# Copyright (c) 2012-2019 by the GalSim developers team on GitHub
# https://github.com/GalSim-developers
#
# This file is part of GalSim: The modular galaxy image simulation toolkit.
# https://github.com/GalSim-developers/GalSim
#
# GalSim is free software: redistribution and use in source and binary forms,
# with or without modification, are permitted provided that the following
# conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
#    list of conditions, and the disclaimer given in the accompanying LICENSE
#    file.
# 2. Redistributions in binary form must reproduce the above copyright notice,
#    this list of conditions, and the disclaimer given in the documentation
#    and/or other materials provided with the distribution.
#

import numpy as np
import math

from . import _galsim
from .gsobject import GSObject
from .gsparams import GSParams
from .utilities import lazy_property, doc_inherit
from .errors import GalSimIncompatibleValuesError, GalSimNotImplementedError, convert_cpp_errors


class Airy(GSObject):
    """A class describing the surface brightness profile for an Airy disk (perfect
    diffraction-limited PSF for a circular aperture), with an optional central obscuration.

    For more information, refer to

    http://en.wikipedia.org/wiki/Airy_disc

    The Airy profile is defined in terms of the diffraction angle, which is a function of the
    ratio lambda / D, where lambda is the wavelength of the light (say in the middle of the
    bandpass you are using) and D is the diameter of the telescope.

    The natural units for this value is radians, which is not normally a convenient unit to use for
    other `GSObject` dimensions.  Assuming that the other sky coordinates you are using are all in
    arcsec (e.g. the pixel scale when you draw the image, the size of the galaxy, etc.), then you
    should convert this to arcsec as well::

        >>> lam = 700  # nm
        >>> diam = 4.0    # meters
        >>> lam_over_diam = (lam * 1.e-9) / diam  # radians
        >>> lam_over_diam *= 206265  # Convert to arcsec
        >>> airy = galsim.Airy(lam_over_diam)

    To make this process a bit simpler, we recommend instead providing the wavelength and diameter
    separately using the parameters ``lam`` (in nm) and ``diam`` (in m).  GalSim will then convert
    this to any of the normal kinds of angular units using the ``scale_unit`` parameter::

        >>> airy = galsim.Airy(lam=lam, diam=diam, scale_unit=galsim.arcsec)

    When drawing images, the scale_unit should match the unit used for the pixel scale or the WCS.
    e.g. in this case, a pixel scale of 0.2 arcsec/pixel would be specified as ``pixel_scale=0.2``.

    Parameters:
        lam_over_diam:  The parameter that governs the scale size of the profile.
                        See above for details about calculating it.
        lam:            Lambda (wavelength) in units of nanometers.  Must be supplied with
                        ``diam``, and in this case, image scales (``scale``) should be specified
                        in units of ``scale_unit``.
        diam:           Telescope diameter in units of meters.  Must be supplied with
                        ``lam``, and in this case, image scales (``scale``) should be specified
                        in units of ``scale_unit``.
        obscuration:    The linear dimension of a central obscuration as a fraction of the
                        pupil dimension.  [default: 0]
        flux:           The flux (in photons/cm^2/s) of the profile. [default: 1]
        scale_unit:     Units to use for the sky coordinates when calculating lam/diam if these
                        are supplied separately.  Note that the results of using properties like
                        `fwhm` will be returned in units of ``scale_unit`` as well.  Should
                        be either a `galsim.AngleUnit` or a string that can be used to construct
                        one (e.g., 'arcsec', 'radians', etc.).  [default: galsim.arcsec]
        gsparams:       An optional `GSParams` argument. [default: None]
    """
    _req_params = { }
    _opt_params = { "flux" : float , "obscuration" : float, "diam" : float,
                    "scale_unit" : str }
    # Note that this is not quite right; it's true that either lam_over_diam or lam should be
    # supplied, but if lam is supplied then diam is required.  Errors in which parameters are used
    # may be caught either by config or by the python code itself, depending on the particular
    # error.
    _single_params = [{ "lam_over_diam" : float , "lam" : float } ]
    _takes_rng = False

    # For an unobscured Airy, we have the following factor which can be derived using the
    # integral result given in the Wikipedia page (http://en.wikipedia.org/wiki/Airy_disk),
    # solved for half total flux using the free online tool Wolfram Alpha.
    # At www.wolframalpha.com:
    # Type "Solve[BesselJ0(x)^2+BesselJ1(x)^2=1/2]" ... and divide the result by pi
    _hlr_factor = 0.5348321477242647
    _fwhm_factor = 1.028993969962188

    _has_hard_edges = False
    _is_axisymmetric = True
    _is_analytic_x = True
    _is_analytic_k = True

    def __init__(self, lam_over_diam=None, lam=None, diam=None, obscuration=0., flux=1.,
                 scale_unit=None, gsparams=None):
        from .angle import arcsec, radians, AngleUnit

        self._obscuration = float(obscuration)
        self._flux = float(flux)
        self._gsparams = GSParams.check(gsparams)

        # Parse arguments: either lam_over_diam in arbitrary units, or lam in nm and diam in m.
        # If the latter, then get lam_over_diam in units of scale_unit, as specified in
        # docstring.
        if lam_over_diam is not None:
            if lam is not None or diam is not None:
                raise GalSimIncompatibleValuesError(
                    "If specifying lam_over_diam, then do not specify lam or diam",
                    lam_over_diam=lam_over_diam, lam=lam, diam=diam)
            self._lod = float(lam_over_diam)
        else:
            if lam is None or diam is None:
                raise GalSimIncompatibleValuesError(
                    "If not specifying lam_over_diam, then specify lam AND diam",
                    lam_over_diam=lam_over_diam, lam=lam, diam=diam)
            # In this case we're going to use scale_unit, so parse it in case of string input:
            if isinstance(scale_unit, str):
                scale_unit = AngleUnit.from_name(scale_unit)
            elif scale_unit is None:
                scale_unit = arcsec
            self._lod = (1.e-9*float(lam)/float(diam))*(radians/scale_unit)

    @lazy_property
    def _sbp(self):
        with convert_cpp_errors():
            return _galsim.SBAiry(self._lod, self._obscuration, self._flux, self.gsparams._gsp)

    @property
    def lam_over_diam(self):
        """The input lambda/diam value.
        """
        return self._lod
    @property
    def obscuration(self):
        """The input obscuration.
        """
        return self._obscuration

    @property
    def half_light_radius(self):
        """The half light radius of this Airy profile (only supported for obscuration = 0.).
        """
        if self.obscuration == 0.:
            return self.lam_over_diam * Airy._hlr_factor
        else:
            # In principle can find the half light radius as a function of lam_over_diam and
            # obscuration too, but it will be much more involved...!
            raise GalSimNotImplementedError(
                    "Half light radius calculation not implemented for Airy "
                    "objects with non-zero obscuration.")

    @property
    def fwhm(self):
        """The FWHM of this Airy profile (only supported for obscuration = 0.).
        """
        # As above, likewise, FWHM only easy to define for unobscured Airy
        if self.obscuration == 0.:
            return self.lam_over_diam * Airy._fwhm_factor
        else:
            # In principle can find the FWHM as a function of lam_over_diam and obscuration too,
            # but it will be much more involved...!
            raise GalSimNotImplementedError(
                    "FWHM calculation not implemented for Airy "
                    "objects with non-zero obscuration.")

    def __eq__(self, other):
        return (self is other or
                (isinstance(other, Airy) and
                 self.lam_over_diam == other.lam_over_diam and
                 self.obscuration == other.obscuration and
                 self.flux == other.flux and
                 self.gsparams == other.gsparams))

    def __hash__(self):
        return hash(("galsim.Airy", self.lam_over_diam, self.obscuration, self.flux,
                     self.gsparams))

    def __repr__(self):
        return 'galsim.Airy(lam_over_diam=%r, obscuration=%r, flux=%r, gsparams=%r)'%(
            self.lam_over_diam, self.obscuration, self.flux, self.gsparams)

    def __str__(self):
        s = 'galsim.Airy(lam_over_diam=%s'%self.lam_over_diam
        if self.obscuration != 0.:
            s += ', obscuration=%s'%self.obscuration
        if self.flux != 1.0:
            s += ', flux=%s'%self.flux
        s += ')'
        return s

    def __getstate__(self):
        d = self.__dict__.copy()
        d.pop('_sbp',None)
        return d

    def __setstate__(self, d):
        self.__dict__ = d

    @property
    def _maxk(self):
        return 2.*math.pi / self._lod

    @property
    def _stepk(self):
        return self._sbp.stepK()

    @property
    def _max_sb(self):
        return self._sbp.maxSB()

    @doc_inherit
    def _xValue(self, pos):
        return self._sbp.xValue(pos._p)

    @doc_inherit
    def _kValue(self, kpos):
        return self._sbp.kValue(kpos._p)

    @doc_inherit
    def _drawReal(self, image):
        self._sbp.draw(image._image, image.scale)

    @doc_inherit
    def _shoot(self, photons, rng):
        self._sbp.shoot(photons._pa, rng._rng)

    @doc_inherit
    def _drawKImage(self, image):
        self._sbp.drawK(image._image, image.scale)

    @doc_inherit
    def withFlux(self, flux):
        return Airy(lam_over_diam=self.lam_over_diam, obscuration=self.obscuration,
                    flux=flux, gsparams=self.gsparams)
