pycobertura report

# This file is adapted from the Astropy package template, which is licensed
# under a 3-clause BSD style license - see licenses/TEMPLATE_LICENSE.rst

# Packages may add whatever they like to this file, but
# should keep this content at the top.
# ----------------------------------------------------------------------------
from ._astropy_init import *   # noqa
# ----------------------------------------------------------------------------

__all__ = ('omp',)


class Omp:
    """OpenMP runtime settings.

    Attributes
    ----------
    num_threads : int
        Adjust the number of OpenMP threads. Getting and setting this attribute
        call :man:`omp_get_num_threads` and :man:`omp_set_num_threads`
        respectively.

    """

    @property
    def num_threads(self):
        from .core import get_num_threads
        return get_num_threads()

    @num_threads.setter
    def num_threads(self, value):
        from .core import set_num_threads
        set_num_threads(value)


omp = Omp()
del Omp

#
# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""
Distance distribution functions from [1]_, [2]_, [3]_.

References
----------
.. [1] Singer, Chen, & Holz, 2016. "Going the Distance: Mapping Host Galaxies
   of LIGO and Virgo Sources in Three Dimensions Using Local Cosmography and
   Targeted Follow-up." ApJL, 829, L15.
   :doi:`10.3847/2041-8205/829/1/L15`

.. [2] Singer, Chen, & Holz, 2016. "Supplement: 'Going the Distance: Mapping
   Host Galaxies of LIGO and Virgo Sources in Three Dimensions Using Local
   Cosmography and Targeted Follow-up' (2016, ApJL, 829, L15)." ApJS, 226, 10.
   :doi:`10.3847/0067-0049/226/1/10`

.. [3] https://asd.gsfc.nasa.gov/Leo.Singer/going-the-distance

"""

import astropy_healpix as ah
import numpy as np
import healpy as hp
import scipy.special
from .core import (conditional_pdf, conditional_cdf, conditional_ppf,
                   moments_to_parameters, parameters_to_moments, volume_render,
                   marginal_pdf, marginal_cdf, marginal_ppf)
from .util.numpy import add_newdoc_ufunc, require_contiguous_aligned

__all__ = ('conditional_pdf', 'conditional_cdf', 'conditional_ppf',
           'moments_to_parameters', 'parameters_to_moments', 'volume_render',
           'marginal_pdf', 'marginal_cdf', 'marginal_ppf', 'ud_grade',
           'conditional_kde', 'cartesian_kde_to_moments', 'principal_axes',
           'parameters_to_moments')


add_newdoc_ufunc(conditional_pdf, """\
Conditional distance probability density function (ansatz).

Parameters
----------
r : `numpy.ndarray`
    Distance (Mpc)
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Returns
-------
pdf : `numpy.ndarray`
    Conditional probability density according to ansatz.

""")
conditional_pdf = require_contiguous_aligned(conditional_pdf)


add_newdoc_ufunc(conditional_cdf, """\
Cumulative conditional distribution of distance (ansatz).

Parameters
----------
r : `numpy.ndarray`
    Distance (Mpc)
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Returns
-------
pdf : `numpy.ndarray`
    Conditional probability density according to ansatz.

Examples
--------
Test against numerical integral of pdf.

>>> import scipy.integrate
>>> distmu = 10.0
>>> distsigma = 5.0
>>> distnorm = 1.0
>>> r = 8.0
>>> expected, _ = scipy.integrate.quad(
...     conditional_pdf, 0, r,
...     (distmu, distsigma, distnorm))
>>> result = conditional_cdf(
...     r, distmu, distsigma, distnorm)
>>> np.testing.assert_almost_equal(result, expected)

""")
conditional_cdf = require_contiguous_aligned(conditional_cdf)


add_newdoc_ufunc(conditional_ppf, """\
Point percent function (inverse cdf) of distribution of distance (ansatz).

Parameters
----------
p : `numpy.ndarray`
    The cumulative distribution function
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Returns
-------
r : `numpy.ndarray`
    Distance at which the cdf is equal to `p`.

Examples
--------
Test against numerical estimate.

>>> import scipy.optimize
>>> distmu = 10.0
>>> distsigma = 5.0
>>> distnorm = 1.0
>>> p = 0.16  # "one-sigma" lower limit
>>> expected_r16 = scipy.optimize.brentq(
... lambda r: conditional_cdf(r, distmu, distsigma, distnorm) - p, 0.0, 100.0)
>>> r16 = conditional_ppf(p, distmu, distsigma, distnorm)
>>> np.testing.assert_almost_equal(r16, expected_r16)

""")
conditional_ppf = require_contiguous_aligned(conditional_ppf)


add_newdoc_ufunc(moments_to_parameters, """\
Convert ansatz moments to parameters.

This function is the inverse of `parameters_to_moments`.

Parameters
----------
distmean : `numpy.ndarray`
    Conditional mean of distance (Mpc)
diststd : `numpy.ndarray`
    Conditional standard deviation of distance (Mpc)

Returns
-------
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

""")
moments_to_parameters = require_contiguous_aligned(moments_to_parameters)


add_newdoc_ufunc(parameters_to_moments, """\
Convert ansatz parameters to moments.

This function is the inverse of `moments_to_parameters`.

Parameters
----------
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)

Returns
-------
distmean : `numpy.ndarray`
    Conditional mean of distance (Mpc)
diststd : `numpy.ndarray`
    Conditional standard deviation of distance (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Examples
--------
For mu=0, sigma=1, the ansatz is a chi distribution with 3 degrees of
freedom, and the moments have simple expressions.

>>> mean, std, norm = parameters_to_moments(0, 1)
>>> expected_mean = 2 * np.sqrt(2 / np.pi)
>>> expected_std = np.sqrt(3 - expected_mean**2)
>>> expected_norm = 2.0
>>> np.testing.assert_allclose(mean, expected_mean)
>>> np.testing.assert_allclose(std, expected_std)
>>> np.testing.assert_allclose(norm, expected_norm)

Check that the moments scale as expected when we vary sigma.

>>> sigma = np.logspace(-8, 8)
>>> mean, std, norm = parameters_to_moments(0, sigma)
>>> np.testing.assert_allclose(mean, expected_mean * sigma)
>>> np.testing.assert_allclose(std, expected_std * sigma)
>>> np.testing.assert_allclose(norm, expected_norm / sigma**2)

Check some more arbitrary values using numerical quadrature:

>>> import scipy.integrate
>>> sigma = 1.0
>>> for mu in np.linspace(-10, 10):
...     mean, std, norm = parameters_to_moments(mu, sigma)
...     moments = np.empty(3)
...     for k in range(3):
...         moments[k], _ = scipy.integrate.quad(
...             lambda r: r**k * conditional_pdf(r, mu, sigma, 1.0),
...             0, np.inf)
...     expected_norm = 1 / moments[0]
...     expected_mean, r2 = moments[1:] * expected_norm
...     expected_std = np.sqrt(r2 - np.square(expected_mean))
...     np.testing.assert_approx_equal(mean, expected_mean, 5)
...     np.testing.assert_approx_equal(std, expected_std, 5)
...     np.testing.assert_approx_equal(norm, expected_norm, 5)

""")
parameters_to_moments = require_contiguous_aligned(parameters_to_moments)


add_newdoc_ufunc(volume_render, """\
Perform volumetric rendering of a 3D sky map.

Parameters
----------
x : `numpy.ndarray`
    X-coordinate in rendered image
y : `numpy.ndarray`
    Y-coordinate in rendered image
max_distance : float
    Limit of integration from `-max_distance` to `+max_distance`
axis0 : int
    Index of axis to assign to x-coordinate
axis1 : int
    Index of axis to assign to y-coordinate
R : `numpy.ndarray`
    Rotation matrix as provided by `principal_axes`
nest : bool
    HEALPix ordering scheme
prob : `numpy.ndarray`
    Marginal probability (pix^-2)
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Returns
-------
image : `numpy.ndarray`
    Rendered image

Examples
--------
Test volume rendering of a normal unit sphere...
First, set up the 3D sky map.

>>> nside = 32
>>> npix = ah.nside_to_npix(nside)
>>> prob = np.ones(npix) / npix
>>> distmu = np.zeros(npix)
>>> distsigma = np.ones(npix)
>>> distnorm = np.ones(npix) * 2.0

The conditional distance distribution should be a chi distribution with
3 degrees of freedom.

>>> from scipy.stats import norm, chi
>>> r = np.linspace(0, 10.0)
>>> actual = conditional_pdf(r, distmu[0], distsigma[0], distnorm[0])
>>> expected = chi(3).pdf(r)
>>> np.testing.assert_almost_equal(actual, expected)

Next, run the volume renderer.

>>> dmax = 4.0
>>> n = 64
>>> s = np.logspace(-dmax, dmax, n)
>>> x, y = np.meshgrid(s, s)
>>> R = np.eye(3)
>>> P = volume_render(x, y, dmax, 0, 1, R, False,
...                   prob, distmu, distsigma, distnorm)

Next, integrate analytically.

>>> P_expected = norm.pdf(x) * norm.pdf(y) * (norm.cdf(dmax) - norm.cdf(-dmax))

Compare the two.

>>> np.testing.assert_almost_equal(P, P_expected, decimal=4)

Check that we get the same answer if the input is in ring ordering.
FIXME: this is a very weak test, because the input sky map is isotropic!

>>> P = volume_render(x, y, dmax, 0, 1, R, True,
...                   prob, distmu, distsigma, distnorm)
>>> np.testing.assert_almost_equal(P, P_expected, decimal=4)

Last, check that we don't have a coordinate singularity at the origin.

>>> x = np.concatenate(([0], np.logspace(1 - n, 0, n) * dmax))
>>> y = 0.0
>>> P = volume_render(x, y, dmax, 0, 1, R, False,
...                   prob, distmu, distsigma, distnorm)
>>> P_expected = norm.pdf(x) * norm.pdf(y) * (norm.cdf(dmax) - norm.cdf(-dmax))
>>> np.testing.assert_allclose(P, P_expected, rtol=1e-4)

""")
volume_render = require_contiguous_aligned(volume_render)


add_newdoc_ufunc(marginal_pdf, """\
Calculate all-sky marginal pdf (ansatz).

Parameters
----------
r : `numpy.ndarray`
    Distance (Mpc)
prob : `numpy.ndarray`
    Marginal probability (pix^-2)
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Returns
-------
pdf : `numpy.ndarray`
    Marginal probability density according to ansatz.

Examples
--------

>>> npix = 12
>>> prob, distmu, distsigma, distnorm = np.random.uniform(size=(4, 12))
>>> r = np.linspace(0, 1)
>>> pdf_expected = np.dot(
...     conditional_pdf(r[:, np.newaxis], distmu, distsigma, distnorm), prob)
>>> pdf = marginal_pdf(r, prob, distmu, distsigma, distnorm)
>>> np.testing.assert_allclose(pdf, pdf_expected, rtol=1e-4)

""")
marginal_pdf = require_contiguous_aligned(marginal_pdf)


add_newdoc_ufunc(marginal_cdf, """\
Calculate all-sky marginal cdf (ansatz).

Parameters
----------
r : `numpy.ndarray`
    Distance (Mpc)
prob : `numpy.ndarray`
    Marginal probability (pix^-2)
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Returns
-------
cdf : `numpy.ndarray`
    Marginal cumulative probability according to ansatz.

Examples
--------

>>> npix = 12
>>> prob, distmu, distsigma, distnorm = np.random.uniform(size=(4, 12))
>>> r = np.linspace(0, 1)
>>> cdf_expected = np.dot(
...     conditional_cdf(r[:, np.newaxis], distmu, distsigma, distnorm), prob)
>>> cdf = marginal_cdf(r, prob, distmu, distsigma, distnorm)
>>> np.testing.assert_allclose(cdf, cdf_expected, rtol=1e-4)

""")
marginal_cdf = require_contiguous_aligned(marginal_cdf)


add_newdoc_ufunc(marginal_ppf, """\
Point percent function (inverse cdf) of marginal distribution of distance
(ansatz).

Parameters
----------
p : `numpy.ndarray`
    The cumulative distribution function
prob : `numpy.ndarray`
    Marginal probability (pix^-2)
distmu : `numpy.ndarray`
    Distance location parameter (Mpc)
distsigma : `numpy.ndarray`
    Distance scale parameter (Mpc)
distnorm : `numpy.ndarray`
    Distance normalization factor (Mpc^-2)

Returns
-------
r : `numpy.ndarray`
    Distance at which the cdf is equal to `p`.

Examples
--------

>>> from astropy.utils.misc import NumpyRNGContext
>>> npix = 12
>>> with NumpyRNGContext(0):
...     prob, distmu, distsigma, distnorm = np.random.uniform(size=(4, 12))
>>> r_expected = np.linspace(0.4, 0.7)
>>> cdf = marginal_cdf(r_expected, prob, distmu, distsigma, distnorm)
>>> r = marginal_ppf(cdf, prob, distmu, distsigma, distnorm)
>>> np.testing.assert_allclose(r, r_expected, rtol=1e-4)

""")
marginal_ppf = require_contiguous_aligned(marginal_ppf)


def ud_grade(prob, distmu, distsigma, *args, **kwargs):
    """
    Upsample or downsample a distance-resolved sky map.

    Parameters
    ----------
    prob : `numpy.ndarray`
        Marginal probability (pix^-2)
    distmu : `numpy.ndarray`
        Distance location parameter (Mpc)
    distsigma : `numpy.ndarray`
        Distance scale parameter (Mpc)
    *args, **kwargs :
        Additional arguments to `healpy.ud_grade` (e.g.,
        `nside`, `order_in`, `order_out`).

    Returns
    -------
    prob : `numpy.ndarray`
        Resampled marginal probability (pix^-2)
    distmu : `numpy.ndarray`
        Resampled distance location parameter (Mpc)
    distsigma : `numpy.ndarray`
        Resampled distance scale parameter (Mpc)
    distnorm : `numpy.ndarray`
        Resampled distance normalization factor (Mpc^-2)

    """
    bad = ~(np.isfinite(distmu) & np.isfinite(distsigma))
    distmean, diststd, _ = parameters_to_moments(distmu, distsigma)
    distmean[bad] = 0
    diststd[bad] = 0
    distmean = hp.ud_grade(prob * distmu, *args, power=-2, **kwargs)
    diststd = hp.ud_grade(prob * np.square(diststd), *args, power=-2, **kwargs)
    prob = hp.ud_grade(prob, *args, power=-2, **kwargs)
    distmean /= prob
    diststd = np.sqrt(diststd / prob)
    bad = ~hp.ud_grade(~bad, *args, power=-2, **kwargs)
    distmean[bad] = np.inf
    diststd[bad] = 1
    distmu, distsigma, distnorm = moments_to_parameters(distmean, diststd)
    return prob, distmu, distsigma, distnorm


def _conditional_kde(n, X, Cinv, W):
    Cinv_n = np.dot(Cinv, n)
    cinv = np.dot(n, Cinv_n)
    x = np.dot(Cinv_n, X) / cinv
    w = W * (0.5 / np.pi) * np.sqrt(np.linalg.det(Cinv) / cinv) * np.exp(
        0.5 * (np.square(x) * cinv - (np.dot(Cinv, X) * X).sum(0)))
    return x, cinv, w


def conditional_kde(n, datasets, inverse_covariances, weights):
    return [
        _conditional_kde(n, X, Cinv, W)
        for X, Cinv, W in zip(datasets, inverse_covariances, weights)]


def cartesian_kde_to_moments(n, datasets, inverse_covariances, weights):
    """
    Calculate the marginal probability, conditional mean, and conditional
    standard deviation of a mixture of three-dimensional kernel density
    estimators (KDEs), in a given direction specified by a unit vector.

    Parameters
    ----------
    n : `numpy.ndarray`
        A unit vector; an array of length 3.
    datasets : list of `numpy.ndarray`
        A list 2D Numpy arrays specifying the sample points of the KDEs.
        The first dimension of each array is 3.
    inverse_covariances: list of `numpy.ndarray`
        An array of 3x3 matrices specifying the inverses of the covariance
        matrices of the KDEs. The list has the same length as the datasets
        parameter.
    weights : list
        A list of floating-point weights.

    Returns
    -------
    prob : float
        The marginal probability in direction n, integrated over all distances.
    mean : float
        The conditional mean in direction n.
    std : float
        The conditional standard deviation in direction n.

    Examples
    --------
    >>> # Some imports
    >>> import scipy.stats
    >>> import scipy.integrate
    >>> # Construct random dataset for KDE
    >>> np.random.seed(0)
    >>> nclusters = 5
    >>> ndata = np.random.randint(0, 1000, nclusters)
    >>> covs = [np.random.uniform(0, 1, size=(3, 3)) for _ in range(nclusters)]
    >>> covs = [_ + _.T + 3 * np.eye(3) for _ in covs]
    >>> means = np.random.uniform(-1, 1, size=(nclusters, 3))
    >>> datasets = [np.random.multivariate_normal(m, c, n).T
    ...     for m, c, n in zip(means, covs, ndata)]
    >>> weights = ndata / float(np.sum(ndata))
    >>>
    >>> # Construct set of KDEs
    >>> kdes = [scipy.stats.gaussian_kde(_) for _ in datasets]
    >>>
    >>> # Random unit vector n
    >>> n = np.random.normal(size=3)
    >>> n /= np.sqrt(np.sum(np.square(n)))
    >>>
    >>> # Analytically evaluate conditional mean and std. dev. in direction n
    >>> datasets = [_.dataset for _ in kdes]
    >>> inverse_covariances = [_.inv_cov for _ in kdes]
    >>> result_prob, result_mean, result_std = cartesian_kde_to_moments(
    ...     n, datasets, inverse_covariances, weights)
    >>>
    >>> # Numerically integrate conditional distance moments
    >>> def rkbar(k):
    ...     def integrand(r):
    ...         return r ** k * np.sum([kde(r * n) * weight
    ...             for kde, weight in zip(kdes, weights)])
    ...     integral, err = scipy.integrate.quad(integrand, 0, np.inf)
    ...     return integral
    ...
    >>> r0bar = rkbar(2)
    >>> r1bar = rkbar(3)
    >>> r2bar = rkbar(4)
    >>>
    >>> # Extract conditional mean and std. dev.
    >>> r1bar /= r0bar
    >>> r2bar /= r0bar
    >>> expected_prob = r0bar
    >>> expected_mean = r1bar
    >>> expected_std = np.sqrt(r2bar - np.square(r1bar))
    >>>
    >>> # Check that the two methods give almost the same result
    >>> np.testing.assert_almost_equal(result_prob, expected_prob)
    >>> np.testing.assert_almost_equal(result_mean, expected_mean)
    >>> np.testing.assert_almost_equal(result_std, expected_std)
    >>>
    >>> # Check that KDE is normalized over unit sphere.
    >>> nside = 32
    >>> npix = ah.nside_to_npix(nside)
    >>> prob, _, _ = np.transpose([cartesian_kde_to_moments(
    ...     np.asarray(hp.pix2vec(nside, ipix)),
    ...     datasets, inverse_covariances, weights)
    ...     for ipix in range(npix)])
    >>> result_integral = prob.sum() * hp.nside2pixarea(nside)
    >>> np.testing.assert_almost_equal(result_integral, 1.0, decimal=4)

    """
    # Initialize moments of conditional KDE.
    r0bar = 0
    r1bar = 0
    r2bar = 0

    # Loop over KDEs.
    for X, Cinv, W in zip(datasets, inverse_covariances, weights):
        x, cinv, w = _conditional_kde(n, X, Cinv, W)

        # Accumulate moments of conditional KDE.
        c = 1 / cinv
        x2 = np.square(x)
        a = scipy.special.ndtr(x * np.sqrt(cinv))
        b = np.sqrt(0.5 / np.pi * c) * np.exp(-0.5 * cinv * x2)
        r0bar_ = (x2 + c) * a + x * b
        r1bar_ = x * (x2 + 3 * c) * a + (x2 + 2 * c) * b
        r2bar_ = (x2 * x2 + 6 * x2 * c + 3 * c * c) * a + x * (x2 + 5 * c) * b
        r0bar += np.mean(w * r0bar_)
        r1bar += np.mean(w * r1bar_)
        r2bar += np.mean(w * r2bar_)

    # Normalize moments.
    with np.errstate(invalid='ignore'):
        r1bar /= r0bar
        r2bar /= r0bar
    var = r2bar - np.square(r1bar)

    # Handle invalid values.
    if var >= 0:
        mean = r1bar
        std = np.sqrt(var)
    else:
        mean = np.inf
        std = 1.0
    prob = r0bar

    # Done!
    return prob, mean, std


def principal_axes(prob, distmu, distsigma, nest=False):
    npix = len(prob)
    nside = ah.npix_to_nside(npix)
    good = np.isfinite(prob) & np.isfinite(distmu) & np.isfinite(distsigma)
    ipix = np.flatnonzero(good)
    distmean, diststd, _ = parameters_to_moments(distmu[good], distsigma[good])
    mass = prob[good] * (np.square(diststd) + np.square(distmean))
    xyz = np.asarray(hp.pix2vec(nside, ipix, nest=nest))
    cov = np.dot(xyz * mass, xyz.T)
    L, V = np.linalg.eigh(cov)
    if np.linalg.det(V) < 0:
        V = -V
    return V


def parameters_to_marginal_moments(prob, distmu, distsigma):
    """Calculate the marginal (integrated all-sky) mean and standard deviation
    of distance from the ansatz parameters.

    Parameters
    ----------
    prob : `numpy.ndarray`
        Marginal probability (pix^-2)
    distmu : `numpy.ndarray`
        Distance location parameter (Mpc)
    distsigma : `numpy.ndarray`
        Distance scale parameter (Mpc)

    Returns
    -------
    distmean : float
        Mean distance (Mpc)
    diststd : float
        Std. deviation of distance (Mpc)

    """
    good = np.isfinite(prob) & np.isfinite(distmu) & np.isfinite(distsigma)
    prob = prob[good]
    distmu = distmu[good]
    distsigma = distsigma[good]
    distmean, diststd, _ = parameters_to_moments(distmu, distsigma)
    rbar = (prob * distmean).sum()
    r2bar = (prob * (np.square(diststd) + np.square(distmean))).sum()
    return rbar, np.sqrt(r2bar - np.square(rbar))


del add_newdoc_ufunc, require_contiguous_aligned

#
# Copyright (C) 2013-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""
Multiresolution HEALPix trees
"""
import astropy_healpix as ah
from astropy import units as u
import numpy as np
import healpy as hp
import collections
import itertools

__all__ = ('HEALPIX_MACHINE_ORDER', 'HEALPIX_MACHINE_NSIDE', 'HEALPixTree',
           'adaptive_healpix_histogram', 'interpolate_nested',
           'reconstruct_nested')


# Maximum 64-bit HEALPix resolution.
HEALPIX_MACHINE_ORDER = 29
HEALPIX_MACHINE_NSIDE = ah.level_to_nside(HEALPIX_MACHINE_ORDER)


_HEALPixTreeVisitExtra = collections.namedtuple(
    'HEALPixTreeVisit', 'nside full_nside ipix ipix0 ipix1 value')


_HEALPixTreeVisit = collections.namedtuple(
    'HEALPixTreeVisit', 'nside ipix')


class HEALPixTree:
    """Data structure used internally by the function
    adaptive_healpix_histogram()."""

    def __init__(
            self, samples, max_samples_per_pixel, max_order,
            order=0, needs_sort=True):
        if needs_sort:
            samples = np.sort(samples)
        if len(samples) >= max_samples_per_pixel and order < max_order:
            # All nodes have 4 children, except for the root node,
            # which has 12.
            nchildren = 12 if order == 0 else 4
            self.samples = None
            self.children = [
                HEALPixTree(
                    [], max_samples_per_pixel, max_order, order=order + 1)
                for i in range(nchildren)]
            for ipix, samples in itertools.groupby(
                    samples, self.key_for_order(order)):
                self.children[ipix % nchildren] = HEALPixTree(
                    list(samples), max_samples_per_pixel, max_order,
                    order=order + 1, needs_sort=False)
        else:
            # There are few enough samples that we can make this cell a leaf.
            self.samples = list(samples)
            self.children = None

    @staticmethod
    def key_for_order(order):
        """Create a function that downsamples full-resolution pixel indices."""
        return lambda ipix: ipix >> np.int64(
            2 * (HEALPIX_MACHINE_ORDER - order))

    @property
    def order(self):
        """Return the maximum HEALPix order required to represent this tree,
        which is the same as the tree depth."""
        if self.children is None:
            return 0
        else:
            return 1 + max(child.order for child in self.children)

    def _visit(self, order, full_order, ipix, extra):
        if self.children is None:
            nside = 1 << order
            full_nside = 1 << order
            ipix0 = ipix << 2 * (full_order - order)
            ipix1 = (ipix + 1) << 2 * (full_order - order)
            if extra:
                yield _HEALPixTreeVisitExtra(
                    nside, full_nside, ipix, ipix0, ipix1, self.samples)
            else:
                yield _HEALPixTreeVisit(nside, ipix)
        else:
            for i, child in enumerate(self.children):
                yield from child._visit(
                    order + 1, full_order, (ipix << 2) + i, extra)

    def _visit_depthfirst(self, extra):
        order = self.order
        for ipix, child in enumerate(self.children):
            yield from child._visit(0, order, ipix, extra)

    def _visit_breadthfirst(self, extra):
        return sorted(
            self._visit_depthfirst(extra), lambda _: (_.nside, _.ipix))

    def visit(self, order='depthfirst', extra=True):
        """Traverse the leaves of the HEALPix tree.

        Parameters
        ----------
        order : string, optional
            Traversal order: 'depthfirst' (the default) or 'breadthfirst'.

        extra : bool
            Whether to output extra information about the pixel
            (default is True).

        Yields
        ------
        nside : int
            The HEALPix resolution of the node.

        full_nside : int, present if extra=True
            The HEALPix resolution of the deepest node in the tree.

        ipix : int
            The nested HEALPix index of the node.

        ipix0 : int, present if extra=True
            The start index of the range of pixels spanned by the node at the
            resolution `full_nside`.

        ipix1 : int, present if extra=True
            The end index of the range of pixels spanned by the node at the
            resolution `full_nside`.

        samples : list, present if extra=True
            The list of samples contained in the node.

        Examples
        --------

        >>> ipix = np.arange(12) * HEALPIX_MACHINE_NSIDE**2
        >>> tree = HEALPixTree(ipix, max_samples_per_pixel=1, max_order=1)
        >>> [tuple(_) for _ in tree.visit(extra=False)]
        [(1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11)]
        """
        funcs = {'depthfirst': self._visit_depthfirst,
                 'breadthfirst': self._visit_breadthfirst}
        func = funcs[order]
        yield from func(extra)

    @property
    def flat_bitmap(self):
        """Return flattened HEALPix representation."""
        m = np.empty(ah.nside_to_npix(ah.level_to_nside(self.order)))
        for nside, full_nside, ipix, ipix0, ipix1, samples in self.visit():
            pixarea = ah.nside_to_pixel_area(nside).to_value(u.sr)
            m[ipix0:ipix1] = len(samples) / pixarea
        return m


def adaptive_healpix_histogram(
        theta, phi, max_samples_per_pixel, nside=-1, max_nside=-1, nest=False):
    """Adaptively histogram the posterior samples represented by the
    (theta, phi) points using a recursively subdivided HEALPix tree. Nodes are
    subdivided until each leaf contains no more than max_samples_per_pixel
    samples. Finally, the tree is flattened to a fixed-resolution HEALPix image
    with a resolution appropriate for the depth of the tree. If nside is
    specified, the result is resampled to another desired HEALPix resolution.
    """
    # Calculate pixel index of every sample, at the maximum 64-bit resolution.
    #
    # At this resolution, each pixel is only 0.2 mas across; we'll use the
    # 64-bit pixel indices as a proxy for the true sample coordinates so that
    # we don't have to do any trigonometry (aside from the initial hp.ang2pix
    # call).
    ipix = hp.ang2pix(HEALPIX_MACHINE_NSIDE, theta, phi, nest=True)

    # Build tree structure.
    if nside == -1 and max_nside == -1:
        max_order = HEALPIX_MACHINE_ORDER
    elif nside == -1:
        max_order = ah.nside_to_level(max_nside)
    elif max_nside == -1:
        max_order = ah.nside_to_level(nside)
    else:
        max_order = ah.nside_to_level(min(nside, max_nside))
    tree = HEALPixTree(ipix, max_samples_per_pixel, max_order)

    # Compute a flattened bitmap representation of the tree.
    p = tree.flat_bitmap

    # If requested, resample the tree to the output resolution.
    if nside != -1:
        p = hp.ud_grade(p, nside, order_in='NESTED', order_out='NESTED')

    # Normalize.
    p /= np.sum(p)

    if not nest:
        p = hp.reorder(p, n2r=True)

    # Done!
    return p


def _interpolate_level(m):
    """Recursive multi-resolution interpolation. Modifies `m` in place."""
    # Determine resolution.
    npix = len(m)

    if npix > 12:
        # Determine which pixels comprise multi-pixel tiles.
        ipix = np.flatnonzero(
            (m[0::4] == m[1::4]) &
            (m[0::4] == m[2::4]) &
            (m[0::4] == m[3::4]))

        if len(ipix):
            ipix = 4 * ipix + np.expand_dims(np.arange(4, dtype=np.intp), 1)
            ipix = ipix.T.ravel()

            nside = ah.npix_to_nside(npix)

            # Downsample.
            m_lores = hp.ud_grade(
                m, nside // 2, order_in='NESTED', order_out='NESTED')

            # Interpolate recursively.
            _interpolate_level(m_lores)

            # Record interpolated multi-pixel tiles.
            m[ipix] = hp.get_interp_val(
                m_lores, *hp.pix2ang(nside, ipix, nest=True), nest=True)


def interpolate_nested(m, nest=False):
    """
    Apply bilinear interpolation to a multiresolution HEALPix map, assuming
    that runs of pixels containing identical values are nodes of the tree. This
    smooths out the stair-step effect that may be noticeable in contour plots.

    Here is how it works. Consider a coarse tile surrounded by base tiles, like
    this::

                +---+---+
                |   |   |
                +-------+
                |   |   |
        +---+---+---+---+---+---+
        |   |   |       |   |   |
        +-------+       +-------+
        |   |   |       |   |   |
        +---+---+---+---+---+---+
                |   |   |
                +-------+
                |   |   |
                +---+---+

    The value within the central coarse tile is computed by downsampling the
    sky map (averaging the fine tiles), upsampling again (with bilinear
    interpolation), and then finally copying the interpolated values within the
    coarse tile back to the full-resolution sky map. This process is applied
    recursively at all successive HEALPix resolutions.

    Note that this method suffers from a minor discontinuity artifact at the
    edges of regions of coarse tiles, because it temporarily treats the
    bordering fine tiles as constant. However, this artifact seems to have only
    a minor effect on generating contour plots.

    Parameters
    ----------

    m: `~numpy.ndarray`
        a HEALPix array

    nest: bool, default: False
        Whether the input array is stored in the `NESTED` indexing scheme
        (True) or the `RING` indexing scheme (False).

    """
    # Convert to nest indexing if necessary, and make sure that we are working
    # on a copy.
    if nest:
        m = m.copy()
    else:
        m = hp.reorder(m, r2n=True)

    _interpolate_level(m)

    # Convert to back ring indexing if necessary
    if not nest:
        m = hp.reorder(m, n2r=True)

    # Done!
    return m


def _reconstruct_nested_breadthfirst(m, extra):
    m = np.asarray(m)
    max_npix = len(m)
    max_nside = ah.npix_to_nside(max_npix)
    max_order = ah.nside_to_level(max_nside)
    seen = np.zeros(max_npix, dtype=bool)

    for order in range(max_order + 1):
        nside = ah.level_to_nside(order)
        npix = ah.nside_to_npix(nside)
        skip = max_npix // npix
        if skip > 1:
            b = m.reshape(-1, skip)
            a = b[:, 0].reshape(-1, 1)
            b = b[:, 1:]
            aseen = seen.reshape(-1, skip)
            eq = ((a == b) | ((a != a) & (b != b))).all(1) & (~aseen).all(1)
        else:
            eq = ~seen
        for ipix in np.flatnonzero(eq):
            ipix0 = ipix * skip
            ipix1 = (ipix + 1) * skip
            seen[ipix0:ipix1] = True
            if extra:
                yield _HEALPixTreeVisitExtra(
                    nside, max_nside, ipix, ipix0, ipix1, m[ipix0])
            else:
                yield _HEALPixTreeVisit(nside, ipix)


def _reconstruct_nested_depthfirst(m, extra):
    result = sorted(
        _reconstruct_nested_breadthfirst(m, True),
        key=lambda _: _.ipix0)
    if not extra:
        result = (_HEALPixTreeVisit(_.nside, _.ipix) for _ in result)
    return result


def reconstruct_nested(m, order='depthfirst', extra=True):
    """Reconstruct the leaves of a multiresolution tree.

    Parameters
    ----------
    m : `~numpy.ndarray`
        A HEALPix array in the NESTED ordering scheme.

    order : {'depthfirst', 'breadthfirst'}, optional
        Traversal order: 'depthfirst' (the default) or 'breadthfirst'.

    extra : bool
        Whether to output extra information about the pixel (default is True).

    Yields
    ------
    nside : int
        The HEALPix resolution of the node.

    full_nside : int, present if extra=True
        The HEALPix resolution of the deepest node in the tree.

    ipix : int
        The nested HEALPix index of the node.

    ipix0 : int, present if extra=True
        The start index of the range of pixels spanned by the node at the
        resolution `full_nside`.

    ipix1 : int, present if extra=True
        The end index of the range of pixels spanned by the node at the
        resolution `full_nside`.

    value : list, present if extra=True
        The value of the map at the node.

    Examples
    --------

    An nside=1 array of all zeros:

    >>> m = np.zeros(12)
    >>> result = reconstruct_nested(m, order='breadthfirst', extra=False)
    >>> [tuple(_) for _ in result]
    [(1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11)]

    An nside=1 array of distinct values:

    >>> m = range(12)
    >>> result = reconstruct_nested(m, order='breadthfirst', extra=False)
    >>> [tuple(_) for _ in result]
    [(1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11)]

    An nside=8 array of zeros:

    >>> m = np.zeros(768)
    >>> result = reconstruct_nested(m, order='breadthfirst', extra=False)
    >>> [tuple(_) for _ in result]
    [(1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11)]

    An nside=2 array, all zeros except for four consecutive distinct elements:

    >>> m = np.zeros(48); m[:4] = range(4)
    >>> result = reconstruct_nested(m, order='breadthfirst', extra=False)
    >>> [tuple(_) for _ in result]
    [(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 0), (2, 1), (2, 2), (2, 3)]

    Same, but in depthfirst order:

    >>> result = reconstruct_nested(m, order='depthfirst', extra=False)
    >>> [tuple(_) for _ in result]
    [(2, 0), (2, 1), (2, 2), (2, 3), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11)]

    An nside=2 array, all elements distinct except for four consecutive zeros:

    >>> m = np.arange(48); m[:4] = 0
    >>> result = reconstruct_nested(m, order='breadthfirst', extra=False)
    >>> [tuple(_) for _ in result]
    [(1, 0), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 15), (2, 16), (2, 17), (2, 18), (2, 19), (2, 20), (2, 21), (2, 22), (2, 23), (2, 24), (2, 25), (2, 26), (2, 27), (2, 28), (2, 29), (2, 30), (2, 31), (2, 32), (2, 33), (2, 34), (2, 35), (2, 36), (2, 37), (2, 38), (2, 39), (2, 40), (2, 41), (2, 42), (2, 43), (2, 44), (2, 45), (2, 46), (2, 47)]
    """
    funcs = {'depthfirst': _reconstruct_nested_depthfirst,
             'breadthfirst': _reconstruct_nested_breadthfirst}
    func = funcs[order]
    yield from func(m, extra)

#
# Copyright (C) 2012-2020  Will M. Farr <will.farr@ligo.org>
#                          Leo P. Singer <leo.singer@ligo.org>
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#

import copyreg
from functools import partial

from astropy.coordinates import SkyCoord
from astropy.utils.misc import NumpyRNGContext
import healpy as hp
import logging
import numpy as np
from scipy.stats import gaussian_kde

from . import distance
from . import moc
from .coordinates import EigenFrame
from .util import progress_map

log = logging.getLogger()

__all__ = ('BoundedKDE', 'Clustered2DSkyKDE', 'Clustered3DSkyKDE',
           'Clustered2Plus1DSkyKDE')


class BoundedKDE(gaussian_kde):
    """Density estimation using a KDE on bounded domains.

    Bounds can be any combination of low or high (if no bound, set to
    ``float('inf')`` or ``float('-inf')``), and can be periodic or
    non-periodic.  Cannot handle topologies that have
    multi-dimensional periodicities; will only handle topologies that
    are direct products of (arbitrary numbers of) R, [0,1], and S1.

    Parameters
    ----------
    pts : :class:`numpy.ndarray`
        ``(Ndim, Npts)`` shaped array of points (as in :class:`gaussian_kde`).
    low
        Lower bounds; if ``None``, assume no lower bounds.
    high
        Upper bounds; if ``None``, assume no upper bounds.
    periodic
        Boolean array giving periodicity in each dimension; if
        ``None`` assume no dimension is periodic.
    bw_method : optional
        Bandwidth estimation method (see :class:`gaussian_kde`).

    """

    def __init__(self, pts, low=-np.inf, high=np.inf, periodic=False,
                 bw_method=None):

        super().__init__(pts, bw_method=bw_method)
        self._low = np.broadcast_to(
            low, self.d).astype(self.dataset.dtype)
        self._high = np.broadcast_to(
            high, self.d).astype(self.dataset.dtype)
        self._periodic = np.broadcast_to(
            periodic, self.d).astype(bool)

    def evaluate(self, pts):
        """Evaluate the KDE at the given points."""
        pts = np.atleast_2d(pts)
        d, m = pts.shape
        if d != self.d and d == 1 and m == self.d:
            pts = pts.T

        pts_orig = pts
        pts = np.copy(pts_orig)

        den = super().evaluate(pts)

        for i, (low, high, period) in enumerate(zip(self._low, self._high,
                                                    self._periodic)):
            if period:
                p = high - low

                pts[i, :] += p
                den += super().evaluate(pts)

                pts[i, :] -= 2.0 * p
                den += super().evaluate(pts)

                pts[i, :] = pts_orig[i, :]

            else:
                if not np.isneginf(low):
                    pts[i, :] = 2.0 * low - pts[i, :]
                    den += super().evaluate(pts)
                    pts[i, :] = pts_orig[i, :]

                if not np.isposinf(high):
                    pts[i, :] = 2.0 * high - pts[i, :]
                    den += super().evaluate(pts)
                    pts[i, :] = pts_orig[i, :]

        return den

    __call__ = evaluate

    def quantile(self, pt):
        """Quantile of ``pt``, evaluated by a greedy algorithm.

        Parameters
        ----------
        pt
            The point at which the quantile value is to be computed.

        Notes
        -----
        The quantile of ``pt`` is the fraction of points used to construct the
        KDE that have a lower KDE density than ``pt``.

        """
        return np.count_nonzero(self(self.dataset) < self(pt)) / self.n


def km_assign(mus, cov, pts):
    """Implement the assignment step in the k-means algorithm.

    Given a set of centers, ``mus``, a covariance matrix used to produce a
    metric on the space, ``cov``, and a set of points, ``pts`` (shape ``(npts,
    ndim)``), assigns each point to its nearest center, returning an array of
    indices of shape ``(npts,)`` giving the assignments.
    """
    k = mus.shape[0]
    n = pts.shape[0]

    dists = np.zeros((k, n))

    for i, mu in enumerate(mus):
        dx = pts - mu
        try:
            dists[i, :] = np.sum(dx * np.linalg.solve(cov, dx.T).T, axis=1)
        except np.linalg.LinAlgError:
            dists[i, :] = np.nan

    return np.nanargmin(dists, axis=0)


def km_centroids(pts, assign, k):
    """Implement the centroid-update step of the k-means algorithm.

    Given a set of points, ``pts``, of shape ``(npts, ndim)``, and an
    assignment of each point to a region, ``assign``, and the number of means,
    ``k``, returns an array of shape ``(k, ndim)`` giving the centroid of each
    region.
    """
    mus = np.zeros((k, pts.shape[1]))
    for i in range(k):
        sel = assign == i
        if np.sum(sel) > 0:
            mus[i, :] = np.mean(pts[sel, :], axis=0)
        else:
            mus[i, :] = pts[np.random.randint(pts.shape[0]), :]

    return mus


def k_means(pts, k):
    """Perform k-means clustering on the set of points.

    Parameters
    ----------
    pts
        Array of shape ``(npts, ndim)`` giving the points on which k-means is
        to operate.
    k
        Positive integer giving the number of regions.

    Returns
    -------
    centroids
        An ``(k, ndim)`` array giving the centroid of each region.
    assign
        An ``(npts,)`` array of integers between 0 (inclusive) and k
        (exclusive) indicating the assignment of each point to a region.

    """
    assert pts.shape[0] > k, 'must have more points than means'

    cov = np.cov(pts, rowvar=0)

    mus = np.random.permutation(pts)[:k, :]
    assign = km_assign(mus, cov, pts)
    while True:
        old_assign = assign

        mus = km_centroids(pts, assign, k)
        assign = km_assign(mus, cov, pts)

        if np.all(assign == old_assign):
            break

    return mus, assign


def _cluster(cls, pts, trials, i, seed, jobs):
    k = i // trials
    if k == 0:
        raise ValueError('Expected at least one cluster')
    try:
        if k == 1:
            assign = np.zeros(len(pts), dtype=np.intp)
        else:
            with NumpyRNGContext(i + seed):
                _, assign = k_means(pts, k)
        obj = cls(pts, assign=assign)
    except np.linalg.LinAlgError:
        return -np.inf,
    else:
        return obj.bic, k, obj.kdes


class ClusteredKDE:

    def __init__(self, pts, max_k=40, trials=5, assign=None, jobs=1):
        self.jobs = jobs
        if assign is None:
            log.info('clustering ...')
            # Make sure that each thread gets a different random number state.
            # We start by drawing a random integer s in the main thread, and
            # then the i'th subprocess will seed itself with the integer i + s.
            #
            # The seed must be an unsigned 32-bit integer, so if there are n
            # threads, then s must be drawn from the interval [0, 2**32 - n).
            seed = np.random.randint(0, 2**32 - max_k * trials)
            func = partial(_cluster, type(self), pts, trials, seed=seed,
                           jobs=jobs)
            self.bic, self.k, self.kdes = max(
                self._map(func, range(trials, (max_k + 1) * trials)),
                key=lambda items: items[:2])
        else:
            # Build KDEs for each cluster, skipping degenerate clusters
            self.kdes = []
            npts, ndim = pts.shape
            self.k = assign.max() + 1
            for i in range(self.k):
                sel = (assign == i)
                cluster_pts = pts[sel, :]
                # Equivalent to but faster than len(set(pts))
                nuniq = len(np.unique(cluster_pts, axis=0))
                # Skip if there are fewer unique points than dimensions
                if nuniq <= ndim:
                    continue
                try:
                    kde = gaussian_kde(cluster_pts.T)
                except (np.linalg.LinAlgError, ValueError):
                    # If there are fewer unique points than degrees of freedom,
                    # then the KDE will fail because the covariance matrix is
                    # singular. In that case, don't bother adding that cluster.
                    pass
                else:
                    self.kdes.append(kde)

            # Calculate BIC
            # The number of parameters is:
            #
            # * ndim for each centroid location
            #
            # * (ndim+1)*ndim/2 Kernel covariances for each cluster
            #
            # * one weighting factor for the cluster (minus one for the
            #   overall constraint that the weights must sum to one)
            nparams = (self.k * ndim +
                       0.5 * self.k * (ndim + 1) * ndim + self.k - 1)
            with np.errstate(divide='ignore'):
                self.bic = (
                    np.sum(np.log(self.eval_kdes(pts))) -
                    0.5 * nparams * np.log(npts))

    def eval_kdes(self, pts):
        pts = pts.T
        return sum(w * kde(pts) for w, kde in zip(self.weights, self.kdes))

    def __call__(self, pts):
        return self.eval_kdes(pts)

    @property
    def weights(self):
        """Get the cluster weights: the fraction of the points within each
        cluster.
        """
        w = np.asarray([kde.n for kde in self.kdes])
        return w / np.sum(w)

    def _map(self, func, items):
        return progress_map(func, items, jobs=self.jobs)


class SkyKDE(ClusteredKDE):

    @classmethod
    def transform(cls, pts):
        """Override in sub-classes to transform points."""
        raise NotImplementedError

    def __init__(self, pts, max_k=40, trials=5, assign=None, jobs=1):
        if assign is None:
            pts = self.transform(pts)
        super().__init__(
            pts, max_k=max_k, trials=trials, assign=assign, jobs=jobs)

    def __call__(self, pts):
        return super().__call__(self.transform(pts))

    def as_healpix(self, top_nside=16, rounds=8):
        return moc.bayestar_adaptive_grid(self, top_nside=top_nside,
                                          rounds=rounds)


# We have to put in some hooks to make instances of Clustered2DSkyKDE picklable
# because we dynamically create subclasses with different values of the 'frame'
# class variable. This gets even trickier because we need both the class and
# instance objects to be picklable.


class _Clustered2DSkyKDEMeta(type):  # noqa: N802
    """Metaclass to make dynamically created subclasses of Clustered2DSkyKDE
    picklable.
    """


def _Clustered2DSkyKDEMeta_pickle(cls):  # noqa: N802
    """Pickle dynamically created subclasses of Clustered2DSkyKDE."""
    return type, (cls.__name__, cls.__bases__, {'frame': cls.frame})


# Register function to pickle subclasses of Clustered2DSkyKDE.
copyreg.pickle(_Clustered2DSkyKDEMeta, _Clustered2DSkyKDEMeta_pickle)


def _Clustered2DSkyKDE_factory(name, frame):  # noqa: N802
    """Unpickle instances of dynamically created subclasses of
    Clustered2DSkyKDE.

    FIXME: In Python 3, we could make this a class method of Clustered2DSkyKDE.
    Unfortunately, Python 2 is picky about pickling bound class methods.
    """
    new_cls = type(name, (Clustered2DSkyKDE,), {'frame': frame})
    return super(Clustered2DSkyKDE, Clustered2DSkyKDE).__new__(new_cls)


class Clustered2DSkyKDE(SkyKDE, metaclass=_Clustered2DSkyKDEMeta):
    r"""Represents a kernel-density estimate of a sky-position PDF that has
    been decomposed into clusters, using a different kernel for each
    cluster.

    The estimated PDF is

    .. math::

      p\left( \vec{\theta} \right) = \sum_{i = 0}^{k-1} \frac{N_i}{N}
      \sum_{\vec{x} \in C_i} N\left[\vec{x}, \Sigma_i\right]\left( \vec{\theta}
      \right)

    where :math:`C_i` is the set of points belonging to cluster
    :math:`i`, :math:`N_i` is the number of points in this cluster,
    :math:`\Sigma_i` is the optimally-converging KDE covariance
    associated to cluster :math:`i`.

    The number of clusters, :math:`k` is chosen to maximize the `BIC
    <http://en.wikipedia.org/wiki/Bayesian_information_criterion>`_
    for the given set of points being drawn from the clustered KDE.
    The points are assigned to clusters using the k-means algorithm,
    with a decorrelated metric.  The overall clustering behavior is
    similar to the well-known `X-Means
    <http://www.cs.cmu.edu/~dpelleg/download/xmeans.pdf>`_ algorithm.
    """

    frame = None

    @classmethod
    def transform(cls, pts):
        pts = SkyCoord(*pts.T, unit='rad').transform_to(cls.frame).spherical
        return np.column_stack((pts.lon.rad, np.sin(pts.lat.rad)))

    def __new__(cls, pts, *args, **kwargs):
        frame = EigenFrame.for_coords(SkyCoord(*pts.T, unit='rad'))
        name = '{:s}_{:x}'.format(cls.__name__, id(frame))
        new_cls = type(name, (cls,), {'frame': frame})
        return super().__new__(new_cls)

    def __reduce__(self):
        """Pickle instances of dynamically created subclasses of
        Clustered2DSkyKDE.
        """
        factory_args = self.__class__.__name__, self.frame
        return _Clustered2DSkyKDE_factory, factory_args, self.__dict__

    def eval_kdes(self, pts):
        base = super().eval_kdes
        dphis = (0.0, 2 * np.pi, -2 * np.pi)
        phi, z = pts.T
        return sum(base(np.column_stack((phi + dphi, z))) for dphi in dphis)


class Clustered3DSkyKDE(SkyKDE):
    """Like :class:`Clustered2DSkyKDE`, but clusters in 3D
    space.  Can compute volumetric posterior density (per cubic Mpc),
    and also produce Healpix maps of the mean and standard deviation
    of the log-distance.
    """

    @classmethod
    def transform(cls, pts):
        return SkyCoord(*pts.T, unit='rad').cartesian.xyz.value.T

    def __call__(self, pts, distances=False):
        """Given an array of positions in RA, DEC, compute the marginal sky
        posterior and optinally the conditional distance parameters.
        """
        func = partial(distance.cartesian_kde_to_moments,
                       datasets=[_.dataset for _ in self.kdes],
                       inverse_covariances=[_.inv_cov for _ in self.kdes],
                       weights=self.weights)
        probdensity, mean, std = zip(*self._map(func, self.transform(pts)))
        if distances:
            mu, sigma, norm = distance.moments_to_parameters(mean, std)
            return probdensity, mu, sigma, norm
        else:
            return probdensity

    def posterior_spherical(self, pts):
        """Evaluate the posterior probability density in spherical polar
        coordinates, as a function of (ra, dec, distance).
        """
        return super().__call__(pts)

    def as_healpix(self, top_nside=16):
        """Return a HEALPix multi-order map of the posterior density and
        conditional distance distribution parameters.
        """
        m = super().as_healpix(top_nside=top_nside)
        order, ipix = moc.uniq2nest(m['UNIQ'])
        nside = 2 ** order.astype(int)
        theta, phi = hp.pix2ang(nside, ipix, nest=True)
        p = np.column_stack((phi, 0.5 * np.pi - theta))
        print('evaluating distance layers ...')
        _, m['DISTMU'], m['DISTSIGMA'], m['DISTNORM'] = self(p, distances=True)
        return m


class Clustered2Plus1DSkyKDE(Clustered3DSkyKDE):
    """A hybrid sky map estimator that uses a 2D clustered KDE for the marginal
    distribution as a function of (RA, Dec) and a 3D clustered KDE for the
    conditional distance distribution.
    """

    def __init__(self, pts, max_k=40, trials=5, assign=None, jobs=1):
        if assign is None:
            self.twod = Clustered2DSkyKDE(
                pts, max_k=max_k, trials=trials, assign=assign, jobs=jobs)
        super().__init__(
            pts, max_k=max_k, trials=trials, assign=assign, jobs=jobs)

    def __call__(self, pts, distances=False):
        probdensity = self.twod(pts)
        if distances:
            _, distmu, distsigma, distnorm = super().__call__(
                pts, distances=True)
            return probdensity, distmu, distsigma, distnorm
        else:
            return probdensity

    def posterior_spherical(self, pts):
        """Evaluate the posterior probability density in spherical polar
        coordinates, as a function of (ra, dec, distance).
        """
        return self(pts) * super().posterior_spherical(pts) / super().__call__(
            pts)

#
# Copyright (C) 2017-2023  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""
Support for HEALPix UNIQ pixel indexing [1]_ and multi-order coverage (MOC)
maps [2]_.

References
----------
.. [1] Reinecke & Hivon, 2015. "Efficient data structures for masks on 2D
       grids." AA 580, A132. :doi:`10.1051/0004-6361/201526549`
.. [2] Boch et al., 2014. "MOC - HEALPix Multi-Order Coverage map." IVOA
       Recommendation <http://ivoa.net/documents/MOC/>.

"""

from astropy import table
from astropy import units as u
import astropy_healpix as ah
import numpy as np
from numpy.lib.recfunctions import repack_fields

from .core import nest2uniq, uniq2nest, uniq2order, uniq2pixarea, uniq2ang
from .core import rasterize as _rasterize
from .util.numpy import add_newdoc_ufunc, require_contiguous_aligned

__all__ = ('nest2uniq', 'uniq2nest', 'uniq2order', 'uniq2pixarea',
           'uniq2ang', 'rasterize', 'bayestar_adaptive_grid')


add_newdoc_ufunc(nest2uniq, """\
Convert a pixel index from NESTED to NUNIQ ordering.

Parameters
----------
order : `numpy.ndarray`
    HEALPix resolution order, the logarithm base 2 of `nside`
ipix : `numpy.ndarray`
    NESTED pixel index

Returns
-------
uniq : `numpy.ndarray`
    NUNIQ pixel index

""")
nest2uniq = require_contiguous_aligned(nest2uniq)


add_newdoc_ufunc(uniq2order, """\
Determine the HEALPix resolution order of a HEALPix NESTED index.

Parameters
----------
uniq : `numpy.ndarray`
    NUNIQ pixel index

Returns
-------
order : `numpy.ndarray`
    HEALPix resolution order, the logarithm base 2 of `nside`

""")
uniq2order = require_contiguous_aligned(uniq2order)


add_newdoc_ufunc(uniq2pixarea, """\
Determine the area of a HEALPix NESTED index.

Parameters
----------
uniq : `numpy.ndarray`
    NUNIQ pixel index

Returns
-------
area : `numpy.ndarray`
    The pixel's area in steradians

""")
uniq2pixarea = require_contiguous_aligned(uniq2pixarea)


add_newdoc_ufunc(uniq2nest, """\
Convert a pixel index from NUNIQ to NESTED ordering.

Parameters
----------
uniq : `numpy.ndarray`
    NUNIQ pixel index

Returns
-------
order : `numpy.ndarray`
    HEALPix resolution order (logarithm base 2 of `nside`)
ipix : `numpy.ndarray`
    NESTED pixel index

""")
uniq2nest = require_contiguous_aligned(uniq2nest)


def rasterize(moc_data, order=None):
    """Convert a multi-order HEALPix dataset to fixed-order NESTED ordering.

    Parameters
    ----------
    moc_data : `numpy.ndarray`
        A multi-order HEALPix dataset stored as a Numpy record array whose
        first column is called UNIQ and contains the NUNIQ pixel index. Every
        point on the unit sphere must be contained in exactly one pixel in the
        dataset.
    order : int, optional
        The desired output resolution order, or :obj:`None` for the maximum
        resolution present in the dataset.

    Returns
    -------
    nested_data : `numpy.ndarray`
        A fixed-order, NESTED-ordering HEALPix dataset with all of the columns
        that were in moc_data, with the exception of the UNIQ column.

    """
    if order is None or order < 0:
        order = -1
    else:
        orig_order, orig_nest = uniq2nest(moc_data['UNIQ'])
        to_downsample = order < orig_order
        if np.any(to_downsample):
            to_keep = table.Table(moc_data[~to_downsample], copy=False)
            orig_order = orig_order[to_downsample]
            orig_nest = orig_nest[to_downsample]
            to_downsample = table.Table(moc_data[to_downsample], copy=False)

            ratio = 1 << (2 * np.int64(orig_order - order))
            weights = 1.0 / ratio
            for colname, column in to_downsample.columns.items():
                if colname != 'UNIQ':
                    column *= weights
            to_downsample['UNIQ'] = nest2uniq(order, orig_nest // ratio)
            to_downsample = to_downsample.group_by(
                'UNIQ').groups.aggregate(np.sum)

            moc_data = table.vstack((to_keep, to_downsample))

    # Ensure that moc_data has appropriate padding for each of its columns to
    # be properly aligned in order to avoid undefined behavior.
    moc_data = repack_fields(np.asarray(moc_data), align=True)

    return _rasterize(moc_data, order=order)


def bayestar_adaptive_grid(probdensity, *args, top_nside=16, rounds=8,
                           **kwargs):
    """Create a sky map by evaluating a function on an adaptive grid.

    Perform the BAYESTAR adaptive mesh refinement scheme as described in
    Section VI of Singer & Price 2016, PRD, 93, 024013
    :doi:`10.1103/PhysRevD.93.024013`. This computes the sky map
    using a provided analytic function and refines the grid, dividing the
    highest 25% into subpixels and then recalculating their values. The extra
    given args and kwargs will be passed to the given probdensity function.

    Parameters
    ----------
    probdensity : callable
        Probability density function. The first argument consists of
        column-stacked array of right ascension and declination in radians.
        The return value must be a 1D array of the probability density in
        inverse steradians with the same length as the argument.
    top_nside : int
        HEALPix NSIDE resolution of initial evaluation of the sky map
    rounds : int
        Number of refinement rounds, including the initial sky map evaluation

    Returns
    -------
    skymap : astropy.table.Table
        An astropy Table with UNIQ and PROBDENSITY columns, representing
        a multi-ordered sky map
    """
    top_npix = ah.nside_to_npix(top_nside)
    nrefine = top_npix // 4
    cells = zip([0] * nrefine, [top_nside // 2] * nrefine, range(nrefine))
    for iround in range(rounds + 1):
        print('adaptive refinement round {} of {} ...'.format(
            iround, rounds))
        cells = sorted(cells, key=lambda p_n_i: p_n_i[0] / p_n_i[1]**2)
        new_nside, new_ipix = np.transpose([
            (nside * 2, ipix * 4 + i)
            for _, nside, ipix in cells[-nrefine:] for i in range(4)])
        ra, dec = ah.healpix_to_lonlat(new_ipix, new_nside, order='nested')
        p = probdensity(np.column_stack((ra.value, dec.value)),
                        *args, **kwargs)
        cells[-nrefine:] = zip(p, new_nside, new_ipix)

    """Return a HEALPix multi-order map of the posterior density."""
    post, nside, ipix = zip(*cells)
    post = np.asarray(list(post))
    nside = np.asarray(list(nside))
    ipix = np.asarray(list(ipix))

    # Make sure that sky map is normalized (it should be already)
    post /= np.sum(post * ah.nside_to_pixel_area(nside).to_value(u.sr))

    # Convert from NESTED to UNIQ pixel indices
    order = np.log2(nside).astype(int)
    uniq = nest2uniq(order.astype(np.int8), ipix)

    # Done!
    return table.Table([uniq, post], names=['UNIQ', 'PROBDENSITY'],
                       copy=False)


del add_newdoc_ufunc, require_contiguous_aligned

#
# Copyright (C) 2013-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""
Rapid sky localization with BAYESTAR [1]_.

References
----------
.. [1] Singer & Price, 2016. "Rapid Bayesian position reconstruction for
       gravitational-wave transients." PRD, 93, 024013.
       :doi:`10.1103/PhysRevD.93.024013`

"""
import inspect
import logging
import os
import sys
from textwrap import wrap

from astropy.table import Column, Table
from astropy import units as u
import lal
import lalsimulation
import numpy as np

from .. import distance
from . import filter
from ..io.hdf5 import write_samples
from ..io.fits import metadata_for_version_module
from ..io.events.base import Event
from . import filter  # noqa
from ..kde import Clustered2Plus1DSkyKDE
from .. import moc
from .. import healpix_tree
from .. import version
from .. import core
from ..core import (antenna_factor, signal_amplitude_model,
                    log_posterior_toa_phoa_snr as _log_posterior_toa_phoa_snr)
from ..util.numpy import require_contiguous_aligned
from ..util.stopwatch import Stopwatch
from .ez_emcee import ez_emcee

__all__ = ('derasterize', 'localize', 'rasterize', 'antenna_factor',
           'signal_amplitude_model')

log = logging.getLogger('BAYESTAR')

_RESCALE_LOGLIKELIHOOD = 0.83

antenna_factor = require_contiguous_aligned(antenna_factor)
signal_amplitude_model = require_contiguous_aligned(signal_amplitude_model)
_log_posterior_toa_phoa_snr = require_contiguous_aligned(
    _log_posterior_toa_phoa_snr)


# Wrap so that ufunc parameter names are known
def log_posterior_toa_phoa_snr(
        ra, sin_dec, distance, u, twopsi, t, min_distance, max_distance,
        prior_distance_power, cosmology, gmst, sample_rate, epochs, snrs,
        responses, locations, horizons,
        rescale_loglikelihood=_RESCALE_LOGLIKELIHOOD):
    return _log_posterior_toa_phoa_snr(
        ra, sin_dec, distance, u, twopsi, t, min_distance, max_distance,
        prior_distance_power, cosmology, gmst, sample_rate, epochs, snrs,
        responses, locations, horizons, rescale_loglikelihood)


# Wrap so that fixed parameter values are pulled from keyword arguments
def log_post(params, *args, **kwargs):
    # Names of parameters
    keys = ('ra', 'sin_dec', 'distance', 'u', 'twopsi', 't')

    params = list(params.T)
    kwargs = dict(kwargs)

    return log_posterior_toa_phoa_snr(
        *(kwargs.pop(key) if key in kwargs else params.pop(0) for key in keys),
        *args, **kwargs)


def localize_emcee(args, xmin, xmax, chain_dump=None):
    # Gather posterior samples
    chain = ez_emcee(log_post, xmin, xmax, args=args, vectorize=True)

    # Transform back from sin_dec to dec and cos_inclination to inclination
    chain[:, 1] = np.arcsin(chain[:, 1])
    chain[:, 3] = np.arccos(chain[:, 3])

    # Optionally save posterior sample chain to file.
    if chain_dump:
        _, ndim = chain.shape
        names = 'ra dec distance inclination twopsi time'.split()[:ndim]
        write_samples(Table(rows=chain, names=names, copy=False), chain_dump,
                      path='/bayestar/posterior_samples', overwrite=True)

    # Pass a random subset of 1000 points to the KDE, to save time.
    pts = np.random.permutation(chain)[:1000, :3]
    ckde = Clustered2Plus1DSkyKDE(pts)
    return ckde.as_healpix()


def condition(
        event, waveform='o2-uberbank', f_low=30.0,
        enable_snr_series=True, f_high_truncate=0.95):

    if len(event.singles) == 0:
        raise ValueError('Cannot localize an event with zero detectors.')

    singles = event.singles
    if not enable_snr_series:
        singles = [single for single in singles if single.snr is not None]

    ifos = [single.detector for single in singles]

    # Extract SNRs from table.
    snrs = np.ma.asarray([
        np.ma.masked if single.snr is None else single.snr
        for single in singles])

    # Look up physical parameters for detector.
    detectors = [lalsimulation.DetectorPrefixToLALDetector(str(ifo))
                 for ifo in ifos]
    responses = np.asarray([det.response for det in detectors])
    locations = np.asarray([det.location for det in detectors]) / lal.C_SI

    # Power spectra for each detector.
    psds = [single.psd for single in singles]
    psds = [filter.InterpolatedPSD(filter.abscissa(psd), psd.data.data,
                                   f_high_truncate=f_high_truncate)
            for psd in psds]

    log.debug('calculating templates')
    H = filter.sngl_inspiral_psd(waveform, f_min=f_low, **event.template_args)

    log.debug('calculating noise PSDs')
    HS = [filter.signal_psd_series(H, S) for S in psds]

    # Signal models for each detector.
    log.debug('calculating Fisher matrix elements')
    signal_models = [filter.SignalModel(_) for _ in HS]

    # Get SNR=1 horizon distances for each detector.
    horizons = np.asarray([signal_model.get_horizon_distance()
                           for signal_model in signal_models])

    weights = np.ma.asarray([
        1 / np.square(signal_model.get_crb_toa_uncert(snr))
        for signal_model, snr in zip(signal_models, snrs)])

    # Center detector array.
    locations -= (np.sum(locations * weights.reshape(-1, 1), axis=0) /
                  np.sum(weights))

    if enable_snr_series:
        snr_series = [single.snr_series for single in singles]
        if all(s is None for s in snr_series):
            snr_series = None
    else:
        snr_series = None

    # Maximum barycentered arrival time error:
    # |distance from array barycenter to furthest detector| / c + 5 ms.
    # For LHO+LLO, this is 15.0 ms.
    # For an arbitrary terrestrial detector network, the maximum is 26.3 ms.
    max_abs_t = np.max(
        np.sqrt(np.sum(np.square(locations), axis=1))) + 0.005

    # Calculate a minimum arrival time prior for low-bandwidth signals.
    # This is important for early-warning events, for which the light travel
    # time between detectors may be only a tiny fraction of the template
    # autocorrelation time.
    #
    # The period of the autocorrelation function is 2 pi times the timing
    # uncertainty at SNR=1 (see Eq. (24) of [1]_). We want a quarter period:
    # there is a factor of a half because we want the first zero crossing,
    # and another factor of a half because the SNR time series will be cropped
    # to a two-sided interval.
    max_acor_t = max(0.5 * np.pi * signal_model.get_crb_toa_uncert(1)
                     for signal_model in signal_models)
    max_abs_t = max(max_abs_t, max_acor_t)

    if snr_series is None:
        log.warning("No SNR time series found, so we are creating a "
                    "zero-noise SNR time series from the whitened template's "
                    "autocorrelation sequence. The sky localization "
                    "uncertainty may be underestimated.")

        acors, sample_rates = zip(
            *[filter.autocorrelation(_, max_abs_t) for _ in HS])
        sample_rate = sample_rates[0]
        deltaT = 1 / sample_rate
        nsamples = len(acors[0])
        assert all(sample_rate == _ for _ in sample_rates)
        assert all(nsamples == len(_) for _ in acors)
        nsamples = nsamples * 2 - 1

        snr_series = []
        for acor, single in zip(acors, singles):
            series = lal.CreateCOMPLEX8TimeSeries(
                'fake SNR', 0, 0, deltaT, lal.StrainUnit, nsamples)
            series.epoch = single.time - 0.5 * (nsamples - 1) * deltaT
            acor = np.concatenate((np.conj(acor[:0:-1]), acor))
            series.data.data = single.snr * filter.exp_i(single.phase) * acor
            snr_series.append(series)

    # Ensure that all of the SNR time series have the same sample rate.
    # FIXME: for now, the Python wrapper expects all of the SNR time series to
    # also be the same length.
    deltaT = snr_series[0].deltaT
    sample_rate = 1 / deltaT
    if any(deltaT != series.deltaT for series in snr_series):
        raise ValueError('BAYESTAR does not yet support SNR time series with '
                         'mixed sample rates')

    # Ensure that all of the SNR time series have odd lengths.
    if any(len(series.data.data) % 2 == 0 for series in snr_series):
        raise ValueError('SNR time series must have odd lengths')

    # Trim time series to the desired length.
    max_abs_n = int(np.ceil(max_abs_t * sample_rate))
    desired_length = 2 * max_abs_n - 1
    for i, series in enumerate(snr_series):
        length = len(series.data.data)
        if length > desired_length:
            snr_series[i] = lal.CutCOMPLEX8TimeSeries(
                series, length // 2 + 1 - max_abs_n, desired_length)

    # FIXME: for now, the Python wrapper expects all of the SNR time sries to
    # also be the same length.
    nsamples = len(snr_series[0].data.data)
    if any(nsamples != len(series.data.data) for series in snr_series):
        raise ValueError('BAYESTAR does not yet support SNR time series of '
                         'mixed lengths')

    # Perform sanity checks that the middle sample of the SNR time series match
    # the sngl_inspiral records to the nearest sample (plus the smallest
    # representable LIGOTimeGPS difference of 1 nanosecond).
    for ifo, single, series in zip(ifos, singles, snr_series):
        shift = np.abs(0.5 * (nsamples - 1) * series.deltaT +
                       float(series.epoch - single.time))
        if shift >= deltaT + 1e-8:
            raise ValueError('BAYESTAR expects the SNR time series to be '
                             'centered on the single-detector trigger times, '
                             'but {} was off by {} s'.format(ifo, shift))

    # Extract the TOAs in GPS nanoseconds from the SNR time series, assuming
    # that the trigger happened in the middle.
    toas_ns = [series.epoch.ns() + 1e9 * 0.5 * (len(series.data.data) - 1) *
               series.deltaT for series in snr_series]

    # Collect all of the SNR series in one array.
    snr_series = np.vstack([series.data.data for series in snr_series])

    # Center times of arrival and compute GMST at mean arrival time.
    # Pre-center in integer nanoseconds to preserve precision of
    # initial datatype.
    epoch = sum(toas_ns) // len(toas_ns)
    toas = 1e-9 * (np.asarray(toas_ns) - epoch)
    mean_toa = np.average(toas, weights=weights)
    toas -= mean_toa
    epoch += int(np.round(1e9 * mean_toa))
    epoch = lal.LIGOTimeGPS(0, int(epoch))

    # Translate SNR time series back to time of first sample.
    toas -= 0.5 * (nsamples - 1) * deltaT

    # Convert complex SNRS to amplitude and phase
    snrs_abs = np.abs(snr_series)
    snrs_arg = filter.unwrap(np.angle(snr_series))
    snrs = np.stack((snrs_abs, snrs_arg), axis=-1)

    return epoch, sample_rate, toas, snrs, responses, locations, horizons


def condition_prior(horizons, min_distance=None, max_distance=None,
                    prior_distance_power=None, cosmology=False):
    if cosmology:
        log.warning('Enabling cosmological prior. This feature is UNREVIEWED.')

    # If minimum distance is not specified, then default to 0 Mpc.
    if min_distance is None:
        min_distance = 0

    # If maximum distance is not specified, then default to the SNR=4
    # horizon distance of the most sensitive detector.
    if max_distance is None:
        max_distance = max(horizons) / 4

    # If prior_distance_power is not specified, then default to 2
    # (p(r) ~ r^2, uniform in volume).
    if prior_distance_power is None:
        prior_distance_power = 2

    # Raise an exception if 0 Mpc is the minimum effective distance and the
    # prior is of the form r**k for k<0
    if min_distance == 0 and prior_distance_power < 0:
        raise ValueError(('Prior is a power law r^k with k={}, '
                          'undefined at min_distance=0').format(
                              prior_distance_power))

    return min_distance, max_distance, prior_distance_power, cosmology


def localize(
        event, waveform='o2-uberbank', f_low=30.0,
        min_inclination=0, max_inclination=np.pi / 2,
        min_distance=None, max_distance=None, prior_distance_power=None,
        cosmology=False, mcmc=False, chain_dump=None,
        enable_snr_series=True, f_high_truncate=0.95,
        rescale_loglikelihood=_RESCALE_LOGLIKELIHOOD):
    """Localize a compact binary signal using the BAYESTAR algorithm.

    Parameters
    ----------
    event : `ligo.skymap.io.events.Event`
        The event candidate.
    waveform : str, optional
        The name of the waveform approximant.
    f_low : float, optional
        The low frequency cutoff.
    min_distance, max_distance : float, optional
        The limits of integration over luminosity distance, in Mpc
        (default: determine automatically from detector sensitivity).
    prior_distance_power : int, optional
        The power of distance that appears in the prior
        (default: 2, uniform in volume).
    cosmology: bool, optional
        Set to enable a uniform in comoving volume prior (default: false).
    mcmc : bool, optional
        Set to use MCMC sampling rather than more accurate Gaussian quadrature.
    chain_dump : str, optional
        Save posterior samples to this filename if `mcmc` is set.
    enable_snr_series : bool, optional
        Set to False to disable SNR time series.
    f_high_truncate : float, optional
        Truncate the noise power spectral densities at this factor times the
        highest sampled frequency to suppress artifacts caused by incorrect
        PSD conditioning by some matched filter pipelines.

    Returns
    -------
    skymap : `astropy.table.Table`
        A 3D sky map in multi-order HEALPix format.

    """
    # Hide event parameters, but show all other arguments
    def formatvalue(value):
        if isinstance(value, Event):
            return '=...'
        else:
            return '=' + repr(value)

    frame = inspect.currentframe()
    argstr = inspect.formatargvalues(*inspect.getargvalues(frame),
                                     formatvalue=formatvalue)

    stopwatch = Stopwatch()
    stopwatch.start()

    epoch, sample_rate, toas, snrs, responses, locations, horizons = \
        condition(event, waveform=waveform, f_low=f_low,
                  enable_snr_series=enable_snr_series,
                  f_high_truncate=f_high_truncate)

    min_distance, max_distance, prior_distance_power, cosmology = \
        condition_prior(horizons, min_distance, max_distance,
                        prior_distance_power, cosmology)

    gmst = lal.GreenwichMeanSiderealTime(epoch)

    # Time and run sky localization.
    log.debug('starting computationally-intensive section')
    if mcmc:
        max_abs_t = 2 * snrs.data.shape[1] / sample_rate
        if min_inclination != 0 or max_inclination != np.pi / 2:
            log.warn('inclination limits are not supported for MCMC mode')
        args = (min_distance, max_distance, prior_distance_power, cosmology,
                gmst, sample_rate, toas, snrs, responses, locations, horizons,
                rescale_loglikelihood)
        skymap = localize_emcee(
            args=args,
            xmin=[0, -1, min_distance, -1, 0, 0],
            xmax=[2 * np.pi, 1, max_distance, 1, 2 * np.pi, 2 * max_abs_t],
            chain_dump=chain_dump)
    else:
        args = (min_inclination, max_inclination, min_distance, max_distance,
                prior_distance_power, cosmology, gmst, sample_rate, toas, snrs,
                responses, locations, horizons, rescale_loglikelihood)
        skymap, log_bci, log_bsn = core.toa_phoa_snr(*args)
        skymap = Table(skymap, copy=False)
        skymap.meta['log_bci'] = log_bci
        skymap.meta['log_bsn'] = log_bsn

    # Convert distance moments to parameters
    try:
        distmean = skymap.columns.pop('DISTMEAN')
        diststd = skymap.columns.pop('DISTSTD')
    except KeyError:
        distmean, diststd, _ = distance.parameters_to_moments(
            skymap['DISTMU'], skymap['DISTSIGMA'])
    else:
        skymap['DISTMU'], skymap['DISTSIGMA'], skymap['DISTNORM'] = \
            distance.moments_to_parameters(distmean, diststd)

    # Add marginal distance moments
    good = np.isfinite(distmean) & np.isfinite(diststd)
    prob = (moc.uniq2pixarea(skymap['UNIQ']) * skymap['PROBDENSITY'])[good]
    distmean = distmean[good]
    diststd = diststd[good]
    rbar = (prob * distmean).sum()
    r2bar = (prob * (np.square(diststd) + np.square(distmean))).sum()
    skymap.meta['distmean'] = rbar
    skymap.meta['diststd'] = np.sqrt(r2bar - np.square(rbar))

    stopwatch.stop()
    end_time = lal.GPSTimeNow()
    log.info('finished computationally-intensive section in %s', stopwatch)

    # Fill in metadata and return.
    program, _ = os.path.splitext(os.path.basename(sys.argv[0]))
    skymap.meta.update(metadata_for_version_module(version))
    skymap.meta['creator'] = 'BAYESTAR'
    skymap.meta['origin'] = 'LIGO/Virgo/KAGRA'
    skymap.meta['gps_time'] = float(epoch)
    skymap.meta['runtime'] = stopwatch.real
    skymap.meta['instruments'] = {single.detector for single in event.singles}
    skymap.meta['gps_creation_time'] = end_time
    skymap.meta['history'] = [
        '',
        'Generated by calling the following Python function:',
        *wrap('{}.{}{}'.format(__name__, frame.f_code.co_name, argstr), 72),
        '',
        'This was the command line that started the program:',
        *wrap(' '.join([program] + sys.argv[1:]), 72)]

    return skymap


def rasterize(skymap, order=None):
    orig_order, _ = moc.uniq2nest(skymap['UNIQ'].max())

    # Determine whether we need to do nontrivial downsampling.
    downsampling = (order is not None and 0 <= order < orig_order
                    and 'DISTMU' in skymap.dtype.fields.keys())

    # If we are downsampling, then convert from distance parameters to
    # distance moments times probability density so that the averaging
    # that is automatically done by moc.rasterize() correctly marginalizes
    # the moments.
    if downsampling:
        skymap = Table(skymap, copy=True, meta=skymap.meta)

        probdensity = skymap['PROBDENSITY']
        distmu = skymap.columns.pop('DISTMU')
        distsigma = skymap.columns.pop('DISTSIGMA')

        bad = ~(np.isfinite(distmu) & np.isfinite(distsigma))
        distmean, diststd, _ = distance.parameters_to_moments(
            distmu, distsigma)
        distmean[bad] = np.nan
        diststd[bad] = np.nan
        skymap['DISTMEAN'] = probdensity * distmean
        skymap['DISTVAR'] = probdensity * (
            np.square(diststd) + np.square(distmean))

    skymap = Table(moc.rasterize(skymap, order=order),
                   meta=skymap.meta, copy=False)

    # If we are downsampling, then convert back to distance parameters.
    if downsampling:
        distmean = skymap.columns.pop('DISTMEAN') / skymap['PROBDENSITY']
        diststd = np.sqrt(
            skymap.columns.pop('DISTVAR') / skymap['PROBDENSITY']
            - np.square(distmean))
        skymap['DISTMU'], skymap['DISTSIGMA'], skymap['DISTNORM'] = \
            distance.moments_to_parameters(
                distmean, diststd)

    skymap.rename_column('PROBDENSITY', 'PROB')
    skymap['PROB'] *= 4 * np.pi / len(skymap)
    skymap['PROB'].unit = u.pixel ** -1
    return skymap


def derasterize(skymap):
    skymap.rename_column('PROB', 'PROBDENSITY')
    skymap['PROBDENSITY'] *= len(skymap) / (4 * np.pi)
    skymap['PROBDENSITY'].unit = u.steradian ** -1
    nside, _, ipix, _, _, value = zip(
        *healpix_tree.reconstruct_nested(skymap))
    nside = np.asarray(nside)
    ipix = np.asarray(ipix)
    value = np.stack(value)
    uniq = (4 * np.square(nside) + ipix)
    old_units = [column.unit for column in skymap.columns.values()]
    skymap = Table(value, meta=skymap.meta, copy=False)
    for old_unit, column in zip(old_units, skymap.columns.values()):
        column.unit = old_unit
    skymap.add_column(Column(uniq, name='UNIQ'), 0)
    skymap.sort('UNIQ')
    return skymap


def test():
    """Run BAYESTAR C unit tests.

    Examples
    --------
    >>> test()
    0

    """
    return int(core.test())


del require_contiguous_aligned

# Copyright (C) 2018-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
import numpy as np
from tqdm import tqdm

from .ptemcee import Sampler

__all__ = ('ez_emcee',)


def logp(x, lo, hi):
    return np.where(((x >= lo) & (x <= hi)).all(-1), 0.0, -np.inf)


def ez_emcee(log_prob_fn, lo, hi, nindep=200,
             ntemps=10, nwalkers=None, nburnin=500,
             args=(), kwargs={}, **options):
    r'''Fire-and-forget MCMC sampling using `ptemcee.Sampler`, featuring
    automated convergence monitoring, progress tracking, and thinning.

    The parameters are bounded in the finite interval described by ``lo`` and
    ``hi`` (including ``-np.inf`` and ``np.inf`` for half-infinite or infinite
    domains).

    If run in an interactive terminal, live progress is shown including the
    current sample number, the total required number of samples, time elapsed
    and estimated time remaining, acceptance fraction, and autocorrelation
    length.

    Sampling terminates when all chains have accumulated the requested number
    of independent samples.

    Parameters
    ----------
    log_prob_fn : callable
        The log probability function. It should take as its argument the
        parameter vector as an of length ``ndim``, or if it is vectorized, a 2D
        array with ``ndim`` columns.
    lo : list, `numpy.ndarray`
        List of lower limits of parameters, of length ``ndim``.
    hi : list, `numpy.ndarray`
        List of upper limits of parameters, of length ``ndim``.
    nindep : int, optional
        Minimum number of independent samples.
    ntemps : int, optional
        Number of temperatures.
    nwalkers : int, optional
        Number of walkers. The default is 4 times the number of dimensions.
    nburnin : int, optional
        Number of samples to discard during burn-in phase.

    Returns
    -------
    chain : `numpy.ndarray`
        The thinned and flattened posterior sample chain,
        with at least ``nindep`` * ``nwalkers`` rows
        and exactly ``ndim`` columns.

    Other parameters
    ----------------
    kwargs :
        Extra keyword arguments for `ptemcee.Sampler`.
        *Tip:* Consider setting the `pool` or `vectorized` keyword arguments in
        order to speed up likelihood evaluations.

    Notes
    -----
    The autocorrelation length, which has a complexity of :math:`O(N \log N)`
    in the number of samples, is recalculated at geometrically progressing
    intervals so that its amortized complexity per sample is constant. (In
    simpler terms, as the chains grow longer and the autocorrelation length
    takes longer to compute, we update it less frequently so that it is never
    more expensive than sampling the chain in the first place.)

    Examples
    --------
    >>> from ligo.skymap.bayestar.ez_emcee import ez_emcee
    >>> from matplotlib import pyplot as plt
    >>> import numpy as np
    >>>
    >>> def log_prob(params):
    ...     """Eggbox function"""
    ...     return 5 * np.log((2 + np.cos(0.5 * params).prod(-1)))
    ...
    >>> lo = [-3*np.pi, -3*np.pi]
    >>> hi = [+3*np.pi, +3*np.pi]
    >>> chain = ez_emcee(log_prob, lo, hi, vectorize=True)   # doctest: +SKIP
    Sampling:  51%|██  | 8628/16820 [00:04<00:04, 1966.74it/s, accept=0.535, acl=62]
    >>> plt.plot(chain[:, 0], chain[:, 1], '.')   # doctest: +SKIP

    .. image:: eggbox.png

    '''  # noqa: E501
    lo = np.asarray(lo)
    hi = np.asarray(hi)
    ndim = len(lo)

    if nwalkers is None:
        nwalkers = 4 * ndim

    nsteps = 64

    with tqdm(total=nburnin + nindep * nsteps) as progress:

        sampler = Sampler(nwalkers, ndim, log_prob_fn, logp,
                          ntemps=ntemps, loglargs=args, loglkwargs=kwargs,
                          logpargs=[lo, hi], random=np.random, **options)
        pos = np.random.uniform(lo, hi, (ntemps, nwalkers, ndim))

        # Burn in
        progress.set_description('Burning in')
        for pos, _, _ in sampler.sample(
                pos, iterations=nburnin, storechain=False):
            progress.update()

        sampler.reset()
        acl = np.nan
        while not np.isfinite(acl) or sampler.time < nindep * acl:

            # Advance the chain
            progress.total = nburnin + max(sampler.time + nsteps,
                                           nindep * acl)
            progress.set_description('Sampling')
            for pos, _, _ in sampler.sample(pos, iterations=nsteps):
                progress.update()

            # Refresh convergence statistics
            progress.set_description('Checking')
            acl = sampler.get_autocorr_time()[0].max()
            if np.isfinite(acl):
                acl = max(1, int(np.ceil(acl)))
            accept = np.mean(sampler.acceptance_fraction[0])
            progress.set_postfix(acl=acl, accept=accept)

            # The autocorrelation time calculation has complexity N log N in
            # the number of posterior samples. Only refresh the autocorrelation
            # length estimate on logarithmically spaced samples so that the
            # amortized complexity per sample is constant.
            nsteps *= 2

    chain = sampler.chain[0, :, ::acl, :]
    s = chain.shape
    return chain.reshape((-1, s[-1]))

#
# Copyright (C) 2013-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Utility functions for BAYESTAR that are related to matched filtering."""
from contextlib import contextmanager
import logging
import math

import lal
import lalsimulation
import numpy as np
from scipy import interpolate
from scipy import fftpack as fft
from scipy import linalg

log = logging.getLogger('BAYESTAR')


@contextmanager
def lal_ndebug():
    """Temporarily disable lal error messages, except for memory errors."""
    mask = ~(lal.LALERRORBIT |
             lal.LALWARNINGBIT |
             lal.LALINFOBIT |
             lal.LALTRACEBIT)
    old_level = lal.GetDebugLevel()
    lal.ClobberDebugLevel(old_level & mask)
    try:
        yield
    finally:
        lal.ClobberDebugLevel(old_level)


def unwrap(y, *args, **kwargs):
    """Unwrap phases while skipping NaN or infinite values.

    This is a simple wrapper around :meth:`numpy.unwrap` that can handle
    invalid values.

    Examples
    --------
    >>> t = np.arange(0, 2 * np.pi, 0.5)
    >>> y = np.exp(1j * t)
    >>> unwrap(np.angle(y))
    array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. , 5.5, 6. ])
    >>> y[3] = y[4] = y[7] = np.nan
    >>> unwrap(np.angle(y))
    array([0. , 0.5, 1. , nan, nan, 2.5, 3. , nan, 4. , 4.5, 5. , 5.5, 6. ])
    """
    good = np.isfinite(y)
    result = np.empty_like(y)
    result[~good] = y[~good]
    result[good] = np.unwrap(y[good], *args, **kwargs)
    return result


def ceil_pow_2(n):
    """Return the least integer power of 2 that is greater than or equal to n.

    Examples
    --------
    >>> ceil_pow_2(128.0)
    128.0
    >>> ceil_pow_2(0.125)
    0.125
    >>> ceil_pow_2(129.0)
    256.0
    >>> ceil_pow_2(0.126)
    0.25
    >>> ceil_pow_2(1.0)
    1.0

    """
    # frexp splits floats into mantissa and exponent, ldexp does the opposite.
    # For positive numbers, mantissa is in [0.5, 1.).
    mantissa, exponent = math.frexp(n)
    return math.ldexp(
        1 if mantissa >= 0 else float('nan'),
        exponent - 1 if mantissa == 0.5 else exponent
    )


def abscissa(series):
    """Produce the independent variable for a lal TimeSeries or
    FrequencySeries.
    """
    try:
        delta = series.deltaT
        x0 = float(series.epoch)
    except AttributeError:
        delta = series.deltaF
        x0 = series.f0
    return x0 + delta * np.arange(len(series.data.data))


def exp_i(phi):
    return np.cos(phi) + np.sin(phi) * 1j


def truncated_ifft(y, nsamples_out=None):
    r"""Truncated inverse FFT.

    See http://www.fftw.org/pruned.html for a discussion of related algorithms.

    Perform inverse FFT to obtain truncated autocorrelation time series.
    This makes use of a folded DFT for a speedup of::

        log(nsamples)/log(nsamples_out)

    over directly computing the inverse FFT and truncating. Here is how it
    works. Say we have a frequency-domain signal X[k], for 0 ≤ k ≤ N - 1. We
    want to compute its DFT x[n], for 0 ≤ n ≤ M, where N is divisible by M:
    N = cM, for some integer c. The DFT is::

               N - 1
               ______
               \           2 π i k n
        x[n] =  \     exp[-----------] Y[k]
               /               N
              /------
               k = 0

               c - 1   M - 1
               ______  ______
               \       \           2 π i n (m c + j)
             =  \       \     exp[------------------] Y[m c + j]
               /       /                 c M
              /------ /------
               j = 0   m = 0

               c - 1                     M - 1
               ______                    ______
               \           2 π i n j     \           2 π i n m
             =  \     exp[-----------]    \     exp[-----------] Y[m c + j]
               /               N         /               M
              /------                   /------
               j = 0                     m = 0

    So: we split the frequency series into c deinterlaced sub-signals, each of
    length M, compute the DFT of each sub-signal, and add them back together
    with complex weights.

    Parameters
    ----------
    y : `numpy.ndarray`
        Complex input vector.
    nsamples_out : int, optional
        Length of output vector. By default, same as length of input vector.

    Returns
    -------
    x : `numpy.ndarray`
        The first nsamples_out samples of the IFFT of x, zero-padded if

    Examples
    --------
    First generate the IFFT of a random signal:

    >>> nsamples_out = 1024
    >>> y = np.random.randn(nsamples_out) + np.random.randn(nsamples_out) * 1j
    >>> x = fft.ifft(y)

    Now check that the truncated IFFT agrees:

    >>> np.allclose(x, truncated_ifft(y), rtol=1e-15)
    True
    >>> np.allclose(x, truncated_ifft(y, 1024), rtol=1e-15)
    True
    >>> np.allclose(x[:128], truncated_ifft(y, 128), rtol=1e-15)
    True
    >>> np.allclose(x[:1], truncated_ifft(y, 1), rtol=1e-15)
    True
    >>> np.allclose(x[:32], truncated_ifft(y, 32), rtol=1e-15)
    True
    >>> np.allclose(x[:63], truncated_ifft(y, 63), rtol=1e-15)
    True
    >>> np.allclose(x[:25], truncated_ifft(y, 25), rtol=1e-15)
    True
    >>> truncated_ifft(y, 1025)
    Traceback (most recent call last):
      ...
    ValueError: Input is too short: you gave me an input of length 1024, but you asked for an IFFT of length 1025.

    """  # noqa: E501
    nsamples = len(y)
    if nsamples_out is None:
        nsamples_out = nsamples
    elif nsamples_out > nsamples:
        raise ValueError(
            'Input is too short: you gave me an input of length {0}, '
            'but you asked for an IFFT of length {1}.'.format(
                nsamples, nsamples_out))
    elif nsamples & (nsamples - 1):
        raise NotImplementedError(
            'I am too lazy to implement for nsamples that is '
            'not a power of 2.')

    # Find number of FFTs.
    # FIXME: only works if nsamples is a power of 2.
    # Would be better to find the smallest divisor of nsamples that is
    # greater than or equal to nsamples_out.
    nsamples_batch = int(ceil_pow_2(nsamples_out))
    c = nsamples // nsamples_batch

    # FIXME: Implement for real-to-complex FFTs as well.
    twiddle = exp_i(2 * np.pi * np.arange(nsamples_batch) / nsamples)

    x = fft.ifft(y.reshape(nsamples_batch, c).T)

    result = x[-1]
    for row in x[-2::-1]:
        result *= twiddle  # FIXME: check stability of this recurrence relation
        result += row

    # Now need to truncate remaining samples.
    if nsamples_out < nsamples_batch:
        result = result[:nsamples_out]

    return result / c


@lal_ndebug()
def get_approximant_and_orders_from_string(s):
    """Determine the approximant, amplitude order, and phase order for a string
    of the form "TaylorT4threePointFivePN". In this example, the waveform is
    "TaylorT4" and the phase order is 7 (twice 3.5). If the input contains the
    substring "restricted" or "Restricted", then the amplitude order is taken
    to be 0. Otherwise, the amplitude order is the same as the phase order.
    """
    # SWIG-wrapped functions apparently do not understand Unicode, but
    # often the input argument will come from a Unicode XML file.
    s = str(s)
    approximant = lalsimulation.GetApproximantFromString(s)
    try:
        phase_order = lalsimulation.GetOrderFromString(s)
    except RuntimeError:
        phase_order = -1
    if 'restricted' in s or 'Restricted' in s:
        amplitude_order = 0
    else:
        amplitude_order = phase_order
    return approximant, amplitude_order, phase_order


def get_f_lso(mass1, mass2):
    """Calculate the GW frequency during the last stable orbit of a compact
    binary.
    """
    return 1 / (6 ** 1.5 * np.pi * (mass1 + mass2) * lal.MTSUN_SI)


def sngl_inspiral_psd(waveform, mass1, mass2,
                      f_min=10, f_final=None, f_ref=None, **kwargs):
    # FIXME: uberbank mass criterion. Should find a way to get this from
    # pipeline output metadata.
    if waveform == 'o1-uberbank':
        log.warning('Template is unspecified; '
                    'using ER8/O1 uberbank criterion')
        if mass1 + mass2 < 4:
            waveform = 'TaylorF2threePointFivePN'
        else:
            waveform = 'SEOBNRv2_ROM_DoubleSpin'
    elif waveform == 'o2-uberbank':
        log.warning('Template is unspecified; '
                    'using ER10/O2 uberbank criterion')
        if mass1 + mass2 < 4:
            waveform = 'TaylorF2threePointFivePN'
        else:
            waveform = 'SEOBNRv4_ROM'
    approx, ampo, phaseo = get_approximant_and_orders_from_string(waveform)
    log.info('Selected template: %s', waveform)

    # Generate conditioned template.
    params = lal.CreateDict()
    lalsimulation.SimInspiralWaveformParamsInsertPNPhaseOrder(params, phaseo)
    lalsimulation.SimInspiralWaveformParamsInsertPNAmplitudeOrder(params, ampo)
    hplus, hcross = lalsimulation.SimInspiralFD(
        m1=float(mass1) * lal.MSUN_SI, m2=float(mass2) * lal.MSUN_SI,
        S1x=float(kwargs.get('spin1x') or 0),
        S1y=float(kwargs.get('spin1y') or 0),
        S1z=float(kwargs.get('spin1z') or 0),
        S2x=float(kwargs.get('spin2x') or 0),
        S2y=float(kwargs.get('spin2y') or 0),
        S2z=float(kwargs.get('spin2z') or 0),
        distance=1e6 * lal.PC_SI, inclination=0, phiRef=0,
        longAscNodes=0, eccentricity=0, meanPerAno=0,
        deltaF=0, f_min=f_min,
        # Note: code elsewhere ensures that the sample rate is at least two
        # times f_final; the factor of 2 below is just a safety factor to make
        # sure that the sample rate is 2-4 times f_final.
        f_max=ceil_pow_2(2 * (f_final or 2048)),
        f_ref=float(f_ref or 0),
        LALparams=params, approximant=approx)

    # Force `plus' and `cross' waveform to be in quadrature.
    h = 0.5 * (hplus.data.data + 1j * hcross.data.data)

    # For inspiral-only waveforms, nullify frequencies beyond ISCO.
    # FIXME: the waveform generation functions pick the end frequency
    # automatically. Shouldn't SimInspiralFD?
    inspiral_only_waveforms = (
        lalsimulation.TaylorF2,
        lalsimulation.SpinTaylorF2,
        lalsimulation.TaylorF2RedSpin,
        lalsimulation.TaylorF2RedSpinTidal,
        lalsimulation.SpinTaylorT4Fourier)
    if approx in inspiral_only_waveforms:
        h[abscissa(hplus) >= get_f_lso(mass1, mass2)] = 0

    # Throw away any frequencies above high frequency cutoff
    h[abscissa(hplus) >= (f_final or 2048)] = 0

    # Drop Nyquist frequency.
    if len(h) % 2:
        h = h[:-1]

    # Create output frequency series.
    psd = lal.CreateREAL8FrequencySeries(
        'signal PSD', 0, hplus.f0, hcross.deltaF, hplus.sampleUnits**2, len(h))
    psd.data.data = abs2(h)

    # Done!
    return psd


def signal_psd_series(H, S):
    n = H.data.data.size
    f = H.f0 + np.arange(1, n) * H.deltaF
    ret = lal.CreateREAL8FrequencySeries(
        'signal PSD / noise PSD', 0, H.f0, H.deltaF, lal.DimensionlessUnit, n)
    ret.data.data[0] = 0
    ret.data.data[1:] = H.data.data[1:] / S(f)
    return ret


def autocorrelation(H, out_duration, normalize=True):
    """Calculate the complex autocorrelation sequence a(t), for t >= 0, of an
    inspiral signal.

    Parameters
    ----------
    H : lal.REAL8FrequencySeries
        Signal PSD series.
    S : callable
        Noise power spectral density function.

    Returns
    -------
    acor : `numpy.ndarray`
        The complex-valued autocorrelation sequence.
    sample_rate : float
        The sample rate.

    """
    # Compute duration of template, rounded up to a power of 2.
    H_len = H.data.data.size
    nsamples = 2 * H_len
    sample_rate = nsamples * H.deltaF

    # Compute autopower spectral density.
    power = np.empty(nsamples, H.data.data.dtype)
    power[:H_len] = H.data.data
    power[H_len:] = 0

    # Determine length of output FFT.
    nsamples_out = int(np.ceil(out_duration * sample_rate))

    acor = truncated_ifft(power, nsamples_out)
    if normalize:
        acor /= np.abs(acor[0])

    # If we have done this right, then the zeroth sample represents lag 0
    if np.all(np.isreal(H.data.data)):
        assert np.argmax(np.abs(acor)) == 0
        assert np.isreal(acor[0])

    # Done!
    return acor, float(sample_rate)


def abs2(y):
    """Return the absolute value squared, :math:`|z|^2` ,for a complex number
    :math:`z`, without performing a square root.
    """
    return np.square(y.real) + np.square(y.imag)


class vectorize_swig_psd_func:  # noqa: N801
    """Create a vectorized Numpy function from a SWIG-wrapped PSD function.
    SWIG does not provide enough information for Numpy to determine the number
    of input arguments, so we can't just use np.vectorize.
    """

    def __init__(self, str):
        self.__func = getattr(lalsimulation, str + 'Ptr')
        self.__npyfunc = np.frompyfunc(getattr(lalsimulation, str), 1, 1)

    def __call__(self, f):
        fa = np.asarray(f)
        df = np.diff(fa)
        if fa.ndim == 1 and df.size > 1 and np.all(df[0] == df[1:]):
            fa = np.concatenate((fa, [fa[-1] + df[0]]))
            ret = lal.CreateREAL8FrequencySeries(
                None, 0, fa[0], df[0], lal.DimensionlessUnit, fa.size)
            lalsimulation.SimNoisePSD(ret, 0, self.__func)
            ret = ret.data.data[:-1]
        else:
            ret = self.__npyfunc(f)
        if not np.isscalar(ret):
            ret = ret.astype(float)
        return ret


class InterpolatedPSD(interpolate.interp1d):
    """Create a (linear in log-log) interpolating function for a discretely
    sampled power spectrum S(f).
    """

    def __init__(self, f, S, f_high_truncate=1.0, fill_value=np.inf):
        assert f_high_truncate <= 1.0
        f = np.asarray(f)
        S = np.asarray(S)

        # Exclude DC if present
        if f[0] == 0:
            f = f[1:]
            S = S[1:]
        # FIXME: This is a hack to fix an issue with the detection pipeline's
        # PSD conditioning. Remove this when the issue is fixed upstream.
        if f_high_truncate < 1.0:
            log.warning(
                'Truncating PSD at %g of maximum frequency to suppress '
                'rolloff artifacts. This option may be removed in the future.',
                f_high_truncate)
            keep = (f <= f_high_truncate * max(f))
            f = f[keep]
            S = S[keep]
        super().__init__(
            np.log(f), np.log(S),
            kind='linear', bounds_error=False, fill_value=np.log(fill_value))
        self._f_min = min(f)
        self._f_max = max(f)

    @property
    def f_min(self):
        return self._f_min

    @property
    def f_max(self):
        return self._f_max

    def __call__(self, f):
        f_min = np.min(f)
        f_max = np.max(f)
        if f_min < self._f_min:
            log.warning('Assuming PSD is infinite at %g Hz because PSD is '
                        'only sampled down to %g Hz', f_min, self._f_min)
        if f_max > self._f_max:
            log.warning('Assuming PSD is infinite at %g Hz because PSD is '
                        'only sampled up to %g Hz', f_max, self._f_max)
        return np.where(
            (f >= self._f_min) & (f <= self._f_max),
            np.exp(super().__call__(np.log(f))),
            np.exp(self.fill_value))


class SignalModel:
    """Class to speed up computation of signal/noise-weighted integrals and
    Barankin and Cramér-Rao lower bounds on time and phase estimation.

    Note that the autocorrelation series and the moments are related,
    as shown below.

    Examples
    --------
    Create signal model:

    >>> from . import filter
    >>> sngl = lambda: None
    >>> H = filter.sngl_inspiral_psd(
    ...     'TaylorF2threePointFivePN', mass1=1.4, mass2=1.4)
    >>> S = vectorize_swig_psd_func('SimNoisePSDaLIGOZeroDetHighPower')
    >>> W = filter.signal_psd_series(H, S)
    >>> sm = SignalModel(W)

    Compute one-sided autocorrelation function:

    >>> out_duration = 0.1
    >>> a, sample_rate = filter.autocorrelation(W, out_duration)

    Restore negative time lags using symmetry:

    >>> a = np.concatenate((a[:0:-1].conj(), a))

    Compute the first 2 frequency moments by taking derivatives of the
    autocorrelation sequence using centered finite differences.
    The nth frequency moment should be given by (-1j)^n a^(n)(t).

    >>> acor_moments = []
    >>> for i in range(2):
    ...     acor_moments.append(a[len(a) // 2])
    ...     a = -0.5j * sample_rate * (a[2:] - a[:-2])
    >>> assert np.all(np.isreal(acor_moments))
    >>> acor_moments = np.real(acor_moments)

    Compute the first 2 frequency moments using this class.

    >>> quad_moments = [sm.get_sn_moment(i) for i in range(2)]

    Compare them.

    >>> for i, (am, qm) in enumerate(zip(acor_moments, quad_moments)):
    ...     assert np.allclose(am, qm, rtol=0.05)

    """

    def __init__(self, h):
        """Create a TaylorF2 signal model with the given masses, PSD function
        S(f), PN amplitude order, and low-frequency cutoff.
        """
        # Find indices of first and last nonzero samples.
        nonzero = np.flatnonzero(h.data.data)
        first_nonzero = nonzero[0]
        last_nonzero = nonzero[-1]

        # Frequency sample points
        self.dw = 2 * np.pi * h.deltaF
        f = h.f0 + h.deltaF * np.arange(first_nonzero, last_nonzero + 1)
        self.w = 2 * np.pi * f

        # Throw away leading and trailing zeros.
        h = h.data.data[first_nonzero:last_nonzero + 1]

        self.denom_integrand = 4 / (2 * np.pi) * h
        self.den = np.trapz(self.denom_integrand, dx=self.dw)

    def get_horizon_distance(self, snr_thresh=1):
        return np.sqrt(self.den) / snr_thresh

    def get_sn_average(self, func):
        """Get the average of a function of angular frequency, weighted by the
        signal to noise per unit angular frequency.
        """
        num = np.trapz(func(self.w) * self.denom_integrand, dx=self.dw)
        return num / self.den

    def get_sn_moment(self, power):
        """Get the average of angular frequency to the given power, weighted by
        the signal to noise per unit frequency.
        """
        return self.get_sn_average(lambda w: w**power)

    def get_crb(self, snr):
        """Get the Cramér-Rao bound, or inverse Fisher information matrix,
        describing the phase and time estimation covariance.
        """
        w1 = self.get_sn_moment(1)
        w2 = self.get_sn_moment(2)
        fisher = np.asarray(((1, -w1), (-w1, w2)))
        return linalg.inv(fisher) / np.square(snr)

    # FIXME: np.vectorize doesn't work on unbound instance methods. The
    # excluded keyword, added in Numpy 1.7, could be used here to exclude the
    # zeroth argument, self.
    def __get_crb_toa_uncert(self, snr):
        return np.sqrt(self.get_crb(snr)[1, 1])

    def get_crb_toa_uncert(self, snr):
        return np.frompyfunc(self.__get_crb_toa_uncert, 1, 1)(snr)

#
# Copyright (C) 2013-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Sub-sample interpolation for matched filter time series.

Example
-------
.. plot::
   :context: reset
   :include-source:
   :align: center

    from ligo.skymap.bayestar.interpolation import interpolate_max
    from matplotlib import pyplot as plt
    import numpy as np

    z = np.asarray([ 9.135017 -2.8185585j,  9.995214 -1.1222992j,
                    10.682851 +0.8188147j, 10.645139 +3.0268786j,
                     9.713133 +5.5589147j,  7.9043484+7.9039335j,
                     5.511646 +9.333084j ,  2.905198 +9.715742j ,
                     0.5302934+9.544538j ])

    amp = np.abs(z)
    arg = np.rad2deg(np.unwrap(np.angle(z)))
    arg -= (np.median(arg) // 360) * 360
    imax = np.argmax(amp)
    window = 4

    fig, (ax_amp, ax_arg) = plt.subplots(2, 1, figsize=(5, 6), sharex=True)
    ax_arg.set_xlabel('Sample index')
    ax_amp.set_ylabel('Amplitude')
    ax_arg.set_ylabel('Phase')
    args, kwargs = ('.-',), dict(color='lightgray', label='data')
    ax_amp.plot(amp, *args, **kwargs)
    ax_arg.plot(arg, *args, **kwargs)
    for method in ['lanczos', 'catmull-rom',
                   'quadratic-fit', 'nearest-neighbor']:
        i, y = interpolate_max(imax, z, window, method)
        amp = np.abs(y)
        arg = np.rad2deg(np.angle(y))
        args, kwargs = ('o',), dict(mfc='none', label=method)
        ax_amp.plot(i, amp, *args, **kwargs)
        ax_arg.plot(i, arg, *args, **kwargs)
    ax_arg.legend()
    fig.tight_layout()

"""
import numpy as np
from scipy import optimize

from .filter import abs2, exp_i, unwrap

__all__ = ('interpolate_max',)


#
# Lanczos interpolation
#


def lanczos(t, a):
    """The Lanczos kernel."""
    return np.where(np.abs(t) < a, np.sinc(t) * np.sinc(t / a), 0)


def lanczos_interpolant(t, y):
    """An interpolant constructed by convolution of the Lanczos kernel with
    a set of discrete samples at unit intervals.
    """
    a = len(y) // 2
    return sum(lanczos(t - i + a, a) * yi for i, yi in enumerate(y))


def lanczos_interpolant_utility_func(t, y):
    """Utility function for Lanczos interpolation."""
    return -abs2(lanczos_interpolant(t, y))


def interpolate_max_lanczos(imax, y, window_length):
    """Find the time and maximum absolute value of a time series by Lanczos
    interpolation.
    """
    yi = y[(imax - window_length):(imax + window_length + 1)]
    tmax = optimize.fminbound(
        lanczos_interpolant_utility_func, -1., 1., (yi,), xtol=1e-5)
    tmax = tmax.item()
    ymax = lanczos_interpolant(tmax, yi).item()
    return imax + tmax, ymax


#
# Catmull-Rom spline interpolation, real and imaginary parts
#


def poly_catmull_rom(y):
    return np.poly1d([
        -0.5 * y[0] + 1.5 * y[1] - 1.5 * y[2] + 0.5 * y[3],
        y[0] - 2.5 * y[1] + 2 * y[2] - 0.5 * y[3],
        -0.5 * y[0] + 0.5 * y[2],
        y[1]
    ])


def interpolate_max_catmull_rom_even(y):

    # Construct Catmull-Rom interpolating polynomials for
    # real and imaginary parts
    poly_re = poly_catmull_rom(y.real)
    poly_im = poly_catmull_rom(y.imag)

    # Find the roots of d(|y|^2)/dt as approximated
    roots = (poly_re * poly_re.deriv() + poly_im * poly_im.deriv()).r

    # Find which of the two matched interior points has a greater magnitude
    t_max = 0.
    y_max = y[1]
    y_max_abs2 = abs2(y_max)

    new_t_max = 1.
    new_y_max = y[2]
    new_y_max_abs2 = abs2(new_y_max)

    if new_y_max_abs2 > y_max_abs2:
        t_max = new_t_max
        y_max = new_y_max
        y_max_abs2 = new_y_max_abs2

    # Find any real root in (0, 1) that has a magnitude greater than the
    # greatest endpoint
    for root in roots:
        if np.isreal(root) and 0 < root < 1:
            new_t_max = np.real(root)
            new_y_max = poly_re(new_t_max) + poly_im(new_t_max) * 1j
            new_y_max_abs2 = abs2(new_y_max)
            if new_y_max_abs2 > y_max_abs2:
                t_max = new_t_max
                y_max = new_y_max
                y_max_abs2 = new_y_max_abs2

    # Done
    return t_max, y_max


def interpolate_max_catmull_rom(imax, y, window_length):
    t_max, y_max = interpolate_max_catmull_rom_even(y[imax - 2:imax + 2])
    y_max_abs2 = abs2(y_max)
    t_max = t_max - 1

    new_t_max, new_y_max = interpolate_max_catmull_rom_even(
        y[imax - 1:imax + 3])
    new_y_max_abs2 = abs2(new_y_max)

    if new_y_max_abs2 > y_max_abs2:
        t_max = new_t_max
        y_max = new_y_max
        y_max_abs2 = new_y_max_abs2

    return imax + t_max, y_max


#
# Catmull-Rom spline interpolation, amplitude and phase
#


def interpolate_max_catmull_rom_amp_phase_even(y):

    # Construct Catmull-Rom interpolating polynomials for
    # real and imaginary parts
    poly_abs = poly_catmull_rom(np.abs(y))
    poly_arg = poly_catmull_rom(unwrap(np.angle(y)))

    # Find the roots of d(|y|)/dt as approximated
    roots = poly_abs.r

    # Find which of the two matched interior points has a greater magnitude
    t_max = 0.
    y_max = y[1]
    y_max_abs2 = abs2(y_max)

    new_t_max = 1.
    new_y_max = y[2]
    new_y_max_abs2 = abs2(new_y_max)

    if new_y_max_abs2 > y_max_abs2:
        t_max = new_t_max
        y_max = new_y_max
        y_max_abs2 = new_y_max_abs2

    # Find any real root in (0, 1) that has a magnitude greater than the
    # greatest endpoint
    for root in roots:
        if np.isreal(root) and 0 < root < 1:
            new_t_max = np.real(root)
            new_y_max = poly_abs(new_t_max) * exp_i(poly_arg(new_t_max))
            new_y_max_abs2 = abs2(new_y_max)
            if new_y_max_abs2 > y_max_abs2:
                t_max = new_t_max
                y_max = new_y_max
                y_max_abs2 = new_y_max_abs2

    # Done
    return t_max, y_max


def interpolate_max_catmull_rom_amp_phase(imax, y, window_length):
    t_max, y_max = interpolate_max_catmull_rom_amp_phase_even(
        y[imax - 2:imax + 2])
    y_max_abs2 = abs2(y_max)
    t_max = t_max - 1

    new_t_max, new_y_max = interpolate_max_catmull_rom_amp_phase_even(
        y[imax - 1:imax + 3])
    new_y_max_abs2 = abs2(new_y_max)

    if new_y_max_abs2 > y_max_abs2:
        t_max = new_t_max
        y_max = new_y_max
        y_max_abs2 = new_y_max_abs2

    return imax + t_max, y_max


#
# Quadratic fit
#


def interpolate_max_quadratic_fit(imax, y, window_length):
    """Quadratic fit to absolute value of y. Note that this one does not alter
    the value at the maximum.
    """
    t = np.arange(-window_length, window_length + 1.)
    y = y[imax - window_length:imax + window_length + 1]
    y_abs = np.abs(y)
    a, b, c = np.polyfit(t, y_abs, 2)

    # Find which of the two matched interior points has a greater magnitude
    t_max = -1.
    y_max = y[window_length - 1]
    y_max_abs = y_abs[window_length - 1]

    new_t_max = 1.
    new_y_max = y[window_length + 1]
    new_y_max_abs = y_abs[window_length + 1]

    if new_y_max_abs > y_max_abs:
        t_max = new_t_max
        y_max = new_y_max
        y_max_abs = new_y_max_abs

    # Determine if the global extremum of the polynomial is a
    # local maximum in (-1, 1)
    new_t_max = -0.5 * b / a
    new_y_max_abs = c - 0.25 * np.square(b) / a
    if -1 < new_t_max < 1 and new_y_max_abs > y_max_abs:
        t_max = new_t_max
        y_max_abs = new_y_max_abs
        y_phase = np.interp(t_max, t, np.unwrap(np.angle(y)))
        y_max = y_max_abs * exp_i(y_phase)

    return imax + t_max, y_max


#
# Nearest neighbor interpolation
#


def interpolate_max_nearest_neighbor(imax, y, window_length):
    """Trivial, nearest-neighbor interpolation."""
    return imax, y[imax]


#
# Set default interpolation scheme
#


_interpolants = {
    'catmull-rom-amp-phase': interpolate_max_catmull_rom_amp_phase,
    'catmull-rom': interpolate_max_catmull_rom,
    'lanczos': interpolate_max_lanczos,
    'nearest-neighbor': interpolate_max_nearest_neighbor,
    'quadratic-fit': interpolate_max_quadratic_fit}


def interpolate_max(imax, y, window_length, method='catmull-rom-amp-phase'):
    """Perform sub-sample interpolation to find the phase and amplitude
    at the maximum of the absolute value of a complex series.

    Parameters
    ----------
    imax : int
        The index of the maximum sample in the series.
    y : `numpy.ndarray`
        The complex series.
    window_length : int
        The window of the interpolation function for the `lanczos` and
        `quadratic-fit` methods. The interpolation will consider a sliding
        window of `2 * window_length + 1` samples centered on `imax`.
    method : {'catmull-rom-amp-phase', 'catmull-rom', 'lanczos', 'nearest-neighbor', 'quadratic-fit'}
        The interpolation method. Can be any of the following:

        * `catmull-rom-amp-phase`: Catmull-Rom cubic splines on amplitude and phase
          The `window_length` parameter is ignored (understood to be 2).
        * `catmull-rom`: Catmull-Rom cubic splines on real and imaginary parts
          The `window_length` parameter is ignored (understood to be 2).
        * `lanczos`: Lanczos filter interpolation
        * `nearest-neighbor`: Nearest neighbor (e.g., no interpolation).
          The `window_length` parameter is ignored (understood to be 0).
        * `quadratic-fit`: Fit the absolute value of the SNR to a quadratic
          function and the phase to a linear function.

    Returns
    -------
    imax_interp : float
        The interpolated index of the maximum sample, which should be between
        `imax - 0.5` and `imax + 0.5`.
    ymax_interp : complex
        The interpolated value at the maximum.

    """  # noqa: E501
    return _interpolants[method](imax, np.asarray(y), window_length)

# FIXME: Remove this file if https://github.com/willvousden/ptemcee/pull/6
# is merged
import numpy as np
import ptemcee.sampler

__all__ = ('Sampler',)


class VectorLikePriorEvaluator(ptemcee.sampler.LikePriorEvaluator):

    def __call__(self, x):
        s = x.shape
        x = x.reshape((-1, x.shape[-1]))

        lp = self.logp(x, *self.logpargs, **self.logpkwargs)
        if np.any(np.isnan(lp)):
            raise ValueError('Prior function returned NaN.')

        ll = np.empty_like(lp)
        bad = (lp == -np.inf)
        ll[bad] = 0
        ll[~bad] = self.logl(x[~bad], *self.loglargs, **self.loglkwargs)
        if np.any(np.isnan(ll)):
            raise ValueError('Log likelihood function returned NaN.')

        return ll.reshape(s[:-1]), lp.reshape(s[:-1])


class Sampler(ptemcee.sampler.Sampler):
    """Patched version of :class:`ptemcee.Sampler` that supports the
    `vectorize` option of :class:`emcee.EnsembleSampler`.
    """

    def __init__(self, nwalkers, dim, logl, logp,  # noqa: N803
                 ntemps=None, Tmax=None, betas=None,  # noqa: N803
                 threads=1, pool=None, a=2.0,
                 loglargs=[], logpargs=[],
                 loglkwargs={}, logpkwargs={},
                 adaptation_lag=10000, adaptation_time=100,
                 random=None, vectorize=False):
        super().__init__(nwalkers, dim, logl, logp,
                         ntemps=ntemps, Tmax=Tmax, betas=betas,
                         threads=threads, pool=pool, a=a, loglargs=loglargs,
                         logpargs=logpargs, loglkwargs=loglkwargs,
                         logpkwargs=logpkwargs, adaptation_lag=adaptation_lag,
                         adaptation_time=adaptation_time, random=random)
        self._vectorize = vectorize
        if vectorize:
            self._likeprior = VectorLikePriorEvaluator(logl, logp,
                                                       loglargs, logpargs,
                                                       loglkwargs, logpkwargs)

    def _evaluate(self, ps):
        if self._vectorize:
            return self._likeprior(ps)
        else:
            return super().evaluate(ps)

import os
import pkgutil

__all__ = ()

# Import all symbols from all submodules of this module.
for _, module, _ in pkgutil.iter_modules([os.path.dirname(__file__)]):
    if module not in {'tests'}:
        exec('from . import {0};'
             '__all__ += getattr({0}, "__all__", ());'
             'from .{0} import *'.format(module))
    del module

# Clean up
del os, pkgutil

#
# Copyright (C) 2018-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Astropy coordinate frames to visualize triangulation rings from pairs of
gravitational-wave detectors. These are useful for generating plots similar to
Fig. 2 of the GW150914 localization and follow-up paper [1]_.

Example
-------
.. plot::
   :context: reset
   :include-source:
   :align: center

    from astropy.coordinates import EarthLocation
    from astropy.time import Time
    from ligo.skymap.coordinates import DetectorFrame
    from ligo.skymap.io import read_sky_map
    import ligo.skymap.plot
    from matplotlib import pyplot as plt

    # Download GW150914 localization
    url = 'https://dcc.ligo.org/public/0122/P1500227/012/bayestar_gstlal_C01.fits.gz'
    m, meta = ligo.skymap.io.read_sky_map(url)

    # Plot sky map on an orthographic projection
    fig = plt.figure(figsize=(5, 5))
    ax = fig.add_subplot(
        111, projection='astro globe', center='130d -70d')
    ax.imshow_hpx(m, cmap='cylon')

    # Hide the original ('RA', 'Dec') ticks
    for coord in ax.coords:
        coord.set_ticks_visible(False)
        coord.set_ticklabel_visible(False)

    # Construct Hanford-Livingston detector frame at the time of the event
    frame = DetectorFrame(site_1=EarthLocation.of_site('H1'),
                          site_2=EarthLocation.of_site('L1'),
                          obstime=Time(meta['gps_time'], format='gps'))

    # Draw grid for detector frame
    ax.get_coords_overlay(frame).grid()

References
----------
.. [1] LSC/Virgo et al., 2016. "Localization and Broadband Follow-up of the
       Gravitational-wave Transient GW150914." ApJL 826, L13.
       :doi:`10.3847/2041-8205/826/1/L13`

"""  # noqa: E501
from astropy.coordinates import (
    CartesianRepresentation, DynamicMatrixTransform, EarthLocationAttribute,
    frame_transform_graph, ITRS, SphericalRepresentation)
from astropy.coordinates.matrix_utilities import matrix_transpose
from astropy import units as u
import numpy as np

__all__ = ('DetectorFrame',)


class DetectorFrame(ITRS):
    """A coordinate frames to visualize triangulation rings from pairs of
    gravitational-wave detectors.
    """

    site_1 = EarthLocationAttribute()
    site_2 = EarthLocationAttribute()

    default_representation = SphericalRepresentation


@frame_transform_graph.transform(DynamicMatrixTransform, ITRS, DetectorFrame)
def itrs_to_detectorframe(from_coo, to_frame):
    e_z = CartesianRepresentation(u.Quantity(to_frame.site_1.geocentric) -
                                  u.Quantity(to_frame.site_2.geocentric))
    e_z /= e_z.norm()
    e_x = CartesianRepresentation(0, 0, 1).cross(e_z)
    e_x /= e_x.norm()
    e_y = e_z.cross(e_x)

    return np.row_stack((e_x.xyz.value,
                         e_y.xyz.value,
                         e_z.xyz.value))


@frame_transform_graph.transform(DynamicMatrixTransform, DetectorFrame, ITRS)
def detectorframe_to_itrs(from_coo, to_frame):
    return matrix_transpose(itrs_to_detectorframe(to_frame, from_coo))

#
# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""
Astropy coordinate frame for eigendecomposition of a cloud of points or a 3D
sky map.
"""

from astropy.coordinates import (
    BaseCoordinateFrame, CartesianRepresentation, DynamicMatrixTransform,
    frame_transform_graph, ICRS, SphericalRepresentation)
from astropy.coordinates import CartesianRepresentationAttribute
from astropy.units import dimensionless_unscaled
import numpy as np

from ..distance import principal_axes

__all__ = ('EigenFrame',)


class EigenFrame(BaseCoordinateFrame):
    """A coordinate frame that has its axes aligned with the principal
    components of a cloud of points.
    """

    e_x = CartesianRepresentationAttribute(
        default=CartesianRepresentation(1, 0, 0, unit=dimensionless_unscaled),
        unit=dimensionless_unscaled)
    e_y = CartesianRepresentationAttribute(
        default=CartesianRepresentation(0, 1, 0, unit=dimensionless_unscaled),
        unit=dimensionless_unscaled)
    e_z = CartesianRepresentationAttribute(
        default=CartesianRepresentation(0, 0, 1, unit=dimensionless_unscaled),
        unit=dimensionless_unscaled)

    default_representation = SphericalRepresentation

    @classmethod
    def for_coords(cls, coords):
        """Create a coordinate frame that has its axes aligned with the
        principal components of a cloud of points.

        Parameters
        ----------
        coords : `astropy.coordinates.SkyCoord`
            A cloud of points

        Returns
        -------
        frame : `EigenFrame`
            A new coordinate frame

        """
        v = coords.icrs.cartesian.xyz.value
        _, r = np.linalg.eigh(np.dot(v, v.T))
        r = r[:, ::-1]  # Order by descending eigenvalue
        e_x, e_y, e_z = CartesianRepresentation(r, unit=dimensionless_unscaled)
        return cls(e_x=e_x, e_y=e_y, e_z=e_z)

    @classmethod
    def for_skymap(cls, prob, distmu, distsigma, nest=False):
        """Create a coordinate frame that has its axes aligned with the
        principal components of a 3D sky map.

        Parameters
        ----------
        prob : `numpy.ndarray`
            Marginal probability (pix^-2)
        distmu : `numpy.ndarray`
            Distance location parameter (Mpc)
        distsigma : `numpy.ndarray`
            Distance scale parameter (Mpc)
        distnorm : `numpy.ndarray`
            Distance normalization factor (Mpc^-2)
        nest : bool, default=False
            Indicates whether the input sky map is in nested rather than
            ring-indexed HEALPix coordinates (default: ring).

        Returns
        -------
        frame : `EigenFrame`
            A new coordinate frame

        """
        r = principal_axes(prob, distmu, distsigma, nest=nest)
        r = r[:, ::-1]  # Order by descending eigenvalue
        e_x, e_y, e_z = CartesianRepresentation(r, unit=dimensionless_unscaled)
        return cls(e_x=e_x, e_y=e_y, e_z=e_z)


@frame_transform_graph.transform(DynamicMatrixTransform, ICRS, EigenFrame)
def icrs_to_eigenframe(from_coo, to_frame):
    return np.row_stack((to_frame.e_x.xyz.value,
                         to_frame.e_y.xyz.value,
                         to_frame.e_z.xyz.value))


@frame_transform_graph.transform(DynamicMatrixTransform, EigenFrame, ICRS)
def eigenframe_to_icrs(from_coo, to_frame):
    return np.column_stack((from_coo.e_x.xyz.value,
                            from_coo.e_y.xyz.value,
                            from_coo.e_z.xyz.value))

import os
import pkgutil

__all__ = ()

# Import all symbols from all submodules of this module.
for _, module, _ in pkgutil.iter_modules([os.path.dirname(__file__)]):
    if module not in {'tests'}:
        exec('from . import {0};'
             '__all__ += getattr({0}, "__all__", ());'
             'from .{0} import *'.format(module))
    del module

# Clean up
del os, pkgutil

#!/usr/bin/env python
#
# Copyright (C) 2013-2022  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Reading and writing HEALPix FITS files.

An example FITS header looks like this:

.. code-block:: sh

    $ fitsheader test.fits.gz
    # HDU 0 in test.fits.gz
    SIMPLE  =                    T / conforms to FITS standard
    BITPIX  =                    8 / array data type
    NAXIS   =                    0 / number of array dimensions
    EXTEND  =                    T

    # HDU 1 in test.fits.gz
    XTENSION= 'BINTABLE'           / binary table extension
    BITPIX  =                    8 / array data type
    NAXIS   =                    2 / number of array dimensions
    NAXIS1  =                 4096 / length of dimension 1
    NAXIS2  =                  192 / length of dimension 2
    PCOUNT  =                    0 / number of group parameters
    GCOUNT  =                    1 / number of groups
    TFIELDS =                    1 / number of table fields
    TTYPE1  = 'PROB    '
    TFORM1  = '1024E   '
    TUNIT1  = 'pix-1   '
    PIXTYPE = 'HEALPIX '           / HEALPIX pixelisation
    ORDERING= 'RING    '           / Pixel ordering scheme, either RING or NESTED
    COORDSYS= 'C       '           / Ecliptic, Galactic or Celestial (equatorial)
    EXTNAME = 'xtension'           / name of this binary table extension
    NSIDE   =                  128 / Resolution parameter of HEALPIX
    FIRSTPIX=                    0 / First pixel # (0 based)
    LASTPIX =               196607 / Last pixel # (0 based)
    INDXSCHM= 'IMPLICIT'           / Indexing: IMPLICIT or EXPLICIT
    OBJECT  = 'FOOBAR 12345'       / Unique identifier for this event
    REFERENC= 'http://www.youtube.com/watch?v=0ccKPSVQcFk' / URL of this event
    DATE-OBS= '2013-04-08T21:37:32.25' / UTC date of the observation
    MJD-OBS =      56391.151064815 / modified Julian date of the observation
    DATE    = '2013-04-08T21:50:32' / UTC date of file creation
    CREATOR = 'fits.py '           / Program that created this file
    RUNTIME =                 21.5 / Runtime in seconds of the CREATOR program
"""  # noqa: E501

import logging
import healpy as hp
import numpy as np
from astropy.io import fits
from astropy.time import Time
from astropy import units as u
from ligo.lw import lsctables
import itertools
import astropy_healpix as ah
from astropy.table import Table
from .. import moc
from ..util.ilwd import ilwd_to_int

log = logging.getLogger()

__all__ = ("read_sky_map", "write_sky_map")


def gps_to_iso8601(gps_time):
    """Convert a floating-point GPS time in seconds to an ISO 8601 date string.

    Parameters
    ----------
    gps : float
        Time in seconds since GPS epoch

    Returns
    -------
    iso8601 : str
        ISO 8601 date string (with fractional seconds)

    Examples
    --------
    >>> gps_to_iso8601(1000000000.01)
    '2011-09-14T01:46:25.010000'
    >>> gps_to_iso8601(1000000000)
    '2011-09-14T01:46:25.000000'
    >>> gps_to_iso8601(1000000000.999999)
    '2011-09-14T01:46:25.999999'
    >>> gps_to_iso8601(1000000000.9999999)
    '2011-09-14T01:46:26.000000'
    >>> gps_to_iso8601(1000000814.999999)
    '2011-09-14T01:59:59.999999'
    >>> gps_to_iso8601(1000000814.9999999)
    '2011-09-14T02:00:00.000000'

    """
    return Time(float(gps_time), format='gps', precision=6).utc.isot


def iso8601_to_gps(iso8601):
    """Convert an ISO 8601 date string to a floating-point GPS time in seconds.

    Parameters
    ----------
    iso8601 : str
        ISO 8601 date string (with fractional seconds)

    Returns
    -------
    gps : float
        Time in seconds since GPS epoch

    Examples
    --------
    >>> gps_to_iso8601(1129501781.2)
    '2015-10-21T22:29:24.200000'
    >>> iso8601_to_gps('2015-10-21T22:29:24.2')
    1129501781.2

    """
    return Time(iso8601, scale='utc').gps


def gps_to_mjd(gps_time):
    """Convert a floating-point GPS time in seconds to a modified Julian day.

    Parameters
    ----------
    gps_time : float
        Time in seconds since GPS epoch

    Returns
    -------
    mjd : float
        Modified Julian day

    Examples
    --------
    >>> '%.9f' % round(gps_to_mjd(1129501781.2), 9)
    '57316.937085648'

    """
    return Time(gps_time, format='gps').utc.mjd


def identity(x):
    return x


def instruments_to_fits(value):
    if not isinstance(value, str):
        value = str(lsctables.instrumentsproperty.set(value))
    return value


def instruments_from_fits(value):
    return {str(ifo) for ifo in lsctables.instrumentsproperty.get(value)}


def metadata_for_version_module(version):
    return {'vcs_version': version.__spec__.parent + ' ' + version.version}


def normalize_objid(objid):
    try:
        return int(objid)
    except ValueError:
        try:
            return ilwd_to_int(objid)
        except ValueError:
            return str(objid)


DEFAULT_NUNIQ_NAMES = ('PROBDENSITY', 'DISTMU', 'DISTSIGMA', 'DISTNORM')
DEFAULT_NUNIQ_UNITS = (u.steradian**-1, u.Mpc, u.Mpc, u.Mpc**-2)
DEFAULT_NESTED_NAMES = ('PROB', 'DISTMU', 'DISTSIGMA', 'DISTNORM')
DEFAULT_NESTED_UNITS = (u.pix**-1, u.Mpc, u.Mpc, u.Mpc**-2)
FITS_META_MAPPING = (
    ('objid', 'OBJECT', 'Unique identifier for this event',
     normalize_objid, normalize_objid),
    ('url', 'REFERENC', 'URL of this event', identity, identity),
    ('instruments', 'INSTRUME', 'Instruments that triggered this event',
     instruments_to_fits, instruments_from_fits),
    ('gps_time', 'DATE-OBS', 'UTC date of the observation',
     gps_to_iso8601, iso8601_to_gps),
    ('gps_time', 'MJD-OBS', 'modified Julian date of the observation',
     gps_to_mjd, None),
    ('gps_creation_time', 'DATE', 'UTC date of file creation',
     gps_to_iso8601, iso8601_to_gps),
    ('creator', 'CREATOR', 'Program that created this file',
     identity, identity),
    ('origin', 'ORIGIN', 'Organization responsible for this FITS file',
     identity, identity),
    ('runtime', 'RUNTIME', 'Runtime in seconds of the CREATOR program',
     identity, identity),
    ('distmean', 'DISTMEAN', 'Posterior mean distance (Mpc)',
     identity, identity),
    ('diststd', 'DISTSTD', 'Posterior standard deviation of distance (Mpc)',
     identity, identity),
    ('log_bci', 'LOGBCI', 'Log Bayes factor: coherent vs. incoherent',
     identity, identity),
    ('log_bsn', 'LOGBSN', 'Log Bayes factor: signal vs. noise',
     identity, identity),
    ('vcs_version', 'VCSVERS', 'Software version',
     identity, identity),
    ('vcs_revision', 'VCSREV', 'Software revision (Git)',
     identity, identity),
    ('build_date', 'DATE-BLD', 'Software build date',
     identity, identity))


def write_sky_map(filename, m, **kwargs):
    """Write a gravitational-wave sky map to a file, populating the header
    with optional metadata.

    Parameters
    ----------
    filename: str
        Path to the optionally gzip-compressed FITS file.

    m : `astropy.table.Table`, `numpy.array`
        If a Numpy record array or astorpy.table.Table instance, and has a
        column named 'UNIQ', then interpret the input as NUNIQ-style
        multi-order map [1]_. Otherwise, interpret as a NESTED or RING ordered
        map.

    **kwargs
        Additional metadata to add to FITS header. If m is an
        `astropy.table.Table` instance, then the header is initialized from
        both `m.meta` and `kwargs`.

    References
    ----------
    .. [1] Górski, K.M., Wandelt, B.D., Hivon, E., Hansen, F.K., & Banday, A.J.
        2017. The HEALPix Primer. The Unique Identifier scheme.
        http://healpix.sourceforge.net/html/intronode4.htm#SECTION00042000000000000000

    Examples
    --------
    Test header contents:

    >>> order = 9
    >>> nside = 2 ** order
    >>> npix = ah.nside_to_npix(nside)
    >>> prob = np.ones(npix, dtype=float) / npix

    >>> import tempfile
    >>> from ligo.skymap import version
    >>> with tempfile.NamedTemporaryFile(suffix='.fits') as f:
    ...     write_sky_map(f.name, prob, nest=True,
    ...                   vcs_version='foo 1.0', vcs_revision='bar',
    ...                   build_date='2018-01-01T00:00:00')
    ...     for card in fits.getheader(f.name, 1).cards:
    ...         print(str(card).rstrip())
    XTENSION= 'BINTABLE'           / binary table extension
    BITPIX  =                    8 / array data type
    NAXIS   =                    2 / number of array dimensions
    NAXIS1  =                    8 / length of dimension 1
    NAXIS2  =              3145728 / length of dimension 2
    PCOUNT  =                    0 / number of group parameters
    GCOUNT  =                    1 / number of groups
    TFIELDS =                    1 / number of table fields
    TTYPE1  = 'PROB    '
    TFORM1  = 'D       '
    TUNIT1  = 'pix-1   '
    PIXTYPE = 'HEALPIX '           / HEALPIX pixelisation
    ORDERING= 'NESTED  '           / Pixel ordering scheme: RING, NESTED, or NUNIQ
    COORDSYS= 'C       '           / Ecliptic, Galactic or Celestial (equatorial)
    NSIDE   =                  512 / Resolution parameter of HEALPIX
    INDXSCHM= 'IMPLICIT'           / Indexing: IMPLICIT or EXPLICIT
    VCSVERS = 'foo 1.0 '           / Software version
    VCSREV  = 'bar     '           / Software revision (Git)
    DATE-BLD= '2018-01-01T00:00:00' / Software build date

    >>> uniq = moc.nest2uniq(np.uint8(order), np.arange(npix))
    >>> probdensity = prob / hp.nside2pixarea(nside)
    >>> moc_data = np.rec.fromarrays(
    ...     [uniq, probdensity], names=['UNIQ', 'PROBDENSITY'])
    >>> with tempfile.NamedTemporaryFile(suffix='.fits') as f:
    ...     write_sky_map(f.name, moc_data,
    ...                   vcs_version='foo 1.0', vcs_revision='bar',
    ...                   build_date='2018-01-01T00:00:00')
    ...     for card in fits.getheader(f.name, 1).cards:
    ...         print(str(card).rstrip())
    XTENSION= 'BINTABLE'           / binary table extension
    BITPIX  =                    8 / array data type
    NAXIS   =                    2 / number of array dimensions
    NAXIS1  =                   16 / length of dimension 1
    NAXIS2  =              3145728 / length of dimension 2
    PCOUNT  =                    0 / number of group parameters
    GCOUNT  =                    1 / number of groups
    TFIELDS =                    2 / number of table fields
    TTYPE1  = 'UNIQ    '
    TFORM1  = 'K       '
    TTYPE2  = 'PROBDENSITY'
    TFORM2  = 'D       '
    TUNIT2  = 'sr-1    '
    PIXTYPE = 'HEALPIX '           / HEALPIX pixelisation
    ORDERING= 'NUNIQ   '           / Pixel ordering scheme: RING, NESTED, or NUNIQ
    COORDSYS= 'C       '           / Ecliptic, Galactic or Celestial (equatorial)
    MOCORDER=                    9 / MOC resolution (best order)
    INDXSCHM= 'EXPLICIT'           / Indexing: IMPLICIT or EXPLICIT
    VCSVERS = 'foo 1.0 '           / Software version
    VCSREV  = 'bar     '           / Software revision (Git)
    DATE-BLD= '2018-01-01T00:00:00' / Software build date

    """  # noqa: E501
    log.debug('normalizing metadata')
    if isinstance(m, Table) or (isinstance(m, np.ndarray) and m.dtype.names):
        m = Table(m, copy=False)
    else:
        if np.ndim(m) == 1:
            m = [m]
        m = Table(m, names=DEFAULT_NESTED_NAMES[:len(m)], copy=False)
    m.meta.update(kwargs)

    if 'UNIQ' in m.colnames:
        default_names = DEFAULT_NUNIQ_NAMES
        default_units = DEFAULT_NUNIQ_UNITS
        extra_header = [
            ('PIXTYPE', 'HEALPIX',
             'HEALPIX pixelisation'),
            ('ORDERING', 'NUNIQ',
             'Pixel ordering scheme: RING, NESTED, or NUNIQ'),
            ('COORDSYS', 'C',
             'Ecliptic, Galactic or Celestial (equatorial)'),
            ('MOCORDER', moc.uniq2order(m['UNIQ'].max()),
             'MOC resolution (best order)'),
            ('INDXSCHM', 'EXPLICIT',
             'Indexing: IMPLICIT or EXPLICIT')]
        # Ignore nest keyword argument if present
        m.meta.pop('nest', False)
    else:
        default_names = DEFAULT_NESTED_NAMES
        default_units = DEFAULT_NESTED_UNITS
        ordering = 'NESTED' if m.meta.pop('nest', False) else 'RING'
        extra_header = [
            ('PIXTYPE', 'HEALPIX',
             'HEALPIX pixelisation'),
            ('ORDERING', ordering,
             'Pixel ordering scheme: RING, NESTED, or NUNIQ'),
            ('COORDSYS', 'C',
             'Ecliptic, Galactic or Celestial (equatorial)'),
            ('NSIDE', ah.npix_to_nside(len(m)),
             'Resolution parameter of HEALPIX'),
            ('INDXSCHM', 'IMPLICIT',
             'Indexing: IMPLICIT or EXPLICIT')]

    for key, rows in itertools.groupby(FITS_META_MAPPING, lambda row: row[0]):
        try:
            value = m.meta.pop(key)
        except KeyError:
            pass
        else:
            for row in rows:
                _, fits_key, fits_comment, to_fits, _ = row
                if to_fits is not None:
                    extra_header.append(
                        (fits_key, to_fits(value), fits_comment))

    for default_name, default_unit in zip(default_names, default_units):
        try:
            col = m[default_name]
        except KeyError:
            pass
        else:
            if not col.unit:
                col.unit = default_unit

    log.debug('converting from Astropy table to FITS HDU list')
    hdu = fits.table_to_hdu(m)
    hdu.header.extend(extra_header)
    hdulist = fits.HDUList([fits.PrimaryHDU(), hdu])
    log.debug('saving')
    hdulist.writeto(filename, overwrite=True)


def read_sky_map(filename, nest=False, distances=False, moc=False, **kwargs):
    """Read a LIGO/Virgo/KAGRA-type sky map and return a tuple of the HEALPix
    array and a dictionary of metadata from the header.

    Parameters
    ----------
    filename: string
        Path to the optionally gzip-compressed FITS file.

    nest: bool, optional
        If omitted or False, then detect the pixel ordering in the FITS file
        and rearrange if necessary to RING indexing before returning.

        If True, then detect the pixel ordering and rearrange if necessary to
        NESTED indexing before returning.

        If None, then preserve the ordering from the FITS file.

        Regardless of the value of this option, the ordering used in the FITS
        file is indicated as the value of the 'nest' key in the metadata
        dictionary.

    distances: bool, optional
        If true, then read also read the additional HEALPix layers representing
        the conditional mean and standard deviation of distance as a function
        of sky location.

    moc: bool, optional
        If true, then preserve multi-order structure if present.

    Examples
    --------
    Test that we can read a legacy IDL-compatible file
    (https://bugs.ligo.org/redmine/issues/5168):

    >>> import tempfile
    >>> with tempfile.NamedTemporaryFile(suffix='.fits') as f:
    ...     nside = 512
    ...     npix = ah.nside_to_npix(nside)
    ...     ipix_nest = np.arange(npix)
    ...     hp.write_map(f.name, ipix_nest, nest=True, column_names=['PROB'])
    ...     m, meta = read_sky_map(f.name)
    ...     np.testing.assert_array_equal(m, hp.ring2nest(nside, ipix_nest))

    """
    m = Table.read(filename, format='fits', **kwargs)

    # Remove some keys that we do not need
    for key in (
            'PIXTYPE', 'EXTNAME', 'NSIDE', 'FIRSTPIX', 'LASTPIX', 'INDXSCHM',
            'MOCORDER'):
        m.meta.pop(key, None)

    if m.meta.pop('COORDSYS', 'C') != 'C':
        raise ValueError('ligo.skymap only reads and writes sky maps in '
                         'equatorial coordinates.')

    try:
        value = m.meta.pop('ORDERING')
    except KeyError:
        pass
    else:
        if value == 'RING':
            m.meta['nest'] = False
        elif value == 'NESTED':
            m.meta['nest'] = True
        elif value == 'NUNIQ':
            pass
        else:
            raise ValueError(
                'ORDERING card in header has unknown value: {0}'.format(value))

    for fits_key, rows in itertools.groupby(
            FITS_META_MAPPING, lambda row: row[1]):
        try:
            value = m.meta.pop(fits_key)
        except KeyError:
            pass
        else:
            for row in rows:
                key, _, _, _, from_fits = row
                if from_fits is not None:
                    m.meta[key] = from_fits(value)

    # FIXME: Fermi GBM HEALPix maps use the column name 'PROBABILITY',
    # instead of the LIGO/Virgo/KAGRA convention of 'PROB'.
    #
    # Fermi may change to our convention in the future, but for now we
    # rename the column.
    if 'PROBABILITY' in m.colnames:
        m.rename_column('PROBABILITY', 'PROB')

    # For a long time, we produced files with a UNIQ column that was an
    # unsigned integer. Cast it here to a signed integer so that the user
    # can handle old or new sky maps the same way.
    if 'UNIQ' in m.colnames:
        m['UNIQ'] = m['UNIQ'].astype(np.int64)

    if 'UNIQ' not in m.colnames:
        m = Table([col.ravel() for col in m.columns.values()], meta=m.meta)

    if 'UNIQ' in m.colnames and not moc:
        from ..bayestar import rasterize
        m = rasterize(m)
        m.meta['nest'] = True
    elif 'UNIQ' not in m.colnames and moc:
        from ..bayestar import derasterize
        if not m.meta['nest']:
            npix = len(m)
            nside = ah.npix_to_nside(npix)
            m = m[hp.nest2ring(nside, np.arange(npix))]
        m = derasterize(m)
        m.meta.pop('nest', None)

    if 'UNIQ' not in m.colnames:
        npix = len(m)
        nside = ah.npix_to_nside(npix)

        if nest is None:
            pass
        elif m.meta['nest'] and not nest:
            m = m[hp.ring2nest(nside, np.arange(npix))]
        elif not m.meta['nest'] and nest:
            m = m[hp.nest2ring(nside, np.arange(npix))]

    if moc:
        return m
    elif distances:
        return tuple(
            np.asarray(m[name]) for name in DEFAULT_NESTED_NAMES), m.meta
    else:
        return np.asarray(m[DEFAULT_NESTED_NAMES[0]]), m.meta


if __name__ == '__main__':
    import os
    nside = 128
    npix = ah.nside_to_npix(nside)
    prob = np.random.random(npix)
    prob /= sum(prob)

    write_sky_map(
        'test.fits.gz', prob,
        objid='FOOBAR 12345',
        gps_time=1049492268.25,
        creator=os.path.basename(__file__),
        url='http://www.youtube.com/watch?v=0ccKPSVQcFk',
        origin='LIGO Scientific Collaboration',
        runtime=21.5)

    print(read_sky_map('test.fits.gz'))

# Copyright (C) 2016-2022  Leo Singer, John Veitch
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Read HDF5 posterior sample chain HDF5 files."""

import numpy as np
import h5py
from astropy.table import Column, Table

# Constants from lalinference module
POSTERIOR_SAMPLES = 'posterior_samples'
LINEAR = 0
CIRCULAR = 1
FIXED = 2
OUTPUT = 3

__all__ = ('read_samples', 'write_samples')


def _identity(x):
    return x


_colname_map = (('rightascension', 'ra', _identity),
                ('right_ascension', 'ra', _identity),
                ('declination', 'dec', _identity),
                ('logdistance', 'dist', np.exp),
                ('distance', 'dist', _identity),
                ('luminosity_distance', 'dist', _identity),
                ('polarisation', 'psi', _identity),
                ('chirpmass', 'mc', _identity),
                ('chirp_mass', 'mc', _identity),
                ('a_spin1', 'a1', _identity),
                ('a_1', 'a1', _identity),
                ('a_spin2', 'a2', _identity),
                ('a_2', 'a2', _identity),
                ('tilt_spin1', 'tilt1', _identity),
                ('tilt_1', 'tilt1', _identity),
                ('tilt_spin2', 'tilt2', _identity),
                ('tilt_2', 'tilt2', _identity),
                ('geocent_time', 'time', _identity))


def _remap_colnames(table):
    for old_name, new_name, func in _colname_map:
        if old_name in table.colnames:
            table[new_name] = func(table.columns.pop(old_name))


def _find_table(group, tablename):
    """Recursively search an HDF5 group or file for a dataset by name.

    Parameters
    ----------
    group : `h5py.File` or `h5py.Group`
        The file or group to search
    tablename : str
        The name of the table to search for

    Returns
    -------
    dataset : `h5py.Dataset`
        The dataset whose name is `tablename`

    Raises
    ------
    KeyError
        If the table is not found or if multiple matching tables are found

    Examples
    --------
    Check that we can find a file by name:

    >>> import os.path
    >>> import tempfile
    >>> table = Table(np.eye(3), names=['a', 'b', 'c'])
    >>> with tempfile.TemporaryDirectory() as dir:
    ...     filename = os.path.join(dir, 'test.hdf5')
    ...     table.write(filename, path='foo/bar', append=True)
    ...     table.write(filename, path='foo/bat', append=True)
    ...     table.write(filename, path='foo/xyzzy/bat', append=True)
    ...     with h5py.File(filename, 'r') as f:
    ...         _find_table(f, 'bar')
    <HDF5 dataset "bar": shape (3,), type "|V24">

    Check that an exception is raised if the table is not found:

    >>> with tempfile.TemporaryDirectory() as dir:
    ...     filename = os.path.join(dir, 'test.hdf5')
    ...     table.write(filename, path='foo/bar', append=True)
    ...     table.write(filename, path='foo/bat', append=True)
    ...     table.write(filename, path='foo/xyzzy/bat', append=True)
    ...     with h5py.File(filename, 'r') as f:
    ...         _find_table(f, 'plugh')
    Traceback (most recent call last):
        ...
    KeyError: 'Table not found: plugh'

    Check that an exception is raised if multiple tables are found:

    >>> with tempfile.TemporaryDirectory() as dir:
    ...     filename = os.path.join(dir, 'test.hdf5')
    ...     table.write(filename, path='foo/bar', append=True)
    ...     table.write(filename, path='foo/bat', append=True)
    ...     table.write(filename, path='foo/xyzzy/bat', append=True)
    ...     with h5py.File(filename, 'r') as f:
    ...         _find_table(f, 'bat')
    Traceback (most recent call last):
        ...
    KeyError: 'Multiple tables called bat exist: foo/bat, foo/xyzzy/bat'

    """
    results = {}

    def visitor(key, value):
        _, _, name = key.rpartition('/')
        if name == tablename:
            results[key] = value

    group.visititems(visitor)

    if len(results) == 0:
        raise KeyError('Table not found: {0}'.format(tablename))

    if len(results) > 1:
        raise KeyError('Multiple tables called {0} exist: {1}'.format(
            tablename, ', '.join(sorted(results.keys()))))

    table, = results.values()
    return table


def read_samples(filename, path=None, tablename=POSTERIOR_SAMPLES):
    """Read an HDF5 sample chain file.

    Parameters
    ----------
    filename : str
        The path of the HDF5 file on the filesystem.
    path : str, optional
        The path of the dataset within the HDF5 file.
    tablename : str, optional
        The name of table to search for recursively within the HDF5 file.
        By default, search for 'posterior_samples'.

    Returns
    -------
    chain : `astropy.table.Table`
        The sample chain as an Astropy table.

    Examples
    --------
    Test reading a file written using the Python API:

    >>> import os.path
    >>> import tempfile
    >>> table = Table([
    ...     Column(np.ones(10), name='foo', meta={'vary': FIXED}),
    ...     Column(np.arange(10), name='bar', meta={'vary': LINEAR}),
    ...     Column(np.arange(10) * np.pi, name='bat', meta={'vary': CIRCULAR}),
    ...     Column(np.arange(10), name='baz', meta={'vary': OUTPUT})
    ... ])
    >>> with tempfile.TemporaryDirectory() as dir:
    ...     filename = os.path.join(dir, 'test.hdf5')
    ...     write_samples(table, filename, path='foo/bar/posterior_samples')
    ...     len(read_samples(filename))
    10

    Test reading a file that was written using the LAL HDF5 C API:

    >>> from importlib.resources import files
    >>> with files('ligo.skymap.io.tests.data').joinpath(
    ...         'test.hdf5').open('rb') as f:
    ...     table = read_samples(f)
    >>> table.colnames
    ['uvw', 'opq', 'lmn', 'ijk', 'def', 'abc', 'ghi', 'rst']

    """
    with h5py.File(filename, 'r') as f:
        if path is not None:  # Look for a given path
            table = f[path]
        else:  # Look for a given table name
            table = _find_table(f, tablename)
        table = Table.read(table)

    # Restore vary types.
    for i, column in enumerate(table.columns.values()):
        column.meta['vary'] = table.meta.get(
            'FIELD_{0}_VARY'.format(i), OUTPUT)

    # Restore fixed columns from table attributes.
    for key, value in table.meta.items():
        # Skip attributes from H5TB interface
        # (https://www.hdfgroup.org/HDF5/doc/HL/H5TB_Spec.html).
        if key == 'CLASS' or key == 'VERSION' or key == 'TITLE' or \
                key.startswith('FIELD_'):
            continue
        table.add_column(Column([value] * len(table), name=key,
                         meta={'vary': FIXED}))

    # Delete remaining table attributes.
    table.meta.clear()

    # Normalize column names.
    _remap_colnames(table)

    # Done!
    return table


def write_samples(table, filename, metadata=None, **kwargs):
    """Write an HDF5 sample chain file.

    Parameters
    ----------
    table : `astropy.table.Table`
        The sample chain as an Astropy table.
    filename : str
        The path of the HDF5 file on the filesystem.
    metadata: dict (optional)
        Dictionary of (path, value) pairs of metadata attributes
        to add to the output file
    kwargs: dict
        Any keyword arguments for `astropy.table.Table.write`.

    Examples
    --------
    Check that we catch columns that are supposed to be FIXED but are not:

    >>> table = Table([
    ...     Column(np.arange(10), name='foo', meta={'vary': FIXED})
    ... ])
    >>> write_samples(table, 'bar.hdf5', 'bat/baz')
    Traceback (most recent call last):
        ...
    AssertionError: 
    Arrays are not equal
    Column foo is a fixed column, but its values are not identical
    ...

    And now try writing an arbitrary example to a temporary file.

    >>> import os.path
    >>> import tempfile
    >>> table = Table([
    ...     Column(np.ones(10), name='foo', meta={'vary': FIXED}),
    ...     Column(np.arange(10), name='bar', meta={'vary': LINEAR}),
    ...     Column(np.arange(10) * np.pi, name='bat', meta={'vary': CIRCULAR}),
    ...     Column(np.arange(10), name='baz', meta={'vary': OUTPUT}),
    ...     Column(np.ones(10), name='plugh'),
    ...     Column(np.arange(10), name='xyzzy')
    ... ])
    >>> with tempfile.TemporaryDirectory() as dir:
    ...     write_samples(
    ...         table, os.path.join(dir, 'test.hdf5'), path='bat/baz',
    ...         metadata={'bat/baz': {'widget': 'shoephone'}})

    """  # noqa: W291
    # Copy the table so that we do not modify the original.
    table = table.copy()

    # Make sure that all tables have a 'vary' type.
    for column in table.columns.values():
        if 'vary' not in column.meta:
            if np.all(column[0] == column[1:]):
                column.meta['vary'] = FIXED
            else:
                column.meta['vary'] = OUTPUT
    # Reconstruct table attributes.
    for colname, column in tuple(table.columns.items()):
        if column.meta['vary'] == FIXED:
            np.testing.assert_array_equal(column[1:], column[0],
                                          'Column {0} is a fixed column, but '
                                          'its values are not identical'
                                          .format(column.name))
            table.meta[colname] = column[0]
            del table[colname]
    for i, column in enumerate(table.columns.values()):
        table.meta['FIELD_{0}_VARY'.format(i)] = column.meta.pop('vary')
    table.write(filename, format='hdf5', **kwargs)
    if metadata:
        with h5py.File(filename, 'r+') as hdf:
            for internal_path, attributes in metadata.items():
                for key, value in attributes.items():
                    try:
                        hdf[internal_path].attrs[key] = value
                    except KeyError:
                        raise KeyError(
                            'Unable to set metadata {0}[{1}] = {2}'.format(
                                internal_path, key, value))

import os
import pkgutil

__all__ = ()

# Import all symbols from all submodules of this module.
for _, module, _ in pkgutil.iter_modules([os.path.dirname(__file__)]):
    if module not in {'tests'}:
        exec('from . import {0};'
             '__all__ += getattr({0}, "__all__", ());'
             'from .{0} import *'.format(module))
    del module

# Clean up
del os, pkgutil

# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Base classes for reading events from search pipelines."""

from abc import ABCMeta, abstractmethod
from collections.abc import Mapping

__all__ = ('EventSource', 'Event', 'SingleEvent')


def _fmt(obj, keys):
    kvs = ', '.join('{}={!r}'.format(key, getattr(obj, key)) for key in keys)
    return '<{}({})>'.format(obj.__class__.__name__, kvs)


class EventSource(Mapping):
    """Abstraction of a source of coincident events.

    This is a mapping from event IDs (which may be any hashable type, but are
    generally integers or strings) to instances of `Event`.
    """

    def __str__(self):
        try:
            length = len(self)
        except (NotImplementedError, TypeError):
            contents = '...'
        else:
            contents = '...{} items...'.format(length)
        return '<{}({{{}}})>'.format(self.__class__.__name__, contents)

    def __repr__(self):
        try:
            len(self)
        except NotImplementedError:
            contents = '...'
        else:
            contents = ', '.join('{}: {!r}'.format(key, value)
                                 for key, value in self.items())
        return '{}({{{}}})'.format(self.__class__.__name__, contents)


class Event(metaclass=ABCMeta):
    """Abstraction of a coincident trigger.

    Attributes
    ----------
    singles : list, tuple
        Sequence of `SingleEvent`
    template_args : dict
        Dictionary of template parameters

    """

    @property
    @abstractmethod
    def singles(self):
        raise NotImplementedError

    @property
    @abstractmethod
    def template_args(self):
        raise NotImplementedError

    __str_keys = ('singles',)

    def __str__(self):
        return _fmt(self, self.__str_keys)

    __repr__ = __str__


class SingleEvent(metaclass=ABCMeta):
    """Abstraction of a single-detector trigger.

    Attributes
    ----------
    detector : str
        Instrument name (e.g. 'H1')
    snr : float
        Signal to noise ratio
    phase : float
        Phase on arrival
    time : float
        GPS time on arrival
    zerolag_time : float
        GPS time on arrival in zero-lag data, without time slides applied
    psd : `REAL8FrequencySeries`
        Power spectral density
    snr_series : `COMPLEX8TimeSeries`
        SNR time series

    """

    @property
    @abstractmethod
    def detector(self):
        raise NotImplementedError

    @property
    @abstractmethod
    def snr(self):
        raise NotImplementedError

    @property
    @abstractmethod
    def phase(self):
        raise NotImplementedError

    @property
    @abstractmethod
    def time(self):
        raise NotImplementedError

    @property
    @abstractmethod
    def zerolag_time(self):
        raise NotImplementedError

    @property
    @abstractmethod
    def psd(self):
        raise NotImplementedError

    @property
    def snr_series(self):
        return None

    __str_keys = ('detector', 'snr', 'phase', 'time')

    def __str__(self):
        keys = self.__str_keys
        if self.time != self.zerolag_time:
            keys += ('zerolag_time',)
        return _fmt(self, keys)

    __repr__ = __str__

# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Modify events by artificially disabling specified detectors."""
from .base import Event, EventSource

__all__ = ('DetectorDisabledEventSource', 'DetectorDisabledError')


class DetectorDisabledError(ValueError):
    pass


class DetectorDisabledEventSource(EventSource):

    def __init__(self, base_source, disabled_detectors, raises=True):
        self.base_source = base_source
        self.disabled_detectors = set(disabled_detectors)
        self.raises = raises

    def __iter__(self):
        return iter(self.base_source)

    def __getitem__(self, key):
        return DetectorDisabledEvent(self, self.base_source[key])

    def __len__(self):
        return len(self.base_source)


class DetectorDisabledEvent(Event):

    def __init__(self, source, base_event):
        self.source = source
        self.base_event = base_event

    @property
    def singles(self):
        disabled_detectors = self.source.disabled_detectors
        if self.source.raises:
            detectors = {s.detector for s in self.base_event.singles}
            if not detectors & disabled_detectors:
                raise DetectorDisabledError(
                    'Disabling detectors {{{}}} would have no effect on this '
                    'event with detectors {{{}}}'.format(
                        ' '.join(sorted(disabled_detectors)),
                        ' '.join(sorted(detectors))))
            if not detectors - disabled_detectors:
                raise DetectorDisabledError(
                    'Disabling detectors {{{}}} would exclude all data for '
                    'this event with detectors {{{}}}'.format(
                        ' '.join(sorted(disabled_detectors)),
                        ' '.join(sorted(detectors))))
        return tuple(s for s in self.base_event.singles
                     if s.detector not in disabled_detectors)

    @property
    def template_args(self):
        return self.base_event.template_args


open = DetectorDisabledEventSource

# Copyright (C) 2017-2022  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
import logging

from ligo.gracedb import rest
from ligo.lw import ligolw

from .base import EventSource
from .ligolw import LigoLWEventSource, _read_xml

__all__ = ('GraceDBEventSource',)

log = logging.getLogger('BAYESTAR')


def _has_psds(xmldoc):
    for elem in xmldoc.getElementsByTagName(ligolw.LIGO_LW.tagName):
        if elem.hasAttribute('Name') and elem.Name == 'REAL8FrequencySeries':
            return True
    return False


class GraceDBEventSource(EventSource):
    """Read events from GraceDB.

    Parameters
    ----------
    graceids : list
        List of GraceDB ID strings.
    client : `ligo.gracedb.rest.GraceDb`, optional
        Client object

    Returns
    -------
    `~ligo.skymap.io.events.EventSource`

    """

    def __init__(self, graceids, client=None):
        if client is None:
            client = rest.GraceDb()
        self._client = client
        self._graceids = graceids

    def __iter__(self):
        return iter(self._graceids)

    def __getitem__(self, graceid):
        coinc_file, _ = _read_xml(self._client.files(graceid, 'coinc.xml'))
        if _has_psds(coinc_file):
            psd_file = coinc_file
        else:
            log.warning('The coinc.xml should contain a PSD, but it does not. '
                        'Attempting to download psd.xml.gz.')
            psd_file = self._client.files(graceid, 'psd.xml.gz')
        event, = LigoLWEventSource(
            coinc_file, psd_file=psd_file, coinc_def=None).values()
        return event

    def __len__(self):
        return len(self._graceids)


open = GraceDBEventSource

# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Read events from PyCBC-style HDF5 output."""
from operator import itemgetter
from itertools import groupby

import h5py
import numpy as np
import lal
from ligo.segments import segment, segmentlist

from .base import Event, EventSource, SingleEvent

__all__ = ('HDFEventSource',)


class _psd_segment(segment):  # noqa: N801

    def __new__(cls, psd, *args):
        return segment.__new__(cls, *args)

    def __init__(self, psd, *args):
        self.psd = psd


def _hdf_file(f):
    if isinstance(f, h5py.File):
        return f
    elif hasattr(f, 'read') and hasattr(f, 'name'):
        return h5py.File(f.name, 'r')
    else:
        return h5py.File(f, 'r')


def _classify_hdf_file(f, sample):
    if sample in f:
        return 'coincs'
    for key, value in f.items():
        if isinstance(value, h5py.Group):
            if 'psds' in value:
                return 'psds'
            if 'snr' in value and 'coa_phase' in value and 'end_time' in value:
                return 'triggers'
    if 'parameters' in f.attrs:
        return 'bank'
    raise ValueError('Unrecognized PyCBC file type')


class HDFEventSource(EventSource):
    """Read events from PyCBC-style HDF5 files.

    Parameters
    ----------
    *files : list of str, file-like object, or `h5py.File` objects
        The PyCBC coinc, bank, psds, and triggers files, in any order.

    Returns
    -------
    `~ligo.skymap.io.events.EventSource`

    """

    def __init__(self, *files, **kwargs):
        sample = kwargs.get('sample', 'foreground')

        # Open the files and split them into coinc files, bank files, psds,
        # and triggers.
        key = itemgetter(0)
        files = [_hdf_file(f) for f in files]
        files = sorted(
            [(_classify_hdf_file(f, sample), f) for f in files], key=key)
        files = {key: list(v[1] for v in value)
                 for key, value in groupby(files, key)}

        try:
            coinc_file, = files['coincs']
        except (KeyError, ValueError):
            raise ValueError('You must provide exactly one coinc file.')
        try:
            bank_file, = files['bank']
        except (KeyError, ValueError):
            raise ValueError(
                'You must provide exactly one template bank file.')
        try:
            psd_files = files['psds']
        except KeyError:
            raise ValueError('You must provide PSD files.')
        try:
            trigger_files = files['triggers']
        except KeyError:
            raise ValueError('You must provide trigger files.')

        self._bank = bank_file

        key_prefix = 'detector_'
        detector_nums, self._ifos = zip(*sorted(
            (int(key[len(key_prefix):]), value)
            for key, value in coinc_file.attrs.items()
            if key.startswith(key_prefix)))

        coinc_group = coinc_file[sample]
        self._timeslide_interval = coinc_file.attrs.get(
            'timeslide_interval', 0)
        self._template_ids = coinc_group['template_id']
        self._timeslide_ids = coinc_group.get(
            'timeslide_id', np.zeros(len(self)))
        self._trigger_ids = [
            coinc_group['trigger_id{}'.format(detector_num)]
            for detector_num in detector_nums]

        triggers = {}
        for f in trigger_files:
            (ifo, group), = f.items()
            triggers[ifo] = [
                group['snr'], group['coa_phase'], group['end_time']]
        self._triggers = tuple(triggers[ifo] for ifo in self._ifos)

        psdseglistdict = {}
        for psd_file in psd_files:
            (ifo, group), = psd_file.items()
            psd = [group['psds'][str(i)] for i in range(len(group['psds']))]
            psdseglistdict[ifo] = segmentlist(
                _psd_segment(*segargs) for segargs in zip(
                    psd, group['start_time'], group['end_time']))
        self._psds = [psdseglistdict[ifo] for ifo in self._ifos]

    def __getitem__(self, id):
        return HDFEvent(self, id)

    def __iter__(self):
        return iter(range(len(self)))

    def __len__(self):
        return len(self._template_ids)


class HDFEvent(Event):

    def __init__(self, source, id):
        self._source = source
        self._id = id

    @property
    def singles(self):
        return tuple(
            HDFSingleEvent(
                ifo, self._id, i, trigger_ids[self._id],
                self._source._timeslide_interval, triggers,
                self._source._timeslide_ids, psds
            )
            for i, (ifo, trigger_ids, triggers, psds) in enumerate(zip(
                self._source._ifos, self._source._trigger_ids,
                self._source._triggers, self._source._psds
            ))
        )

    @property
    def template_args(self):
        bank = self._source._bank
        bank_id = self._source._template_ids[self._id]
        return {key: value[bank_id] for key, value in bank.items()}


class HDFSingleEvent(SingleEvent):

    def __init__(
            self, detector, _coinc_id, _detector_num, _trigger_id,
            _timeslide_interval, _triggers, _timeslide_ids, _psds):
        self._detector = detector
        self._coinc_id = _coinc_id
        self._detector_num = _detector_num
        self._trigger_id = _trigger_id
        self._timeslide_interval = _timeslide_interval
        self._triggers = _triggers
        self._timeslide_ids = _timeslide_ids
        self._psds = _psds

    @property
    def detector(self):
        return self._detector

    @property
    def snr(self):
        return self._triggers[0][self._trigger_id]

    @property
    def phase(self):
        return self._triggers[1][self._trigger_id]

    @property
    def time(self):
        value = self.zerolag_time

        # PyCBC does not specify which detector is time-shifted in time slides.
        # Since PyCBC's coincidence format currently supports only two
        # detectors, we arbitrarily apply half of the time slide to each
        # detector.
        shift = self._timeslide_ids[self._coinc_id] * self._timeslide_interval
        if self._detector_num == 0:
            value -= 0.5 * shift
        elif self._detector_num == 1:
            value += 0.5 * shift
        else:
            raise AssertionError('This line should not be reached')
        return value

    @property
    def zerolag_time(self):
        return self._triggers[2][self._trigger_id]

    @property
    def psd(self):
        try:
            psd = self._psds[self._psds.find(self.zerolag_time)].psd
        except ValueError:
            raise ValueError(
                'No PSD found for detector {} at zero-lag GPS time {}'.format(
                    self.detector, self.zerolag_time))

        dyn_range_fac = psd.file.attrs['dynamic_range_factor']
        flow = psd.file.attrs['low_frequency_cutoff']
        df = psd.attrs['delta_f']
        kmin = int(flow / df)

        fseries = lal.CreateREAL8FrequencySeries(
            'psd', 0, kmin * df, df,
            lal.DimensionlessUnit, len(psd) - kmin)
        fseries.data.data = psd[kmin:] / np.square(dyn_range_fac)
        return fseries


open = HDFEventSource

# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Read events from pipedown/GstLal-style XML output."""
from collections import OrderedDict, defaultdict
import errno
from functools import lru_cache
import itertools
import logging
import operator
import os.path

from ligo.lw import array, lsctables, param, table
from ligo.lw.ligolw import Element, LIGOLWContentHandler, LIGO_LW
from ligo.lw.lsctables import (
    CoincDefTable, CoincMapTable, CoincTable, ProcessTable, ProcessParamsTable,
    SnglInspiralTable, TimeSlideID, TimeSlideTable)
from ligo.lw.utils import load_filename, load_fileobj
import lal
import lal.series
from lalinspiral.thinca import InspiralCoincDef

from .base import Event, EventSource, SingleEvent
from ...util import ilwd

__all__ = ('LigoLWEventSource',)

log = logging.getLogger('BAYESTAR')


@ilwd.use_in
@array.use_in
@lsctables.use_in
@param.use_in
@table.use_in
class ContentHandler(LIGOLWContentHandler):
    pass


def _read_xml(f, fallbackpath=None):
    if f is None:
        doc = filename = None
    elif isinstance(f, Element):
        doc = f
        filename = ''
    elif isinstance(f, str):
        try:
            doc = load_filename(f, contenthandler=ContentHandler)
        except IOError as e:
            if e.errno == errno.ENOENT and fallbackpath and \
                    not os.path.isabs(f):
                f = os.path.join(fallbackpath, f)
                doc = load_filename(f, contenthandler=ContentHandler)
            else:
                raise
        filename = f
    else:
        doc = load_fileobj(f, contenthandler=ContentHandler)
        try:
            filename = f.name
        except AttributeError:
            filename = ''
    return doc, filename


class LigoLWEventSource(OrderedDict, EventSource):
    """Read events from LIGO-LW XML files.

    Parameters
    ----------
    f : str, file-like object, or `ligo.lw.ligolw.Document`
        The name of the file, or the file object, or the XML document object,
        containing the trigger tables.
    psd_file : str, file-like object, or `ligo.lw.ligolw.Document`
        The name of the file, or the file object, or the XML document object,
        containing the PSDs. If not supplied, then PSDs will be read
        automatically from any files mentioned in ``--reference-psd`` command
        line arguments stored in the ProcessParams table.
    coinc_def : `ligo.lw.lsctables.CoincDef`, optional
        An optional coinc definer to limit which events are read.
    fallbackpath : str, optional
        A directory to search for PSD files whose ``--reference-psd`` command
        line arguments have relative paths. By default, the current working
        directory and the directory containing file ``f`` are searched.

    Returns
    -------
    `~ligo.skymap.io.events.EventSource`

    """

    def __init__(self, f, psd_file=None, coinc_def=InspiralCoincDef,
                 fallbackpath=None, **kwargs):
        doc, filename = _read_xml(f)
        self._fallbackpath = (
            os.path.dirname(filename) if filename else fallbackpath)
        self._psds_for_file = lru_cache(maxsize=None)(self._psds_for_file)
        super().__init__(self._make_events(doc, psd_file, coinc_def))

    _template_keys = '''mass1 mass2
                        spin1x spin1y spin1z spin2x spin2y spin2z
                        f_final'''.split()

    _invert_phases = {
        'pycbc': False,
        'gstlal_inspiral': True,
        'gstlal_inspiral_postcohspiir_online': True,  # FIXME: wild guess
        'bayestar_realize_coincs': True,
        'bayestar-realize-coincs': True,
        'MBTAOnline': True
    }

    @classmethod
    def _phase_convention(cls, program):
        try:
            return cls._invert_phases[program]
        except KeyError:
            raise KeyError(
                ('The pipeline "{}" is unknown, so the phase '
                 'convention could not be deduced.').format(program))

    def _psds_for_file(self, f):
        doc, _ = _read_xml(f, self._fallbackpath)
        return lal.series.read_psd_xmldoc(doc, root_name=None)

    def _make_events(self, doc, psd_file, coinc_def):
        # Look up necessary tables.
        coinc_table = CoincTable.get_table(doc)
        coinc_map_table = CoincMapTable.get_table(doc)
        sngl_inspiral_table = SnglInspiralTable.get_table(doc)
        try:
            time_slide_table = TimeSlideTable.get_table(doc)
        except ValueError:
            offsets_by_time_slide_id = None
        else:
            offsets_by_time_slide_id = time_slide_table.as_dict()

        # Indices to speed up lookups by ID.
        key = operator.attrgetter('coinc_event_id')
        event_ids_by_coinc_event_id = {
            coinc_event_id:
                tuple(coinc_map.event_id for coinc_map in coinc_maps
                      if coinc_map.table_name == SnglInspiralTable.tableName)
            for coinc_event_id, coinc_maps
            in itertools.groupby(sorted(coinc_map_table, key=key), key=key)}
        sngl_inspirals_by_event_id = {
            row.event_id: row for row in sngl_inspiral_table}

        # Filter rows by coinc_def if requested.
        if coinc_def is not None:
            coinc_def_table = CoincDefTable.get_table(doc)
            coinc_def_ids = {
                row.coinc_def_id for row in coinc_def_table
                if (row.search, row.search_coinc_type) ==
                (coinc_def.search, coinc_def.search_coinc_type)}
            coinc_table = [
                row for row in coinc_table
                if row.coinc_def_id in coinc_def_ids]

        snr_dict = dict(self._snr_series_by_sngl_inspiral(doc))

        process_table = ProcessTable.get_table(doc)
        program_for_process_id = {
            row.process_id: row.program for row in process_table}

        try:
            process_params_table = ProcessParamsTable.get_table(doc)
        except ValueError:
            psd_filenames_by_process_id = {}
        else:
            psd_filenames_by_process_id = {
                process_param.process_id: process_param.value
                for process_param in process_params_table
                if process_param.param == '--reference-psd'}

        ts0 = TimeSlideID(0)
        for time_slide_id in {coinc.time_slide_id for coinc in coinc_table}:
            if offsets_by_time_slide_id is None and time_slide_id == ts0:
                log.warning(
                    'Time slide record is missing for %s, '
                    'guessing that this is zero-lag', time_slide_id)

        for program in {program_for_process_id[coinc.process_id]
                        for coinc in coinc_table}:
            invert_phases = self._phase_convention(program)
            if invert_phases:
                log.warning(
                    'Using anti-FINDCHIRP phase convention; inverting phases. '
                    'This is currently the default and it is appropriate for '
                    'gstlal and MBTA but not pycbc as of observing run 1 '
                    '("O1"). The default setting is likely to change in the '
                    'future.')

        for coinc in coinc_table:
            coinc_event_id = coinc.coinc_event_id
            coinc_event_num = int(coinc_event_id)
            sngls = [sngl_inspirals_by_event_id[event_id] for event_id
                     in event_ids_by_coinc_event_id[coinc_event_id]]
            if offsets_by_time_slide_id is None and coinc.time_slide_id == ts0:
                offsets = defaultdict(float)
            else:
                offsets = offsets_by_time_slide_id[coinc.time_slide_id]

            template_args = [
                {key: getattr(sngl, key) for key in self._template_keys}
                for sngl in sngls]
            if any(d != template_args[0] for d in template_args[1:]):
                raise ValueError(
                    'Template arguments are not identical for all detectors!')
            template_args = template_args[0]

            invert_phases = self._phase_convention(
                program_for_process_id[coinc.process_id])

            singles = tuple(LigoLWSingleEvent(
                self, sngl.ifo, sngl.snr, sngl.coa_phase,
                float(sngl.end + offsets[sngl.ifo]), float(sngl.end),
                psd_file or psd_filenames_by_process_id.get(sngl.process_id),
                snr_dict.get(sngl.event_id), invert_phases)
                for sngl in sngls)

            event = LigoLWEvent(coinc_event_num, singles, template_args)

            yield coinc_event_num, event

    @classmethod
    def _snr_series_by_sngl_inspiral(cls, doc):
        for elem in doc.getElementsByTagName(LIGO_LW.tagName):
            try:
                if elem.Name != lal.COMPLEX8TimeSeries.__name__:
                    continue
                array.get_array(elem, 'snr')
                event_id = param.get_pyvalue(elem, 'event_id')
            except (AttributeError, ValueError):
                continue
            else:
                yield event_id, lal.series.parse_COMPLEX8TimeSeries(elem)


class LigoLWEvent(Event):

    def __init__(self, id, singles, template_args):
        self._id = id
        self._singles = singles
        self._template_args = template_args

    @property
    def singles(self):
        return self._singles

    @property
    def template_args(self):
        return self._template_args


class LigoLWSingleEvent(SingleEvent):

    def __init__(self, source, detector, snr, phase, time, zerolag_time,
                 psd_file, snr_series, invert_phases):
        self._source = source
        self._detector = detector
        self._snr = snr
        self._phase = phase
        self._time = time
        self._zerolag_time = zerolag_time
        self._psd_file = psd_file
        self._snr_series = snr_series
        self._invert_phases = invert_phases

    @property
    def detector(self):
        return self._detector

    @property
    def snr(self):
        return self._snr

    @property
    def phase(self):
        value = self._phase
        if value is not None and self._invert_phases:
            value *= -1
        return value

    @property
    def time(self):
        return self._time

    @property
    def zerolag_time(self):
        return self._zerolag_time

    @property
    def psd(self):
        return self._source._psds_for_file(self._psd_file)[self._detector]

    @property
    def snr_series(self):
        value = self._snr_series
        if self._invert_phases and value is not None:
            value = lal.CutCOMPLEX8TimeSeries(value, 0, len(value.data.data))
            value.data.data = value.data.data.conj()
        return value


open = LigoLWEventSource

# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Read events from either HDF or LIGO-LW files."""
import builtins
import sqlite3

from ligo.lw.ligolw import Element
import h5py

from . import hdf, ligolw, sqlite

__all__ = ('MagicEventSource', 'open')


def _read_file_header(f, nbytes=16):
    """Read the first 16 bytes of a file

    This is presumed to include the characters that declare the
    file type.

    Parameters
    ----------
    f : file, str
        A file object or the path to a file

    Returns
    -------
    header : bytes
        A string (hopefully) describing the file type

    """
    try:
        pos = f.tell()
    except AttributeError:
        with builtins.open(f, "rb") as fobj:
            return fobj.read(nbytes)
    try:
        return f.read(nbytes)
    finally:
        f.seek(pos)


def MagicEventSource(f, *args, **kwargs):  # noqa: N802
    """Read events from LIGO-LW XML, LIGO-LW SQlite, or HDF5 files. The format
    is determined automatically using the :manpage:`file(1)` command, and then
    the file is opened using :obj:`.ligolw.open`, :obj:`.sqlite.open`, or
    :obj:`.hdf.open`, as appropriate.

    Returns
    -------
    `~ligo.skymap.io.events.EventSource`

    """
    if isinstance(f, h5py.File):
        opener = hdf.open
    elif isinstance(f, sqlite3.Connection):
        opener = sqlite.open
    elif isinstance(f, Element):
        opener = ligolw.open
    else:
        fileheader = _read_file_header(f)
        if fileheader.startswith(b'\x89HDF\r\n\x1a\n'):
            opener = hdf.open
        elif fileheader.startswith(b'SQLite format 3'):
            opener = sqlite.open
        elif fileheader.startswith((
                b'<?xml',  # XML
                b'\x1f\x8b\x08',  # GZIP
        )):
            opener = ligolw.open
        else:
            raise IOError('Unknown file format')
    return opener(f, *args, **kwargs)


open = MagicEventSource

# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""Read events from a GstLal-style SQLite output."""
import os
import sqlite3

from ligo.lw import dbtables

from ...util import sqlite
from .ligolw import LigoLWEventSource

__all__ = ('SQLiteEventSource',)


class SQLiteEventSource(LigoLWEventSource):
    """Read events from LIGO-LW SQLite files.

    Parameters
    ----------
    f : str, file-like object, or `sqlite3.Connection` instance
        The SQLite database.

    Returns
    -------
    `~ligo.skymap.io.events.EventSource`

    """

    def __init__(self, f, *args, **kwargs):
        if isinstance(f, sqlite3.Connection):
            db = f
            filename = sqlite.get_filename(f)
        else:
            if hasattr(f, 'read'):
                filename = f.name
                f.close()
            else:
                filename = f
            db = sqlite.open(filename, 'r')
        super().__init__(dbtables.get_xml(db), *args, **kwargs)
        self._fallbackpath = os.path.dirname(filename) if filename else None


open = SQLiteEventSource

import os
import pkgutil

__all__ = ()

# Import all symbols from all submodules of this module.
for _, module, _ in pkgutil.iter_modules([os.path.dirname(__file__)]):
    if module not in {'tests'}:
        exec('from . import {0};'
             '__all__ += getattr({0}, "__all__", ());'
             'from .{0} import *'.format(module))
    del module

# Clean up
del os, pkgutil

#
# Copyright (C) 2012-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.
#
"""
Axes subclasses for astronomical mapmaking.

This module adds several :class:`astropy.visualization.wcsaxes.WCSAxes`
subclasses to the Matplotlib projection registry. The projections have names of
the form :samp:`{astro_or_geo_or_galactic} [{lon_units}] {projection}`.

:samp:`{astro_or_geo_or_galactic}` may be ``astro``, ``geo``, or ``galactic``.
It controls the reference frame, either celestial (ICRS), terrestrial (ITRS),
or galactic.

:samp:`{lon_units}` may be ``hours`` or ``degrees``. It controls the units of
the longitude axis. If omitted, ``astro`` implies ``hours`` and ``geo`` implies
degrees.

:samp:`{projection}` may be any of the following:

* ``aitoff`` for the Aitoff all-sky projection

* ``mollweide`` for the Mollweide all-sky projection

* ``globe`` for an orthographic projection, like the three-dimensional view of
  the Earth from a distant satellite

* ``zoom`` for a gnomonic projection suitable for visualizing small zoomed-in
  patches

All projections support the ``center`` argument, while some support additional
arguments. The ``globe`` projections also support the ``rotate`` argument, and
the ``zoom`` projections also supports the ``radius`` and ``rotate`` arguments.

Examples
--------
.. plot::
   :context: reset
   :include-source:
   :align: center

    import ligo.skymap.plot
    from matplotlib import pyplot as plt
    ax = plt.axes(projection='astro hours mollweide')
    ax.grid()

.. plot::
   :context: reset
   :include-source:
   :align: center

    import ligo.skymap.plot
    from matplotlib import pyplot as plt
    ax = plt.axes(projection='geo aitoff')
    ax.grid()

.. plot::
   :context: reset
   :include-source:
   :align: center

    import ligo.skymap.plot
    from matplotlib import pyplot as plt
    ax = plt.axes(projection='astro zoom',
                  center='5h -32d', radius='5 deg', rotate='20 deg')
    ax.grid()

.. plot::
   :context: reset
   :include-source:
   :align: center

    import ligo.skymap.plot
    from matplotlib import pyplot as plt
    ax = plt.axes(projection='geo globe', center='-50d +23d')
    ax.grid()

Insets
------
You can use insets to link zoom-in views between axes. There are two supported
styles of insets: rectangular and circular (loupe). The example below shows
both kinds of insets.

.. plot::
   :context: reset
   :include-source:
   :align: center

    import ligo.skymap.plot
    from matplotlib import pyplot as plt
    fig = plt.figure(figsize=(9, 4), dpi=100)

    ax_globe = plt.axes(
        [0.1, 0.1, 0.8, 0.8],
        projection='astro degrees globe',
        center='120d +23d')

    ax_zoom_rect = plt.axes(
        [0.0, 0.2, 0.4, 0.4],
        projection='astro degrees zoom',
        center='150d +30d',
        radius='9 deg')

    ax_zoom_circle = plt.axes(
        [0.55, 0.1, 0.6, 0.6],
        projection='astro degrees zoom',
        center='120d +10d',
        radius='5 deg')

    ax_globe.mark_inset_axes(ax_zoom_rect)
    ax_globe.connect_inset_axes(ax_zoom_rect, 'upper left')
    ax_globe.connect_inset_axes(ax_zoom_rect, 'lower right')

    ax_globe.mark_inset_circle(ax_zoom_circle, '120d +10d', '4 deg')
    ax_globe.connect_inset_circle(ax_zoom_circle, '120d +10d', '4 deg')

    ax_globe.grid()
    ax_zoom_rect.grid()
    ax_zoom_circle.grid()

    for ax in [ax_globe, ax_zoom_rect, ax_zoom_circle]:
        ax.set_facecolor('none')
        for key in ['ra', 'dec']:
            ax.coords[key].set_auto_axislabel(False)

Complete Example
----------------
The following example demonstrates most of the features of this module.

.. plot::
   :context: reset
   :include-source:
   :align: center

    from astropy.coordinates import SkyCoord
    from astropy.io import fits
    from astropy import units as u
    import ligo.skymap.plot
    from matplotlib import pyplot as plt

    url = 'https://dcc.ligo.org/public/0146/G1701985/001/bayestar_no_virgo.fits.gz'
    center = SkyCoord.from_name('NGC 4993')

    fig = plt.figure(figsize=(4, 4), dpi=100)

    ax = plt.axes(
        [0.05, 0.05, 0.9, 0.9],
        projection='astro globe',
        center=center)

    ax_inset = plt.axes(
        [0.59, 0.3, 0.4, 0.4],
        projection='astro zoom',
        center=center,
        radius=10*u.deg)

    for key in ['ra', 'dec']:
        ax_inset.coords[key].set_ticklabel_visible(False)
        ax_inset.coords[key].set_ticks_visible(False)
    ax.grid()
    ax.mark_inset_axes(ax_inset)
    ax.connect_inset_axes(ax_inset, 'upper left')
    ax.connect_inset_axes(ax_inset, 'lower left')
    ax_inset.scalebar((0.1, 0.1), 5 * u.deg).label()
    ax_inset.compass(0.9, 0.1, 0.2)

    ax.imshow_hpx(url, cmap='cylon')
    ax_inset.imshow_hpx(url, cmap='cylon')
    ax_inset.plot(
        center.ra.deg, center.dec.deg,
        transform=ax_inset.get_transform('world'),
        marker=ligo.skymap.plot.reticle(),
        markersize=30,
        markeredgewidth=3)

"""  # noqa: E501
from itertools import product

from astropy.coordinates import SkyCoord, UnitSphericalRepresentation
from astropy.io.fits import Header
from astropy.time import Time
from astropy.visualization.wcsaxes import SphericalCircle, WCSAxes
from astropy.visualization.wcsaxes.formatter_locator import (
    AngleFormatterLocator)
from astropy.visualization.wcsaxes.frame import EllipticalFrame
from astropy.wcs import WCS
from astropy import units as u
from matplotlib import rcParams
from matplotlib.offsetbox import AnchoredOffsetbox
from matplotlib.patches import ConnectionPatch, FancyArrowPatch, PathPatch
from matplotlib.path import Path
from matplotlib.projections import projection_registry
import numpy as np
from reproject import reproject_from_healpix
from scipy.optimize import minimize_scalar
from .angle import reference_angle_deg, wrapped_angle_deg

__all__ = ['AutoScaledWCSAxes', 'ScaleBar']


class WCSInsetPatch(PathPatch):
    """Subclass of `matplotlib.patches.PathPatch` for marking the outline of
    one `astropy.visualization.wcsaxes.WCSAxes` inside another.
    """

    def __init__(self, ax, *args, **kwargs):
        self._ax = ax
        super().__init__(
            None, *args, fill=False,
            edgecolor=ax.coords.frame.get_color(),
            linewidth=ax.coords.frame.get_linewidth(),
            **kwargs)

    def get_path(self):
        frame = self._ax.coords.frame
        return frame.patch.get_path().interpolated(50).transformed(
            frame.transform)


class WCSInsetConnectionPatch(ConnectionPatch):
    """Patch to connect an inset WCS axes inside another WCS axes.

    Notes
    -----
    FIXME: This class assumes that the projection of the circle in figure-inch
    coordinates *is* a circle. It will have noticable artifacts if the
    projection is very distorted."""

    _corners_map = {1: 3, 2: 1, 3: 0, 4: 2}

    def __init__(self, ax, ax_inset, loc, **kwargs):
        try:
            loc = AnchoredOffsetbox.codes[loc]
        except KeyError:
            loc = int(loc)
        corners = ax_inset.viewLim.corners()
        transform = (ax_inset.coords.frame.transform +
                     ax.coords.frame.transform.inverted())
        xy_inset = corners[self._corners_map[loc]]
        xy = transform.transform_point(xy_inset)
        super().__init__(
            xy, xy_inset, 'data', 'data', axesA=ax, axesB=ax_inset,
            color=ax_inset.coords.frame.get_color(),
            linewidth=ax_inset.coords.frame.get_linewidth(),
            **kwargs)


class WCSCircleInsetConnectionPatch(PathPatch):
    """Patch to connect a circular inset WCS axes inside another WCS axes."""

    def __init__(self, ax1, ax2, coord, radius, sign, *args, **kwargs):
        self._axs = (ax1, ax2)
        self._coord = coord.icrs
        self._radius = radius
        self._sign = sign
        super().__init__(None, *args, **kwargs, clip_on=False, transform=None)

    def get_path(self):
        # Calculate the position and radius of the inset in figure-inch
        # coordinates.
        offset = self._coord.directional_offset_by(0 * u.deg, self._radius)
        transforms = [ax.get_transform('world') for ax in self._axs]
        centers = np.asarray([
            tx.transform_point((self._coord.ra.deg, self._coord.dec.deg))
            for tx in transforms])
        offsets = np.asarray([
            tx.transform_point((offset.ra.deg, offset.dec.deg))
            for tx in transforms])

        # Plot outer tangents.
        r0, r1 = np.sqrt(np.sum(np.square(centers - offsets), axis=-1))
        dx, dy = np.diff(centers, axis=0).ravel()
        gamma = -np.arctan(dy / dx)
        beta = np.arcsin((r1 - r0) / np.sqrt(np.square(dx) + np.square(dy)))
        alpha = gamma - self._sign * beta
        p0 = centers[0] + self._sign * np.asarray([
            r0 * np.sin(alpha), r0 * np.cos(alpha)])
        p1 = centers[1] + self._sign * np.asarray([
            r1 * np.sin(alpha), r1 * np.cos(alpha)])
        return Path(np.row_stack((p0, p1)), np.asarray([
            Path.MOVETO, Path.LINETO]))


class AutoScaledWCSAxes(WCSAxes):
    """Axes base class. The pixel scale is adjusted to the DPI of the image,
    and there are a variety of convenience methods.
    """

    name = 'astro wcs'

    def __init__(self, *args, header, obstime=None, **kwargs):
        super().__init__(*args, aspect=1, **kwargs)
        h = Header(header, copy=True)
        naxis1 = h['NAXIS1']
        naxis2 = h['NAXIS2']
        scale = min(self.bbox.width / naxis1, self.bbox.height / naxis2)
        h['NAXIS1'] = int(np.ceil(naxis1 * scale))
        h['NAXIS2'] = int(np.ceil(naxis2 * scale))
        scale1 = h['NAXIS1'] / naxis1
        scale2 = h['NAXIS2'] / naxis2
        h['CRPIX1'] = (h['CRPIX1'] - 1) * (h['NAXIS1'] - 1) / (naxis1 - 1) + 1
        h['CRPIX2'] = (h['CRPIX2'] - 1) * (h['NAXIS2'] - 1) / (naxis2 - 1) + 1
        h['CDELT1'] /= scale1
        h['CDELT2'] /= scale2
        if obstime is not None:
            h['MJD-OBS'] = Time(obstime).utc.mjd
            h['DATE-OBS'] = Time(obstime).utc.isot
        self.reset_wcs(WCS(h))
        self.set_xlim(-0.5, h['NAXIS1'] - 0.5)
        self.set_ylim(-0.5, h['NAXIS2'] - 0.5)
        self._header = h

    @property
    def header(self):
        return self._header

    def mark_inset_axes(self, ax, *args, **kwargs):
        """Outline the footprint of another WCSAxes inside this one.

        Parameters
        ----------
        ax : `astropy.visualization.wcsaxes.WCSAxes`
            The other axes.

        Other parameters
        ----------------
        args :
            Extra arguments for `matplotlib.patches.PathPatch`
        kwargs :
            Extra keyword arguments for `matplotlib.patches.PathPatch`

        Returns
        -------
        patch : `matplotlib.patches.PathPatch`

        """
        return self.add_patch(WCSInsetPatch(
            ax, *args, transform=self.get_transform('world'), **kwargs))

    def mark_inset_circle(self, ax, center, radius, *args, **kwargs):
        """Outline a circle in this and another Axes to create a loupe.

        Parameters
        ----------
        ax : `astropy.visualization.wcsaxes.WCSAxes`
            The other axes.
        coord : `astropy.coordinates.SkyCoord`
            The center of the circle.
        radius : `astropy.units.Quantity`
            The radius of the circle in units that are compatible with degrees.

        Other parameters
        ----------------
        args :
            Extra arguments for `matplotlib.patches.PathPatch`
        kwargs :
            Extra keyword arguments for `matplotlib.patches.PathPatch`

        Returns
        -------
        patch1 : `matplotlib.patches.PathPatch`
            The outline of the circle in these Axes.
        patch2 : `matplotlib.patches.PathPatch`
            The outline of the circle in the other Axes.
        """
        center = SkyCoord(
            center, representation_type=UnitSphericalRepresentation).icrs
        radius = u.Quantity(radius)
        args = ((center.ra, center.dec), radius, *args)
        kwargs = {'facecolor': 'none',
                  'edgecolor': rcParams['axes.edgecolor'],
                  'linewidth': rcParams['axes.linewidth'],
                  **kwargs}
        for ax in (self, ax):
            ax.add_patch(SphericalCircle(*args, **kwargs,
                                         transform=ax.get_transform('world')))

    def connect_inset_axes(self, ax, loc, *args, **kwargs):
        """Connect a corner of another WCSAxes to the matching point inside
        this one.

        Parameters
        ----------
        ax : `astropy.visualization.wcsaxes.WCSAxes`
            The other axes.
        loc : int, str
            Which corner to connect. For valid values, see
            `matplotlib.offsetbox.AnchoredOffsetbox`.

        Other parameters
        ----------------
        args :
            Extra arguments for `matplotlib.patches.ConnectionPatch`
        kwargs :
            Extra keyword arguments for `matplotlib.patches.ConnectionPatch`

        Returns
        -------
        patch : `matplotlib.patches.ConnectionPatch`

        """
        return self.add_patch(WCSInsetConnectionPatch(
            self, ax, loc, *args, **kwargs))

    def connect_inset_circle(self, ax, center, radius, *args, **kwargs):
        """Connect a circle in this and another Axes to create a loupe.

        Parameters
        ----------
        ax : `astropy.visualization.wcsaxes.WCSAxes`
            The other axes.
        coord : `astropy.coordinates.SkyCoord`
            The center of the circle.
        radius : `astropy.units.Quantity`
            The radius of the circle in units that are compatible with degrees.

        Other parameters
        ----------------
        args :
            Extra arguments for `matplotlib.patches.PathPatch`
        kwargs :
            Extra keyword arguments for `matplotlib.patches.PathPatch`

        Returns
        -------
        patch1, patch2 : `matplotlib.patches.ConnectionPatch`
            The two connecting patches.
        """
        center = SkyCoord(
            center, representation_type=UnitSphericalRepresentation).icrs
        radius = u.Quantity(radius)
        kwargs = {'color': rcParams['axes.edgecolor'],
                  'linewidth': rcParams['axes.linewidth'],
                  **kwargs}
        for sign in (-1, 1):
            self.add_patch(WCSCircleInsetConnectionPatch(
                self, ax, center, radius, sign, *args, **kwargs))

    def compass(self, x, y, size):
        """Add a compass to indicate the north and east directions.

        Parameters
        ----------
        x, y : float
            Position of compass vertex in axes coordinates.
        size : float
            Size of compass in axes coordinates.

        """
        xy = x, y
        scale = self.wcs.pixel_scale_matrix
        scale /= np.sqrt(np.abs(np.linalg.det(scale)))
        return [self.annotate(label, xy, xy + size * n,
                              self.transAxes, self.transAxes,
                              ha='center', va='center',
                              arrowprops=dict(arrowstyle='<-',
                                              shrinkA=0.0, shrinkB=0.0))
                for n, label, ha, va in zip(scale, 'EN',
                                            ['right', 'center'],
                                            ['center', 'bottom'])]

    def scalebar(self, *args, **kwargs):
        """Add scale bar.

        Parameters
        ----------
        xy : tuple
            The axes coordinates of the scale bar.
        length : `astropy.units.Quantity`
            The length of the scale bar in angle-compatible units.

        Other parameters
        ----------------
        args :
            Extra arguments for `matplotlib.patches.FancyArrowPatch`
        kwargs :
            Extra keyword arguments for `matplotlib.patches.FancyArrowPatch`

        Returns
        -------
        patch : `matplotlib.patches.FancyArrowPatch`

        """
        return self.add_patch(ScaleBar(self, *args, **kwargs))

    def _reproject_hpx(self, data, hdu_in=None, order='bilinear',
                       nested=False, field=0, smooth=None):
        if isinstance(data, np.ndarray):
            data = (data, self.header['RADESYS'])

        # It's normal for reproject_from_healpix to produce some Numpy invalid
        # value warnings for points that land outside the projection.
        with np.errstate(invalid='ignore'):
            img, mask = reproject_from_healpix(
                data, self.header, hdu_in=hdu_in, order=order, nested=nested,
                field=field)
        img = np.ma.array(img, mask=~mask.astype(bool))

        if smooth is not None:
            # Infrequently used imports
            from astropy.convolution import convolve_fft, Gaussian2DKernel

            pixsize = np.mean(np.abs(self.wcs.wcs.cdelt)) * u.deg
            smooth = (smooth / pixsize).to(u.dimensionless_unscaled).value
            kernel = Gaussian2DKernel(smooth)
            # Ignore divide by zero warnings for pixels that have no valid
            # neighbors.
            with np.errstate(invalid='ignore'):
                img = convolve_fft(img, kernel, fill_value=np.nan)

        return img

    def contour_hpx(self, data, hdu_in=None, order='bilinear', nested=False,
                    field=0, smooth=None, **kwargs):
        """Add contour levels for a HEALPix data set.

        Parameters
        ----------
        data : `numpy.ndarray` or str or `~astropy.io.fits.TableHDU` or `~astropy.io.fits.BinTableHDU` or tuple
            The HEALPix data set. If this is a `numpy.ndarray`, then it is
            interpreted as the HEALPix array in the same coordinate system as
            the axes. Otherwise, the input data can be any type that is
            understood by `reproject.reproject_from_healpix`.
        smooth : `astropy.units.Quantity`, optional
            An optional smoothing length in angle-compatible units.

        Other parameters
        ----------------
        hdu_in, order, nested, field, smooth :
            Extra arguments for `reproject.reproject_from_healpix`
        kwargs :
            Extra keyword arguments for `matplotlib.axes.Axes.contour`

        Returns
        -------
        countours : `matplotlib.contour.QuadContourSet`

        """  # noqa: E501
        img = self._reproject_hpx(data, hdu_in=hdu_in, order=order,
                                  nested=nested, field=field, smooth=smooth)
        return self.contour(img, **kwargs)

    def contourf_hpx(self, data, hdu_in=None, order='bilinear', nested=False,
                     field=0, smooth=None, **kwargs):
        """Add filled contour levels for a HEALPix data set.

        Parameters
        ----------
        data : `numpy.ndarray` or str or `~astropy.io.fits.TableHDU` or `~astropy.io.fits.BinTableHDU` or tuple
            The HEALPix data set. If this is a `numpy.ndarray`, then it is
            interpreted as the HEALPix array in the same coordinate system as
            the axes. Otherwise, the input data can be any type that is
            understood by `reproject.reproject_from_healpix`.
        smooth : `astropy.units.Quantity`, optional
            An optional smoothing length in angle-compatible units.

        Other parameters
        ----------------
        hdu_in, order, nested, field, smooth :
            Extra arguments for `reproject.reproject_from_healpix`
        kwargs :
            Extra keyword arguments for `matplotlib.axes.Axes.contour`

        Returns
        -------
        contours : `matplotlib.contour.QuadContourSet`

        """  # noqa: E501
        img = self._reproject_hpx(data, hdu_in=hdu_in, order=order,
                                  nested=nested, field=field, smooth=smooth)
        return self.contourf(img, **kwargs)

    def imshow_hpx(self, data, hdu_in=None, order='bilinear', nested=False,
                   field=0, smooth=None, **kwargs):
        """Add an image for a HEALPix data set.

        Parameters
        ----------
        data : `numpy.ndarray` or str or `~astropy.io.fits.TableHDU` or `~astropy.io.fits.BinTableHDU` or tuple
            The HEALPix data set. If this is a `numpy.ndarray`, then it is
            interpreted as the HEALPix array in the same coordinate system as
            the axes. Otherwise, the input data can be any type that is
            understood by `reproject.reproject_from_healpix`.
        smooth : `astropy.units.Quantity`, optional
            An optional smoothing length in angle-compatible units.

        Other parameters
        ----------------
        hdu_in, order, nested, field, smooth :
            Extra arguments for `reproject.reproject_from_healpix`
        kwargs :
            Extra keyword arguments for `matplotlib.axes.Axes.contour`

        Returns
        -------
        image : `matplotlib.image.AxesImage`

        """  # noqa: E501
        img = self._reproject_hpx(data, hdu_in=hdu_in, order=order,
                                  nested=nested, field=field, smooth=smooth)
        return self.imshow(img, **kwargs)


class ScaleBar(FancyArrowPatch):

    def _func(self, dx, x, y):
        p1, p2 = self._transAxesToWorld.transform([[x, y], [x + dx, y]])
        p1 = SkyCoord(*p1, unit=u.deg)
        p2 = SkyCoord(*p2, unit=u.deg)
        return np.square((p1.separation(p2) - self._length).value)

    def __init__(self, ax, xy, length, *args, **kwargs):
        x, y = xy
        self._ax = ax
        self._length = u.Quantity(length)
        self._transAxesToWorld = (
            (ax.transAxes - ax.transData) + ax.coords.frame.transform)
        dx = minimize_scalar(
            self._func, args=xy, bounds=[0, 1 - x], method='bounded').x
        custom_kwargs = kwargs
        kwargs = dict(
            capstyle='round',
            color='black',
            linewidth=rcParams['lines.linewidth'],
        )
        kwargs.update(custom_kwargs)
        super().__init__(
            xy, (x + dx, y),
            *args,
            arrowstyle='-',
            shrinkA=0.0,
            shrinkB=0.0,
            transform=ax.transAxes,
            **kwargs)

    def label(self, **kwargs):
        (x0, y), (x1, _) = self._posA_posB
        s = ' {0.value:g}{0.unit:unicode}'.format(self._length)
        return self._ax.text(
            0.5 * (x0 + x1), y, s,
            ha='center', va='bottom', transform=self._ax.transAxes, **kwargs)


class Astro:
    _crval1 = 180
    _xcoord = 'RA--'
    _ycoord = 'DEC-'
    _radesys = 'ICRS'


class GeoAngleFormatterLocator(AngleFormatterLocator):

    def formatter(self, values, spacing):
        return super().formatter(
            reference_angle_deg(values.to(u.deg).value) * u.deg, spacing)


class Geo:
    _crval1 = 0
    _radesys = 'ITRS'
    _xcoord = 'TLON'
    _ycoord = 'TLAT'

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.invert_xaxis()
        fl = self.coords[0]._formatter_locator
        self.coords[0]._formatter_locator = GeoAngleFormatterLocator(
            values=fl.values,
            number=fl.number,
            spacing=fl.spacing,
            format=fl.format,
            format_unit=fl.format_unit)


class GalacticAngleFormatterLocator(AngleFormatterLocator):

    def formatter(self, values, spacing):
        return super().formatter(
            wrapped_angle_deg(values.to(u.deg).value) * u.deg, spacing)


class Galactic:
    _crval1 = 0
    _radesys = 'GALACTIC'
    _xcoord = 'GLON'
    _ycoord = 'GLAT'

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        fl = self.coords[0]._formatter_locator
        self.coords[0]._formatter_locator = GalacticAngleFormatterLocator(
            values=fl.values,
            number=fl.number,
            spacing=fl.spacing,
            format=fl.format,
            format_unit=fl.format_unit)


class Degrees:
    """WCS axes with longitude axis in degrees."""

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.coords[0].set_format_unit(u.degree)


class Hours:
    """WCS axes with longitude axis in hour angle."""

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.coords[0].set_format_unit(u.hourangle)


class Globe(AutoScaledWCSAxes):

    def __init__(self, *args, center='0d 0d', rotate=None, **kwargs):
        center = SkyCoord(
            center, representation_type=UnitSphericalRepresentation).icrs
        header = {
            'NAXIS': 2,
            'NAXIS1': 180,
            'NAXIS2': 180,
            'CRPIX1': 90.5,
            'CRPIX2': 90.5,
            'CRVAL1': center.ra.deg,
            'CRVAL2': center.dec.deg,
            'CDELT1': -2 / np.pi,
            'CDELT2': 2 / np.pi,
            'CTYPE1': self._xcoord + '-SIN',
            'CTYPE2': self._ycoord + '-SIN',
            'RADESYS': self._radesys}
        if rotate is not None:
            header['LONPOLE'] = u.Quantity(rotate).to_value(u.deg)
        super().__init__(
            *args, frame_class=EllipticalFrame, header=header, **kwargs)


class Zoom(AutoScaledWCSAxes):

    def __init__(self, *args, center='0d 0d', radius='1 deg', rotate=None,
                 **kwargs):
        center = SkyCoord(
            center, representation_type=UnitSphericalRepresentation).icrs
        radius = u.Quantity(radius).to(u.deg).value
        header = {
            'NAXIS': 2,
            'NAXIS1': 512,
            'NAXIS2': 512,
            'CRPIX1': 256.5,
            'CRPIX2': 256.5,
            'CRVAL1': center.ra.deg,
            'CRVAL2': center.dec.deg,
            'CDELT1': -radius / 256,
            'CDELT2': radius / 256,
            'CTYPE1': self._xcoord + '-TAN',
            'CTYPE2': self._ycoord + '-TAN',
            'RADESYS': self._radesys}
        if rotate is not None:
            header['LONPOLE'] = u.Quantity(rotate).to_value(u.deg)
        super().__init__(*args, header=header, **kwargs)


class AllSkyAxes(AutoScaledWCSAxes):
    """Base class for a multi-purpose all-sky projection."""

    def __init__(self, *args, center=None, **kwargs):
        if center is None:
            center = f"{self._crval1}d 0d"
        center = SkyCoord(
            center, representation_type=UnitSphericalRepresentation).icrs
        header = {
            'NAXIS': 2,
            'NAXIS1': 360,
            'NAXIS2': 180,
            'CRPIX1': 180.5,
            'CRPIX2': 90.5,
            'CRVAL1': center.ra.deg,
            'CRVAL2': center.dec.deg,
            'CDELT1': -2 * np.sqrt(2) / np.pi,
            'CDELT2': 2 * np.sqrt(2) / np.pi,
            'CTYPE1': self._xcoord + '-' + self._wcsprj,
            'CTYPE2': self._ycoord + '-' + self._wcsprj,
            'RADESYS': self._radesys}
        super().__init__(
            *args, frame_class=EllipticalFrame, header=header, **kwargs)
        self.coords[0].set_ticks(spacing=45 * u.deg)
        self.coords[1].set_ticks(spacing=30 * u.deg)
        self.coords[0].set_ticklabel(exclude_overlapping=True)
        self.coords[1].set_ticklabel(exclude_overlapping=True)


class Aitoff(AllSkyAxes):
    _wcsprj = 'AIT'


class Mollweide(AllSkyAxes):
    _wcsprj = 'MOL'


moddict = globals()

#
# Create subclasses and register all projections:
# '{astro|geo|galactic} {hours|degrees} {aitoff|globe|mollweide|zoom}'
#
bases1 = (Astro, Geo, Galactic)
bases2 = (Hours, Degrees)
bases3 = (Aitoff, Globe, Mollweide, Zoom)
for bases in product(bases1, bases2, bases3):
    class_name = ''.join(cls.__name__ for cls in bases) + 'Axes'
    projection = ' '.join(cls.__name__.lower() for cls in bases)
    new_class = type(class_name, bases, {'name': projection})
    projection_registry.register(new_class)
    moddict[class_name] = new_class
    __all__.append(class_name)

#
# Create some synonyms:
# 'astro' will be short for 'astro hours',
# 'geo' will be short for 'geo degrees'
#

bases2 = (Hours, Degrees, Degrees)
for base1, base2 in zip(bases1, bases2):
    for base3 in (Aitoff, Globe, Mollweide, Zoom):
        bases = (base1, base2, base3)
        orig_class_name = ''.join(cls.__name__ for cls in bases) + 'Axes'
        orig_class = moddict[orig_class_name]
        class_name = ''.join(cls.__name__ for cls in (base1, base3)) + 'Axes'
        projection = ' '.join(cls.__name__.lower() for cls in (base1, base3))
        new_class = type(class_name, (orig_class,), {'name': projection})
        projection_registry.register(new_class)
        moddict[class_name] = new_class
        __all__.append(class_name)

del class_name, moddict, projection, projection_registry, new_class
__all__ = tuple(__all__)

#
# Copyright (C) 2012-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
"""Angle utilities."""
import numpy as np

__all__ = ('reference_angle', 'reference_angle_deg',
           'wrapped_angle', 'wrapped_angle_deg')


def reference_angle(a):
    """Convert an angle to a reference angle between -pi and pi."""
    a = np.mod(a, 2 * np.pi)
    return np.where(a <= np.pi, a, a - 2 * np.pi)


def reference_angle_deg(a):
    """Convert an angle to a reference angle between -180 and 180 degrees."""
    a = np.mod(a, 360)
    return np.where(a <= 180, a, a - 360)


def wrapped_angle(a):
    """Convert an angle to a reference angle between 0 and 2*pi."""
    return np.mod(a, 2 * np.pi)


def wrapped_angle_deg(a):
    """Convert an angle to a reference angle between 0 and 2*pi."""
    return np.mod(a, 360)

#
# Copyright (C) 2017-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
"""Backdrops for astronomical plots."""

from importlib.resources import files
import json
import warnings

from astropy.io import fits
from astropy.time import Time
from astropy.utils.data import download_file
from astropy.wcs import WCS
from matplotlib.image import imread
import numpy as np
from PIL.Image import DecompressionBombWarning
from reproject import reproject_interp

__all__ = ('bluemarble', 'blackmarble', 'coastlines', 'mellinger',
           'reproject_interp_rgb')


def big_imread(*args, **kwargs):
    """Wrapper for imread() that suppresses warnings when loading very large
    images (usually tiffs). Most of the all-sky images that we use in this
    module are large enough to trigger this warning:

        DecompressionBombWarning: Image size (91125000 pixels) exceeds limit of
        89478485 pixels, could be decompression bomb DOS attack.
    """
    with warnings.catch_warnings():
        warnings.simplefilter('ignore', DecompressionBombWarning)
        img = imread(*args, **kwargs)
    return img


def mellinger():
    """Get the Mellinger Milky Way panorama.

    Retrieve, cache, and return the Mellinger Milky Way panorama. See
    http://www.milkywaysky.com.

    Returns
    -------
    `astropy.io.fits.ImageHDU`
        A FITS WCS image in ICRS coordinates.

    Examples
    --------
    .. plot::
       :context: reset
       :include-source:
       :align: center

        from astropy.visualization import (ImageNormalize,
                                           AsymmetricPercentileInterval)
        from astropy.wcs import WCS
        from matplotlib import pyplot as plt
        from ligo.skymap.plot import mellinger
        from reproject import reproject_interp

        ax = plt.axes(projection='astro hours aitoff')
        backdrop = mellinger()
        backdrop_wcs = WCS(backdrop.header).dropaxis(-1)
        interval = AsymmetricPercentileInterval(45, 98)
        norm = ImageNormalize(backdrop.data, interval)
        backdrop_reprojected = np.asarray([
            reproject_interp((layer, backdrop_wcs), ax.header)[0]
            for layer in norm(backdrop.data)])
        backdrop_reprojected = np.rollaxis(backdrop_reprojected, 0, 3)
        ax.imshow(backdrop_reprojected)

    """
    url = 'http://galaxy.phy.cmich.edu/~axel/mwpan2/mwpan2_RGB_3600.fits'
    hdu, = fits.open(url, cache=True)
    return hdu


def bluemarble(t, resolution='low'):
    """Get the "Blue Marble" image.

    Retrieve, cache, and return the NASA/NOAO/NPP "Blue Marble" image showing
    landforms and oceans.

    See https://visibleearth.nasa.gov/view.php?id=74117.

    Parameters
    ----------
    t : `astropy.time.Time`
        Time to embed in the WCS header.
    resolution : {'low', 'high'}
        Specify which version to use: the "low" resolution version (5400x2700
        pixels, the default) or the "high" resolution version (21600x10800
        pixels).

    Returns
    -------
    `astropy.io.fits.ImageHDU`
        A FITS WCS image in ICRS coordinates.

    Examples
    --------
    .. plot::
       :context: reset
       :include-source:
       :align: center

        from matplotlib import pyplot as plt
        from ligo.skymap.plot import bluemarble, reproject_interp_rgb

        obstime = '2017-08-17 12:41:04'
        ax = plt.axes(projection='geo degrees aitoff', obstime=obstime)
        ax.imshow(reproject_interp_rgb(bluemarble(obstime), ax.header))

    """
    variants = {
        'low': '5400x2700',
        'high': '21600x10800'
    }

    url = ('https://eoimages.gsfc.nasa.gov/images/imagerecords/74000/74117/'
           'world.200408.3x{}.png'.format(variants[resolution]))
    img = big_imread(download_file(url, cache=True))
    height, width, ndim = img.shape
    gmst_deg = Time(t).sidereal_time('mean', 'greenwich').deg
    header = fits.Header(dict(
        NAXIS=3,
        NAXIS1=ndim, NAXIS2=width, NAXIS3=height,
        CRPIX2=width / 2, CRPIX3=height / 2,
        CRVAL2=gmst_deg % 360, CRVAL3=0,
        CDELT2=360 / width,
        CDELT3=-180 / height,
        CTYPE2='RA---CAR',
        CTYPE3='DEC--CAR',
        RADESYSa='ICRS').items())
    return fits.ImageHDU(img[:, :, :], header)


def blackmarble(t, resolution='low'):
    """Get the "Black Marble" image.

    Get the NASA/NOAO/NPP image showing city lights, at the sidereal time given
    by t. See https://visibleearth.nasa.gov/view.php?id=79765.

    Parameters
    ----------
    t : `astropy.time.Time`
        Time to embed in the WCS header.
    resolution : {'low', 'mid', 'high'}
        Specify which version to use: the "low" resolution version (3600x1800
        pixels, the default), the "mid" resolution version (13500x6750 pixels),
        or the "high" resolution version (54000x27000 pixels).

    Returns
    -------
    `astropy.io.fits.ImageHDU`
        A FITS WCS image in ICRS coordinates.

    Examples
    --------
    .. plot::
       :context: reset
       :include-source:
       :align: center

        from matplotlib import pyplot as plt
        from ligo.skymap.plot import blackmarble, reproject_interp_rgb

        obstime = '2017-08-17 12:41:04'
        ax = plt.axes(projection='geo degrees aitoff', obstime=obstime)
        ax.imshow(reproject_interp_rgb(blackmarble(obstime), ax.header))

    """
    variants = {
        'low': '3600x1800',
        'high': '13500x6750',
        'mid': '54000x27000'
    }

    url = ('http://eoimages.gsfc.nasa.gov/images/imagerecords/79000/79765/'
           'dnb_land_ocean_ice.2012.{}_geo.tif'.format(variants[resolution]))
    img = big_imread(download_file(url, cache=True))
    height, width, ndim = img.shape
    gmst_deg = Time(t).sidereal_time('mean', 'greenwich').deg
    header = fits.Header(dict(
        NAXIS=3,
        NAXIS1=ndim, NAXIS2=width, NAXIS3=height,
        CRPIX2=width / 2, CRPIX3=height / 2,
        CRVAL2=gmst_deg % 360, CRVAL3=0,
        CDELT2=360 / width,
        CDELT3=-180 / height,
        CTYPE2='RA---CAR',
        CTYPE3='DEC--CAR',
        RADESYSa='ICRS').items())
    return fits.ImageHDU(img[:, :, :], header)


def reproject_interp_rgb(input_data, *args, **kwargs):
    data = input_data.data
    wcs = WCS(input_data.header).celestial
    return np.moveaxis(np.stack([
        reproject_interp((data[:, :, i], wcs),
                         *args, **kwargs)[0].astype(data.dtype)
        for i in range(3)]), 0, -1)


def coastlines():
    with files(__package__).joinpath(
            'ne_simplified_coastline.json').open() as f:
        geoms = json.load(f)['geometries']
    return [coord for geom in geoms for coord in zip(*geom['coordinates'])]

#
# Copyright (C) 2019-2023  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
"""Bullet charts for Bayes factors."""

from matplotlib import pyplot as plt
import numpy as np

__all__ = ('plot_bayes_factor',)


def plot_bayes_factor(logb,
                      values=(1, 3, 5),
                      labels=('', 'strong', 'very strong'),
                      xlim=7, title=None, palette='RdYlBu',
                      var_label="B"):
    """Visualize a Bayes factor as a `bullet graph`_.

    Make a bar chart of a log Bayes factor as compared to a set of subjective
    threshold values. By default, use the thresholds from
    Kass & Raftery (1995).

    .. _`bullet graph`: https://en.wikipedia.org/wiki/Bullet_graph

    Parameters
    ----------
    logb : float
        The natural logarithm of the Bayes factor.
    values : list
        A list of floating point values for human-friendly confidence levels.
    labels : list
        A list of string labels for human-friendly confidence levels.
    xlim : float
        Limits of plot (`-xlim` to `+xlim`).
    title : str
        Title for plot.
    palette : str
        Color palette.
    var_label : str
        The variable symbol used in plotting

    Returns
    -------
    fig : Matplotlib figure
    ax : Matplotlib axes

    Examples
    --------

    .. plot::
       :include-source:

        from ligo.skymap.plot.bayes_factor import plot_bayes_factor
        plot_bayes_factor(6.3, title='BAYESTAR is awesome')

    """
    with plt.style.context('seaborn-v0_8-notebook'):
        fig, ax = plt.subplots(figsize=(6, 1.7), tight_layout=True)
        ax.set_xlim(-xlim, xlim)
        ax.set_ylim(-0.5, 0.5)
        ax.set_yticks([])
        ax.set_title(title)
        ax.set_ylabel(r'$\ln\,{}$'.format(var_label), rotation=0,
                      rotation_mode='anchor',
                      ha='right', va='center')

        # Add human-friendly labels
        ticks = (*(-x for x in reversed(values)), 0, *values)
        ticklabels = (
            *(f'{s}\nevidence\nagainst'.strip() for s in reversed(labels)), '',
            *(f'{s}\nevidence\nfor'.strip() for s in labels))
        ax.set_xticks(ticks)
        ax.set_xticklabels(ticklabels)
        plt.setp(ax.get_xticklines(), visible=False)
        plt.setp(ax.get_xticklabels()[:len(ticks) // 2], ha='right')
        plt.setp(ax.get_xticklabels()[len(ticks) // 2:], ha='left')

        # Plot colored bands for confidence thresholds
        fmt = plt.FuncFormatter(lambda x, _: f'{x:+g}'.replace('+0', '0'))
        ax2 = ax.twiny()
        ax2.set_xlim(*ax.get_xlim())
        ax2.set_xticks(ticks)
        ax2.xaxis.set_major_formatter(fmt)
        levels = (-xlim, *ticks, xlim)
        colors = plt.get_cmap(palette)(np.arange(1, len(levels)) / len(levels))
        ax.barh(0, np.diff(levels), 1, levels[:-1],
                linewidth=plt.rcParams['xtick.major.width'],
                color=colors, edgecolor='white')

        # Plot bar for log Bayes factor value
        ax.barh(0, logb, 0.5, color='black',
                linewidth=plt.rcParams['xtick.major.width'],
                edgecolor='white')

        for ax_ in fig.axes:
            ax_.grid(False)
            for spine in ax_.spines.values():
                spine.set_visible(False)

    return fig, ax

#
# Copyright (C) 2014-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
"""Register some extra Matplotlib color maps"""

from importlib.resources import files

from matplotlib import colormaps
from matplotlib import colors
import numpy as np

__all__ = ()


for name in ['cylon']:
    # Read in color map RGB data.
    with files(__package__).joinpath(f'{name}.csv').open() as f:
        data = np.loadtxt(f, delimiter=',')

    # Create color map.
    cmap = colors.LinearSegmentedColormap.from_list(name, data)
    # Assign in module.
    locals().update({name: cmap})
    # Register with Matplotlib.
    colormaps.register(cmap=cmap, force=True)

    # Generate reversed color map.
    name += '_r'
    data = data[::-1]
    cmap = colors.LinearSegmentedColormap.from_list(name, data)
    # Assign in module.
    locals().update({name: cmap})
    # Register with Matplotlib.
    colormaps.register(cmap=cmap, force=True)

#
# Copyright (C) 2014-2018  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
"""RGB data for the "Cylon red" color map.

A print- and screen-friendly color map designed specifically for plotting
LSC/Virgo sky maps. The color map is constructed in CIE Lab space, following
a linear ramp in lightness (the `l` coordinate) and a cubic spline in color
components (the `a` and `b` coordinates).

This particular color map was selected from 20 random realizations of this
construction."""

if __name__ == '__main__':  # pragma: no cover
    from colormath.color_conversions import convert_color
    from colormath.color_objects import LabColor, sRGBColor
    from scipy.interpolate import interp1d
    import numpy as np

    def lab_to_rgb(*args):
        """Convert Lab color to sRGB, with components clipped to (0, 1)."""
        Lab = LabColor(*args)
        sRGB = convert_color(Lab, sRGBColor)
        return np.clip(sRGB.get_value_tuple(), 0, 1)

    L_samples = np.linspace(100, 0, 5)

    a_samples = (
        33.34664938,
        98.09940562,
        84.48361516,
        76.62970841,
        21.43276891)

    b_samples = (
        62.73345997,
        2.09003022,
        37.28252236,
        76.22507582,
        16.24862535)

    L = np.linspace(100, 0, 255)
    a = interp1d(L_samples, a_samples[::-1], 'cubic')(L)
    b = interp1d(L_samples, b_samples[::-1], 'cubic')(L)

    for line in __doc__.splitlines():
        print('#', line)
    for L, a, b in zip(L, a, b):
        print(*lab_to_rgb(L, a, b), sep=',')

#
# Copyright (C) 2016-2019  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
"""Specialized markers."""

from matplotlib.path import Path
import numpy as np

__all__ = ('earth', 'reticle')


earth = Path.unit_circle()
verts = np.concatenate([earth.vertices, [[-1, 0], [1, 0], [0, -1], [0, 1]]])
codes = np.concatenate([earth.codes, [Path.MOVETO, Path.LINETO] * 2])
earth = Path(verts, codes)
del verts, codes
earth.__doc__ = """
The Earth symbol (circle and cross).

Examples
--------
.. plot::
   :context: reset
   :include-source:
   :align: center

    from matplotlib import pyplot as plt
    from ligo.skymap.plot.marker import earth

    plt.plot(0, 0, markersize=20, markeredgewidth=2,
             markerfacecolor='none', marker=earth)

"""


def reticle(inner=0.5, outer=1.0, angle=0.0, which='lrtb'):
    """Create a reticle or crosshairs marker.

    Parameters
    ----------
    inner : float
        Distance from the origin to the inside of the crosshairs.
    outer : float
        Distance from the origin to the outside of the crosshairs.
    angle : float
        Rotation in degrees; 0 for a '+' orientation and 45 for 'x'.

    Returns
    -------
    path : `matplotlib.path.Path`
        The new marker path, suitable for passing to Matplotlib functions
        (e.g., `plt.plot(..., marker=reticle())`)

    Examples
    --------
    .. plot::
       :context: reset
       :include-source:
       :align: center

        from matplotlib import pyplot as plt
        from ligo.skymap.plot.marker import reticle

        markers = [reticle(inner=0),
                   reticle(which='lt'),
                   reticle(which='lt', angle=45)]

        fig, ax = plt.subplots(figsize=(6, 2))
        ax.set_xlim(-0.5, 2.5)
        ax.set_ylim(-0.5, 0.5)
        for x, marker in enumerate(markers):
            ax.plot(x, 0, markersize=20, markeredgewidth=2, marker=marker)

    """
    angle = np.deg2rad(angle)
    x = np.cos(angle)
    y = np.sin(angle)
    rotation = [[x, y], [-y, x]]
    vertdict = {'l': [-1, 0], 'r': [1, 0], 'b': [0, -1], 't': [0, 1]}
    verts = [vertdict[direction] for direction in which]
    codes = [Path.MOVETO, Path.LINETO] * len(verts)
    verts = np.dot(verts, rotation)
    verts = np.swapaxes([inner * verts, outer * verts], 0, 1).reshape(-1, 2)
    return Path(verts, codes)

#
# Copyright (C) 2012-2020  Leo Singer
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
"""Plotting tools for drawing polygons."""
import numpy as np
import healpy as hp

from .angle import reference_angle, wrapped_angle

__all__ = ('subdivide_vertices', 'cut_dateline',
           'cut_prime_meridian', 'make_rect_poly')


def subdivide_vertices(vertices, subdivisions):
    """Subdivide a list of vertices by inserting subdivisions additional
    vertices between each original pair of vertices using linear
    interpolation.
    """
    subvertices = np.empty((subdivisions * len(vertices), vertices.shape[1]))
    frac = np.atleast_2d(
        np.arange(subdivisions + 1, dtype=float) / subdivisions).T.repeat(
            vertices.shape[1], 1)
    for i in range(len(vertices)):
        subvertices[i * subdivisions:(i + 1) * subdivisions] = \
            frac[:0:-1, :] * \
            np.expand_dims(vertices[i - 1, :], 0).repeat(subdivisions, 0) + \
            frac[:-1, :] * \
            np.expand_dims(vertices[i, :], 0).repeat(subdivisions, 0)
    return subvertices


def cut_dateline(vertices):
    """Cut a polygon across the dateline, possibly splitting it into multiple
    polygons. Vertices consist of (longitude, latitude) pairs where longitude
    is always given in terms of a reference angle (between -π and π).

    This routine is not meant to cover all possible cases; it will only work
    for convex polygons that extend over less than a hemisphere.
    """
    vertices = vertices.copy()
    vertices[:, 0] += np.pi
    vertices = cut_prime_meridian(vertices)
    for v in vertices:
        v[:, 0] -= np.pi
    return vertices


def cut_prime_meridian(vertices):
    """Cut a polygon across the prime meridian, possibly splitting it into
    multiple polygons. Vertices consist of (longitude, latitude) pairs where
    longitude is always given in terms of a wrapped angle (between 0 and 2π).

    This routine is not meant to cover all possible cases; it will only work
    for convex polygons that extend over less than a hemisphere.
    """
    from shapely import geometry

    # Ensure that the list of vertices does not contain a repeated endpoint.
    if (vertices[0] == vertices[-1]).all():
        vertices = vertices[:-1]

    # Ensure that the longitudes are wrapped from 0 to 2π.
    vertices = np.column_stack((wrapped_angle(vertices[:, 0]), vertices[:, 1]))

    # Test if the segment consisting of points i-1 and i croses the meridian.
    #
    # If the two longitudes are in [0, 2π), then the shortest arc connecting
    # them crosses the meridian if the difference of the angles is greater
    # than π.
    phis = vertices[:, 0]
    phi0, phi1 = np.sort(np.row_stack((np.roll(phis, 1), phis)), axis=0)
    crosses_meridian = (phi1 - phi0 > np.pi)

    # Count the number of times that the polygon crosses the meridian.
    meridian_crossings = np.sum(crosses_meridian)

    if meridian_crossings == 0:
        # There were zero meridian crossings, so we can use the
        # original vertices as is.
        out_vertices = [vertices]
    elif meridian_crossings == 1:
        # There was one meridian crossing, so the polygon encloses the pole.
        # Any meridian-crossing edge has to be extended
        # into a curve following the nearest polar edge of the map.
        i, = np.flatnonzero(crosses_meridian)
        v0 = vertices[i - 1]
        v1 = vertices[i]

        # Find the latitude at which the meridian crossing occurs by
        # linear interpolation.
        delta_lon = abs(reference_angle(v1[0] - v0[0]))
        lat = (abs(reference_angle(v0[0])) / delta_lon * v0[1] +
               abs(reference_angle(v1[0])) / delta_lon * v1[1])

        # FIXME: Use this simple heuristic to decide which pole to enclose.
        sign_lat = np.sign(np.sum(vertices[:, 1]))

        # Find the closer of the left or the right map boundary for
        # each vertex in the line segment.
        lon_0 = 0. if v0[0] < np.pi else 2 * np.pi
        lon_1 = 0. if v1[0] < np.pi else 2 * np.pi

        # Set the output vertices to the polar cap plus the original
        # vertices.
        out_vertices = [
            np.vstack((
                vertices[:i],
                [[lon_0, lat],
                 [lon_0, sign_lat * np.pi / 2],
                 [lon_1, sign_lat * np.pi / 2],
                 [lon_1, lat]],
                vertices[i:]))]
    elif meridian_crossings == 2:
        # Since the polygon is assumed to be convex, if there is an even number
        # of meridian crossings, we know that the polygon does not enclose
        # either pole. Then we can use ordinary Euclidean polygon intersection
        # algorithms.

        out_vertices = []

        # Construct polygon representing map boundaries.
        frame_poly = geometry.Polygon(np.asarray([
            [0., 0.5 * np.pi],
            [0., -0.5 * np.pi],
            [2 * np.pi, -0.5 * np.pi],
            [2 * np.pi, 0.5 * np.pi]]))

        # Intersect with polygon re-wrapped to lie in [-π, π) or [π, 3π).
        for shift in [0, 2 * np.pi]:
            poly = geometry.Polygon(np.column_stack((
                reference_angle(vertices[:, 0]) + shift, vertices[:, 1])))
            intersection = poly.intersection(frame_poly)
            if intersection:
                assert isinstance(intersection, geometry.Polygon)
                assert intersection.is_simple
                out_vertices += [np.asarray(intersection.exterior)]
    else:
        # There were more than two intersections. Not implemented!
        raise NotImplementedError('The polygon intersected the map boundaries '
                                  'two or more times, so it is probably not '
                                  'simple and convex.')

    # Done!
    return out_vertices


def make_rect_poly(width, height, theta, phi, subdivisions=10):
    """Create a Polygon patch representing a rectangle with half-angles width
    and height rotated from the north pole to (theta, phi).
    """
    # Convert width and height to radians, then to Cartesian coordinates.
    w = np.sin(np.deg2rad(width))
    h = np.sin(np.deg2rad(height))

    # Generate vertices of rectangle.
    v = np.asarray([[-w, -h], [w, -h], [w, h], [-w, h]])

    # Subdivide.
    v = subdivide_vertices(v, subdivisions)

    # Project onto sphere by calculating z-coord from normalization condition.
    v = np.hstack((v, np.sqrt(1. - np.expand_dims(np.square(v).sum(1), 1))))

    # Transform vertices.
    v = np.dot(v, hp.rotator.euler_matrix_new(phi, theta, 0, Y=True))

    # Convert to spherical polar coordinates.
    thetas, phis = hp.vec2ang(v)

    # Return list of vertices as longitude, latitude pairs.
    return np.column_stack((wrapped_angle(phis), 0.5 * np.pi - thetas))