcs'``).
    cls : class or None
        The class of object to create.  Should be a
        `~astropy.coordinates.SkyCoord` subclass.  If None, defaults to
        `~astropy.coordinates.SkyCoord`.

    Returns
    -------
    coords : Whatever ``cls`` is (a subclass of `~astropy.coordinates.SkyCoord`)
        The celestial coordinates

    See Also
    --------
    astropy.coordinates.SkyCoord.from_pixel
    """

    from .. import units as u
    from . import WCSSUB_CELESTIAL
    from ..coordinates import SkyCoord, UnitSphericalRepresentation

    # we have to do this instead of actually setting the default to SkyCoord
    # because importing SkyCoord at the module-level leads to circular
    # dependencies.
    if cls is None:
        cls = SkyCoord

    if _has_distortion(wcs) and wcs.naxis != 2:
        raise ValueError("Can only handle WCS with distortions for 2-dimensional WCS")

    # Keep only the celestial part of the axes, also re-orders lon/lat
    wcs = wcs.sub([WCSSUB_CELESTIAL])

    if wcs.naxis != 2:
        raise ValueError("WCS should contain celestial component")

    # Check which frame the WCS uses
    frame = wcs_to_celestial_frame(wcs)

    # Check what unit the WCS gives
    lon_unit = u.Unit(wcs.wcs.cunit[0])
    lat_unit = u.Unit(wcs.wcs.cunit[1])

    # Convert pixel coordinates to celestial coordinates
    if mode == 'all':
        lon, lat = wcs.all_pix2world(xp, yp, origin)
    elif mode == 'wcs':
        lon, lat = wcs.wcs_pix2world(xp, yp, origin)
    else:
        raise ValueError("mode should be either 'all' or 'wcs'")

    # Add units to longitude/latitude
    lon = lon * lon_unit
    lat = lat * lat_unit

    # Create a SkyCoord-like object
    data = UnitSphericalRepresentation(lon=lon, lat=lat)
    coords = cls(frame.realize_frame(data))

    return coords
