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

import pytest

import numpy as np
from numpy.testing import assert_equal, assert_allclose

from astropy.utils.compat.optional_deps import HAS_SCIPY, HAS_MPMATH  # noqa

from astropy.stats import funcs
from astropy import units as u
from astropy.utils.misc import NumpyRNGContext


def test_median_absolute_deviation():
    with NumpyRNGContext(12345):
        # test that it runs
        randvar = np.random.randn(10000)
        mad = funcs.median_absolute_deviation(randvar)

        # test whether an array is returned if an axis is used
        randvar = randvar.reshape((10, 1000))
        mad = funcs.median_absolute_deviation(randvar, axis=1)
        assert len(mad) == 10
        assert mad.size < randvar.size
        mad = funcs.median_absolute_deviation(randvar, axis=0)
        assert len(mad) == 1000
        assert mad.size < randvar.size
        # Test some actual values in a 3 dimensional array
        x = np.arange(3 * 4 * 5)
        a = np.array([sum(x[:i + 1]) for i in range(len(x))]).reshape(3, 4, 5)
        mad = funcs.median_absolute_deviation(a)
        assert mad == 389.5
        mad = funcs.median_absolute_deviation(a, axis=0)
        assert_allclose(mad, [[210., 230., 250., 270., 290.],
                              [310., 330., 350., 370., 390.],
                              [410., 430., 450., 470., 490.],
                              [510., 530., 550., 570., 590.]])
        mad = funcs.median_absolute_deviation(a, axis=1)
        assert_allclose(mad, [[27.5, 32.5, 37.5, 42.5, 47.5],
                              [127.5, 132.5, 137.5, 142.5, 147.5],
                              [227.5, 232.5, 237.5, 242.5, 247.5]])
        mad = funcs.median_absolute_deviation(a, axis=2)
        assert_allclose(mad, [[3., 8., 13., 18.],
                              [23., 28., 33., 38.],
                              [43., 48., 53., 58.]])


def test_median_absolute_deviation_masked():
    # Based on the changes introduces in #4658

    # normal masked arrays without masked values are handled like normal
    # numpy arrays
    array = np.ma.array([1, 2, 3])
    assert funcs.median_absolute_deviation(array) == 1

    # masked numpy arrays return something different (rank 0 masked array)
    # but one can still compare it without np.all!
    array = np.ma.array([1, 4, 3], mask=[0, 1, 0])
    assert funcs.median_absolute_deviation(array) == 1
    # Just cross check if that's identical to the function on the unmasked
    # values only
    assert funcs.median_absolute_deviation(array) == (
        funcs.median_absolute_deviation(array[~array.mask]))

    # Multidimensional masked array
    array = np.ma.array([[1, 4], [2, 2]], mask=[[1, 0], [0, 0]])
    funcs.median_absolute_deviation(array)
    assert funcs.median_absolute_deviation(array) == 0
    # Just to compare it with the data without mask:
    assert funcs.median_absolute_deviation(array.data) == 0.5

    # And check if they are also broadcasted correctly
    np.testing.assert_array_equal(
        funcs.median_absolute_deviation(array, axis=0).data, [0, 1])
    np.testing.assert_array_equal(
        funcs.median_absolute_deviation(array, axis=1).data, [0, 0])


def test_median_absolute_deviation_nans():
    array = np.array([[1, 4, 3, np.nan],
                      [2, 5, np.nan, 4]])
    assert_equal(funcs.median_absolute_deviation(array, func=np.nanmedian,
                                                 axis=1), [1, 1])

    array = np.ma.masked_invalid(array)
    assert funcs.median_absolute_deviation(array) == 1


def test_median_absolute_deviation_nans_masked():
    """
    Regression test to ensure ignore_nan=True gives same results for
    ndarray and masked arrays that contain +/-inf.
    """

    data1 = np.array([1., np.nan, 2, np.inf])
    data2 = np.ma.masked_array(data1, mask=False)
    mad1 = funcs.median_absolute_deviation(data1, ignore_nan=True)
    mad2 = funcs.median_absolute_deviation(data2, ignore_nan=True)
    assert_equal(mad1, mad2)

    # ensure that input masked array is not modified
    assert np.isnan(data2[1])


def test_median_absolute_deviation_multidim_axis():
    array = np.ones((5, 4, 3)) * np.arange(5)[:, np.newaxis, np.newaxis]
    mad1 = funcs.median_absolute_deviation(array, axis=(1, 2))
    mad2 = funcs.median_absolute_deviation(array, axis=(2, 1))
    assert_equal(mad1, np.zeros(5))
    assert_equal(mad1, mad2)


def test_median_absolute_deviation_quantity():
    # Based on the changes introduces in #4658

    # Just a small test that this function accepts Quantities and returns a
    # quantity
    a = np.array([1, 16, 5]) * u.m
    mad = funcs.median_absolute_deviation(a)
    # Check for the correct unit and that the result is identical to the
    # result without units.
    assert mad.unit == a.unit
    assert mad.value == funcs.median_absolute_deviation(a.value)


@pytest.mark.skipif('not HAS_SCIPY')
def test_binom_conf_interval():

    # Test Wilson and Jeffreys interval for corner cases:
    # Corner cases: k = 0, k = n, confidence_level = 0., confidence_level = 1.
    n = 5
    k = [0, 4, 5]
    for conf in [0., 0.5, 1.]:
        res = funcs.binom_conf_interval(k, n, confidence_level=conf, interval='wilson')
        assert ((res >= 0.) & (res <= 1.)).all()
        res = funcs.binom_conf_interval(k, n, confidence_level=conf, interval='jeffreys')
        assert ((res >= 0.) & (res <= 1.)).all()

    # Test Jeffreys interval accuracy against table in Brown et al. (2001).
    # (See `binom_conf_interval` docstring for reference.)
    k = [0, 1, 2, 3, 4]
    n = 7
    conf = 0.95
    result = funcs.binom_conf_interval(k, n, confidence_level=conf, interval='jeffreys')
    table = np.array([[0.000, 0.016, 0.065, 0.139, 0.234],
                      [0.292, 0.501, 0.648, 0.766, 0.861]])
    assert_allclose(result, table, atol=1.e-3, rtol=0.)

    # Test scalar version
    result = np.array([funcs.binom_conf_interval(kval, n, confidence_level=conf,
                                                 interval='jeffreys')
                       for kval in k]).transpose()
    assert_allclose(result, table, atol=1.e-3, rtol=0.)

    # Test flat
    result = funcs.binom_conf_interval(k, n, confidence_level=conf, interval='flat')
    table = np.array([[0., 0.03185, 0.08523, 0.15701, 0.24486],
                      [0.36941, 0.52650, 0.65085, 0.75513, 0.84298]])
    assert_allclose(result, table, atol=1.e-3, rtol=0.)

    # Test Wald interval
    result = funcs.binom_conf_interval(0, 5, interval='wald')
    assert_allclose(result, 0.)  # conf interval is [0, 0] when k = 0
    result = funcs.binom_conf_interval(5, 5, interval='wald')
    assert_allclose(result, 1.)  # conf interval is [1, 1] when k = n
    result = funcs.binom_conf_interval(500, 1000, confidence_level=0.68269,
                                       interval='wald')
    assert_allclose(result[0], 0.5 - 0.5 / np.sqrt(1000.))
    assert_allclose(result[1], 0.5 + 0.5 / np.sqrt(1000.))

    # Test shapes
    k = 3
    n = 7
    for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
        result = funcs.binom_conf_interval(k, n, interval=interval)
        assert result.shape == (2,)

    k = np.array(k)
    for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
        result = funcs.binom_conf_interval(k, n, interval=interval)
        assert result.shape == (2,)

    n = np.array(n)
    for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
        result = funcs.binom_conf_interval(k, n, interval=interval)
        assert result.shape == (2,)

    k = np.array([1, 3, 5])
    for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
        result = funcs.binom_conf_interval(k, n, interval=interval)
        assert result.shape == (2, 3)

    n = np.array([5, 5, 5])
    for interval in ['wald', 'wilson', 'jeffreys', 'flat']:
        result = funcs.binom_conf_interval(k, n, interval=interval)
        assert result.shape == (2, 3)


@pytest.mark.skipif('not HAS_SCIPY')
def test_binned_binom_proportion():

    # Check that it works.
    nbins = 20
    x = np.linspace(0., 10., 100)  # Guarantee an `x` in every bin.
    success = np.ones(len(x), dtype=bool)
    bin_ctr, bin_hw, p, perr = funcs.binned_binom_proportion(x, success,
                                                             bins=nbins)

    # Check shape of outputs
    assert bin_ctr.shape == (nbins,)
    assert bin_hw.shape == (nbins,)
    assert p.shape == (nbins,)
    assert perr.shape == (2, nbins)

    # Check that p is 1 in all bins, since success = True for all `x`.
    assert (p == 1.).all()

    # Check that p is 0 in all bins if success = False for all `x`.
    success[:] = False
    bin_ctr, bin_hw, p, perr = funcs.binned_binom_proportion(x, success,
                                                             bins=nbins)
    assert (p == 0.).all()


def test_binned_binom_proportion_exception():
    with pytest.raises(ValueError):
        funcs.binned_binom_proportion([0], [1, 2], confidence_level=0.75)


def test_signal_to_noise_oir_ccd():

    result = funcs.signal_to_noise_oir_ccd(1, 25, 0, 0, 0, 1)
    assert 5.0 == result
    # check to make sure gain works
    result = funcs.signal_to_noise_oir_ccd(1, 5, 0, 0, 0, 1, 5)
    assert 5.0 == result

    # now add in sky, dark current, and read noise
    # make sure the snr goes down
    result = funcs.signal_to_noise_oir_ccd(1, 25, 1, 0, 0, 1)
    assert result < 5.0
    result = funcs.signal_to_noise_oir_ccd(1, 25, 0, 1, 0, 1)
    assert result < 5.0
    result = funcs.signal_to_noise_oir_ccd(1, 25, 0, 0, 1, 1)
    assert result < 5.0

    # make sure snr increases with time
    result = funcs.signal_to_noise_oir_ccd(2, 25, 0, 0, 0, 1)
    assert result > 5.0


def test_bootstrap():
    bootarr = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 0])
    # test general bootstrapping
    answer = np.array([[7, 4, 8, 5, 7, 0, 3, 7, 8, 5],
                       [4, 8, 8, 3, 6, 5, 2, 8, 6, 2]])
    with NumpyRNGContext(42):
        assert_equal(answer, funcs.bootstrap(bootarr, 2))

    # test with a bootfunction
    with NumpyRNGContext(42):
        bootresult = np.mean(funcs.bootstrap(bootarr, 10000, bootfunc=np.mean))
        assert_allclose(np.mean(bootarr), bootresult, atol=0.01)


@pytest.mark.skipif('not HAS_SCIPY')
def test_bootstrap_multiple_outputs():

    from scipy.stats import spearmanr

    # test a bootfunc with several output values
    # return just bootstrapping with one output from bootfunc
    with NumpyRNGContext(42):
        bootarr = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 0],
                            [4, 8, 8, 3, 6, 5, 2, 8, 6, 2]]).T

        answer = np.array((0.19425, 0.02094))

        def bootfunc(x): return spearmanr(x)[0]

        bootresult = funcs.bootstrap(bootarr, 2,
                                     bootfunc=bootfunc)

        assert_allclose(answer, bootresult, atol=1e-3)

    # test a bootfunc with several output values
    # return just bootstrapping with the second output from bootfunc
    with NumpyRNGContext(42):
        bootarr = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 0],
                            [4, 8, 8, 3, 6, 5, 2, 8, 6, 2]]).T

        answer = np.array((0.5907,
                           0.9541))

        def bootfunc(x): return spearmanr(x)[1]

        bootresult = funcs.bootstrap(bootarr, 2,
                                     bootfunc=bootfunc)

        assert_allclose(answer, bootresult, atol=1e-3)

    # return just bootstrapping with two outputs from bootfunc
    with NumpyRNGContext(42):
        answer = np.array(((0.1942, 0.5907),
                           (0.0209, 0.9541),
                           (0.4286, 0.2165)))

        def bootfunc(x): return spearmanr(x)

        bootresult = funcs.bootstrap(bootarr, 3,
                                     bootfunc=bootfunc)

        assert bootresult.shape == (3, 2)
        assert_allclose(answer, bootresult, atol=1e-3)


def test_mad_std():
    with NumpyRNGContext(12345):
        data = np.random.normal(5, 2, size=(100, 100))
        assert_allclose(funcs.mad_std(data), 2.0, rtol=0.05)


def test_mad_std_scalar_return():
    with NumpyRNGContext(12345):
        data = np.random.normal(5, 2, size=(10, 10))
        # make a masked array with no masked points
        data = np.ma.masked_where(np.isnan(data), data)
        rslt = funcs.mad_std(data)
        # want a scalar result, NOT a masked array
        assert np.isscalar(rslt)

        data[5, 5] = np.nan

        rslt = funcs.mad_std(data, ignore_nan=True)
        assert np.isscalar(rslt)
        rslt = funcs.mad_std(data)
        assert np.isscalar(rslt)
        assert np.isnan(rslt)


def test_mad_std_warns():
    with NumpyRNGContext(12345):
        data = np.random.normal(5, 2, size=(10, 10))
        data[5, 5] = np.nan
        rslt = funcs.mad_std(data, ignore_nan=False)
        assert np.isnan(rslt)


@pytest.mark.filterwarnings('ignore:Invalid value encountered in median')
def test_mad_std_withnan():
    with NumpyRNGContext(12345):
        data = np.empty([102, 102])
        data[:] = np.nan
        data[1:-1, 1:-1] = np.random.normal(5, 2, size=(100, 100))
        assert_allclose(funcs.mad_std(data, ignore_nan=True), 2.0, rtol=0.05)

    assert np.isnan(funcs.mad_std([1, 2, 3, 4, 5, np.nan]))
    assert_allclose(funcs.mad_std([1, 2, 3, 4, 5, np.nan], ignore_nan=True),
                    1.482602218505602)


def test_mad_std_with_axis():
    data = np.array([[1, 2, 3, 4],
                     [4, 3, 2, 1]])
    # results follow data symmetry
    result_axis0 = np.array([2.22390333, 0.74130111, 0.74130111,
                             2.22390333])
    result_axis1 = np.array([1.48260222, 1.48260222])
    assert_allclose(funcs.mad_std(data, axis=0), result_axis0)
    assert_allclose(funcs.mad_std(data, axis=1), result_axis1)


def test_mad_std_with_axis_and_nan():
    data = np.array([[1, 2, 3, 4, np.nan],
                     [4, 3, 2, 1, np.nan]])
    # results follow data symmetry
    result_axis0 = np.array([2.22390333, 0.74130111, 0.74130111,
                             2.22390333, np.nan])
    result_axis1 = np.array([1.48260222, 1.48260222])

    with pytest.warns(RuntimeWarning,
                      match=r'All-NaN slice encountered'):
        assert_allclose(funcs.mad_std(data, axis=0, ignore_nan=True), result_axis0)
        assert_allclose(funcs.mad_std(data, axis=1, ignore_nan=True), result_axis1)


def test_mad_std_with_axis_and_nan_array_type():
    # mad_std should return a masked array if given one, and not otherwise
    data = np.array([[1, 2, 3, 4, np.nan],
                     [4, 3, 2, 1, np.nan]])

    with pytest.warns(RuntimeWarning,
                      match=r'All-NaN slice encountered'):
        result = funcs.mad_std(data, axis=0, ignore_nan=True)
    assert not np.ma.isMaskedArray(result)

    data = np.ma.masked_where(np.isnan(data), data)
    result = funcs.mad_std(data, axis=0, ignore_nan=True)
    assert np.ma.isMaskedArray(result)


def test_gaussian_fwhm_to_sigma():
    fwhm = (2.0 * np.sqrt(2.0 * np.log(2.0)))
    assert_allclose(funcs.gaussian_fwhm_to_sigma * fwhm, 1.0, rtol=1.0e-6)


def test_gaussian_sigma_to_fwhm():
    sigma = 1.0 / (2.0 * np.sqrt(2.0 * np.log(2.0)))
    assert_allclose(funcs.gaussian_sigma_to_fwhm * sigma, 1.0, rtol=1.0e-6)


def test_gaussian_sigma_to_fwhm_to_sigma():
    assert_allclose(funcs.gaussian_fwhm_to_sigma *
                    funcs.gaussian_sigma_to_fwhm, 1.0)


def test_poisson_conf_interval_rootn():
    assert_allclose(funcs.poisson_conf_interval(16, interval='root-n'),
                    (12, 20))


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize('interval', ['root-n-0',
                                      'pearson',
                                      'sherpagehrels',
                                      'frequentist-confidence'])
def test_poisson_conf_large(interval):
    n = 100
    assert_allclose(funcs.poisson_conf_interval(n, interval='root-n'),
                    funcs.poisson_conf_interval(n, interval=interval),
                    rtol=2e-2)


def test_poisson_conf_array_rootn0_zero():
    n = np.zeros((3, 4, 5))
    assert_allclose(funcs.poisson_conf_interval(n, interval='root-n-0'),
                    funcs.poisson_conf_interval(n[0, 0, 0], interval='root-n-0')[:, None, None, None] * np.ones_like(n))  # noqa: E501

    assert not np.any(np.isnan(
        funcs.poisson_conf_interval(n, interval='root-n-0')))


@pytest.mark.skipif('not HAS_SCIPY')
def test_poisson_conf_array_frequentist_confidence_zero():
    n = np.zeros((3, 4, 5))
    assert_allclose(
        funcs.poisson_conf_interval(n, interval='frequentist-confidence'),
        funcs.poisson_conf_interval(n[0, 0, 0], interval='frequentist-confidence')[:, None, None, None] * np.ones_like(n))  # noqa: E501

    assert not np.any(np.isnan(
        funcs.poisson_conf_interval(n, interval='root-n-0')))


def test_poisson_conf_list_rootn0_zero():
    n = [0, 0, 0]
    assert_allclose(funcs.poisson_conf_interval(n, interval='root-n-0'),
                    [[0, 0, 0], [1, 1, 1]])

    assert not np.any(np.isnan(
        funcs.poisson_conf_interval(n, interval='root-n-0')))


def test_poisson_conf_array_rootn0():
    n = 7 * np.ones((3, 4, 5))
    assert_allclose(funcs.poisson_conf_interval(n, interval='root-n-0'),
                    funcs.poisson_conf_interval(n[0, 0, 0], interval='root-n-0')[:, None, None, None] * np.ones_like(n))  # noqa: E501

    n[1, 2, 3] = 0
    assert not np.any(np.isnan(
        funcs.poisson_conf_interval(n, interval='root-n-0')))


@pytest.mark.skipif('not HAS_SCIPY')
def test_poisson_conf_array_fc():
    n = 7 * np.ones((3, 4, 5))
    assert_allclose(
        funcs.poisson_conf_interval(n, interval='frequentist-confidence'),
        funcs.poisson_conf_interval(n[0, 0, 0], interval='frequentist-confidence')[:, None, None, None] * np.ones_like(n))  # noqa: E501

    n[1, 2, 3] = 0
    assert not np.any(np.isnan(
        funcs.poisson_conf_interval(n, interval='frequentist-confidence')))


@pytest.mark.skipif('not HAS_SCIPY')
def test_poisson_conf_frequentist_confidence_gehrels():
    """Test intervals against those published in Gehrels 1986"""
    nlh = np.array([(0, 0, 1.841),
                    (1, 0.173, 3.300),
                    (2, 0.708, 4.638),
                    (3, 1.367, 5.918),
                    (4, 2.086, 7.163),
                    (5, 2.840, 8.382),
                    (6, 3.620, 9.584),
                    (7, 4.419, 10.77),
                    (8, 5.232, 11.95),
                    (9, 6.057, 13.11),
                    (10, 6.891, 14.27),
                    ])
    assert_allclose(
        funcs.poisson_conf_interval(nlh[:, 0],
                                    interval='frequentist-confidence'),
        nlh[:, 1:].T, rtol=0.001, atol=0.001)


@pytest.mark.skipif('not HAS_SCIPY')
def test_poisson_conf_frequentist_confidence_gehrels_2sigma():
    """Test intervals against those published in Gehrels 1986

    Note: I think there's a typo (transposition of digits) in Gehrels 1986,
    specifically for the two-sigma lower limit for 3 events; they claim
    0.569 but this function returns 0.59623...

    """
    nlh = np.array([(0, 2, 0, 3.783),
                    (1, 2, 2.30e-2, 5.683),
                    (2, 2, 0.230, 7.348),
                    (3, 2, 0.596, 8.902),
                    (4, 2, 1.058, 10.39),
                    (5, 2, 1.583, 11.82),
                    (6, 2, 2.153, 13.22),
                    (7, 2, 2.758, 14.59),
                    (8, 2, 3.391, 15.94),
                    (9, 2, 4.046, 17.27),
                    (10, 2, 4.719, 18.58)])
    assert_allclose(
        funcs.poisson_conf_interval(nlh[:, 0], sigma=2,
                                    interval='frequentist-confidence').T,
        nlh[:, 2:], rtol=0.01)


@pytest.mark.skipif('not HAS_SCIPY')
def test_poisson_conf_frequentist_confidence_gehrels_3sigma():
    """Test intervals against those published in Gehrels 1986"""
    nlh = np.array([(0, 3, 0, 6.608),
                    (1, 3, 1.35e-3, 8.900),
                    (2, 3, 5.29e-2, 10.87),
                    (3, 3, 0.212, 12.68),
                    (4, 3, 0.465, 14.39),
                    (5, 3, 0.792, 16.03),
                    (6, 3, 1.175, 17.62),
                    (7, 3, 1.603, 19.17),
                    (8, 3, 2.068, 20.69),
                    (9, 3, 2.563, 22.18),
                    (10, 3, 3.084, 23.64),
                    ])
    assert_allclose(
        funcs.poisson_conf_interval(nlh[:, 0], sigma=3,
                                    interval='frequentist-confidence').T,
        nlh[:, 2:], rtol=0.01, verbose=True)


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize('n', [0, 1, 2, 3, 10, 20, 100])
def test_poisson_conf_gehrels86(n):
    assert_allclose(
        funcs.poisson_conf_interval(n, interval='sherpagehrels')[1],
        funcs.poisson_conf_interval(n, interval='frequentist-confidence')[1],
        rtol=0.02)


@pytest.mark.skipif('not HAS_SCIPY')
def test_scipy_poisson_limit():
    '''Test that the lower-level routine gives the snae number.

    Test numbers are from table1 1, 3 in
    Kraft, Burrows and Nousek in
    `ApJ 374, 344 (1991) <https://ui.adsabs.harvard.edu/abs/1991ApJ...374..344K>`_
    '''
    assert_allclose(funcs._scipy_kraft_burrows_nousek(5, 2.5, .99),
                    (0, 10.67), rtol=1e-3)
    assert_allclose(funcs._scipy_kraft_burrows_nousek(np.int32(5.), 2.5, .99),
                    (0, 10.67), rtol=1e-3)
    assert_allclose(funcs._scipy_kraft_burrows_nousek(np.int64(5.), 2.5, .99),
                    (0, 10.67), rtol=1e-3)
    assert_allclose(funcs._scipy_kraft_burrows_nousek(5, np.float32(2.5), .99),
                    (0, 10.67), rtol=1e-3)
    assert_allclose(funcs._scipy_kraft_burrows_nousek(5, np.float64(2.5), .99),
                    (0, 10.67), rtol=1e-3)
    assert_allclose(funcs._scipy_kraft_burrows_nousek(5, 2.5, np.float32(.99)),
                    (0, 10.67), rtol=1e-3)
    assert_allclose(funcs._scipy_kraft_burrows_nousek(5, 2.5, np.float64(.99)),
                    (0, 10.67), rtol=1e-3)
    conf = funcs.poisson_conf_interval([5, 6], 'kraft-burrows-nousek',
                                       background=[2.5, 2.],
                                       confidence_level=[.99, .9])
    assert_allclose(conf[:, 0], (0, 10.67), rtol=1e-3)
    assert_allclose(conf[:, 1], (0.81, 8.99), rtol=5e-3)


@pytest.mark.skipif('not HAS_MPMATH')
def test_mpmath_poisson_limit():
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(1., .1, .99),
                    (0.00, 6.54), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(1., .5, .95),
                    (0.00, 4.36), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(5., 0., .99),
                    (1.17, 13.32), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(5., 2.5, .99),
                    (0, 10.67), rtol=1e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(np.int32(6), 2., .9),
                    (0.81, 8.99), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(np.int64(6), 2., .9),
                    (0.81, 8.99), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(6., np.float32(2.), .9),
                    (0.81, 8.99), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(6., np.float64(2.), .9),
                    (0.81, 8.99), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(6., 2., np.float32(.9)),
                    (0.81, 8.99), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(6., 2., np.float64(.9)),
                    (0.81, 8.99), rtol=5e-3)
    assert_allclose(funcs._mpmath_kraft_burrows_nousek(5., 2.5, .99),
                    (0, 10.67), rtol=1e-3)

    assert_allclose(funcs.poisson_conf_interval(
        n=160, background=154.543,
        confidence_level=.95, interval='kraft-burrows-nousek')[:, 0], (0, 30.30454909))
    # For this one we do not have the "true" answer from the publication,
    # but we want to make sure that it at least runs without error
    # see https://github.com/astropy/astropy/issues/9596
    _ = funcs._mpmath_kraft_burrows_nousek(1000., 900., .9)


@pytest.mark.skipif('not HAS_SCIPY')
def test_poisson_conf_value_errors():
    with pytest.raises(ValueError, match='Only sigma=1 supported'):
        funcs.poisson_conf_interval([5, 6], 'root-n', sigma=2)

    with pytest.raises(ValueError, match='background not supported'):
        funcs.poisson_conf_interval([5, 6], 'pearson', background=[2.5, 2.])

    with pytest.raises(ValueError, match='confidence_level not supported'):
        funcs.poisson_conf_interval([5, 6], 'sherpagehrels',
                                    confidence_level=[2.5, 2.])

    with pytest.raises(ValueError, match='Invalid method'):
        funcs.poisson_conf_interval(1, 'foo')


@pytest.mark.skipif('not HAS_SCIPY')
def test_poisson_conf_kbn_value_errors():
    with pytest.raises(ValueError, match='number between 0 and 1'):
        funcs.poisson_conf_interval(5, 'kraft-burrows-nousek',
                                    background=2.5,
                                    confidence_level=99)

    with pytest.raises(ValueError, match='Set confidence_level for method'):
        funcs.poisson_conf_interval(5, 'kraft-burrows-nousek',
                                    background=2.5)

    with pytest.raises(ValueError, match='Background must be'):
        funcs.poisson_conf_interval(5, 'kraft-burrows-nousek',
                                    background=-2.5,
                                    confidence_level=.99)

    with pytest.raises(TypeError, match='Number of counts must be integer'):
        funcs.poisson_conf_interval(5., 'kraft-burrows-nousek',
                                    background=2.5, confidence_level=.99)

    with pytest.raises(TypeError, match='Number of counts must be integer'):
        funcs.poisson_conf_interval([5., 6.], 'kraft-burrows-nousek',
                                    background=[2.5, 2.],
                                    confidence_level=[.99, .9])


@pytest.mark.skipif('HAS_SCIPY or HAS_MPMATH')
def test_poisson_limit_nodependencies():
    with pytest.raises(ImportError):
        funcs.poisson_conf_interval(20, interval='kraft-burrows-nousek',
                                    background=10., confidence_level=.95)


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize('N', [10, 100, 1000, 10000])
def test_uniform(N):
    with NumpyRNGContext(12345):
        assert funcs.kuiper(np.random.random(N))[1] > 0.01


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize('N,M', [(100, 100),
                                 (20, 100),
                                 (100, 20),
                                 (10, 20),
                                 (5, 5),
                                 (1000, 100)])
def test_kuiper_two_uniform(N, M):
    with NumpyRNGContext(12345):
        assert funcs.kuiper_two(np.random.random(N),
                                np.random.random(M))[1] > 0.01


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize('N,M', [(100, 100),
                                 (20, 100),
                                 (100, 20),
                                 (10, 20),
                                 (5, 5),
                                 (1000, 100)])
def test_kuiper_two_nonuniform(N, M):
    with NumpyRNGContext(12345):
        assert funcs.kuiper_two(np.random.random(N)**2,
                                np.random.random(M)**2)[1] > 0.01


@pytest.mark.skipif('not HAS_SCIPY')
def test_detect_kuiper_two_different():
    with NumpyRNGContext(12345):
        D, f = funcs.kuiper_two(np.random.random(500) * 0.5,
                                np.random.random(500))
        assert f < 0.01


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize('N,M', [(100, 100),
                                 (20, 100),
                                 (100, 20),
                                 (10, 20),
                                 (5, 5),
                                 (1000, 100)])
def test_fpp_kuiper_two(N, M):
    from scipy.stats import binom

    with NumpyRNGContext(12345):
        R = 100
        fpp = 0.05
        fps = 0
        for i in range(R):
            D, f = funcs.kuiper_two(np.random.random(N), np.random.random(M))
            if f < fpp:
                fps += 1
        assert binom(R, fpp).sf(fps - 1) > 0.005
        assert binom(R, fpp).cdf(fps - 1) > 0.005


@pytest.mark.skipif('not HAS_SCIPY')
def test_kuiper_false_positive_probability():
    fpp = funcs.kuiper_false_positive_probability(0.5353333333333409, 1500.)
    assert fpp == 0


@pytest.mark.skipif('not HAS_SCIPY')
def test_histogram():
    from scipy.stats import chi2

    with NumpyRNGContext(1234):
        a, b = 0.3, 3.14
        s = np.random.uniform(a, b, 10000) % 1

        b, w = funcs.fold_intervals([(a, b, 1. / (b - a))])

        h = funcs.histogram_intervals(16, b, w)
        nn, bb = np.histogram(s, bins=len(h), range=(0, 1))

        uu = np.sqrt(nn)
        nn, uu = len(h) * nn / h / len(s), len(h) * uu / h / len(s)

        c2 = np.sum(((nn - 1) / uu)**2)

        assert chi2(len(h)).cdf(c2) > 0.01
        assert chi2(len(h)).sf(c2) > 0.01


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize("ii,rr", [
    ((4, (0, 1), (1,)), (1, 1, 1, 1)),
    ((2, (0, 1), (1,)), (1, 1)),
    ((4, (0, 0.5, 1), (1, 1)), (1, 1, 1, 1)),
    ((4, (0, 0.5, 1), (1, 2)), (1, 1, 2, 2)),
    ((3, (0, 0.5, 1), (1, 2)), (1, 1.5, 2)),
])
def test_histogram_intervals_known(ii, rr):
    with NumpyRNGContext(1234):
        assert_allclose(funcs.histogram_intervals(*ii), rr)


@pytest.mark.skipif('not HAS_SCIPY')
@pytest.mark.parametrize('N,m,p', [pytest.param(100, 10000, 0.01,
                                                marks=pytest.mark.skip('Test too slow')),
                                   pytest.param(300, 10000, 0.001,
                                                marks=pytest.mark.skip('Test too slow')),
                                   (10, 10000, 0.001),
                                   (3, 10000, 0.001),
                                   ])
def test_uniform_binomial(N, m, p):
    """Check that the false positive probability is right

    In particular, run m trials with N uniformly-distributed photons
    and check that the number of false positives is consistent with
    a binomial distribution. The more trials, the tighter the bounds
    but the longer the runtime.

    """
    from scipy.stats import binom

    with NumpyRNGContext(1234):
        fpps = np.array([funcs.kuiper(np.random.random(N))[1]
                         for i in range(m)])
        assert (fpps >= 0).all()
        assert (fpps <= 1).all()
        low = binom(n=m, p=p).ppf(0.01)
        high = binom(n=m, p=p).ppf(0.99)
        assert (low < sum(fpps < p) < high)