import decimal
import math
import operator
import sys
import warnings
from fractions import Fraction
from functools import partial

import hypothesis
import hypothesis.strategies as st
import pytest
from hypothesis.extra.numpy import arrays

import numpy as np
import numpy.lib._function_base_impl as nfb
from numpy import (
    angle,
    average,
    bartlett,
    blackman,
    corrcoef,
    cov,
    delete,
    diff,
    digitize,
    extract,
    flipud,
    gradient,
    hamming,
    hanning,
    i0,
    insert,
    interp,
    kaiser,
    ma,
    meshgrid,
    piecewise,
    place,
    rot90,
    select,
    setxor1d,
    sinc,
    trapezoid,
    trim_zeros,
    unique,
    unwrap,
    vectorize,
)
from numpy._core.numeric import normalize_axis_tuple
from numpy.exceptions import AxisError
from numpy.random import rand
from numpy.testing import (
    HAS_REFCOUNT,
    IS_WASM,
    NOGIL_BUILD,
    assert_,
    assert_allclose,
    assert_almost_equal,
    assert_array_almost_equal,
    assert_array_equal,
    assert_equal,
    assert_raises,
    assert_raises_regex,
)

np_floats = [np.half, np.single, np.double, np.longdouble]

def get_mat(n):
    data = np.arange(n)
    data = np.add.outer(data, data)
    return data


def _make_complex(real, imag):
    """
    Like real + 1j * imag, but behaves as expected when imag contains non-finite
    values
    """
    ret = np.zeros(np.broadcast(real, imag).shape, np.complex128)
    ret.real = real
    ret.imag = imag
    return ret


class TestRot90:
    def test_basic(self):
        assert_raises(ValueError, rot90, np.ones(4))
        assert_raises(ValueError, rot90, np.ones((2, 2, 2)), axes=(0, 1, 2))
        assert_raises(ValueError, rot90, np.ones((2, 2)), axes=(0, 2))
        assert_raises(ValueError, rot90, np.ones((2, 2)), axes=(1, 1))
        assert_raises(ValueError, rot90, np.ones((2, 2, 2)), axes=(-2, 1))

        a = [[0, 1, 2],
             [3, 4, 5]]
        b1 = [[2, 5],
              [1, 4],
              [0, 3]]
        b2 = [[5, 4, 3],
              [2, 1, 0]]
        b3 = [[3, 0],
              [4, 1],
              [5, 2]]
        b4 = [[0, 1, 2],
              [3, 4, 5]]

        for k in range(-3, 13, 4):
            assert_equal(rot90(a, k=k), b1)
        for k in range(-2, 13, 4):
            assert_equal(rot90(a, k=k), b2)
        for k in range(-1, 13, 4):
            assert_equal(rot90(a, k=k), b3)
        for k in range(0, 13, 4):
            assert_equal(rot90(a, k=k), b4)

        assert_equal(rot90(rot90(a, axes=(0, 1)), axes=(1, 0)), a)
        assert_equal(rot90(a, k=1, axes=(1, 0)), rot90(a, k=-1, axes=(0, 1)))

    def test_axes(self):
        a = np.ones((50, 40, 3))
        assert_equal(rot90(a).shape, (40, 50, 3))
        assert_equal(rot90(a, axes=(0, 2)), rot90(a, axes=(0, -1)))
        assert_equal(rot90(a, axes=(1, 2)), rot90(a, axes=(-2, -1)))

    def test_rotation_axes(self):
        a = np.arange(8).reshape((2, 2, 2))

        a_rot90_01 = [[[2, 3],
                       [6, 7]],
                      [[0, 1],
                       [4, 5]]]
        a_rot90_12 = [[[1, 3],
                       [0, 2]],
                      [[5, 7],
                       [4, 6]]]
        a_rot90_20 = [[[4, 0],
                       [6, 2]],
                      [[5, 1],
                       [7, 3]]]
        a_rot90_10 = [[[4, 5],
                       [0, 1]],
                      [[6, 7],
                       [2, 3]]]

        assert_equal(rot90(a, axes=(0, 1)), a_rot90_01)
        assert_equal(rot90(a, axes=(1, 0)), a_rot90_10)
        assert_equal(rot90(a, axes=(1, 2)), a_rot90_12)

        for k in range(1, 5):
            assert_equal(rot90(a, k=k, axes=(2, 0)),
                         rot90(a_rot90_20, k=k - 1, axes=(2, 0)))

    @pytest.mark.parametrize('k', [2.0, 2.25])
    def test_noninteger_k_deprecation_warning(self, k):
        a = np.array([[1, 2], [3, 4]])
        with pytest.warns(DeprecationWarning,
                          match="not an integer type has been deprecated"):
            b = rot90(a, k=k)
        assert_array_equal(b, np.rot90(a, k=2), strict=True)


class TestFlip:

    def test_axes(self):
        assert_raises(AxisError, np.flip, np.ones(4), axis=1)
        assert_raises(AxisError, np.flip, np.ones((4, 4)), axis=2)
        assert_raises(AxisError, np.flip, np.ones((4, 4)), axis=-3)
        assert_raises(AxisError, np.flip, np.ones((4, 4)), axis=(0, 3))

    def test_basic_lr(self):
        a = get_mat(4)
        b = a[:, ::-1]
        assert_equal(np.flip(a, 1), b)
        a = [[0, 1, 2],
             [3, 4, 5]]
        b = [[2, 1, 0],
             [5, 4, 3]]
        assert_equal(np.flip(a, 1), b)

    def test_basic_ud(self):
        a = get_mat(4)
        b = a[::-1, :]
        assert_equal(np.flip(a, 0), b)
        a = [[0, 1, 2],
             [3, 4, 5]]
        b = [[3, 4, 5],
             [0, 1, 2]]
        assert_equal(np.flip(a, 0), b)

    def test_3d_swap_axis0(self):
        a = np.array([[[0, 1],
                       [2, 3]],
                      [[4, 5],
                       [6, 7]]])

        b = np.array([[[4, 5],
                       [6, 7]],
                      [[0, 1],
                       [2, 3]]])

        assert_equal(np.flip(a, 0), b)

    def test_3d_swap_axis1(self):
        a = np.array([[[0, 1],
                       [2, 3]],
                      [[4, 5],
                       [6, 7]]])

        b = np.array([[[2, 3],
                       [0, 1]],
                      [[6, 7],
                       [4, 5]]])

        assert_equal(np.flip(a, 1), b)

    def test_3d_swap_axis2(self):
        a = np.array([[[0, 1],
                       [2, 3]],
                      [[4, 5],
                       [6, 7]]])

        b = np.array([[[1, 0],
                       [3, 2]],
                      [[5, 4],
                       [7, 6]]])

        assert_equal(np.flip(a, 2), b)

    def test_4d(self):
        a = np.arange(2 * 3 * 4 * 5).reshape(2, 3, 4, 5)
        for i in range(a.ndim):
            assert_equal(np.flip(a, i),
                         np.flipud(a.swapaxes(0, i)).swapaxes(i, 0))

    def test_default_axis(self):
        a = np.array([[1, 2, 3],
                      [4, 5, 6]])
        b = np.array([[6, 5, 4],
                      [3, 2, 1]])
        assert_equal(np.flip(a), b)

    def test_multiple_axes(self):
        a = np.array([[[0, 1],
                       [2, 3]],
                      [[4, 5],
                       [6, 7]]])

        assert_equal(np.flip(a, axis=()), a)

        b = np.array([[[5, 4],
                       [7, 6]],
                      [[1, 0],
                       [3, 2]]])

        assert_equal(np.flip(a, axis=(0, 2)), b)

        c = np.array([[[3, 2],
                       [1, 0]],
                      [[7, 6],
                       [5, 4]]])

        assert_equal(np.flip(a, axis=(1, 2)), c)


class TestAny:

    def test_basic(self):
        y1 = [0, 0, 1, 0]
        y2 = [0, 0, 0, 0]
        y3 = [1, 0, 1, 0]
        assert_(np.any(y1))
        assert_(np.any(y3))
        assert_(not np.any(y2))

    def test_nd(self):
        y1 = [[0, 0, 0], [0, 1, 0], [1, 1, 0]]
        assert_(np.any(y1))
        assert_array_equal(np.any(y1, axis=0), [1, 1, 0])
        assert_array_equal(np.any(y1, axis=1), [0, 1, 1])


class TestAll:

    def test_basic(self):
        y1 = [0, 1, 1, 0]
        y2 = [0, 0, 0, 0]
        y3 = [1, 1, 1, 1]
        assert_(not np.all(y1))
        assert_(np.all(y3))
        assert_(not np.all(y2))
        assert_(np.all(~np.array(y2)))

    def test_nd(self):
        y1 = [[0, 0, 1], [0, 1, 1], [1, 1, 1]]
        assert_(not np.all(y1))
        assert_array_equal(np.all(y1, axis=0), [0, 0, 1])
        assert_array_equal(np.all(y1, axis=1), [0, 0, 1])


@pytest.mark.parametrize("dtype", ["i8", "U10", "object", "datetime64[ms]"])
def test_any_and_all_result_dtype(dtype):
    arr = np.ones(3, dtype=dtype)
    assert np.any(arr).dtype == np.bool
    assert np.all(arr).dtype == np.bool


class TestCopy:

    def test_basic(self):
        a = np.array([[1, 2], [3, 4]])
        a_copy = np.copy(a)
        assert_array_equal(a, a_copy)
        a_copy[0, 0] = 10
        assert_equal(a[0, 0], 1)
        assert_equal(a_copy[0, 0], 10)

    def test_order(self):
        # It turns out that people rely on np.copy() preserving order by
        # default; changing this broke scikit-learn:
        # github.com/scikit-learn/scikit-learn/commit/7842748
        a = np.array([[1, 2], [3, 4]])
        assert_(a.flags.c_contiguous)
        assert_(not a.flags.f_contiguous)
        a_fort = np.array([[1, 2], [3, 4]], order="F")
        assert_(not a_fort.flags.c_contiguous)
        assert_(a_fort.flags.f_contiguous)
        a_copy = np.copy(a)
        assert_(a_copy.flags.c_contiguous)
        assert_(not a_copy.flags.f_contiguous)
        a_fort_copy = np.copy(a_fort)
        assert_(not a_fort_copy.flags.c_contiguous)
        assert_(a_fort_copy.flags.f_contiguous)

    def test_subok(self):
        mx = ma.ones(5)
        assert_(not ma.isMaskedArray(np.copy(mx, subok=False)))
        assert_(ma.isMaskedArray(np.copy(mx, subok=True)))
        # Default behavior
        assert_(not ma.isMaskedArray(np.copy(mx)))


class TestAverage:

    def test_basic(self):
        y1 = np.array([1, 2, 3])
        assert_(average(y1, axis=0) == 2.)
        y2 = np.array([1., 2., 3.])
        assert_(average(y2, axis=0) == 2.)
        y3 = [0., 0., 0.]
        assert_(average(y3, axis=0) == 0.)

        y4 = np.ones((4, 4))
        y4[0, 1] = 0
        y4[1, 0] = 2
        assert_almost_equal(y4.mean(0), average(y4, 0))
        assert_almost_equal(y4.mean(1), average(y4, 1))

        y5 = rand(5, 5)
        assert_almost_equal(y5.mean(0), average(y5, 0))
        assert_almost_equal(y5.mean(1), average(y5, 1))

    @pytest.mark.parametrize(
        'x, axis, expected_avg, weights, expected_wavg, expected_wsum',
        [([1, 2, 3], None, [2.0], [3, 4, 1], [1.75], [8.0]),
         ([[1, 2, 5], [1, 6, 11]], 0, [[1.0, 4.0, 8.0]],
          [1, 3], [[1.0, 5.0, 9.5]], [[4, 4, 4]])],
    )
    def test_basic_keepdims(self, x, axis, expected_avg,
                            weights, expected_wavg, expected_wsum):
        avg = np.average(x, axis=axis, keepdims=True)
        assert avg.shape == np.shape(expected_avg)
        assert_array_equal(avg, expected_avg)

        wavg = np.average(x, axis=axis, weights=weights, keepdims=True)
        assert wavg.shape == np.shape(expected_wavg)
        assert_array_equal(wavg, expected_wavg)

        wavg, wsum = np.average(x, axis=axis, weights=weights, returned=True,
                                keepdims=True)
        assert wavg.shape == np.shape(expected_wavg)
        assert_array_equal(wavg, expected_wavg)
        assert wsum.shape == np.shape(expected_wsum)
        assert_array_equal(wsum, expected_wsum)

    def test_weights(self):
        y = np.arange(10)
        w = np.arange(10)
        actual = average(y, weights=w)
        desired = (np.arange(10) ** 2).sum() * 1. / np.arange(10).sum()
        assert_almost_equal(actual, desired)

        y1 = np.array([[1, 2, 3], [4, 5, 6]])
        w0 = [1, 2]
        actual = average(y1, weights=w0, axis=0)
        desired = np.array([3., 4., 5.])
        assert_almost_equal(actual, desired)

        w1 = [0, 0, 1]
        actual = average(y1, weights=w1, axis=1)
        desired = np.array([3., 6.])
        assert_almost_equal(actual, desired)

        # weights and input have different shapes but no axis is specified
        with pytest.raises(
                TypeError,
                match="Axis must be specified when shapes of a "
                      "and weights differ"):
            average(y1, weights=w1)

        # 2D Case
        w2 = [[0, 0, 1], [0, 0, 2]]
        desired = np.array([3., 6.])
        assert_array_equal(average(y1, weights=w2, axis=1), desired)
        assert_equal(average(y1, weights=w2), 5.)

        y3 = rand(5).astype(np.float32)
        w3 = rand(5).astype(np.float64)

        assert_(np.average(y3, weights=w3).dtype == np.result_type(y3, w3))

        # test weights with `keepdims=False` and `keepdims=True`
        x = np.array([2, 3, 4]).reshape(3, 1)
        w = np.array([4, 5, 6]).reshape(3, 1)

        actual = np.average(x, weights=w, axis=1, keepdims=False)
        desired = np.array([2., 3., 4.])
        assert_array_equal(actual, desired)

        actual = np.average(x, weights=w, axis=1, keepdims=True)
        desired = np.array([[2.], [3.], [4.]])
        assert_array_equal(actual, desired)

    def test_weight_and_input_dims_different(self):
        y = np.arange(12).reshape(2, 2, 3)
        w = np.array([0., 0., 1., .5, .5, 0., 0., .5, .5, 1., 0., 0.])\
            .reshape(2, 2, 3)

        subw0 = w[:, :, 0]
        actual = average(y, axis=(0, 1), weights=subw0)
        desired = np.array([7., 8., 9.])
        assert_almost_equal(actual, desired)

        subw1 = w[1, :, :]
        actual = average(y, axis=(1, 2), weights=subw1)
        desired = np.array([2.25, 8.25])
        assert_almost_equal(actual, desired)

        subw2 = w[:, 0, :]
        actual = average(y, axis=(0, 2), weights=subw2)
        desired = np.array([4.75, 7.75])
        assert_almost_equal(actual, desired)

        # here the weights have the wrong shape for the specified axes
        with pytest.raises(
                ValueError,
                match="Shape of weights must be consistent with "
                      "shape of a along specified axis"):
            average(y, axis=(0, 1, 2), weights=subw0)

        with pytest.raises(
                ValueError,
                match="Shape of weights must be consistent with "
                      "shape of a along specified axis"):
            average(y, axis=(0, 1), weights=subw1)

        # swapping the axes should be same as transposing weights
        actual = average(y, axis=(1, 0), weights=subw0)
        desired = average(y, axis=(0, 1), weights=subw0.T)
        assert_almost_equal(actual, desired)

        # if average over all axes, should have float output
        actual = average(y, axis=(0, 1, 2), weights=w)
        assert_(actual.ndim == 0)

    def test_returned(self):
        y = np.array([[1, 2, 3], [4, 5, 6]])

        # No weights
        avg, scl = average(y, returned=True)
        assert_equal(scl, 6.)

        avg, scl = average(y, 0, returned=True)
        assert_array_equal(scl, np.array([2., 2., 2.]))

        avg, scl = average(y, 1, returned=True)
        assert_array_equal(scl, np.array([3., 3.]))

        # With weights
        w0 = [1, 2]
        avg, scl = average(y, weights=w0, axis=0, returned=True)
        assert_array_equal(scl, np.array([3., 3., 3.]))

        w1 = [1, 2, 3]
        avg, scl = average(y, weights=w1, axis=1, returned=True)
        assert_array_equal(scl, np.array([6., 6.]))

        w2 = [[0, 0, 1], [1, 2, 3]]
        avg, scl = average(y, weights=w2, axis=1, returned=True)
        assert_array_equal(scl, np.array([1., 6.]))

    def test_subclasses(self):
        class subclass(np.ndarray):
            pass
        a = np.array([[1, 2], [3, 4]]).view(subclass)
        w = np.array([[1, 2], [3, 4]]).view(subclass)

        assert_equal(type(np.average(a)), subclass)
        assert_equal(type(np.average(a, weights=w)), subclass)
        # Ensure a possibly returned sum of weights is correct too.
        ra, rw = np.average(a, weights=w, returned=True)
        assert_equal(type(ra), subclass)
        assert_equal(type(rw), subclass)
        # Even if it needs to be broadcast.
        ra, rw = np.average(a, weights=w[0], axis=1, returned=True)
        assert_equal(type(ra), subclass)
        assert_equal(type(rw), subclass)

    def test_upcasting(self):
        types = [('i4', 'i4', 'f8'), ('i4', 'f4', 'f8'), ('f4', 'i4', 'f8'),
                 ('f4', 'f4', 'f4'), ('f4', 'f8', 'f8')]
        for at, wt, rt in types:
            a = np.array([[1, 2], [3, 4]], dtype=at)
            w = np.array([[1, 2], [3, 4]], dtype=wt)
            assert_equal(np.average(a, weights=w).dtype, np.dtype(rt))

    def test_object_dtype(self):
        a = np.array([decimal.Decimal(x) for x in range(10)])
        w = np.array([decimal.Decimal(1) for _ in range(10)])
        w /= w.sum()
        assert_almost_equal(a.mean(0), average(a, weights=w))

    def test_object_no_weights(self):
        a = np.array([decimal.Decimal(x) for x in range(10)])
        m = average(a)
        assert m == decimal.Decimal('4.5')

    def test_average_class_without_dtype(self):
        # see gh-21988
        a = np.array([Fraction(1, 5), Fraction(3, 5)])
        assert_equal(np.average(a), Fraction(2, 5))


class TestSelect:
    choices = [np.array([1, 2, 3]),
               np.array([4, 5, 6]),
               np.array([7, 8, 9])]
    conditions = [np.array([False, False, False]),
                  np.array([False, True, False]),
                  np.array([False, False, True])]

    def _select(self, cond, values, default=0):
        output = []
        for m in range(len(cond)):
            output += [V[m] for V, C in zip(values, cond) if C[m]] or [default]
        return output

    def test_basic(self):
        choices = self.choices
        conditions = self.conditions
        assert_array_equal(select(conditions, choices, default=15),
                           self._select(conditions, choices, default=15))

        assert_equal(len(choices), 3)
        assert_equal(len(conditions), 3)

    def test_broadcasting(self):
        conditions = [np.array(True), np.array([False, True, False])]
        choices = [1, np.arange(12).reshape(4, 3)]
        assert_array_equal(select(conditions, choices), np.ones((4, 3)))
        # default can broadcast too:
        assert_equal(select([True], [0], default=[0]).shape, (1,))

    def test_return_dtype(self):
        assert_equal(select(self.conditions, self.choices, 1j).dtype,
                     np.complex128)
        # But the conditions need to be stronger then the scalar default
        # if it is scalar.
        choices = [choice.astype(np.int8) for choice in self.choices]
        assert_equal(select(self.conditions, choices).dtype, np.int8)

        d = np.array([1, 2, 3, np.nan, 5, 7])
        m = np.isnan(d)
        assert_equal(select([m], [d]), [0, 0, 0, np.nan, 0, 0])

    def test_non_bool_deprecation(self):
        choices = self.choices
        conditions = self.conditions[:]
        conditions[0] = conditions[0].astype(np.int_)
        assert_raises(TypeError, select, conditions, choices)
        conditions[0] = conditions[0].astype(np.uint8)
        assert_raises(TypeError, select, conditions, choices)
        assert_raises(TypeError, select, conditions, choices)

    def test_many_arguments(self):
        # This used to be limited by NPY_MAXARGS == 32
        conditions = [np.array([False])] * 100
        choices = [np.array([1])] * 100
        select(conditions, choices)


class TestInsert:

    def test_basic(self):
        a = [1, 2, 3]
        assert_equal(insert(a, 0, 1), [1, 1, 2, 3])
        assert_equal(insert(a, 3, 1), [1, 2, 3, 1])
        assert_equal(insert(a, [1, 1, 1], [1, 2, 3]), [1, 1, 2, 3, 2, 3])
        assert_equal(insert(a, 1, [1, 2, 3]), [1, 1, 2, 3, 2, 3])
        assert_equal(insert(a, [1, -1, 3], 9), [1, 9, 2, 9, 3, 9])
        assert_equal(insert(a, slice(-1, None, -1), 9), [9, 1, 9, 2, 9, 3])
        assert_equal(insert(a, [-1, 1, 3], [7, 8, 9]), [1, 8, 2, 7, 3, 9])
        b = np.array([0, 1], dtype=np.float64)
        assert_equal(insert(b, 0, b[0]), [0., 0., 1.])
        assert_equal(insert(b, [], []), b)
        assert_equal(insert(a, np.array([True] * 4), 9), [9, 1, 9, 2, 9, 3, 9])
        assert_equal(insert(a, np.array([True, False, True, False]), 9),
                     [9, 1, 2, 9, 3])

    def test_multidim(self):
        a = [[1, 1, 1]]
        r = [[2, 2, 2],
             [1, 1, 1]]
        assert_equal(insert(a, 0, [1]), [1, 1, 1, 1])
        assert_equal(insert(a, 0, [2, 2, 2], axis=0), r)
        assert_equal(insert(a, 0, 2, axis=0), r)
        assert_equal(insert(a, 2, 2, axis=1), [[1, 1, 2, 1]])

        a = np.array([[1, 1], [2, 2], [3, 3]])
        b = np.arange(1, 4).repeat(3).reshape(3, 3)
        c = np.concatenate(
            (a[:, 0:1], np.arange(1, 4).repeat(3).reshape(3, 3).T,
             a[:, 1:2]), axis=1)
        assert_equal(insert(a, [1], [[1], [2], [3]], axis=1), b)
        assert_equal(insert(a, [1], [1, 2, 3], axis=1), c)
        # scalars behave differently, in this case exactly opposite:
        assert_equal(insert(a, 1, [1, 2, 3], axis=1), b)
        assert_equal(insert(a, 1, [[1], [2], [3]], axis=1), c)

        a = np.arange(4).reshape(2, 2)
        assert_equal(insert(a[:, :1], 1, a[:, 1], axis=1), a)
        assert_equal(insert(a[:1, :], 1, a[1, :], axis=0), a)

        # negative axis value
        a = np.arange(24).reshape((2, 3, 4))
        assert_equal(insert(a, 1, a[:, :, 3], axis=-1),
                     insert(a, 1, a[:, :, 3], axis=2))
        assert_equal(insert(a, 1, a[:, 2, :], axis=-2),
                     insert(a, 1, a[:, 2, :], axis=1))

        # invalid axis value
        assert_raises(AxisError, insert, a, 1, a[:, 2, :], axis=3)
        assert_raises(AxisError, insert, a, 1, a[:, 2, :], axis=-4)

        # negative axis value
        a = np.arange(24).reshape((2, 3, 4))
        assert_equal(insert(a, 1, a[:, :, 3], axis=-1),
                     insert(a, 1, a[:, :, 3], axis=2))
        assert_equal(insert(a, 1, a[:, 2, :], axis=-2),
                     insert(a, 1, a[:, 2, :], axis=1))

    def test_0d(self):
        a = np.array(1)
        with pytest.raises(AxisError):
            insert(a, [], 2, axis=0)
        with pytest.raises(TypeError):
            insert(a, [], 2, axis="nonsense")

    def test_subclass(self):
        class SubClass(np.ndarray):
            pass
        a = np.arange(10).view(SubClass)
        assert_(isinstance(np.insert(a, 0, [0]), SubClass))
        assert_(isinstance(np.insert(a, [], []), SubClass))
        assert_(isinstance(np.insert(a, [0, 1], [1, 2]), SubClass))
        assert_(isinstance(np.insert(a, slice(1, 2), [1, 2]), SubClass))
        assert_(isinstance(np.insert(a, slice(1, -2, -1), []), SubClass))
        # This is an error in the future:
        a = np.array(1).view(SubClass)
        assert_(isinstance(np.insert(a, 0, [0]), SubClass))

    def test_index_array_copied(self):
        x = np.array([1, 1, 1])
        np.insert([0, 1, 2], x, [3, 4, 5])
        assert_equal(x, np.array([1, 1, 1]))

    def test_structured_array(self):
        a = np.array([(1, 'a'), (2, 'b'), (3, 'c')],
                     dtype=[('foo', 'i'), ('bar', 'S1')])
        val = (4, 'd')
        b = np.insert(a, 0, val)
        assert_array_equal(b[0], np.array(val, dtype=b.dtype))
        val = [(4, 'd')] * 2
        b = np.insert(a, [0, 2], val)
        assert_array_equal(b[[0, 3]], np.array(val, dtype=b.dtype))

    def test_index_floats(self):
        with pytest.raises(IndexError):
            np.insert([0, 1, 2], np.array([1.0, 2.0]), [10, 20])
        with pytest.raises(IndexError):
            np.insert([0, 1, 2], np.array([], dtype=float), [])

    @pytest.mark.parametrize('idx', [4, -4])
    def test_index_out_of_bounds(self, idx):
        with pytest.raises(IndexError, match='out of bounds'):
            np.insert([0, 1, 2], [idx], [3, 4])


class TestAmax:

    def test_basic(self):
        a = [3, 4, 5, 10, -3, -5, 6.0]
        assert_equal(np.amax(a), 10.0)
        b = [[3, 6.0, 9.0],
             [4, 10.0, 5.0],
             [8, 3.0, 2.0]]
        assert_equal(np.amax(b, axis=0), [8.0, 10.0, 9.0])
        assert_equal(np.amax(b, axis=1), [9.0, 10.0, 8.0])


class TestAmin:

    def test_basic(self):
        a = [3, 4, 5, 10, -3, -5, 6.0]
        assert_equal(np.amin(a), -5.0)
        b = [[3, 6.0, 9.0],
             [4, 10.0, 5.0],
             [8, 3.0, 2.0]]
        assert_equal(np.amin(b, axis=0), [3.0, 3.0, 2.0])
        assert_equal(np.amin(b, axis=1), [3.0, 4.0, 2.0])


class TestPtp:

    def test_basic(self):
        a = np.array([3, 4, 5, 10, -3, -5, 6.0])
        assert_equal(np.ptp(a, axis=0), 15.0)
        b = np.array([[3, 6.0, 9.0],
                      [4, 10.0, 5.0],
                      [8, 3.0, 2.0]])
        assert_equal(np.ptp(b, axis=0), [5.0, 7.0, 7.0])
        assert_equal(np.ptp(b, axis=-1), [6.0, 6.0, 6.0])

        assert_equal(np.ptp(b, axis=0, keepdims=True), [[5.0, 7.0, 7.0]])
        assert_equal(np.ptp(b, axis=(0, 1), keepdims=True), [[8.0]])


class TestCumsum:

    @pytest.mark.parametrize("cumsum", [np.cumsum, np.cumulative_sum])
    def test_basic(self, cumsum):
        ba = [1, 2, 10, 11, 6, 5, 4]
        ba2 = [[1, 2, 3, 4], [5, 6, 7, 9], [10, 3, 4, 5]]
        for ctype in [np.int8, np.uint8, np.int16, np.uint16, np.int32,
                      np.uint32, np.float32, np.float64, np.complex64,
                      np.complex128]:
            a = np.array(ba, ctype)
            a2 = np.array(ba2, ctype)

            tgt = np.array([1, 3, 13, 24, 30, 35, 39], ctype)
            assert_array_equal(cumsum(a, axis=0), tgt)

            tgt = np.array(
                [[1, 2, 3, 4], [6, 8, 10, 13], [16, 11, 14, 18]], ctype)
            assert_array_equal(cumsum(a2, axis=0), tgt)

            tgt = np.array(
                [[1, 3, 6, 10], [5, 11, 18, 27], [10, 13, 17, 22]], ctype)
            assert_array_equal(cumsum(a2, axis=1), tgt)


class TestProd:

    def test_basic(self):
        ba = [1, 2, 10, 11, 6, 5, 4]
        ba2 = [[1, 2, 3, 4], [5, 6, 7, 9], [10, 3, 4, 5]]
        for ctype in [np.int16, np.uint16, np.int32, np.uint32,
                      np.float32, np.float64, np.complex64, np.complex128]:
            a = np.array(ba, ctype)
            a2 = np.array(ba2, ctype)
            if ctype in ['1', 'b']:
                assert_raises(ArithmeticError, np.prod, a)
                assert_raises(ArithmeticError, np.prod, a2, 1)
            else:
                assert_equal(a.prod(axis=0), 26400)
                assert_array_equal(a2.prod(axis=0),
                                   np.array([50, 36, 84, 180], ctype))
                assert_array_equal(a2.prod(axis=-1),
                                   np.array([24, 1890, 600], ctype))


class TestCumprod:

    @pytest.mark.parametrize("cumprod", [np.cumprod, np.cumulative_prod])
    def test_basic(self, cumprod):
        ba = [1, 2, 10, 11, 6, 5, 4]
        ba2 = [[1, 2, 3, 4], [5, 6, 7, 9], [10, 3, 4, 5]]
        for ctype in [np.int16, np.uint16, np.int32, np.uint32,
                      np.float32, np.float64, np.complex64, np.complex128]:
            a = np.array(ba, ctype)
            a2 = np.array(ba2, ctype)
            if ctype in ['1', 'b']:
                assert_raises(ArithmeticError, cumprod, a)
                assert_raises(ArithmeticError, cumprod, a2, 1)
                assert_raises(ArithmeticError, cumprod, a)
            else:
                assert_array_equal(cumprod(a, axis=-1),
                                   np.array([1, 2, 20, 220,
                                             1320, 6600, 26400], ctype))
                assert_array_equal(cumprod(a2, axis=0),
                                   np.array([[1, 2, 3, 4],
                                             [5, 12, 21, 36],
                                             [50, 36, 84, 180]], ctype))
                assert_array_equal(cumprod(a2, axis=-1),
                                   np.array([[1, 2, 6, 24],
                                             [5, 30, 210, 1890],
                                             [10, 30, 120, 600]], ctype))


def test_cumulative_include_initial():
    arr = np.arange(8).reshape((2, 2, 2))

    expected = np.array([
        [[0, 0], [0, 1], [2, 4]], [[0, 0], [4, 5], [10, 12]]
    ])
    assert_array_equal(
        np.cumulative_sum(arr, axis=1, include_initial=True), expected
    )

    expected = np.array([
        [[1, 0, 0], [1, 2, 6]], [[1, 4, 20], [1, 6, 42]]
    ])
    assert_array_equal(
        np.cumulative_prod(arr, axis=2, include_initial=True), expected
    )

    out = np.zeros((3, 2), dtype=np.float64)
    expected = np.array([[0, 0], [1, 2], [4, 6]], dtype=np.float64)
    arr = np.arange(1, 5).reshape((2, 2))
    np.cumulative_sum(arr, axis=0, out=out, include_initial=True)
    assert_array_equal(out, expected)

    expected = np.array([1, 2, 4])
    assert_array_equal(
        np.cumulative_prod(np.array([2, 2]), include_initial=True), expected
    )


class TestDiff:

    def test_basic(self):
        x = [1, 4, 6, 7, 12]
        out = np.array([3, 2, 1, 5])
        out2 = np.array([-1, -1, 4])
        out3 = np.array([0, 5])
        assert_array_equal(diff(x), out)
        assert_array_equal(diff(x, n=2), out2)
        assert_array_equal(diff(x, n=3), out3)

        x = [1.1, 2.2, 3.0, -0.2, -0.1]
        out = np.array([1.1, 0.8, -3.2, 0.1])
        assert_almost_equal(diff(x), out)

        x = [True, True, False, False]
        out = np.array([False, True, False])
        out2 = np.array([True, True])
        assert_array_equal(diff(x), out)
        assert_array_equal(diff(x, n=2), out2)

    def test_axis(self):
        x = np.zeros((10, 20, 30))
        x[:, 1::2, :] = 1
        exp = np.ones((10, 19, 30))
        exp[:, 1::2, :] = -1
        assert_array_equal(diff(x), np.zeros((10, 20, 29)))
        assert_array_equal(diff(x, axis=-1), np.zeros((10, 20, 29)))
        assert_array_equal(diff(x, axis=0), np.zeros((9, 20, 30)))
        assert_array_equal(diff(x, axis=1), exp)
        assert_array_equal(diff(x, axis=-2), exp)
        assert_raises(AxisError, diff, x, axis=3)
        assert_raises(AxisError, diff, x, axis=-4)

        x = np.array(1.11111111111, np.float64)
        assert_raises(ValueError, diff, x)

    def test_nd(self):
        x = 20 * rand(10, 20, 30)
        out1 = x[:, :, 1:] - x[:, :, :-1]
        out2 = out1[:, :, 1:] - out1[:, :, :-1]
        out3 = x[1:, :, :] - x[:-1, :, :]
        out4 = out3[1:, :, :] - out3[:-1, :, :]
        assert_array_equal(diff(x), out1)
        assert_array_equal(diff(x, n=2), out2)
        assert_array_equal(diff(x, axis=0), out3)
        assert_array_equal(diff(x, n=2, axis=0), out4)

    def test_n(self):
        x = list(range(3))
        assert_raises(ValueError, diff, x, n=-1)
        output = [diff(x, n=n) for n in range(1, 5)]
        expected = [[1, 1], [0], [], []]
        assert_(diff(x, n=0) is x)
        for n, (expected_n, output_n) in enumerate(zip(expected, output), start=1):
            assert_(type(output_n) is np.ndarray)
            assert_array_equal(output_n, expected_n)
            assert_equal(output_n.dtype, np.int_)
            assert_equal(len(output_n), max(0, len(x) - n))

    def test_times(self):
        x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64)
        expected = [
            np.array([1, 1], dtype='timedelta64[D]'),
            np.array([0], dtype='timedelta64[D]'),
        ]
        expected.extend([np.array([], dtype='timedelta64[D]')] * 3)
        for n, exp in enumerate(expected, start=1):
            out = diff(x, n=n)
            assert_array_equal(out, exp)
            assert_equal(out.dtype, exp.dtype)

    def test_subclass(self):
        x = ma.array([[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],
                     mask=[[False, False], [True, False],
                           [False, True], [True, True], [False, False]])
        out = diff(x)
        assert_array_equal(out.data, [[1], [1], [1], [1], [1]])
        assert_array_equal(out.mask, [[False], [True],
                                      [True], [True], [False]])
        assert_(type(out) is type(x))

        out3 = diff(x, n=3)
        assert_array_equal(out3.data, [[], [], [], [], []])
        assert_array_equal(out3.mask, [[], [], [], [], []])
        assert_(type(out3) is type(x))

    def test_prepend(self):
        x = np.arange(5) + 1
        assert_array_equal(diff(x, prepend=0), np.ones(5))
        assert_array_equal(diff(x, prepend=[0]), np.ones(5))
        assert_array_equal(np.cumsum(np.diff(x, prepend=0)), x)
        assert_array_equal(diff(x, prepend=[-1, 0]), np.ones(6))

        x = np.arange(4).reshape(2, 2)
        result = np.diff(x, axis=1, prepend=0)
        expected = [[0, 1], [2, 1]]
        assert_array_equal(result, expected)
        result = np.diff(x, axis=1, prepend=[[0], [0]])
        assert_array_equal(result, expected)

        result = np.diff(x, axis=0, prepend=0)
        expected = [[0, 1], [2, 2]]
        assert_array_equal(result, expected)
        result = np.diff(x, axis=0, prepend=[[0, 0]])
        assert_array_equal(result, expected)

        assert_raises(ValueError, np.diff, x, prepend=np.zeros((3, 3)))

        assert_raises(AxisError, diff, x, prepend=0, axis=3)

    def test_append(self):
        x = np.arange(5)
        result = diff(x, append=0)
        expected = [1, 1, 1, 1, -4]
        assert_array_equal(result, expected)
        result = diff(x, append=[0])
        assert_array_equal(result, expected)
        result = diff(x, append=[0, 2])
        expected = expected + [2]
        assert_array_equal(result, expected)

        x = np.arange(4).reshape(2, 2)
        result = np.diff(x, axis=1, append=0)
        expected = [[1, -1], [1, -3]]
        assert_array_equal(result, expected)
        result = np.diff(x, axis=1, append=[[0], [0]])
        assert_array_equal(result, expected)

        result = np.diff(x, axis=0, append=0)
        expected = [[2, 2], [-2, -3]]
        assert_array_equal(result, expected)
        result = np.diff(x, axis=0, append=[[0, 0]])
        assert_array_equal(result, expected)

        assert_raises(ValueError, np.diff, x, append=np.zeros((3, 3)))

        assert_raises(AxisError, diff, x, append=0, axis=3)


class TestDelete:

    def _create_arrays(self):
        a = np.arange(5)
        nd_a = np.arange(5).repeat(2).reshape(1, 5, 2)
        return a, nd_a

    def _check_inverse_of_slicing(self, indices):
        a, nd_a = self._create_arrays()
        a_del = delete(a, indices)
        nd_a_del = delete(nd_a, indices, axis=1)
        msg = f'Delete failed for obj: {indices!r}'
        assert_array_equal(setxor1d(a_del, a[indices, ]), a,
                           err_msg=msg)
        xor = setxor1d(nd_a_del[0, :, 0], nd_a[0, indices, 0])
        assert_array_equal(xor, nd_a[0, :, 0], err_msg=msg)

    def test_slices(self):
        lims = [-6, -2, 0, 1, 2, 4, 5]
        steps = [-3, -1, 1, 3]
        for start in lims:
            for stop in lims:
                for step in steps:
                    s = slice(start, stop, step)
                    self._check_inverse_of_slicing(s)

    def test_fancy(self):
        a, _ = self._create_arrays()
        self._check_inverse_of_slicing(np.array([[0, 1], [2, 1]]))
        with pytest.raises(IndexError):
            delete(a, [100])
        with pytest.raises(IndexError):
            delete(a, [-100])

        self._check_inverse_of_slicing([0, -1, 2, 2])

        self._check_inverse_of_slicing([True, False, False, True, False])

        # not legal, indexing with these would change the dimension
        with pytest.raises(ValueError):
            delete(a, True)
        with pytest.raises(ValueError):
            delete(a, False)

        # not enough items
        with pytest.raises(ValueError):
            delete(a, [False] * 4)

    def test_single(self):
        self._check_inverse_of_slicing(0)
        self._check_inverse_of_slicing(-4)

    def test_0d(self):
        a = np.array(1)
        with pytest.raises(AxisError):
            delete(a, [], axis=0)
        with pytest.raises(TypeError):
            delete(a, [], axis="nonsense")

    def test_subclass(self):
        class SubClass(np.ndarray):
            pass

        a_orig, _ = self._create_arrays()
        a = a_orig.view(SubClass)
        assert_(isinstance(delete(a, 0), SubClass))
        assert_(isinstance(delete(a, []), SubClass))
        assert_(isinstance(delete(a, [0, 1]), SubClass))
        assert_(isinstance(delete(a, slice(1, 2)), SubClass))
        assert_(isinstance(delete(a, slice(1, -2)), SubClass))

    def test_array_order_preserve(self):
        # See gh-7113
        k = np.arange(10).reshape(2, 5, order='F')
        m = delete(k, slice(60, None), axis=1)

        # 'k' is Fortran ordered, and 'm' should have the
        # same ordering as 'k' and NOT become C ordered
        assert_equal(m.flags.c_contiguous, k.flags.c_contiguous)
        assert_equal(m.flags.f_contiguous, k.flags.f_contiguous)

    def test_index_floats(self):
        with pytest.raises(IndexError):
            np.delete([0, 1, 2], np.array([1.0, 2.0]))
        with pytest.raises(IndexError):
            np.delete([0, 1, 2], np.array([], dtype=float))

    @pytest.mark.parametrize("indexer", [np.array([1]), [1]])
    def test_single_item_array(self, indexer):
        a, nd_a = self._create_arrays()
        a_del_int = delete(a, 1)
        a_del = delete(a, indexer)
        assert_equal(a_del_int, a_del)

        nd_a_del_int = delete(nd_a, 1, axis=1)
        nd_a_del = delete(nd_a, np.array([1]), axis=1)
        assert_equal(nd_a_del_int, nd_a_del)

    def test_single_item_array_non_int(self):
        # Special handling for integer arrays must not affect non-integer ones.
        # If `False` was cast to `0` it would delete the element:
        res = delete(np.ones(1), np.array([False]))
        assert_array_equal(res, np.ones(1))

        # Test the more complicated (with axis) case from gh-21840
        x = np.ones((3, 1))
        false_mask = np.array([False], dtype=bool)
        true_mask = np.array([True], dtype=bool)

        res = delete(x, false_mask, axis=-1)
        assert_array_equal(res, x)
        res = delete(x, true_mask, axis=-1)
        assert_array_equal(res, x[:, :0])

        # Object or e.g. timedeltas should *not* be allowed
        with pytest.raises(IndexError):
            delete(np.ones(2), np.array([0], dtype=object))

        with pytest.raises(IndexError):
            # timedeltas are sometimes "integral, but clearly not allowed:
            delete(np.ones(2), np.array([0], dtype="m8[ns]"))


class TestGradient:

    def test_basic(self):
        v = [[1, 1], [3, 4]]
        x = np.array(v)
        dx = [np.array([[2., 3.], [2., 3.]]),
              np.array([[0., 0.], [1., 1.]])]
        assert_array_equal(gradient(x), dx)
        assert_array_equal(gradient(v), dx)

    def test_args(self):
        dx = np.cumsum(np.ones(5))
        dx_uneven = [1., 2., 5., 9., 11.]
        f_2d = np.arange(25).reshape(5, 5)

        # distances must be scalars or have size equal to gradient[axis]
        gradient(np.arange(5), 3.)
        gradient(np.arange(5), np.array(3.))
        gradient(np.arange(5), dx)
        # dy is set equal to dx because scalar
        gradient(f_2d, 1.5)
        gradient(f_2d, np.array(1.5))

        gradient(f_2d, dx_uneven, dx_uneven)
        # mix between even and uneven spaces and
        # mix between scalar and vector
        gradient(f_2d, dx, 2)

        # 2D but axis specified
        gradient(f_2d, dx, axis=1)

        # 2d coordinate arguments are not yet allowed
        assert_raises_regex(ValueError, '.*scalars or 1d',
            gradient, f_2d, np.stack([dx] * 2, axis=-1), 1)

    def test_badargs(self):
        f_2d = np.arange(25).reshape(5, 5)
        x = np.cumsum(np.ones(5))

        # wrong sizes
        assert_raises(ValueError, gradient, f_2d, x, np.ones(2))
        assert_raises(ValueError, gradient, f_2d, 1, np.ones(2))
        assert_raises(ValueError, gradient, f_2d, np.ones(2), np.ones(2))
        # wrong number of arguments
        assert_raises(TypeError, gradient, f_2d, x)
        assert_raises(TypeError, gradient, f_2d, x, axis=(0, 1))
        assert_raises(TypeError, gradient, f_2d, x, x, x)
        assert_raises(TypeError, gradient, f_2d, 1, 1, 1)
        assert_raises(TypeError, gradient, f_2d, x, x, axis=1)
        assert_raises(TypeError, gradient, f_2d, 1, 1, axis=1)

    def test_datetime64(self):
        # Make sure gradient() can handle special types like datetime64
        x = np.array(
            ['1910-08-16', '1910-08-11', '1910-08-10', '1910-08-12',
             '1910-10-12', '1910-12-12', '1912-12-12'],
            dtype='datetime64[D]')
        dx = np.array(
            [-5, -3, 0, 31, 61, 396, 731],
            dtype='timedelta64[D]')
        assert_array_equal(gradient(x), dx)
        assert_(dx.dtype == np.dtype('timedelta64[D]'))

    def test_masked(self):
        # Make sure that gradient supports subclasses like masked arrays
        x = np.ma.array([[1, 1], [3, 4]],
                        mask=[[False, False], [False, False]])
        out = gradient(x)[0]
        assert_equal(type(out), type(x))
        # And make sure that the output and input don't have aliased mask
        # arrays
        assert_(x._mask is not out._mask)
        # Also check that edge_order=2 doesn't alter the original mask
        x2 = np.ma.arange(5)
        x2[2] = np.ma.masked
        np.gradient(x2, edge_order=2)
        assert_array_equal(x2.mask, [False, False, True, False, False])

    def test_second_order_accurate(self):
        # Testing that the relative numerical error is less that 3% for
        # this example problem. This corresponds to second order
        # accurate finite differences for all interior and boundary
        # points.
        x = np.linspace(0, 1, 10)
        dx = x[1] - x[0]
        y = 2 * x ** 3 + 4 * x ** 2 + 2 * x
        analytical = 6 * x ** 2 + 8 * x + 2
        num_error = np.abs((np.gradient(y, dx, edge_order=2) / analytical) - 1)
        assert_(np.all(num_error < 0.03) == True)

        # test with unevenly spaced
        rng = np.random.default_rng(0)
        x = np.sort(rng.random(10))
        y = 2 * x ** 3 + 4 * x ** 2 + 2 * x
        analytical = 6 * x ** 2 + 8 * x + 2
        num_error = np.abs((np.gradient(y, x, edge_order=2) / analytical) - 1)
        assert_(np.all(num_error < 0.03) == True)

    def test_spacing(self):
        f = np.array([0, 2., 3., 4., 5., 5.])
        f = np.tile(f, (6, 1)) + f.reshape(-1, 1)
        x_uneven = np.array([0., 0.5, 1., 3., 5., 7.])
        x_even = np.arange(6.)

        fdx_even_ord1 = np.tile([2., 1.5, 1., 1., 0.5, 0.], (6, 1))
        fdx_even_ord2 = np.tile([2.5, 1.5, 1., 1., 0.5, -0.5], (6, 1))
        fdx_uneven_ord1 = np.tile([4., 3., 1.7, 0.5, 0.25, 0.], (6, 1))
        fdx_uneven_ord2 = np.tile([5., 3., 1.7, 0.5, 0.25, -0.25], (6, 1))

        # evenly spaced
        for edge_order, exp_res in [(1, fdx_even_ord1), (2, fdx_even_ord2)]:
            res1 = gradient(f, 1., axis=(0, 1), edge_order=edge_order)
            res2 = gradient(f, x_even, x_even,
                            axis=(0, 1), edge_order=edge_order)
            res3 = gradient(f, x_even, x_even,
                            axis=None, edge_order=edge_order)
            assert_array_equal(res1, res2)
            assert_array_equal(res2, res3)
            assert_almost_equal(res1[0], exp_res.T)
            assert_almost_equal(res1[1], exp_res)

            res1 = gradient(f, 1., axis=0, edge_order=edge_order)
            res2 = gradient(f, x_even, axis=0, edge_order=edge_order)
            assert_(res1.shape == res2.shape)
            assert_almost_equal(res2, exp_res.T)

            res1 = gradient(f, 1., axis=1, edge_order=edge_order)
            res2 = gradient(f, x_even, axis=1, edge_order=edge_order)
            assert_(res1.shape == res2.shape)
            assert_array_equal(res2, exp_res)

        # unevenly spaced
        for edge_order, exp_res in [(1, fdx_uneven_ord1), (2, fdx_uneven_ord2)]:
            res1 = gradient(f, x_uneven, x_uneven,
                            axis=(0, 1), edge_order=edge_order)
            res2 = gradient(f, x_uneven, x_uneven,
                            axis=None, edge_order=edge_order)
            assert_array_equal(res1, res2)
            assert_almost_equal(res1[0], exp_res.T)
            assert_almost_equal(res1[1], exp_res)

            res1 = gradient(f, x_uneven, axis=0, edge_order=edge_order)
            assert_almost_equal(res1, exp_res.T)

            res1 = gradient(f, x_uneven, axis=1, edge_order=edge_order)
            assert_almost_equal(res1, exp_res)

        # mixed
        res1 = gradient(f, x_even, x_uneven, axis=(0, 1), edge_order=1)
        res2 = gradient(f, x_uneven, x_even, axis=(1, 0), edge_order=1)
        assert_array_equal(res1[0], res2[1])
        assert_array_equal(res1[1], res2[0])
        assert_almost_equal(res1[0], fdx_even_ord1.T)
        assert_almost_equal(res1[1], fdx_uneven_ord1)

        res1 = gradient(f, x_even, x_uneven, axis=(0, 1), edge_order=2)
        res2 = gradient(f, x_uneven, x_even, axis=(1, 0), edge_order=2)
        assert_array_equal(res1[0], res2[1])
        assert_array_equal(res1[1], res2[0])
        assert_almost_equal(res1[0], fdx_even_ord2.T)
        assert_almost_equal(res1[1], fdx_uneven_ord2)

    def test_specific_axes(self):
        # Testing that gradient can work on a given axis only
        v = [[1, 1], [3, 4]]
        x = np.array(v)
        dx = [np.array([[2., 3.], [2., 3.]]),
              np.array([[0., 0.], [1., 1.]])]
        assert_array_equal(gradient(x, axis=0), dx[0])
        assert_array_equal(gradient(x, axis=1), dx[1])
        assert_array_equal(gradient(x, axis=-1), dx[1])
        assert_array_equal(gradient(x, axis=(1, 0)), [dx[1], dx[0]])

        # test axis=None which means all axes
        assert_almost_equal(gradient(x, axis=None), [dx[0], dx[1]])
        # and is the same as no axis keyword given
        assert_almost_equal(gradient(x, axis=None), gradient(x))

        # test vararg order
        assert_array_equal(gradient(x, 2, 3, axis=(1, 0)),
                           [dx[1] / 2.0, dx[0] / 3.0])
        # test maximal number of varargs
        assert_raises(TypeError, gradient, x, 1, 2, axis=1)

        assert_raises(AxisError, gradient, x, axis=3)
        assert_raises(AxisError, gradient, x, axis=-3)
        # assert_raises(TypeError, gradient, x, axis=[1,])

    def test_timedelta64(self):
        # Make sure gradient() can handle special types like timedelta64
        x = np.array(
            [-5, -3, 10, 12, 61, 321, 300],
            dtype='timedelta64[D]')
        dx = np.array(
            [2, 7, 7, 25, 154, 119, -21],
            dtype='timedelta64[D]')
        assert_array_equal(gradient(x), dx)
        assert_(dx.dtype == np.dtype('timedelta64[D]'))

    def test_inexact_dtypes(self):
        for dt in [np.float16, np.float32, np.float64]:
            # dtypes should not be promoted in a different way to what diff does
            x = np.array([1, 2, 3], dtype=dt)
            assert_equal(gradient(x).dtype, np.diff(x).dtype)

    def test_values(self):
        # needs at least 2 points for edge_order ==1
        gradient(np.arange(2), edge_order=1)
        # needs at least 3 points for edge_order ==1
        gradient(np.arange(3), edge_order=2)

        assert_raises(ValueError, gradient, np.arange(0), edge_order=1)
        assert_raises(ValueError, gradient, np.arange(0), edge_order=2)
        assert_raises(ValueError, gradient, np.arange(1), edge_order=1)
        assert_raises(ValueError, gradient, np.arange(1), edge_order=2)
        assert_raises(ValueError, gradient, np.arange(2), edge_order=2)

    @pytest.mark.parametrize('f_dtype', [np.uint8, np.uint16,
                                         np.uint32, np.uint64])
    def test_f_decreasing_unsigned_int(self, f_dtype):
        f = np.array([5, 4, 3, 2, 1], dtype=f_dtype)
        g = gradient(f)
        assert_array_equal(g, [-1] * len(f))

    @pytest.mark.parametrize('f_dtype', [np.int8, np.int16,
                                         np.int32, np.int64])
    def test_f_signed_int_big_jump(self, f_dtype):
        maxint = np.iinfo(f_dtype).max
        x = np.array([1, 3])
        f = np.array([-1, maxint], dtype=f_dtype)
        dfdx = gradient(f, x)
        assert_array_equal(dfdx, [(maxint + 1) // 2] * 2)

    @pytest.mark.parametrize('x_dtype', [np.uint8, np.uint16,
                                         np.uint32, np.uint64])
    def test_x_decreasing_unsigned(self, x_dtype):
        x = np.array([3, 2, 1], dtype=x_dtype)
        f = np.array([0, 2, 4])
        dfdx = gradient(f, x)
        assert_array_equal(dfdx, [-2] * len(x))

    @pytest.mark.parametrize('x_dtype', [np.int8, np.int16,
                                         np.int32, np.int64])
    def test_x_signed_int_big_jump(self, x_dtype):
        minint = np.iinfo(x_dtype).min
        maxint = np.iinfo(x_dtype).max
        x = np.array([-1, maxint], dtype=x_dtype)
        f = np.array([minint // 2, 0])
        dfdx = gradient(f, x)
        assert_array_equal(dfdx, [0.5, 0.5])

    def test_return_type(self):
        res = np.gradient(([1, 2], [2, 3]))
        assert type(res) is tuple


class TestAngle:

    def test_basic(self):
        x = [1 + 3j, np.sqrt(2) / 2.0 + 1j * np.sqrt(2) / 2,
             1, 1j, -1, -1j, 1 - 3j, -1 + 3j]
        y = angle(x)
        yo = [
            np.arctan(3.0 / 1.0),
            np.arctan(1.0), 0, np.pi / 2, np.pi, -np.pi / 2.0,
            -np.arctan(3.0 / 1.0), np.pi - np.arctan(3.0 / 1.0)]
        z = angle(x, deg=True)
        zo = np.array(yo) * 180 / np.pi
        assert_array_almost_equal(y, yo, 11)
        assert_array_almost_equal(z, zo, 11)

    def test_subclass(self):
        x = np.ma.array([1 + 3j, 1, np.sqrt(2) / 2 * (1 + 1j)])
        x[1] = np.ma.masked
        expected = np.ma.array([np.arctan(3.0 / 1.0), 0, np.arctan(1.0)])
        expected[1] = np.ma.masked
        actual = angle(x)
        assert_equal(type(actual), type(expected))
        assert_equal(actual.mask, expected.mask)
        assert_equal(actual, expected)


class TestTrimZeros:

    a = np.array([0, 0, 1, 0, 2, 3, 4, 0])
    b = a.astype(float)
    c = a.astype(complex)
    d = a.astype(object)

    def construct_input_output(self, rng, shape, axis, trim):
        """Construct an input/output test pair for trim_zeros"""
        # Standardize axis to a tuple.
        if axis is None:
            axis = tuple(range(len(shape)))
        elif isinstance(axis, int):
            axis = (len(shape) + axis if axis < 0 else axis,)
        else:
            axis = tuple(len(shape) + ax if ax < 0 else ax for ax in axis)

        # Populate a random interior slice with nonzero entries.
        data = np.zeros(shape)
        i_start = rng.integers(low=0, high=np.array(shape) - 1)
        i_end = rng.integers(low=i_start + 1, high=shape)
        inner_shape = tuple(i_end - i_start)
        inner_data = 1 + rng.random(inner_shape)
        data[tuple(slice(i, j) for i, j in zip(i_start, i_end))] = inner_data

        # Construct the expected output of N-dimensional trim_zeros
        # with the given axis and trim arguments.
        if 'f' not in trim:
            i_start = np.array([None for _ in shape])
        if 'b' not in trim:
            i_end = np.array([None for _ in shape])
        idx = tuple(slice(i, j) if ax in axis else slice(None)
                    for ax, (i, j) in enumerate(zip(i_start, i_end)))
        expected = data[idx]

        return data, expected

    def values(self):
        attr_names = ('a', 'b', 'c', 'd')
        return (getattr(self, name) for name in attr_names)

    def test_basic(self):
        slc = np.s_[2:-1]
        for arr in self.values():
            res = trim_zeros(arr)
            assert_array_equal(res, arr[slc])

    def test_leading_skip(self):
        slc = np.s_[:-1]
        for arr in self.values():
            res = trim_zeros(arr, trim='b')
            assert_array_equal(res, arr[slc])

    def test_trailing_skip(self):
        slc = np.s_[2:]
        for arr in self.values():
            res = trim_zeros(arr, trim='F')
            assert_array_equal(res, arr[slc])

    def test_all_zero(self):
        for _arr in self.values():
            arr = np.zeros_like(_arr, dtype=_arr.dtype)

            res1 = trim_zeros(arr, trim='B')
            assert len(res1) == 0

            res2 = trim_zeros(arr, trim='f')
            assert len(res2) == 0

    def test_size_zero(self):
        arr = np.zeros(0)
        res = trim_zeros(arr)
        assert_array_equal(arr, res)

    @pytest.mark.parametrize(
        'arr',
        [np.array([0, 2**62, 0]),
         np.array([0, 2**63, 0]),
         np.array([0, 2**64, 0])]
    )
    def test_overflow(self, arr):
        slc = np.s_[1:2]
        res = trim_zeros(arr)
        assert_array_equal(res, arr[slc])

    def test_no_trim(self):
        arr = np.array([None, 1, None])
        res = trim_zeros(arr)
        assert_array_equal(arr, res)

    def test_list_to_list(self):
        res = trim_zeros(self.a.tolist())
        assert isinstance(res, list)

    @pytest.mark.parametrize("ndim", (0, 1, 2, 3, 10))
    def test_nd_basic(self, ndim):
        a = np.ones((2,) * ndim)
        b = np.pad(a, (2, 1), mode="constant", constant_values=0)
        res = trim_zeros(b, axis=None)
        assert_array_equal(a, res)

    @pytest.mark.parametrize("ndim", (0, 1, 2, 3))
    def test_allzero(self, ndim):
        a = np.zeros((3,) * ndim)
        res = trim_zeros(a, axis=None)
        assert_array_equal(res, np.zeros((0,) * ndim))

    def test_trim_arg(self):
        a = np.array([0, 1, 2, 0])

        res = trim_zeros(a, trim='f')
        assert_array_equal(res, [1, 2, 0])

        res = trim_zeros(a, trim='b')
        assert_array_equal(res, [0, 1, 2])

    @pytest.mark.parametrize("trim", ("front", ""))
    def test_unexpected_trim_value(self, trim):
        arr = self.a
        with pytest.raises(ValueError, match=r"unexpected character\(s\) in `trim`"):
            trim_zeros(arr, trim=trim)

    @pytest.mark.parametrize("shape, axis", [
        [(5,), None],
        [(5,), ()],
        [(5,), 0],
        [(5, 6), None],
        [(5, 6), ()],
        [(5, 6), 0],
        [(5, 6), (-1,)],
        [(5, 6, 7), None],
        [(5, 6, 7), ()],
        [(5, 6, 7), 1],
        [(5, 6, 7), (0, 2)],
        [(5, 6, 7, 8), None],
        [(5, 6, 7, 8), ()],
        [(5, 6, 7, 8), -2],
        [(5, 6, 7, 8), (0, 1, 3)],
    ])
    @pytest.mark.parametrize("trim", ['fb', 'f', 'b'])
    def test_multiple_axes(self, shape, axis, trim):
        rng = np.random.default_rng(4321)
        data, expected = self.construct_input_output(rng, shape, axis, trim)
        assert_array_equal(trim_zeros(data, axis=axis, trim=trim), expected)


class TestExtins:

    def test_basic(self):
        a = np.array([1, 3, 2, 1, 2, 3, 3])
        b = extract(a > 1, a)
        assert_array_equal(b, [3, 2, 2, 3, 3])

    def test_place(self):
        # Make sure that non-np.ndarray objects
        # raise an error instead of doing nothing
        assert_raises(TypeError, place, [1, 2, 3], [True, False], [0, 1])

        a = np.array([1, 4, 3, 2, 5, 8, 7])
        place(a, [0, 1, 0, 1, 0, 1, 0], [2, 4, 6])
        assert_array_equal(a, [1, 2, 3, 4, 5, 6, 7])

        place(a, np.zeros(7), [])
        assert_array_equal(a, np.arange(1, 8))

        place(a, [1, 0, 1, 0, 1, 0, 1], [8, 9])
        assert_array_equal(a, [8, 2, 9, 4, 8, 6, 9])
        assert_raises_regex(ValueError, "Cannot insert from an empty array",
                            lambda: place(a, [0, 0, 0, 0, 0, 1, 0], []))

        # See Issue #6974
        a = np.array(['12', '34'])
        place(a, [0, 1], '9')
        assert_array_equal(a, ['12', '9'])

    def test_both(self):
        a = rand(10)
        mask = a > 0.5
        ac = a.copy()
        c = extract(mask, a)
        place(a, mask, 0)
        place(a, mask, c)
        assert_array_equal(a, ac)


# _foo1 and _foo2 are used in some tests in TestVectorize.

def _foo1(x, y=1.0):
    return y * math.floor(x)


def _foo2(x, y=1.0, z=0.0):
    return y * math.floor(x) + z


class TestVectorize:

    def test_simple(self):
        def addsubtract(a, b):
            if a > b:
                return a - b
            else:
                return a + b

        f = vectorize(addsubtract)
        r = f([0, 3, 6, 9], [1, 3, 5, 7])
        assert_array_equal(r, [1, 6, 1, 2])

    def test_scalar(self):
        def addsubtract(a, b):
            if a > b:
                return a - b
            else:
                return a + b

        f = vectorize(addsubtract)
        r = f([0, 3, 6, 9], 5)
        assert_array_equal(r, [5, 8, 1, 4])

    def test_large(self):
        x = np.linspace(-3, 2, 10000)
        f = vectorize(lambda x: x)
        y = f(x)
        assert_array_equal(y, x)

    def test_ufunc(self):
        f = vectorize(math.cos)
        args = np.array([0, 0.5 * np.pi, np.pi, 1.5 * np.pi, 2 * np.pi])
        r1 = f(args)
        r2 = np.cos(args)
        assert_array_almost_equal(r1, r2)

    def test_keywords(self):

        def foo(a, b=1):
            return a + b

        f = vectorize(foo)
        args = np.array([1, 2, 3])
        r1 = f(args)
        r2 = np.array([2, 3, 4])
        assert_array_equal(r1, r2)
        r1 = f(args, 2)
        r2 = np.array([3, 4, 5])
        assert_array_equal(r1, r2)

    def test_keywords_with_otypes_order1(self):
        # gh-1620: The second call of f would crash with
        # `ValueError: invalid number of arguments`.
        f = vectorize(_foo1, otypes=[float])
        # We're testing the caching of ufuncs by vectorize, so the order
        # of these function calls is an important part of the test.
        r1 = f(np.arange(3.0), 1.0)
        r2 = f(np.arange(3.0))
        assert_array_equal(r1, r2)

    def test_keywords_with_otypes_order2(self):
        # gh-1620: The second call of f would crash with
        # `ValueError: non-broadcastable output operand with shape ()
        # doesn't match the broadcast shape (3,)`.
        f = vectorize(_foo1, otypes=[float])
        # We're testing the caching of ufuncs by vectorize, so the order
        # of these function calls is an important part of the test.
        r1 = f(np.arange(3.0))
        r2 = f(np.arange(3.0), 1.0)
        assert_array_equal(r1, r2)

    def test_keywords_with_otypes_order3(self):
        # gh-1620: The third call of f would crash with
        # `ValueError: invalid number of arguments`.
        f = vectorize(_foo1, otypes=[float])
        # We're testing the caching of ufuncs by vectorize, so the order
        # of these function calls is an important part of the test.
        r1 = f(np.arange(3.0))
        r2 = f(np.arange(3.0), y=1.0)
        r3 = f(np.arange(3.0))
        assert_array_equal(r1, r2)
        assert_array_equal(r1, r3)

    def test_keywords_with_otypes_several_kwd_args1(self):
        # gh-1620 Make sure different uses of keyword arguments
        # don't break the vectorized function.
        f = vectorize(_foo2, otypes=[float])
        # We're testing the caching of ufuncs by vectorize, so the order
        # of these function calls is an important part of the test.
        r1 = f(10.4, z=100)
        r2 = f(10.4, y=-1)
        r3 = f(10.4)
        assert_equal(r1, _foo2(10.4, z=100))
        assert_equal(r2, _foo2(10.4, y=-1))
        assert_equal(r3, _foo2(10.4))

    def test_keywords_with_otypes_several_kwd_args2(self):
        # gh-1620 Make sure different uses of keyword arguments
        # don't break the vectorized function.
        f = vectorize(_foo2, otypes=[float])
        # We're testing the caching of ufuncs by vectorize, so the order
        # of these function calls is an important part of the test.
        r1 = f(z=100, x=10.4, y=-1)
        r2 = f(1, 2, 3)
        assert_equal(r1, _foo2(z=100, x=10.4, y=-1))
        assert_equal(r2, _foo2(1, 2, 3))

    def test_keywords_no_func_code(self):
        # This needs to test a function that has keywords but
        # no func_code attribute, since otherwise vectorize will
        # inspect the func_code.
        import random
        try:
            vectorize(random.randrange)  # Should succeed
        except Exception:
            raise AssertionError

    def test_keywords2_ticket_2100(self):
        # Test kwarg support: enhancement ticket 2100

        def foo(a, b=1):
            return a + b

        f = vectorize(foo)
        args = np.array([1, 2, 3])
        r1 = f(a=args)
        r2 = np.array([2, 3, 4])
        assert_array_equal(r1, r2)
        r1 = f(b=1, a=args)
        assert_array_equal(r1, r2)
        r1 = f(args, b=2)
        r2 = np.array([3, 4, 5])
        assert_array_equal(r1, r2)

    def test_keywords3_ticket_2100(self):
        # Test excluded with mixed positional and kwargs: ticket 2100
        def mypolyval(x, p):
            _p = list(p)
            res = _p.pop(0)
            while _p:
                res = res * x + _p.pop(0)
            return res

        vpolyval = np.vectorize(mypolyval, excluded=['p', 1])
        ans = [3, 6]
        assert_array_equal(ans, vpolyval(x=[0, 1], p=[1, 2, 3]))
        assert_array_equal(ans, vpolyval([0, 1], p=[1, 2, 3]))
        assert_array_equal(ans, vpolyval([0, 1], [1, 2, 3]))

    def test_keywords4_ticket_2100(self):
        # Test vectorizing function with no positional args.
        @vectorize
        def f(**kw):
            res = 1.0
            for _k in kw:
                res *= kw[_k]
            return res

        assert_array_equal(f(a=[1, 2], b=[3, 4]), [3, 8])

    def test_keywords5_ticket_2100(self):
        # Test vectorizing function with no kwargs args.
        @vectorize
        def f(*v):
            return np.prod(v)

        assert_array_equal(f([1, 2], [3, 4]), [3, 8])

    def test_coverage1_ticket_2100(self):
        def foo():
            return 1

        f = vectorize(foo)
        assert_array_equal(f(), 1)

    def test_assigning_docstring(self):
        def foo(x):
            """Original documentation"""
            return x

        f = vectorize(foo)
        assert_equal(f.__doc__, foo.__doc__)

        doc = "Provided documentation"
        f = vectorize(foo, doc=doc)
        assert_equal(f.__doc__, doc)

    def test_UnboundMethod_ticket_1156(self):
        # Regression test for issue 1156
        class Foo:
            b = 2

            def bar(self, a):
                return a ** self.b

        assert_array_equal(vectorize(Foo().bar)(np.arange(9)),
                           np.arange(9) ** 2)
        assert_array_equal(vectorize(Foo.bar)(Foo(), np.arange(9)),
                           np.arange(9) ** 2)

    def test_execution_order_ticket_1487(self):
        # Regression test for dependence on execution order: issue 1487
        f1 = vectorize(lambda x: x)
        res1a = f1(np.arange(3))
        res1b = f1(np.arange(0.1, 3))
        f2 = vectorize(lambda x: x)
        res2b = f2(np.arange(0.1, 3))
        res2a = f2(np.arange(3))
        assert_equal(res1a, res2a)
        assert_equal(res1b, res2b)

    def test_string_ticket_1892(self):
        # Test vectorization over strings: issue 1892.
        f = np.vectorize(lambda x: x)
        s = '0123456789' * 10
        assert_equal(s, f(s))

    def test_dtype_promotion_gh_29189(self):
        # dtype should not be silently promoted (int32 -> int64)
        dtypes = [np.int16, np.int32, np.int64, np.float16, np.float32, np.float64]

        for dtype in dtypes:
            x = np.asarray([1, 2, 3], dtype=dtype)
            y = np.vectorize(lambda x: x + x)(x)
            assert x.dtype == y.dtype

    def test_cache(self):
        # Ensure that vectorized func called exactly once per argument.
        _calls = [0]

        @vectorize
        def f(x):
            _calls[0] += 1
            return x ** 2

        f.cache = True
        x = np.arange(5)
        assert_array_equal(f(x), x * x)
        assert_equal(_calls[0], len(x))

    def test_otypes(self):
        f = np.vectorize(lambda x: x)
        f.otypes = 'i'
        x = np.arange(5)
        assert_array_equal(f(x), x)

    def test_otypes_object_28624(self):
        # with object otype, the vectorized function should return y
        # wrapped into an object array
        y = np.arange(3)
        f = vectorize(lambda x: y, otypes=[object])

        assert f(None).item() is y
        assert f([None]).item() is y

        y = [1, 2, 3]
        f = vectorize(lambda x: y, otypes=[object])

        assert f(None).item() is y
        assert f([None]).item() is y

    def test_parse_gufunc_signature(self):
        assert_equal(nfb._parse_gufunc_signature('(x)->()'), ([('x',)], [()]))
        assert_equal(nfb._parse_gufunc_signature('(x,y)->()'),
                     ([('x', 'y')], [()]))
        assert_equal(nfb._parse_gufunc_signature('(x),(y)->()'),
                     ([('x',), ('y',)], [()]))
        assert_equal(nfb._parse_gufunc_signature('(x)->(y)'),
                     ([('x',)], [('y',)]))
        assert_equal(nfb._parse_gufunc_signature('(x)->(y),()'),
                     ([('x',)], [('y',), ()]))
        assert_equal(nfb._parse_gufunc_signature('(),(a,b,c),(d)->(d,e)'),
                     ([(), ('a', 'b', 'c'), ('d',)], [('d', 'e')]))

        # Tests to check if whitespaces are ignored
        assert_equal(nfb._parse_gufunc_signature('(x )->()'), ([('x',)], [()]))
        assert_equal(nfb._parse_gufunc_signature('( x , y )->(  )'),
                     ([('x', 'y')], [()]))
        assert_equal(nfb._parse_gufunc_signature('(x),( y) ->()'),
                     ([('x',), ('y',)], [()]))
        assert_equal(nfb._parse_gufunc_signature('(  x)-> (y )  '),
                     ([('x',)], [('y',)]))
        assert_equal(nfb._parse_gufunc_signature(' (x)->( y),( )'),
                     ([('x',)], [('y',), ()]))
        assert_equal(nfb._parse_gufunc_signature(
                     '(  ), ( a,  b,c )  ,(  d)   ->   (d  ,  e)'),
                     ([(), ('a', 'b', 'c'), ('d',)], [('d', 'e')]))

        with assert_raises(ValueError):
            nfb._parse_gufunc_signature('(x)(y)->()')
        with assert_raises(ValueError):
            nfb._parse_gufunc_signature('(x),(y)->')
        with assert_raises(ValueError):
            nfb._parse_gufunc_signature('((x))->(x)')

    def test_signature_simple(self):
        def addsubtract(a, b):
            if a > b:
                return a - b
            else:
                return a + b

        f = vectorize(addsubtract, signature='(),()->()')
        r = f([0, 3, 6, 9], [1, 3, 5, 7])
        assert_array_equal(r, [1, 6, 1, 2])

    def test_signature_mean_last(self):
        def mean(a):
            return a.mean()

        f = vectorize(mean, signature='(n)->()')
        r = f([[1, 3], [2, 4]])
        assert_array_equal(r, [2, 3])

    def test_signature_center(self):
        def center(a):
            return a - a.mean()

        f = vectorize(center, signature='(n)->(n)')
        r = f([[1, 3], [2, 4]])
        assert_array_equal(r, [[-1, 1], [-1, 1]])

    def test_signature_two_outputs(self):
        f = vectorize(lambda x: (x, x), signature='()->(),()')
        r = f([1, 2, 3])
        assert_(isinstance(r, tuple) and len(r) == 2)
        assert_array_equal(r[0], [1, 2, 3])
        assert_array_equal(r[1], [1, 2, 3])

    def test_signature_outer(self):
        f = vectorize(np.outer, signature='(a),(b)->(a,b)')
        r = f([1, 2], [1, 2, 3])
        assert_array_equal(r, [[1, 2, 3], [2, 4, 6]])

        r = f([[[1, 2]]], [1, 2, 3])
        assert_array_equal(r, [[[[1, 2, 3], [2, 4, 6]]]])

        r = f([[1, 0], [2, 0]], [1, 2, 3])
        assert_array_equal(r, [[[1, 2, 3], [0, 0, 0]],
                               [[2, 4, 6], [0, 0, 0]]])

        r = f([1, 2], [[1, 2, 3], [0, 0, 0]])
        assert_array_equal(r, [[[1, 2, 3], [2, 4, 6]],
                               [[0, 0, 0], [0, 0, 0]]])

    def test_signature_computed_size(self):
        f = vectorize(lambda x: x[:-1], signature='(n)->(m)')
        r = f([1, 2, 3])
        assert_array_equal(r, [1, 2])

        r = f([[1, 2, 3], [2, 3, 4]])
        assert_array_equal(r, [[1, 2], [2, 3]])

    def test_signature_excluded(self):

        def foo(a, b=1):
            return a + b

        f = vectorize(foo, signature='()->()', excluded={'b'})
        assert_array_equal(f([1, 2, 3]), [2, 3, 4])
        assert_array_equal(f([1, 2, 3], b=0), [1, 2, 3])

    def test_signature_otypes(self):
        f = vectorize(lambda x: x, signature='(n)->(n)', otypes=['float64'])
        r = f([1, 2, 3])
        assert_equal(r.dtype, np.dtype('float64'))
        assert_array_equal(r, [1, 2, 3])

    def test_signature_invalid_inputs(self):
        f = vectorize(operator.add, signature='(n),(n)->(n)')
        with assert_raises_regex(TypeError, 'wrong number of positional'):
            f([1, 2])
        with assert_raises_regex(
                ValueError, 'does not have enough dimensions'):
            f(1, 2)
        with assert_raises_regex(
                ValueError, 'inconsistent size for core dimension'):
            f([1, 2], [1, 2, 3])

        f = vectorize(operator.add, signature='()->()')
        with assert_raises_regex(TypeError, 'wrong number of positional'):
            f(1, 2)

    def test_signature_invalid_outputs(self):

        f = vectorize(lambda x: x[:-1], signature='(n)->(n)')
        with assert_raises_regex(
                ValueError, 'inconsistent size for core dimension'):
            f([1, 2, 3])

        f = vectorize(lambda x: x, signature='()->(),()')
        with assert_raises_regex(ValueError, 'wrong number of outputs'):
            f(1)

        f = vectorize(lambda x: (x, x), signature='()->()')
        with assert_raises_regex(ValueError, 'wrong number of outputs'):
            f([1, 2])

    def test_size_zero_output(self):
        # see issue 5868
        f = np.vectorize(lambda x: x)
        x = np.zeros([0, 5], dtype=int)
        with assert_raises_regex(ValueError, 'otypes'):
            f(x)

        f.otypes = 'i'
        assert_array_equal(f(x), x)

        f = np.vectorize(lambda x: x, signature='()->()')
        with assert_raises_regex(ValueError, 'otypes'):
            f(x)

        f = np.vectorize(lambda x: x, signature='()->()', otypes='i')
        assert_array_equal(f(x), x)

        f = np.vectorize(lambda x: x, signature='(n)->(n)', otypes='i')
        assert_array_equal(f(x), x)

        f = np.vectorize(lambda x: x, signature='(n)->(n)')
        assert_array_equal(f(x.T), x.T)

        f = np.vectorize(lambda x: [x], signature='()->(n)', otypes='i')
        with assert_raises_regex(ValueError, 'new output dimensions'):
            f(x)

    def test_subclasses(self):
        class subclass(np.ndarray):
            pass

        m = np.array([[1., 0., 0.],
                      [0., 0., 1.],
                      [0., 1., 0.]]).view(subclass)
        v = np.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]]).view(subclass)
        # generalized (gufunc)
        matvec = np.vectorize(np.matmul, signature='(m,m),(m)->(m)')
        r = matvec(m, v)
        assert_equal(type(r), subclass)
        assert_equal(r, [[1., 3., 2.], [4., 6., 5.], [7., 9., 8.]])

        # element-wise (ufunc)
        mult = np.vectorize(lambda x, y: x * y)
        r = mult(m, v)
        assert_equal(type(r), subclass)
        assert_equal(r, m * v)

    def test_name(self):
        # gh-23021
        @np.vectorize
        def f2(a, b):
            return a + b

        assert f2.__name__ == 'f2'

    def test_decorator(self):
        @vectorize
        def addsubtract(a, b):
            if a > b:
                return a - b
            else:
                return a + b

        r = addsubtract([0, 3, 6, 9], [1, 3, 5, 7])
        assert_array_equal(r, [1, 6, 1, 2])

    def test_docstring(self):
        @vectorize
        def f(x):
            """Docstring"""
            return x

        if sys.flags.optimize < 2:
            assert f.__doc__ == "Docstring"

    def test_partial(self):
        def foo(x, y):
            return x + y

        bar = partial(foo, 3)
        vbar = np.vectorize(bar)
        assert vbar(1) == 4

    def test_signature_otypes_decorator(self):
        @vectorize(signature='(n)->(n)', otypes=['float64'])
        def f(x):
            return x

        r = f([1, 2, 3])
        assert_equal(r.dtype, np.dtype('float64'))
        assert_array_equal(r, [1, 2, 3])
        assert f.__name__ == 'f'

    def test_bad_input(self):
        with assert_raises(TypeError):
            A = np.vectorize(pyfunc=3)

    def test_no_keywords(self):
        with assert_raises(TypeError):
            @np.vectorize("string")
            def foo():
                return "bar"

    def test_positional_regression_9477(self):
        # This supplies the first keyword argument as a positional,
        # to ensure that they are still properly forwarded after the
        # enhancement for #9477
        f = vectorize((lambda x: x), ['float64'])
        r = f([2])
        assert_equal(r.dtype, np.dtype('float64'))

    def test_datetime_conversion(self):
        otype = "datetime64[ns]"
        arr = np.array(['2024-01-01', '2024-01-02', '2024-01-03'],
                       dtype='datetime64[ns]')
        assert_array_equal(np.vectorize(lambda x: x, signature="(i)->(j)",
                                        otypes=[otype])(arr), arr)


class TestLeaks:
    class A:
        iters = 20

        def bound(self, *args):
            return 0

        @staticmethod
        def unbound(*args):
            return 0

    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
    @pytest.mark.skipif(NOGIL_BUILD,
                        reason=("Functions are immortalized if a thread is "
                                "launched, making this test flaky"))
    @pytest.mark.parametrize('name, incr', [
            ('bound', A.iters),
            ('unbound', 0),
            ])
    @pytest.mark.thread_unsafe(
        reason="test result depends on the reference count of a global object"
    )
    @pytest.mark.slow
    def test_frompyfunc_leaks(self, name, incr):
        # exposed in gh-11867 as np.vectorized, but the problem stems from
        # frompyfunc.
        # class.attribute = np.frompyfunc(<method>) creates a
        # reference cycle if <method> is a bound class method.
        # It requires a gc collection cycle to break the cycle.
        import gc
        A_func = getattr(self.A, name)
        gc.disable()
        try:
            refcount = sys.getrefcount(A_func)
            for i in range(self.A.iters):
                a = self.A()
                a.f = np.frompyfunc(getattr(a, name), 1, 1)
                out = a.f(np.arange(10))
            a = None
            # A.func is part of a reference cycle if incr is non-zero
            assert_equal(sys.getrefcount(A_func), refcount + incr)
            for i in range(5):
                gc.collect()
            assert_equal(sys.getrefcount(A_func), refcount)
        finally:
            gc.enable()


class TestDigitize:

    def test_forward(self):
        x = np.arange(-6, 5)
        bins = np.arange(-5, 5)
        assert_array_equal(digitize(x, bins), np.arange(11))

    def test_reverse(self):
        x = np.arange(5, -6, -1)
        bins = np.arange(5, -5, -1)
        assert_array_equal(digitize(x, bins), np.arange(11))

    def test_random(self):
        x = rand(10)
        bin = np.linspace(x.min(), x.max(), 10)
        assert_(np.all(digitize(x, bin) != 0))

    def test_right_basic(self):
        x = [1, 5, 4, 10, 8, 11, 0]
        bins = [1, 5, 10]
        default_answer = [1, 2, 1, 3, 2, 3, 0]
        assert_array_equal(digitize(x, bins), default_answer)
        right_answer = [0, 1, 1, 2, 2, 3, 0]
        assert_array_equal(digitize(x, bins, True), right_answer)

    def test_right_open(self):
        x = np.arange(-6, 5)
        bins = np.arange(-6, 4)
        assert_array_equal(digitize(x, bins, True), np.arange(11))

    def test_right_open_reverse(self):
        x = np.arange(5, -6, -1)
        bins = np.arange(4, -6, -1)
        assert_array_equal(digitize(x, bins, True), np.arange(11))

    def test_right_open_random(self):
        x = rand(10)
        bins = np.linspace(x.min(), x.max(), 10)
        assert_(np.all(digitize(x, bins, True) != 10))

    def test_monotonic(self):
        x = [-1, 0, 1, 2]
        bins = [0, 0, 1]
        assert_array_equal(digitize(x, bins, False), [0, 2, 3, 3])
        assert_array_equal(digitize(x, bins, True), [0, 0, 2, 3])
        bins = [1, 1, 0]
        assert_array_equal(digitize(x, bins, False), [3, 2, 0, 0])
        assert_array_equal(digitize(x, bins, True), [3, 3, 2, 0])
        bins = [1, 1, 1, 1]
        assert_array_equal(digitize(x, bins, False), [0, 0, 4, 4])
        assert_array_equal(digitize(x, bins, True), [0, 0, 0, 4])
        bins = [0, 0, 1, 0]
        assert_raises(ValueError, digitize, x, bins)
        bins = [1, 1, 0, 1]
        assert_raises(ValueError, digitize, x, bins)

    def test_casting_error(self):
        x = [1, 2, 3 + 1.j]
        bins = [1, 2, 3]
        assert_raises(TypeError, digitize, x, bins)
        x, bins = bins, x
        assert_raises(TypeError, digitize, x, bins)

    def test_return_type(self):
        # Functions returning indices should always return base ndarrays
        class A(np.ndarray):
            pass
        a = np.arange(5).view(A)
        b = np.arange(1, 3).view(A)
        assert_(not isinstance(digitize(b, a, False), A))
        assert_(not isinstance(digitize(b, a, True), A))

    def test_large_integers_increasing(self):
        # gh-11022
        x = 2**54  # loses precision in a float
        assert_equal(np.digitize(x, [x - 1, x + 1]), 1)

    @pytest.mark.xfail(
        reason="gh-11022: np._core.multiarray._monoticity loses precision")
    def test_large_integers_decreasing(self):
        # gh-11022
        x = 2**54  # loses precision in a float
        assert_equal(np.digitize(x, [x + 1, x - 1]), 1)


class TestUnwrap:

    def test_simple(self):
        # check that unwrap removes jumps greater that 2*pi
        assert_array_equal(unwrap([1, 1 + 2 * np.pi]), [1, 1])
        # check that unwrap maintains continuity
        assert_(np.all(diff(unwrap(rand(10) * 100)) < np.pi))

    def test_period(self):
        # check that unwrap removes jumps greater that 255
        assert_array_equal(unwrap([1, 1 + 256], period=255), [1, 2])
        # check that unwrap maintains continuity
        assert_(np.all(diff(unwrap(rand(10) * 1000, period=255)) < 255))
        # check simple case
        simple_seq = np.array([0, 75, 150, 225, 300])
        wrap_seq = np.mod(simple_seq, 255)
        assert_array_equal(unwrap(wrap_seq, period=255), simple_seq)
        # check custom discont value
        uneven_seq = np.array([0, 75, 150, 225, 300, 430])
        wrap_uneven = np.mod(uneven_seq, 250)
        no_discont = unwrap(wrap_uneven, period=250)
        assert_array_equal(no_discont, [0, 75, 150, 225, 300, 180])
        sm_discont = unwrap(wrap_uneven, period=250, discont=140)
        assert_array_equal(sm_discont, [0, 75, 150, 225, 300, 430])
        assert sm_discont.dtype == wrap_uneven.dtype


@pytest.mark.parametrize(
    "dtype", "O" + np.typecodes["AllInteger"] + np.typecodes["Float"]
)
@pytest.mark.parametrize("M", [0, 1, 10])
class TestFilterwindows:

    def test_hanning(self, dtype: str, M: int) -> None:
        scalar = np.array(M, dtype=dtype)[()]

        w = hanning(scalar)
        if dtype == "O":
            ref_dtype = np.float64
        else:
            ref_dtype = np.result_type(scalar.dtype, np.float64)
        assert w.dtype == ref_dtype

        # check symmetry
        assert_equal(w, flipud(w))

        # check known value
        if scalar < 1:
            assert_array_equal(w, np.array([]))
        elif scalar == 1:
            assert_array_equal(w, np.ones(1))
        else:
            assert_almost_equal(np.sum(w, axis=0), 4.500, 4)

    def test_hamming(self, dtype: str, M: int) -> None:
        scalar = np.array(M, dtype=dtype)[()]

        w = hamming(scalar)
        if dtype == "O":
            ref_dtype = np.float64
        else:
            ref_dtype = np.result_type(scalar.dtype, np.float64)
        assert w.dtype == ref_dtype

        # check symmetry
        assert_equal(w, flipud(w))

        # check known value
        if scalar < 1:
            assert_array_equal(w, np.array([]))
        elif scalar == 1:
            assert_array_equal(w, np.ones(1))
        else:
            assert_almost_equal(np.sum(w, axis=0), 4.9400, 4)

    def test_bartlett(self, dtype: str, M: int) -> None:
        scalar = np.array(M, dtype=dtype)[()]

        w = bartlett(scalar)
        if dtype == "O":
            ref_dtype = np.float64
        else:
            ref_dtype = np.result_type(scalar.dtype, np.float64)
        assert w.dtype == ref_dtype

        # check symmetry
        assert_equal(w, flipud(w))

        # check known value
        if scalar < 1:
            assert_array_equal(w, np.array([]))
        elif scalar == 1:
            assert_array_equal(w, np.ones(1))
        else:
            assert_almost_equal(np.sum(w, axis=0), 4.4444, 4)

    def test_blackman(self, dtype: str, M: int) -> None:
        scalar = np.array(M, dtype=dtype)[()]

        w = blackman(scalar)
        if dtype == "O":
            ref_dtype = np.float64
        else:
            ref_dtype = np.result_type(scalar.dtype, np.float64)
        assert w.dtype == ref_dtype

        # check symmetry
        assert_equal(w, flipud(w))

        # check known value
        if scalar < 1:
            assert_array_equal(w, np.array([]))
        elif scalar == 1:
            assert_array_equal(w, np.ones(1))
        else:
            assert_almost_equal(np.sum(w, axis=0), 3.7800, 4)

    def test_kaiser(self, dtype: str, M: int) -> None:
        scalar = np.array(M, dtype=dtype)[()]

        w = kaiser(scalar, 0)
        if dtype == "O":
            ref_dtype = np.float64
        else:
            ref_dtype = np.result_type(scalar.dtype, np.float64)
        assert w.dtype == ref_dtype

        # check symmetry
        assert_equal(w, flipud(w))

        # check known value
        if scalar < 1:
            assert_array_equal(w, np.array([]))
        elif scalar == 1:
            assert_array_equal(w, np.ones(1))
        else:
            assert_almost_equal(np.sum(w, axis=0), 10, 15)


class TestTrapezoid:

    def test_simple(self):
        x = np.arange(-10, 10, .1)
        r = trapezoid(np.exp(-.5 * x ** 2) / np.sqrt(2 * np.pi), dx=0.1)
        # check integral of normal equals 1
        assert_almost_equal(r, 1, 7)

    def test_ndim(self):
        x = np.linspace(0, 1, 3)
        y = np.linspace(0, 2, 8)
        z = np.linspace(0, 3, 13)

        wx = np.ones_like(x) * (x[1] - x[0])
        wx[0] /= 2
        wx[-1] /= 2
        wy = np.ones_like(y) * (y[1] - y[0])
        wy[0] /= 2
        wy[-1] /= 2
        wz = np.ones_like(z) * (z[1] - z[0])
        wz[0] /= 2
        wz[-1] /= 2

        q = x[:, None, None] + y[None, :, None] + z[None, None, :]

        qx = (q * wx[:, None, None]).sum(axis=0)
        qy = (q * wy[None, :, None]).sum(axis=1)
        qz = (q * wz[None, None, :]).sum(axis=2)

        # n-d `x`
        r = trapezoid(q, x=x[:, None, None], axis=0)
        assert_almost_equal(r, qx)
        r = trapezoid(q, x=y[None, :, None], axis=1)
        assert_almost_equal(r, qy)
        r = trapezoid(q, x=z[None, None, :], axis=2)
        assert_almost_equal(r, qz)

        # 1-d `x`
        r = trapezoid(q, x=x, axis=0)
        assert_almost_equal(r, qx)
        r = trapezoid(q, x=y, axis=1)
        assert_almost_equal(r, qy)
        r = trapezoid(q, x=z, axis=2)
        assert_almost_equal(r, qz)

    def test_masked(self):
        # Testing that masked arrays behave as if the function is 0 where
        # masked
        x = np.arange(5)
        y = x * x
        mask = x == 2
        ym = np.ma.array(y, mask=mask)
        r = 13.0  # sum(0.5 * (0 + 1) * 1.0 + 0.5 * (9 + 16))
        assert_almost_equal(trapezoid(ym, x), r)

        xm = np.ma.array(x, mask=mask)
        assert_almost_equal(trapezoid(ym, xm), r)

        xm = np.ma.array(x, mask=mask)
        assert_almost_equal(trapezoid(y, xm), r)


class TestSinc:

    def test_simple(self):
        assert_(sinc(0) == 1)
        w = sinc(np.linspace(-1, 1, 100))
        # check symmetry
        assert_array_almost_equal(w, flipud(w), 7)

    def test_array_like(self):
        x = [0, 0.5]
        y1 = sinc(np.array(x))
        y2 = sinc(list(x))
        y3 = sinc(tuple(x))
        assert_array_equal(y1, y2)
        assert_array_equal(y1, y3)

    def test_bool_dtype(self):
        x = (np.arange(4, dtype=np.uint8) % 2 == 1)
        actual = sinc(x)
        expected = sinc(x.astype(np.float64))
        assert_allclose(actual, expected)
        assert actual.dtype == np.float64

    @pytest.mark.parametrize('dtype', [np.uint8, np.int16, np.uint64])
    def test_int_dtypes(self, dtype):
        x = np.arange(4, dtype=dtype)
        actual = sinc(x)
        expected = sinc(x.astype(np.float64))
        assert_allclose(actual, expected)
        assert actual.dtype == np.float64

    @pytest.mark.parametrize(
            'dtype',
            [np.float16, np.float32, np.longdouble, np.complex64, np.complex128]
    )
    def test_float_dtypes(self, dtype):
        x = np.arange(4, dtype=dtype)
        assert sinc(x).dtype == x.dtype

    def test_float16_underflow(self):
        x = np.float16(0)
        # before gh-27784, fill value for 0 in input would underflow float16,
        # resulting in nan
        assert_array_equal(sinc(x), np.asarray(1.0))


class TestUnique:

    def test_simple(self):
        x = np.array([4, 3, 2, 1, 1, 2, 3, 4, 0])
        assert_(np.all(unique(x) == [0, 1, 2, 3, 4]))
        assert_(unique(np.array([1, 1, 1, 1, 1])) == np.array([1]))
        x = ['widget', 'ham', 'foo', 'bar', 'foo', 'ham']
        assert_(np.all(unique(x) == ['bar', 'foo', 'ham', 'widget']))
        x = np.array([5 + 6j, 1 + 1j, 1 + 10j, 10, 5 + 6j])
        assert_(np.all(unique(x) == [1 + 1j, 1 + 10j, 5 + 6j, 10]))


class TestCheckFinite:

    def test_simple(self):
        a = [1, 2, 3]
        b = [1, 2, np.inf]
        c = [1, 2, np.nan]
        np.asarray_chkfinite(a)
        assert_raises(ValueError, np.asarray_chkfinite, b)
        assert_raises(ValueError, np.asarray_chkfinite, c)

    def test_dtype_order(self):
        # Regression test for missing dtype and order arguments
        a = [1, 2, 3]
        a = np.asarray_chkfinite(a, order='F', dtype=np.float64)
        assert_(a.dtype == np.float64)


class TestCorrCoef:
    A = np.array(
        [[0.15391142, 0.18045767, 0.14197213],
         [0.70461506, 0.96474128, 0.27906989],
         [0.9297531, 0.32296769, 0.19267156]])
    B = np.array(
        [[0.10377691, 0.5417086, 0.49807457],
         [0.82872117, 0.77801674, 0.39226705],
         [0.9314666, 0.66800209, 0.03538394]])
    res1 = np.array(
        [[1., 0.9379533, -0.04931983],
         [0.9379533, 1., 0.30007991],
         [-0.04931983, 0.30007991, 1.]])
    res2 = np.array(
        [[1., 0.9379533, -0.04931983, 0.30151751, 0.66318558, 0.51532523],
         [0.9379533, 1., 0.30007991, -0.04781421, 0.88157256, 0.78052386],
         [-0.04931983, 0.30007991, 1., -0.96717111, 0.71483595, 0.83053601],
         [0.30151751, -0.04781421, -0.96717111, 1., -0.51366032, -0.66173113],
         [0.66318558, 0.88157256, 0.71483595, -0.51366032, 1., 0.98317823],
         [0.51532523, 0.78052386, 0.83053601, -0.66173113, 0.98317823, 1.]])

    def test_non_array(self):
        assert_almost_equal(np.corrcoef([0, 1, 0], [1, 0, 1]),
                            [[1., -1.], [-1., 1.]])

    def test_simple(self):
        tgt1 = corrcoef(self.A)
        assert_almost_equal(tgt1, self.res1)
        assert_(np.all(np.abs(tgt1) <= 1.0))

        tgt2 = corrcoef(self.A, self.B)
        assert_almost_equal(tgt2, self.res2)
        assert_(np.all(np.abs(tgt2) <= 1.0))

    def test_complex(self):
        x = np.array([[1, 2, 3], [1j, 2j, 3j]])
        res = corrcoef(x)
        tgt = np.array([[1., -1.j], [1.j, 1.]])
        assert_allclose(res, tgt)
        assert_(np.all(np.abs(res) <= 1.0))

    def test_xy(self):
        x = np.array([[1, 2, 3]])
        y = np.array([[1j, 2j, 3j]])
        assert_allclose(np.corrcoef(x, y), np.array([[1., -1.j], [1.j, 1.]]))

    def test_empty(self):
        with warnings.catch_warnings(record=True):
            warnings.simplefilter('always', RuntimeWarning)
            assert_array_equal(corrcoef(np.array([])), np.nan)
            assert_array_equal(corrcoef(np.array([]).reshape(0, 2)),
                               np.array([]).reshape(0, 0))
            assert_array_equal(corrcoef(np.array([]).reshape(2, 0)),
                               np.array([[np.nan, np.nan], [np.nan, np.nan]]))

    def test_extreme(self):
        x = [[1e-100, 1e100], [1e100, 1e-100]]
        with np.errstate(all='raise'):
            c = corrcoef(x)
        assert_array_almost_equal(c, np.array([[1., -1.], [-1., 1.]]))
        assert_(np.all(np.abs(c) <= 1.0))

    @pytest.mark.parametrize("test_type", np_floats)
    def test_corrcoef_dtype(self, test_type):
        cast_A = self.A.astype(test_type)
        res = corrcoef(cast_A, dtype=test_type)
        assert test_type == res.dtype


class TestCov:
    x1 = np.array([[0, 2], [1, 1], [2, 0]]).T
    res1 = np.array([[1., -1.], [-1., 1.]])
    x2 = np.array([0.0, 1.0, 2.0], ndmin=2)
    frequencies = np.array([1, 4, 1])
    x2_repeats = np.array([[0.0], [1.0], [1.0], [1.0], [1.0], [2.0]]).T
    res2 = np.array([[0.4, -0.4], [-0.4, 0.4]])
    unit_frequencies = np.ones(3, dtype=np.int_)
    weights = np.array([1.0, 4.0, 1.0])
    res3 = np.array([[2. / 3., -2. / 3.], [-2. / 3., 2. / 3.]])
    unit_weights = np.ones(3)
    x3 = np.array([0.3942, 0.5969, 0.7730, 0.9918, 0.7964])

    def test_basic(self):
        assert_allclose(cov(self.x1), self.res1)

    def test_complex(self):
        x = np.array([[1, 2, 3], [1j, 2j, 3j]])
        res = np.array([[1., -1.j], [1.j, 1.]])
        assert_allclose(cov(x), res)
        assert_allclose(cov(x, aweights=np.ones(3)), res)

    def test_xy(self):
        x = np.array([[1, 2, 3]])
        y = np.array([[1j, 2j, 3j]])
        assert_allclose(cov(x, y), np.array([[1., -1.j], [1.j, 1.]]))

    def test_empty(self):
        with warnings.catch_warnings(record=True):
            warnings.simplefilter('always', RuntimeWarning)
            assert_array_equal(cov(np.array([])), np.nan)
            assert_array_equal(cov(np.array([]).reshape(0, 2)),
                               np.array([]).reshape(0, 0))
            assert_array_equal(cov(np.array([]).reshape(2, 0)),
                               np.array([[np.nan, np.nan], [np.nan, np.nan]]))

    def test_wrong_ddof(self):
        with warnings.catch_warnings(record=True):
            warnings.simplefilter('always', RuntimeWarning)
            assert_array_equal(cov(self.x1, ddof=5),
                               np.array([[np.inf, -np.inf],
                                         [-np.inf, np.inf]]))

    def test_1D_rowvar(self):
        assert_allclose(cov(self.x3), cov(self.x3, rowvar=False))
        y = np.array([0.0780, 0.3107, 0.2111, 0.0334, 0.8501])
        assert_allclose(cov(self.x3, y), cov(self.x3, y, rowvar=False))

    def test_1D_variance(self):
        assert_allclose(cov(self.x3, ddof=1), np.var(self.x3, ddof=1))

    def test_fweights(self):
        assert_allclose(cov(self.x2, fweights=self.frequencies),
                        cov(self.x2_repeats))
        assert_allclose(cov(self.x1, fweights=self.frequencies),
                        self.res2)
        assert_allclose(cov(self.x1, fweights=self.unit_frequencies),
                        self.res1)
        nonint = self.frequencies + 0.5
        assert_raises(TypeError, cov, self.x1, fweights=nonint)
        f = np.ones((2, 3), dtype=np.int_)
        assert_raises(RuntimeError, cov, self.x1, fweights=f)
        f = np.ones(2, dtype=np.int_)
        assert_raises(RuntimeError, cov, self.x1, fweights=f)
        f = -1 * np.ones(3, dtype=np.int_)
        assert_raises(ValueError, cov, self.x1, fweights=f)

    def test_aweights(self):
        assert_allclose(cov(self.x1, aweights=self.weights), self.res3)
        assert_allclose(cov(self.x1, aweights=3.0 * self.weights),
                        cov(self.x1, aweights=self.weights))
        assert_allclose(cov(self.x1, aweights=self.unit_weights), self.res1)
        w = np.ones((2, 3))
        assert_raises(RuntimeError, cov, self.x1, aweights=w)
        w = np.ones(2)
        assert_raises(RuntimeError, cov, self.x1, aweights=w)
        w = -1.0 * np.ones(3)
        assert_raises(ValueError, cov, self.x1, aweights=w)

    def test_unit_fweights_and_aweights(self):
        assert_allclose(cov(self.x2, fweights=self.frequencies,
                            aweights=self.unit_weights),
                        cov(self.x2_repeats))
        assert_allclose(cov(self.x1, fweights=self.frequencies,
                            aweights=self.unit_weights),
                        self.res2)
        assert_allclose(cov(self.x1, fweights=self.unit_frequencies,
                            aweights=self.unit_weights),
                        self.res1)
        assert_allclose(cov(self.x1, fweights=self.unit_frequencies,
                            aweights=self.weights),
                        self.res3)
        assert_allclose(cov(self.x1, fweights=self.unit_frequencies,
                            aweights=3.0 * self.weights),
                        cov(self.x1, aweights=self.weights))
        assert_allclose(cov(self.x1, fweights=self.unit_frequencies,
                            aweights=self.unit_weights),
                        self.res1)

    @pytest.mark.parametrize("test_type", np_floats)
    def test_cov_dtype(self, test_type):
        cast_x1 = self.x1.astype(test_type)
        res = cov(cast_x1, dtype=test_type)
        assert test_type == res.dtype

    def test_gh_27658(self):
        x = np.ones((3, 1))
        expected = np.cov(x, ddof=0, rowvar=True)
        actual = np.cov(x.T, ddof=0, rowvar=False)
        assert_allclose(actual, expected, strict=True)


class Test_I0:

    def test_simple(self):
        assert_almost_equal(
            i0(0.5),
            np.array(1.0634833707413234))

        # need at least one test above 8, as the implementation is piecewise
        A = np.array([0.49842636, 0.6969809, 0.22011976, 0.0155549, 10.0])
        expected = np.array([1.06307822, 1.12518299, 1.01214991,
                             1.00006049, 2815.71662847])
        assert_almost_equal(i0(A), expected)
        assert_almost_equal(i0(-A), expected)

        B = np.array([[0.827002, 0.99959078],
                      [0.89694769, 0.39298162],
                      [0.37954418, 0.05206293],
                      [0.36465447, 0.72446427],
                      [0.48164949, 0.50324519]])
        assert_almost_equal(
            i0(B),
            np.array([[1.17843223, 1.26583466],
                      [1.21147086, 1.03898290],
                      [1.03633899, 1.00067775],
                      [1.03352052, 1.13557954],
                      [1.05884290, 1.06432317]]))
        # Regression test for gh-11205
        i0_0 = np.i0([0.])
        assert_equal(i0_0.shape, (1,))
        assert_array_equal(np.i0([0.]), np.array([1.]))

    def test_non_array(self):
        a = np.arange(4)

        class array_like:
            __array_interface__ = a.__array_interface__

            def __array_wrap__(self, arr, context, return_scalar):
                return self

        # E.g. pandas series survive ufunc calls through array-wrap:
        assert isinstance(np.abs(array_like()), array_like)
        exp = np.i0(a)
        res = np.i0(array_like())

        assert_array_equal(exp, res)

    def test_complex(self):
        a = np.array([0, 1 + 2j])
        with pytest.raises(TypeError, match="i0 not supported for complex values"):
            res = i0(a)


class TestKaiser:

    def test_simple(self):
        assert_(np.isfinite(kaiser(1, 1.0)))
        assert_almost_equal(kaiser(0, 1.0),
                            np.array([]))
        assert_almost_equal(kaiser(2, 1.0),
                            np.array([0.78984831, 0.78984831]))
        assert_almost_equal(kaiser(5, 1.0),
                            np.array([0.78984831, 0.94503323, 1.,
                                      0.94503323, 0.78984831]))
        assert_almost_equal(kaiser(5, 1.56789),
                            np.array([0.58285404, 0.88409679, 1.,
                                      0.88409679, 0.58285404]))

    def test_int_beta(self):
        kaiser(3, 4)


class TestMeshgrid:

    def test_simple(self):
        [X, Y] = meshgrid([1, 2, 3], [4, 5, 6, 7])
        assert_array_equal(X, np.array([[1, 2, 3],
                                        [1, 2, 3],
                                        [1, 2, 3],
                                        [1, 2, 3]]))
        assert_array_equal(Y, np.array([[4, 4, 4],
                                        [5, 5, 5],
                                        [6, 6, 6],
                                        [7, 7, 7]]))

    def test_single_input(self):
        [X] = meshgrid([1, 2, 3, 4])
        assert_array_equal(X, np.array([1, 2, 3, 4]))

    def test_no_input(self):
        args = []
        assert_array_equal([], meshgrid(*args))
        assert_array_equal([], meshgrid(*args, copy=False))

    def test_indexing(self):
        x = [1, 2, 3]
        y = [4, 5, 6, 7]
        [X, Y] = meshgrid(x, y, indexing='ij')
        assert_array_equal(X, np.array([[1, 1, 1, 1],
                                        [2, 2, 2, 2],
                                        [3, 3, 3, 3]]))
        assert_array_equal(Y, np.array([[4, 5, 6, 7],
                                        [4, 5, 6, 7],
                                        [4, 5, 6, 7]]))

        # Test expected shapes:
        z = [8, 9]
        assert_(meshgrid(x, y)[0].shape == (4, 3))
        assert_(meshgrid(x, y, indexing='ij')[0].shape == (3, 4))
        assert_(meshgrid(x, y, z)[0].shape == (4, 3, 2))
        assert_(meshgrid(x, y, z, indexing='ij')[0].shape == (3, 4, 2))

        assert_raises(ValueError, meshgrid, x, y, indexing='notvalid')

    def test_sparse(self):
        [X, Y] = meshgrid([1, 2, 3], [4, 5, 6, 7], sparse=True)
        assert_array_equal(X, np.array([[1, 2, 3]]))
        assert_array_equal(Y, np.array([[4], [5], [6], [7]]))

    def test_always_tuple(self):
        A = meshgrid([1, 2, 3], [4, 5, 6, 7], sparse=True, copy=False)
        B = meshgrid([], sparse=True, copy=False)
        assert isinstance(A, tuple)
        assert isinstance(B, tuple)

    def test_invalid_arguments(self):
        # Test that meshgrid complains about invalid arguments
        # Regression test for issue #4755:
        # https://github.com/numpy/numpy/issues/4755
        assert_raises(TypeError, meshgrid,
                      [1, 2, 3], [4, 5, 6, 7], indices='ij')

    def test_return_type(self):
        # Test for appropriate dtype in returned arrays.
        # Regression test for issue #5297
        # https://github.com/numpy/numpy/issues/5297
        x = np.arange(0, 10, dtype=np.float32)
        y = np.arange(10, 20, dtype=np.float64)

        X, Y = np.meshgrid(x, y)

        assert_(X.dtype == x.dtype)
        assert_(Y.dtype == y.dtype)

        # copy
        X, Y = np.meshgrid(x, y, copy=True)

        assert_(X.dtype == x.dtype)
        assert_(Y.dtype == y.dtype)

        # sparse
        X, Y = np.meshgrid(x, y, sparse=True)

        assert_(X.dtype == x.dtype)
        assert_(Y.dtype == y.dtype)

    def test_writeback(self):
        # Issue 8561
        X = np.array([1.1, 2.2])
        Y = np.array([3.3, 4.4])
        x, y = np.meshgrid(X, Y, sparse=False, copy=True)

        x[0, :] = 0
        assert_equal(x[0, :], 0)
        assert_equal(x[1, :], X)

    def test_nd_shape(self):
        a, b, c, d, e = np.meshgrid(*([0] * i for i in range(1, 6)))
        expected_shape = (2, 1, 3, 4, 5)
        assert_equal(a.shape, expected_shape)
        assert_equal(b.shape, expected_shape)
        assert_equal(c.shape, expected_shape)
        assert_equal(d.shape, expected_shape)
        assert_equal(e.shape, expected_shape)

    def test_nd_values(self):
        a, b, c = np.meshgrid([0], [1, 2], [3, 4, 5])
        assert_equal(a, [[[0, 0, 0]], [[0, 0, 0]]])
        assert_equal(b, [[[1, 1, 1]], [[2, 2, 2]]])
        assert_equal(c, [[[3, 4, 5]], [[3, 4, 5]]])

    def test_nd_indexing(self):
        a, b, c = np.meshgrid([0], [1, 2], [3, 4, 5], indexing='ij')
        assert_equal(a, [[[0, 0, 0], [0, 0, 0]]])
        assert_equal(b, [[[1, 1, 1], [2, 2, 2]]])
        assert_equal(c, [[[3, 4, 5], [3, 4, 5]]])


class TestPiecewise:

    def test_simple(self):
        # Condition is single bool list
        x = piecewise([0, 0], [True, False], [1])
        assert_array_equal(x, [1, 0])

        # List of conditions: single bool list
        x = piecewise([0, 0], [[True, False]], [1])
        assert_array_equal(x, [1, 0])

        # Conditions is single bool array
        x = piecewise([0, 0], np.array([True, False]), [1])
        assert_array_equal(x, [1, 0])

        # Condition is single int array
        x = piecewise([0, 0], np.array([1, 0]), [1])
        assert_array_equal(x, [1, 0])

        # List of conditions: int array
        x = piecewise([0, 0], [np.array([1, 0])], [1])
        assert_array_equal(x, [1, 0])

        x = piecewise([0, 0], [[False, True]], [lambda x:-1])
        assert_array_equal(x, [0, -1])

        assert_raises_regex(ValueError, '1 or 2 functions are expected',
            piecewise, [0, 0], [[False, True]], [])
        assert_raises_regex(ValueError, '1 or 2 functions are expected',
            piecewise, [0, 0], [[False, True]], [1, 2, 3])

    def test_two_conditions(self):
        x = piecewise([1, 2], [[True, False], [False, True]], [3, 4])
        assert_array_equal(x, [3, 4])

    def test_scalar_domains_three_conditions(self):
        x = piecewise(3, [True, False, False], [4, 2, 0])
        assert_equal(x, 4)

    def test_default(self):
        # No value specified for x[1], should be 0
        x = piecewise([1, 2], [True, False], [2])
        assert_array_equal(x, [2, 0])

        # Should set x[1] to 3
        x = piecewise([1, 2], [True, False], [2, 3])
        assert_array_equal(x, [2, 3])

    def test_0d(self):
        x = np.array(3)
        y = piecewise(x, x > 3, [4, 0])
        assert_(y.ndim == 0)
        assert_(y == 0)

        x = 5
        y = piecewise(x, [True, False], [1, 0])
        assert_(y.ndim == 0)
        assert_(y == 1)

        # With 3 ranges (It was failing, before)
        y = piecewise(x, [False, False, True], [1, 2, 3])
        assert_array_equal(y, 3)

    def test_0d_comparison(self):
        x = 3
        y = piecewise(x, [x <= 3, x > 3], [4, 0])  # Should succeed.
        assert_equal(y, 4)

        # With 3 ranges (It was failing, before)
        x = 4
        y = piecewise(x, [x <= 3, (x > 3) * (x <= 5), x > 5], [1, 2, 3])
        assert_array_equal(y, 2)

        assert_raises_regex(ValueError, '2 or 3 functions are expected',
            piecewise, x, [x <= 3, x > 3], [1])
        assert_raises_regex(ValueError, '2 or 3 functions are expected',
            piecewise, x, [x <= 3, x > 3], [1, 1, 1, 1])

    def test_0d_0d_condition(self):
        x = np.array(3)
        c = np.array(x > 3)
        y = piecewise(x, [c], [1, 2])
        assert_equal(y, 2)

    def test_multidimensional_extrafunc(self):
        x = np.array([[-2.5, -1.5, -0.5],
                      [0.5, 1.5, 2.5]])
        y = piecewise(x, [x < 0, x >= 2], [-1, 1, 3])
        assert_array_equal(y, np.array([[-1., -1., -1.],
                                        [3., 3., 1.]]))

    def test_subclasses(self):
        class subclass(np.ndarray):
            pass
        x = np.arange(5.).view(subclass)
        r = piecewise(x, [x < 2., x >= 4], [-1., 1., 0.])
        assert_equal(type(r), subclass)
        assert_equal(r, [-1., -1., 0., 0., 1.])


class TestBincount:

    def test_simple(self):
        y = np.bincount(np.arange(4))
        assert_array_equal(y, np.ones(4))

    def test_simple2(self):
        y = np.bincount(np.array([1, 5, 2, 4, 1]))
        assert_array_equal(y, np.array([0, 2, 1, 0, 1, 1]))

    def test_simple_weight(self):
        x = np.arange(4)
        w = np.array([0.2, 0.3, 0.5, 0.1])
        y = np.bincount(x, w)
        assert_array_equal(y, w)

    def test_simple_weight2(self):
        x = np.array([1, 2, 4, 5, 2])
        w = np.array([0.2, 0.3, 0.5, 0.1, 0.2])
        y = np.bincount(x, w)
        assert_array_equal(y, np.array([0, 0.2, 0.5, 0, 0.5, 0.1]))

    def test_with_minlength(self):
        x = np.array([0, 1, 0, 1, 1])
        y = np.bincount(x, minlength=3)
        assert_array_equal(y, np.array([2, 3, 0]))
        x = []
        y = np.bincount(x, minlength=0)
        assert_array_equal(y, np.array([]))

    def test_with_minlength_smaller_than_maxvalue(self):
        x = np.array([0, 1, 1, 2, 2, 3, 3])
        y = np.bincount(x, minlength=2)
        assert_array_equal(y, np.array([1, 2, 2, 2]))
        y = np.bincount(x, minlength=0)
        assert_array_equal(y, np.array([1, 2, 2, 2]))

    def test_with_minlength_and_weights(self):
        x = np.array([1, 2, 4, 5, 2])
        w = np.array([0.2, 0.3, 0.5, 0.1, 0.2])
        y = np.bincount(x, w, 8)
        assert_array_equal(y, np.array([0, 0.2, 0.5, 0, 0.5, 0.1, 0, 0]))

    def test_empty(self):
        x = np.array([], dtype=int)
        y = np.bincount(x)
        assert_array_equal(x, y)

    def test_empty_with_minlength(self):
        x = np.array([], dtype=int)
        y = np.bincount(x, minlength=5)
        assert_array_equal(y, np.zeros(5, dtype=int))

    @pytest.mark.parametrize('minlength', [0, 3])
    def test_empty_list(self, minlength):
        assert_array_equal(np.bincount([], minlength=minlength),
                           np.zeros(minlength, dtype=int))

    def test_with_incorrect_minlength(self):
        x = np.array([], dtype=int)
        assert_raises_regex(TypeError,
                            "'str' object cannot be interpreted",
                            lambda: np.bincount(x, minlength="foobar"))
        assert_raises_regex(ValueError,
                            "must not be negative",
                            lambda: np.bincount(x, minlength=-1))

        x = np.arange(5)
        assert_raises_regex(TypeError,
                            "'str' object cannot be interpreted",
                            lambda: np.bincount(x, minlength="foobar"))
        assert_raises_regex(ValueError,
                            "must not be negative",
                            lambda: np.bincount(x, minlength=-1))

    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
    def test_dtype_reference_leaks(self):
        # gh-6805
        intp_refcount = sys.getrefcount(np.dtype(np.intp))
        double_refcount = sys.getrefcount(np.dtype(np.double))

        for j in range(10):
            np.bincount([1, 2, 3])
        assert_equal(sys.getrefcount(np.dtype(np.intp)), intp_refcount)
        assert_equal(sys.getrefcount(np.dtype(np.double)), double_refcount)

        for j in range(10):
            np.bincount([1, 2, 3], [4, 5, 6])
        assert_equal(sys.getrefcount(np.dtype(np.intp)), intp_refcount)
        assert_equal(sys.getrefcount(np.dtype(np.double)), double_refcount)

    @pytest.mark.parametrize("vals", [[[2, 2]], 2])
    def test_error_not_1d(self, vals):
        # Test that values has to be 1-D (both as array and nested list)
        vals_arr = np.asarray(vals)
        with assert_raises(ValueError):
            np.bincount(vals_arr)
        with assert_raises(ValueError):
            np.bincount(vals)

    @pytest.mark.parametrize("vals", [[1.0], [1j], ["1"], [b"1"]])
    def test_error_not_int(self, vals):
        with assert_raises(TypeError):
            np.bincount(vals)

    @pytest.mark.parametrize("dt", np.typecodes["AllInteger"])
    def test_gh_28354(self, dt):
        a = np.array([0, 1, 1, 3, 2, 1, 7], dtype=dt)
        actual = np.bincount(a)
        expected = [1, 3, 1, 1, 0, 0, 0, 1]
        assert_array_equal(actual, expected)

    def test_contiguous_handling(self):
        # check for absence of hard crash
        np.bincount(np.arange(10000)[::2])

    def test_gh_28354_array_like(self):
        class A:
            def __array__(self):
                return np.array([0, 1, 1, 3, 2, 1, 7], dtype=np.uint64)

        a = A()
        actual = np.bincount(a)
        expected = [1, 3, 1, 1, 0, 0, 0, 1]
        assert_array_equal(actual, expected)


class TestInterp:

    def test_exceptions(self):
        assert_raises(ValueError, interp, 0, [], [])
        assert_raises(ValueError, interp, 0, [0], [1, 2])
        assert_raises(ValueError, interp, 0, [0, 1], [1, 2], period=0)
        assert_raises(ValueError, interp, 0, [], [], period=360)
        assert_raises(ValueError, interp, 0, [0], [1, 2], period=360)
        assert_raises(ValueError, interp, [], [], [3, 4, 5])

    def test_empty_x(self):
        # gh-30316
        assert_array_equal(interp([], [], []), np.array([], dtype=np.float64))
        assert_array_equal(interp([], [1, 2], [3, 4]), np.array([], dtype=np.float64))
        assert_array_equal(
            interp([], [], [], period=360), np.array([], dtype=np.float64))
        assert_array_equal(
            interp([], [1, 2], [3 + 4j, 5 + 6j]), np.array([], dtype=np.complex128))

    def test_basic(self):
        x = np.linspace(0, 1, 5)
        y = np.linspace(0, 1, 5)
        x0 = np.linspace(0, 1, 50)
        assert_almost_equal(np.interp(x0, x, y), x0)

    def test_right_left_behavior(self):
        # Needs range of sizes to test different code paths.
        # size ==1 is special cased, 1 < size < 5 is linear search, and
        # size >= 5 goes through local search and possibly binary search.
        for size in range(1, 10):
            xp = np.arange(size, dtype=np.double)
            yp = np.ones(size, dtype=np.double)
            incpts = np.array([-1, 0, size - 1, size], dtype=np.double)
            decpts = incpts[::-1]

            incres = interp(incpts, xp, yp)
            decres = interp(decpts, xp, yp)
            inctgt = np.array([1, 1, 1, 1], dtype=float)
            dectgt = inctgt[::-1]
            assert_equal(incres, inctgt)
            assert_equal(decres, dectgt)

            incres = interp(incpts, xp, yp, left=0)
            decres = interp(decpts, xp, yp, left=0)
            inctgt = np.array([0, 1, 1, 1], dtype=float)
            dectgt = inctgt[::-1]
            assert_equal(incres, inctgt)
            assert_equal(decres, dectgt)

            incres = interp(incpts, xp, yp, right=2)
            decres = interp(decpts, xp, yp, right=2)
            inctgt = np.array([1, 1, 1, 2], dtype=float)
            dectgt = inctgt[::-1]
            assert_equal(incres, inctgt)
            assert_equal(decres, dectgt)

            incres = interp(incpts, xp, yp, left=0, right=2)
            decres = interp(decpts, xp, yp, left=0, right=2)
            inctgt = np.array([0, 1, 1, 2], dtype=float)
            dectgt = inctgt[::-1]
            assert_equal(incres, inctgt)
            assert_equal(decres, dectgt)

    def test_scalar_interpolation_point(self):
        x = np.linspace(0, 1, 5)
        y = np.linspace(0, 1, 5)
        x0 = 0
        assert_almost_equal(np.interp(x0, x, y), x0)
        x0 = .3
        assert_almost_equal(np.interp(x0, x, y), x0)
        x0 = np.float32(.3)
        assert_almost_equal(np.interp(x0, x, y), x0)
        x0 = np.float64(.3)
        assert_almost_equal(np.interp(x0, x, y), x0)
        x0 = np.nan
        assert_almost_equal(np.interp(x0, x, y), x0)

    def test_non_finite_behavior_exact_x(self):
        x = [1, 2, 2.5, 3, 4]
        xp = [1, 2, 3, 4]
        fp = [1, 2, np.inf, 4]
        assert_almost_equal(np.interp(x, xp, fp), [1, 2, np.inf, np.inf, 4])
        fp = [1, 2, np.nan, 4]
        assert_almost_equal(np.interp(x, xp, fp), [1, 2, np.nan, np.nan, 4])

    @pytest.fixture(params=[
        np.float64,
        lambda x: _make_complex(x, 0),
        lambda x: _make_complex(0, x),
        lambda x: _make_complex(x, np.multiply(x, -2))
    ], ids=[
        'real',
        'complex-real',
        'complex-imag',
        'complex-both'
    ])
    def sc(self, request):
        """ scale function used by the below tests """
        return request.param

    def test_non_finite_any_nan(self, sc):
        """ test that nans are propagated """
        assert_equal(np.interp(0.5, [np.nan,      1], sc([     0,     10])), sc(np.nan))
        assert_equal(np.interp(0.5, [     0, np.nan], sc([     0,     10])), sc(np.nan))
        assert_equal(np.interp(0.5, [     0,      1], sc([np.nan,     10])), sc(np.nan))
        assert_equal(np.interp(0.5, [     0,      1], sc([     0, np.nan])), sc(np.nan))

    def test_non_finite_inf(self, sc):
        """ Test that interp between opposite infs gives nan """
        inf = np.inf
        nan = np.nan
        assert_equal(np.interp(0.5, [-inf, +inf], sc([   0,   10])), sc(nan))
        assert_equal(np.interp(0.5, [   0,    1], sc([-inf, +inf])), sc(nan))
        assert_equal(np.interp(0.5, [   0,    1], sc([+inf, -inf])), sc(nan))

        # unless the y values are equal
        assert_equal(np.interp(0.5, [-np.inf, +np.inf], sc([     10,      10])), sc(10))

    def test_non_finite_half_inf_xf(self, sc):
        """ Test that interp where both axes have a bound at inf gives nan """
        inf = np.inf
        nan = np.nan
        assert_equal(np.interp(0.5, [-inf,    1], sc([-inf,   10])), sc(nan))
        assert_equal(np.interp(0.5, [-inf,    1], sc([+inf,   10])), sc(nan))
        assert_equal(np.interp(0.5, [-inf,    1], sc([   0, -inf])), sc(nan))
        assert_equal(np.interp(0.5, [-inf,    1], sc([   0, +inf])), sc(nan))
        assert_equal(np.interp(0.5, [   0, +inf], sc([-inf,   10])), sc(nan))
        assert_equal(np.interp(0.5, [   0, +inf], sc([+inf,   10])), sc(nan))
        assert_equal(np.interp(0.5, [   0, +inf], sc([   0, -inf])), sc(nan))
        assert_equal(np.interp(0.5, [   0, +inf], sc([   0, +inf])), sc(nan))

    def test_non_finite_half_inf_x(self, sc):
        """ Test interp where the x axis has a bound at inf """
        assert_equal(np.interp(0.5, [-np.inf, -np.inf], sc([0, 10])), sc(10))
        assert_equal(np.interp(0.5, [-np.inf, 1      ], sc([0, 10])), sc(10))  # noqa: E202
        assert_equal(np.interp(0.5, [      0, +np.inf], sc([0, 10])), sc(0))
        assert_equal(np.interp(0.5, [+np.inf, +np.inf], sc([0, 10])), sc(0))

    def test_non_finite_half_inf_f(self, sc):
        """ Test interp where the f axis has a bound at inf """
        assert_equal(np.interp(0.5, [0, 1], sc([      0, -np.inf])), sc(-np.inf))
        assert_equal(np.interp(0.5, [0, 1], sc([      0, +np.inf])), sc(+np.inf))
        assert_equal(np.interp(0.5, [0, 1], sc([-np.inf,      10])), sc(-np.inf))
        assert_equal(np.interp(0.5, [0, 1], sc([+np.inf,      10])), sc(+np.inf))
        assert_equal(np.interp(0.5, [0, 1], sc([-np.inf, -np.inf])), sc(-np.inf))
        assert_equal(np.interp(0.5, [0, 1], sc([+np.inf, +np.inf])), sc(+np.inf))

    def test_complex_interp(self):
        # test complex interpolation
        x = np.linspace(0, 1, 5)
        y = np.linspace(0, 1, 5) + (1 + np.linspace(0, 1, 5)) * 1.0j
        x0 = 0.3
        y0 = x0 + (1 + x0) * 1.0j
        assert_almost_equal(np.interp(x0, x, y), y0)
        # test complex left and right
        x0 = -1
        left = 2 + 3.0j
        assert_almost_equal(np.interp(x0, x, y, left=left), left)
        x0 = 2.0
        right = 2 + 3.0j
        assert_almost_equal(np.interp(x0, x, y, right=right), right)
        # test complex non finite
        x = [1, 2, 2.5, 3, 4]
        xp = [1, 2, 3, 4]
        fp = [1, 2 + 1j, np.inf, 4]
        y = [1, 2 + 1j, np.inf + 0.5j, np.inf, 4]
        assert_almost_equal(np.interp(x, xp, fp), y)
        # test complex periodic
        x = [-180, -170, -185, 185, -10, -5, 0, 365]
        xp = [190, -190, 350, -350]
        fp = [5 + 1.0j, 10 + 2j, 3 + 3j, 4 + 4j]
        y = [7.5 + 1.5j, 5. + 1.0j, 8.75 + 1.75j, 6.25 + 1.25j, 3. + 3j, 3.25 + 3.25j,
             3.5 + 3.5j, 3.75 + 3.75j]
        assert_almost_equal(np.interp(x, xp, fp, period=360), y)

    def test_zero_dimensional_interpolation_point(self):
        x = np.linspace(0, 1, 5)
        y = np.linspace(0, 1, 5)
        x0 = np.array(.3)
        assert_almost_equal(np.interp(x0, x, y), x0)

        xp = np.array([0, 2, 4])
        fp = np.array([1, -1, 1])

        actual = np.interp(np.array(1), xp, fp)
        assert_equal(actual, 0)
        assert_(isinstance(actual, np.float64))

        actual = np.interp(np.array(4.5), xp, fp, period=4)
        assert_equal(actual, 0.5)
        assert_(isinstance(actual, np.float64))

    def test_if_len_x_is_small(self):
        xp = np.arange(0, 10, 0.0001)
        fp = np.sin(xp)
        assert_almost_equal(np.interp(np.pi, xp, fp), 0.0)

    def test_period(self):
        x = [-180, -170, -185, 185, -10, -5, 0, 365]
        xp = [190, -190, 350, -350]
        fp = [5, 10, 3, 4]
        y = [7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75]
        assert_almost_equal(np.interp(x, xp, fp, period=360), y)
        x = np.array(x, order='F').reshape(2, -1)
        y = np.array(y, order='C').reshape(2, -1)
        assert_almost_equal(np.interp(x, xp, fp, period=360), y)


quantile_methods = [
    'inverted_cdf', 'averaged_inverted_cdf', 'closest_observation',
    'interpolated_inverted_cdf', 'hazen', 'weibull', 'linear',
    'median_unbiased', 'normal_unbiased', 'nearest', 'lower', 'higher',
    'midpoint']

# Note: Technically, averaged_inverted_cdf and midpoint are not interpolated.
# but NumPy doesn't currently make a difference (at least w.r.t. to promotion).
interpolating_quantile_methods = [
    'averaged_inverted_cdf', 'interpolated_inverted_cdf', 'hazen', 'weibull',
    'linear', 'median_unbiased', 'normal_unbiased', 'midpoint']

methods_supporting_weights = ["inverted_cdf"]


class TestPercentile:

    def test_basic(self):
        x = np.arange(8) * 0.5
        assert_equal(np.percentile(x, 0), 0.)
        assert_equal(np.percentile(x, 100), 3.5)
        assert_equal(np.percentile(x, 50), 1.75)
        x[1] = np.nan
        assert_equal(np.percentile(x, 0), np.nan)
        assert_equal(np.percentile(x, 0, method='nearest'), np.nan)
        assert_equal(np.percentile(x, 0, method='inverted_cdf'), np.nan)
        assert_equal(
            np.percentile(x, 0, method='inverted_cdf',
                          weights=np.ones_like(x)),
            np.nan,
        )

    def test_fraction(self):
        x = [Fraction(i, 2) for i in range(8)]

        p = np.percentile(x, Fraction(0))
        assert_equal(p, Fraction(0))
        assert_equal(type(p), Fraction)

        p = np.percentile(x, Fraction(100))
        assert_equal(p, Fraction(7, 2))
        assert_equal(type(p), Fraction)

        p = np.percentile(x, Fraction(50))
        assert_equal(p, Fraction(7, 4))
        assert_equal(type(p), Fraction)

        p = np.percentile(x, [Fraction(50)])
        assert_equal(p, np.array([Fraction(7, 4)]))
        assert_equal(type(p), np.ndarray)

    def test_api(self):
        d = np.ones(5)
        np.percentile(d, 5, None, None, False)
        np.percentile(d, 5, None, None, False, 'linear')
        o = np.ones((1,))
        np.percentile(d, 5, None, o, False, 'linear')

    def test_complex(self):
        arr_c = np.array([0.5 + 3.0j, 2.1 + 0.5j, 1.6 + 2.3j], dtype='G')
        assert_raises(TypeError, np.percentile, arr_c, 0.5)
        arr_c = np.array([0.5 + 3.0j, 2.1 + 0.5j, 1.6 + 2.3j], dtype='D')
        assert_raises(TypeError, np.percentile, arr_c, 0.5)
        arr_c = np.array([0.5 + 3.0j, 2.1 + 0.5j, 1.6 + 2.3j], dtype='F')
        assert_raises(TypeError, np.percentile, arr_c, 0.5)

    def test_2D(self):
        x = np.array([[1, 1, 1],
                      [1, 1, 1],
                      [4, 4, 3],
                      [1, 1, 1],
                      [1, 1, 1]])
        assert_array_equal(np.percentile(x, 50, axis=0), [1, 1, 1])

    @pytest.mark.parametrize("dtype", np.typecodes["Float"])
    def test_linear_nan_1D(self, dtype):
        # METHOD 1 of H&F
        arr = np.asarray([15.0, np.nan, 35.0, 40.0, 50.0], dtype=dtype)
        res = np.percentile(
            arr,
            40.0,
            method="linear")
        np.testing.assert_equal(res, np.nan)
        np.testing.assert_equal(res.dtype, arr.dtype)

    H_F_TYPE_CODES = [(int_type, np.float64)
                      for int_type in np.typecodes["AllInteger"]
                      ] + [(np.float16, np.float16),
                           (np.float32, np.float32),
                           (np.float64, np.float64),
                           (np.longdouble, np.longdouble),
                           (np.dtype("O"), np.float64)]

    @pytest.mark.parametrize(["function", "quantile"],
                             [(np.quantile, 0.4),
                              (np.percentile, 40.0)])
    @pytest.mark.parametrize(["input_dtype", "expected_dtype"], H_F_TYPE_CODES)
    @pytest.mark.parametrize(["method", "weighted", "expected"],
                              [("inverted_cdf", False, 20),
                              ("inverted_cdf", True, 20),
                              ("averaged_inverted_cdf", False, 27.5),
                              ("closest_observation", False, 20),
                              ("interpolated_inverted_cdf", False, 20),
                              ("hazen", False, 27.5),
                              ("weibull", False, 26),
                              ("linear", False, 29),
                              ("median_unbiased", False, 27),
                              ("normal_unbiased", False, 27.125),
                               ])
    def test_linear_interpolation(self,
                                  function,
                                  quantile,
                                  method,
                                  weighted,
                                  expected,
                                  input_dtype,
                                  expected_dtype):
        expected_dtype = np.dtype(expected_dtype)

        arr = np.asarray([15.0, 20.0, 35.0, 40.0, 50.0], dtype=input_dtype)
        weights = np.ones_like(arr) if weighted else None
        if input_dtype is np.longdouble:
            if function is np.quantile:
                # 0.4 is not exactly representable and it matters
                # for "averaged_inverted_cdf", so we need to cheat.
                quantile = input_dtype("0.4")
            # We want to use nulp, but that does not work for longdouble
            test_function = np.testing.assert_almost_equal
        else:
            test_function = np.testing.assert_array_almost_equal_nulp

        actual = function(arr, quantile, method=method, weights=weights)

        test_function(actual, expected_dtype.type(expected))

        if method in ["inverted_cdf", "closest_observation"]:
            if input_dtype == "O":
                np.testing.assert_equal(np.asarray(actual).dtype, np.float64)
            else:
                np.testing.assert_equal(np.asarray(actual).dtype,
                                        np.dtype(input_dtype))
        else:
            np.testing.assert_equal(np.asarray(actual).dtype,
                                    np.dtype(expected_dtype))

    TYPE_CODES = np.typecodes["AllInteger"] + np.typecodes["Float"] + "O"

    @pytest.mark.parametrize("dtype", TYPE_CODES)
    def test_lower_higher(self, dtype):
        assert_equal(np.percentile(np.arange(10, dtype=dtype), 50,
                                   method='lower'), 4)
        assert_equal(np.percentile(np.arange(10, dtype=dtype), 50,
                                   method='higher'), 5)

    @pytest.mark.parametrize("dtype", TYPE_CODES)
    def test_midpoint(self, dtype):
        assert_equal(np.percentile(np.arange(10, dtype=dtype), 51,
                                   method='midpoint'), 4.5)
        assert_equal(np.percentile(np.arange(9, dtype=dtype) + 1, 50,
                                   method='midpoint'), 5)
        assert_equal(np.percentile(np.arange(11, dtype=dtype), 51,
                                   method='midpoint'), 5.5)
        assert_equal(np.percentile(np.arange(11, dtype=dtype), 50,
                                   method='midpoint'), 5)

    @pytest.mark.parametrize("dtype", TYPE_CODES)
    def test_nearest(self, dtype):
        assert_equal(np.percentile(np.arange(10, dtype=dtype), 51,
                                   method='nearest'), 5)
        assert_equal(np.percentile(np.arange(10, dtype=dtype), 49,
                                   method='nearest'), 4)

    def test_linear_interpolation_extrapolation(self):
        arr = np.random.rand(5)

        actual = np.percentile(arr, 100)
        np.testing.assert_equal(actual, arr.max())

        actual = np.percentile(arr, 0)
        np.testing.assert_equal(actual, arr.min())

    def test_sequence(self):
        x = np.arange(8) * 0.5
        assert_equal(np.percentile(x, [0, 100, 50]), [0, 3.5, 1.75])

    def test_axis(self):
        x = np.arange(12).reshape(3, 4)

        assert_equal(np.percentile(x, (25, 50, 100)), [2.75, 5.5, 11.0])

        r0 = [[2, 3, 4, 5], [4, 5, 6, 7], [8, 9, 10, 11]]
        assert_equal(np.percentile(x, (25, 50, 100), axis=0), r0)

        r1 = [[0.75, 1.5, 3], [4.75, 5.5, 7], [8.75, 9.5, 11]]
        assert_equal(np.percentile(x, (25, 50, 100), axis=1), np.array(r1).T)

        # ensure qth axis is always first as with np.array(old_percentile(..))
        x = np.arange(3 * 4 * 5 * 6).reshape(3, 4, 5, 6)
        assert_equal(np.percentile(x, (25, 50)).shape, (2,))
        assert_equal(np.percentile(x, (25, 50, 75)).shape, (3,))
        assert_equal(np.percentile(x, (25, 50), axis=0).shape, (2, 4, 5, 6))
        assert_equal(np.percentile(x, (25, 50), axis=1).shape, (2, 3, 5, 6))
        assert_equal(np.percentile(x, (25, 50), axis=2).shape, (2, 3, 4, 6))
        assert_equal(np.percentile(x, (25, 50), axis=3).shape, (2, 3, 4, 5))
        assert_equal(
            np.percentile(x, (25, 50, 75), axis=1).shape, (3, 3, 5, 6))
        assert_equal(np.percentile(x, (25, 50),
                                   method="higher").shape, (2,))
        assert_equal(np.percentile(x, (25, 50, 75),
                                   method="higher").shape, (3,))
        assert_equal(np.percentile(x, (25, 50), axis=0,
                                   method="higher").shape, (2, 4, 5, 6))
        assert_equal(np.percentile(x, (25, 50), axis=1,
                                   method="higher").shape, (2, 3, 5, 6))
        assert_equal(np.percentile(x, (25, 50), axis=2,
                                   method="higher").shape, (2, 3, 4, 6))
        assert_equal(np.percentile(x, (25, 50), axis=3,
                                   method="higher").shape, (2, 3, 4, 5))
        assert_equal(np.percentile(x, (25, 50, 75), axis=1,
                                   method="higher").shape, (3, 3, 5, 6))

    def test_scalar_q(self):
        # test for no empty dimensions for compatibility with old percentile
        x = np.arange(12).reshape(3, 4)
        assert_equal(np.percentile(x, 50), 5.5)
        assert_(np.isscalar(np.percentile(x, 50)))
        r0 = np.array([4., 5., 6., 7.])
        assert_equal(np.percentile(x, 50, axis=0), r0)
        assert_equal(np.percentile(x, 50, axis=0).shape, r0.shape)
        r1 = np.array([1.5, 5.5, 9.5])
        assert_almost_equal(np.percentile(x, 50, axis=1), r1)
        assert_equal(np.percentile(x, 50, axis=1).shape, r1.shape)

        out = np.empty(1)
        assert_equal(np.percentile(x, 50, out=out), 5.5)
        assert_equal(out, 5.5)
        out = np.empty(4)
        assert_equal(np.percentile(x, 50, axis=0, out=out), r0)
        assert_equal(out, r0)
        out = np.empty(3)
        assert_equal(np.percentile(x, 50, axis=1, out=out), r1)
        assert_equal(out, r1)

        # test for no empty dimensions for compatibility with old percentile
        x = np.arange(12).reshape(3, 4)
        assert_equal(np.percentile(x, 50, method='lower'), 5.)
        assert_(np.isscalar(np.percentile(x, 50)))
        r0 = np.array([4., 5., 6., 7.])
        c0 = np.percentile(x, 50, method='lower', axis=0)
        assert_equal(c0, r0)
        assert_equal(c0.shape, r0.shape)
        r1 = np.array([1., 5., 9.])
        c1 = np.percentile(x, 50, method='lower', axis=1)
        assert_almost_equal(c1, r1)
        assert_equal(c1.shape, r1.shape)

        out = np.empty((), dtype=x.dtype)
        c = np.percentile(x, 50, method='lower', out=out)
        assert_equal(c, 5)
        assert_equal(out, 5)
        out = np.empty(4, dtype=x.dtype)
        c = np.percentile(x, 50, method='lower', axis=0, out=out)
        assert_equal(c, r0)
        assert_equal(out, r0)
        out = np.empty(3, dtype=x.dtype)
        c = np.percentile(x, 50, method='lower', axis=1, out=out)
        assert_equal(c, r1)
        assert_equal(out, r1)

    def test_exception(self):
        assert_raises(ValueError, np.percentile, [1, 2], 56,
                      method='foobar')
        assert_raises(ValueError, np.percentile, [1], 101)
        assert_raises(ValueError, np.percentile, [1], -1)
        assert_raises(ValueError, np.percentile, [1], list(range(50)) + [101])
        assert_raises(ValueError, np.percentile, [1], list(range(50)) + [-0.1])

    def test_percentile_list(self):
        assert_equal(np.percentile([1, 2, 3], 0), 1)

    @pytest.mark.parametrize(
        "percentile, with_weights",
        [
            (np.percentile, False),
            (partial(np.percentile, method="inverted_cdf"), True),
        ]
    )
    def test_percentile_out(self, percentile, with_weights):
        out_dtype = int if with_weights else float
        x = np.array([1, 2, 3])
        y = np.zeros((3,), dtype=out_dtype)
        p = (1, 2, 3)
        weights = np.ones_like(x) if with_weights else None
        r = percentile(x, p, out=y, weights=weights)
        assert r is y
        assert_equal(percentile(x, p, weights=weights), y)

        x = np.array([[1, 2, 3],
                      [4, 5, 6]])
        y = np.zeros((3, 3), dtype=out_dtype)
        weights = np.ones_like(x) if with_weights else None
        r = percentile(x, p, axis=0, out=y, weights=weights)
        assert r is y
        assert_equal(percentile(x, p, weights=weights, axis=0), y)

        y = np.zeros((3, 2), dtype=out_dtype)
        percentile(x, p, axis=1, out=y, weights=weights)
        assert_equal(percentile(x, p, weights=weights, axis=1), y)

        x = np.arange(12).reshape(3, 4)
        # q.dim > 1, float
        if with_weights:
            r0 = np.array([[0, 1, 2, 3], [4, 5, 6, 7]])
        else:
            r0 = np.array([[2., 3., 4., 5.], [4., 5., 6., 7.]])
        out = np.empty((2, 4), dtype=out_dtype)
        weights = np.ones_like(x) if with_weights else None
        assert_equal(
            percentile(x, (25, 50), axis=0, out=out, weights=weights), r0
        )
        assert_equal(out, r0)
        r1 = np.array([[0.75, 4.75, 8.75], [1.5, 5.5, 9.5]])
        out = np.empty((2, 3))
        assert_equal(np.percentile(x, (25, 50), axis=1, out=out), r1)
        assert_equal(out, r1)

        # q.dim > 1, int
        r0 = np.array([[0, 1, 2, 3], [4, 5, 6, 7]])
        out = np.empty((2, 4), dtype=x.dtype)
        c = np.percentile(x, (25, 50), method='lower', axis=0, out=out)
        assert_equal(c, r0)
        assert_equal(out, r0)
        r1 = np.array([[0, 4, 8], [1, 5, 9]])
        out = np.empty((2, 3), dtype=x.dtype)
        c = np.percentile(x, (25, 50), method='lower', axis=1, out=out)
        assert_equal(c, r1)
        assert_equal(out, r1)

    def test_percentile_empty_dim(self):
        # empty dims are preserved
        d = np.arange(11 * 2).reshape(11, 1, 2, 1)
        assert_array_equal(np.percentile(d, 50, axis=0).shape, (1, 2, 1))
        assert_array_equal(np.percentile(d, 50, axis=1).shape, (11, 2, 1))
        assert_array_equal(np.percentile(d, 50, axis=2).shape, (11, 1, 1))
        assert_array_equal(np.percentile(d, 50, axis=3).shape, (11, 1, 2))
        assert_array_equal(np.percentile(d, 50, axis=-1).shape, (11, 1, 2))
        assert_array_equal(np.percentile(d, 50, axis=-2).shape, (11, 1, 1))
        assert_array_equal(np.percentile(d, 50, axis=-3).shape, (11, 2, 1))
        assert_array_equal(np.percentile(d, 50, axis=-4).shape, (1, 2, 1))

        assert_array_equal(np.percentile(d, 50, axis=2,
                                         method='midpoint').shape,
                           (11, 1, 1))
        assert_array_equal(np.percentile(d, 50, axis=-2,
                                         method='midpoint').shape,
                           (11, 1, 1))

        assert_array_equal(np.array(np.percentile(d, [10, 50], axis=0)).shape,
                           (2, 1, 2, 1))
        assert_array_equal(np.array(np.percentile(d, [10, 50], axis=1)).shape,
                           (2, 11, 2, 1))
        assert_array_equal(np.array(np.percentile(d, [10, 50], axis=2)).shape,
                           (2, 11, 1, 1))
        assert_array_equal(np.array(np.percentile(d, [10, 50], axis=3)).shape,
                           (2, 11, 1, 2))

    def test_percentile_no_overwrite(self):
        a = np.array([2, 3, 4, 1])
        np.percentile(a, [50], overwrite_input=False)
        assert_equal(a, np.array([2, 3, 4, 1]))

        a = np.array([2, 3, 4, 1])
        np.percentile(a, [50])
        assert_equal(a, np.array([2, 3, 4, 1]))

    def test_no_p_overwrite(self):
        p = np.linspace(0., 100., num=5)
        np.percentile(np.arange(100.), p, method="midpoint")
        assert_array_equal(p, np.linspace(0., 100., num=5))
        p = np.linspace(0., 100., num=5).tolist()
        np.percentile(np.arange(100.), p, method="midpoint")
        assert_array_equal(p, np.linspace(0., 100., num=5).tolist())

    def test_percentile_overwrite(self):
        a = np.array([2, 3, 4, 1])
        b = np.percentile(a, [50], overwrite_input=True)
        assert_equal(b, np.array([2.5]))

        b = np.percentile([2, 3, 4, 1], [50], overwrite_input=True)
        assert_equal(b, np.array([2.5]))

    def test_extended_axis(self):
        o = np.random.normal(size=(71, 23))
        x = np.dstack([o] * 10)
        assert_equal(np.percentile(x, 30, axis=(0, 1)), np.percentile(o, 30))
        x = np.moveaxis(x, -1, 0)
        assert_equal(np.percentile(x, 30, axis=(-2, -1)), np.percentile(o, 30))
        x = x.swapaxes(0, 1).copy()
        assert_equal(np.percentile(x, 30, axis=(0, -1)), np.percentile(o, 30))
        x = x.swapaxes(0, 1).copy()

        assert_equal(np.percentile(x, [25, 60], axis=(0, 1, 2)),
                     np.percentile(x, [25, 60], axis=None))
        assert_equal(np.percentile(x, [25, 60], axis=(0,)),
                     np.percentile(x, [25, 60], axis=0))

        d = np.arange(3 * 5 * 7 * 11).reshape((3, 5, 7, 11))
        np.random.shuffle(d.ravel())
        assert_equal(np.percentile(d, 25, axis=(0, 1, 2))[0],
                     np.percentile(d[:, :, :, 0].flatten(), 25))
        assert_equal(np.percentile(d, [10, 90], axis=(0, 1, 3))[:, 1],
                     np.percentile(d[:, :, 1, :].flatten(), [10, 90]))
        assert_equal(np.percentile(d, 25, axis=(3, 1, -4))[2],
                     np.percentile(d[:, :, 2, :].flatten(), 25))
        assert_equal(np.percentile(d, 25, axis=(3, 1, 2))[2],
                     np.percentile(d[2, :, :, :].flatten(), 25))
        assert_equal(np.percentile(d, 25, axis=(3, 2))[2, 1],
                     np.percentile(d[2, 1, :, :].flatten(), 25))
        assert_equal(np.percentile(d, 25, axis=(1, -2))[2, 1],
                     np.percentile(d[2, :, :, 1].flatten(), 25))
        assert_equal(np.percentile(d, 25, axis=(1, 3))[2, 2],
                     np.percentile(d[2, :, 2, :].flatten(), 25))

    def test_extended_axis_invalid(self):
        d = np.ones((3, 5, 7, 11))
        assert_raises(AxisError, np.percentile, d, axis=-5, q=25)
        assert_raises(AxisError, np.percentile, d, axis=(0, -5), q=25)
        assert_raises(AxisError, np.percentile, d, axis=4, q=25)
        assert_raises(AxisError, np.percentile, d, axis=(0, 4), q=25)
        # each of these refers to the same axis twice
        assert_raises(ValueError, np.percentile, d, axis=(1, 1), q=25)
        assert_raises(ValueError, np.percentile, d, axis=(-1, -1), q=25)
        assert_raises(ValueError, np.percentile, d, axis=(3, -1), q=25)

    def test_keepdims(self):
        d = np.ones((3, 5, 7, 11))
        assert_equal(np.percentile(d, 7, axis=None, keepdims=True).shape,
                     (1, 1, 1, 1))
        assert_equal(np.percentile(d, 7, axis=(0, 1), keepdims=True).shape,
                     (1, 1, 7, 11))
        assert_equal(np.percentile(d, 7, axis=(0, 3), keepdims=True).shape,
                     (1, 5, 7, 1))
        assert_equal(np.percentile(d, 7, axis=(1,), keepdims=True).shape,
                     (3, 1, 7, 11))
        assert_equal(np.percentile(d, 7, (0, 1, 2, 3), keepdims=True).shape,
                     (1, 1, 1, 1))
        assert_equal(np.percentile(d, 7, axis=(0, 1, 3), keepdims=True).shape,
                     (1, 1, 7, 1))

        assert_equal(np.percentile(d, [1, 7], axis=(0, 1, 3),
                                   keepdims=True).shape, (2, 1, 1, 7, 1))
        assert_equal(np.percentile(d, [1, 7], axis=(0, 3),
                                   keepdims=True).shape, (2, 1, 5, 7, 1))

    @pytest.mark.parametrize('q', [7, [1, 7]])
    @pytest.mark.parametrize(
        argnames='axis',
        argvalues=[
            None,
            1,
            (1,),
            (0, 1),
            (-3, -1),
        ]
    )
    def test_keepdims_out(self, q, axis):
        d = np.ones((3, 5, 7, 11))
        if axis is None:
            shape_out = (1,) * d.ndim
        else:
            axis_norm = normalize_axis_tuple(axis, d.ndim)
            shape_out = tuple(
                1 if i in axis_norm else d.shape[i] for i in range(d.ndim))
        shape_out = np.shape(q) + shape_out

        out = np.empty(shape_out)
        result = np.percentile(d, q, axis=axis, keepdims=True, out=out)
        assert result is out
        assert_equal(result.shape, shape_out)

    def test_out(self):
        o = np.zeros((4,))
        d = np.ones((3, 4))
        assert_equal(np.percentile(d, 0, 0, out=o), o)
        assert_equal(np.percentile(d, 0, 0, method='nearest', out=o), o)
        o = np.zeros((3,))
        assert_equal(np.percentile(d, 1, 1, out=o), o)
        assert_equal(np.percentile(d, 1, 1, method='nearest', out=o), o)

        o = np.zeros(())
        assert_equal(np.percentile(d, 2, out=o), o)
        assert_equal(np.percentile(d, 2, method='nearest', out=o), o)

    @pytest.mark.parametrize("method, weighted", [
        ("linear", False),
        ("nearest", False),
        ("inverted_cdf", False),
        ("inverted_cdf", True),
    ])
    def test_out_nan(self, method, weighted):
        if weighted:
            kwargs = {"weights": np.ones((3, 4)), "method": method}
        else:
            kwargs = {"method": method}
        with warnings.catch_warnings(record=True):
            warnings.filterwarnings('always', '', RuntimeWarning)
            o = np.zeros((4,))
            d = np.ones((3, 4))
            d[2, 1] = np.nan
            assert_equal(np.percentile(d, 0, 0, out=o, **kwargs), o)

            o = np.zeros((3,))
            assert_equal(np.percentile(d, 1, 1, out=o, **kwargs), o)

            o = np.zeros(())
            assert_equal(np.percentile(d, 1, out=o, **kwargs), o)

    def test_nan_behavior(self):
        a = np.arange(24, dtype=float)
        a[2] = np.nan
        assert_equal(np.percentile(a, 0.3), np.nan)
        assert_equal(np.percentile(a, 0.3, axis=0), np.nan)
        assert_equal(np.percentile(a, [0.3, 0.6], axis=0),
                     np.array([np.nan] * 2))

        a = np.arange(24, dtype=float).reshape(2, 3, 4)
        a[1, 2, 3] = np.nan
        a[1, 1, 2] = np.nan

        # no axis
        assert_equal(np.percentile(a, 0.3), np.nan)
        assert_equal(np.percentile(a, 0.3).ndim, 0)

        # axis0 zerod
        b = np.percentile(np.arange(24, dtype=float).reshape(2, 3, 4), 0.3, 0)
        b[2, 3] = np.nan
        b[1, 2] = np.nan
        assert_equal(np.percentile(a, 0.3, 0), b)

        # axis0 not zerod
        b = np.percentile(np.arange(24, dtype=float).reshape(2, 3, 4),
                          [0.3, 0.6], 0)
        b[:, 2, 3] = np.nan
        b[:, 1, 2] = np.nan
        assert_equal(np.percentile(a, [0.3, 0.6], 0), b)

        # axis1 zerod
        b = np.percentile(np.arange(24, dtype=float).reshape(2, 3, 4), 0.3, 1)
        b[1, 3] = np.nan
        b[1, 2] = np.nan
        assert_equal(np.percentile(a, 0.3, 1), b)
        # axis1 not zerod
        b = np.percentile(
            np.arange(24, dtype=float).reshape(2, 3, 4), [0.3, 0.6], 1)
        b[:, 1, 3] = np.nan
        b[:, 1, 2] = np.nan
        assert_equal(np.percentile(a, [0.3, 0.6], 1), b)

        # axis02 zerod
        b = np.percentile(
            np.arange(24, dtype=float).reshape(2, 3, 4), 0.3, (0, 2))
        b[1] = np.nan
        b[2] = np.nan
        assert_equal(np.percentile(a, 0.3, (0, 2)), b)
        # axis02 not zerod
        b = np.percentile(np.arange(24, dtype=float).reshape(2, 3, 4),
                          [0.3, 0.6], (0, 2))
        b[:, 1] = np.nan
        b[:, 2] = np.nan
        assert_equal(np.percentile(a, [0.3, 0.6], (0, 2)), b)
        # axis02 not zerod with method='nearest'
        b = np.percentile(np.arange(24, dtype=float).reshape(2, 3, 4),
                          [0.3, 0.6], (0, 2), method='nearest')
        b[:, 1] = np.nan
        b[:, 2] = np.nan
        assert_equal(np.percentile(
            a, [0.3, 0.6], (0, 2), method='nearest'), b)

    def test_nan_q(self):
        # GH18830
        with pytest.raises(ValueError, match="Percentiles must be in"):
            np.percentile([1, 2, 3, 4.0], np.nan)
        with pytest.raises(ValueError, match="Percentiles must be in"):
            np.percentile([1, 2, 3, 4.0], [np.nan])
        q = np.linspace(1.0, 99.0, 16)
        q[0] = np.nan
        with pytest.raises(ValueError, match="Percentiles must be in"):
            np.percentile([1, 2, 3, 4.0], q)

    @pytest.mark.parametrize("dtype", ["m8[D]", "M8[s]"])
    @pytest.mark.parametrize("pos", [0, 23, 10])
    def test_nat_basic(self, dtype, pos):
        # TODO: Note that times have dubious rounding as of fixing NaTs!
        # NaT and NaN should behave the same, do basic tests for NaT:
        a = np.arange(0, 24, dtype=dtype)
        a[pos] = "NaT"
        res = np.percentile(a, 30)
        assert res.dtype == dtype
        assert np.isnat(res)
        res = np.percentile(a, [30, 60])
        assert res.dtype == dtype
        assert np.isnat(res).all()

        a = np.arange(0, 24 * 3, dtype=dtype).reshape(-1, 3)
        a[pos, 1] = "NaT"
        res = np.percentile(a, 30, axis=0)
        assert_array_equal(np.isnat(res), [False, True, False])

    @pytest.mark.parametrize("qtype", [np.float16, np.float32])
    @pytest.mark.parametrize("method", quantile_methods)
    def test_percentile_gh_29003(self, qtype, method):
        # test that with float16 or float32 input we do not get overflow
        zero = qtype(0)
        one = qtype(1)
        a = np.zeros(65521, qtype)
        a[:20_000] = one
        z = np.percentile(a, 50, method=method)
        assert z == zero
        assert z.dtype == a.dtype
        z = np.percentile(a, 99, method=method)
        assert z == one
        assert z.dtype == a.dtype

    @pytest.mark.slow
    def test_percentile_gh_29003_Fraction(self):
        zero = Fraction(0)
        one = Fraction(1)
        a = np.array([zero] * 65521)
        a[:20_000] = one
        z = np.percentile(a, 50)
        assert z == zero
        z = np.percentile(a, Fraction(50))
        assert z == zero
        assert np.array(z).dtype == a.dtype

        z = np.percentile(a, 99)
        assert z == one
        # test that with only Fraction input the return type is a Fraction
        z = np.percentile(a, Fraction(99))
        assert z == one
        assert np.array(z).dtype == a.dtype

    @pytest.mark.parametrize("method", interpolating_quantile_methods)
    @pytest.mark.parametrize("q", [50, 10.0])
    def test_q_weak_promotion(self, method, q):
        a = np.array([1, 2, 3, 4, 5], dtype=np.float32)
        value = np.percentile(a, q, method=method)
        assert value.dtype == np.float32

    @pytest.mark.parametrize("method", interpolating_quantile_methods)
    def test_q_strong_promotion(self, method):
        # For interpolating methods, the dtype should be float64, for
        # discrete ones the original int8.  (technically, mid-point has no
        # reason to take into account `q`, but does so anyway.)
        a = np.array([1, 2, 3, 4, 5], dtype=np.float32)
        value = np.percentile(a, np.float64(50), method=method)
        assert value.dtype == np.float64
        # Check that we don't do accidental promotion either:
        value = np.percentile(a, np.float32(50), method=method)
        assert value.dtype == np.float32


class TestQuantile:
    # most of this is already tested by TestPercentile

    def V(self, x, y, alpha):
        # Identification function used in several tests.
        return (x >= y) - alpha

    def test_max_ulp(self):
        x = [0.0, 0.2, 0.4]
        a = np.quantile(x, 0.45)
        # The default linear method would result in 0 + 0.2 * (0.45/2) = 0.18.
        # 0.18 is not exactly representable and the formula leads to a 1 ULP
        # different result. Ensure it is this exact within 1 ULP, see gh-20331.
        np.testing.assert_array_max_ulp(a, 0.18, maxulp=1)

    def test_basic(self):
        x = np.arange(8) * 0.5
        assert_equal(np.quantile(x, 0), 0.)
        assert_equal(np.quantile(x, 1), 3.5)
        assert_equal(np.quantile(x, 0.5), 1.75)

    def test_correct_quantile_value(self):
        a = np.array([True])
        tf_quant = np.quantile(True, False)
        assert_equal(tf_quant, a[0])
        assert_equal(type(tf_quant), a.dtype)
        a = np.array([False, True, True])
        quant_res = np.quantile(a, a)
        assert_array_equal(quant_res, a)
        assert_equal(quant_res.dtype, a.dtype)

    def test_fraction(self):
        # fractional input, integral quantile
        x = [Fraction(i, 2) for i in range(8)]
        q = np.quantile(x, 0)
        assert_equal(q, 0)
        assert_equal(type(q), Fraction)

        q = np.quantile(x, 1)
        assert_equal(q, Fraction(7, 2))
        assert_equal(type(q), Fraction)

        q = np.quantile(x, .5)
        assert_equal(q, 1.75)
        assert isinstance(q, float)

        q = np.quantile(x, Fraction(1, 2))
        assert_equal(q, Fraction(7, 4))
        assert_equal(type(q), Fraction)

        q = np.quantile(x, [Fraction(1, 2)])
        assert_equal(q, np.array([Fraction(7, 4)]))
        assert_equal(type(q), np.ndarray)

        q = np.quantile(x, [[Fraction(1, 2)]])
        assert_equal(q, np.array([[Fraction(7, 4)]]))
        assert_equal(type(q), np.ndarray)

        # repeat with integral input but fractional quantile
        x = np.arange(8)
        assert_equal(np.quantile(x, Fraction(1, 2)), Fraction(7, 2))

    def test_complex(self):
        # gh-22652
        arr_c = np.array([0.5 + 3.0j, 2.1 + 0.5j, 1.6 + 2.3j], dtype='G')
        assert_raises(TypeError, np.quantile, arr_c, 0.5)
        arr_c = np.array([0.5 + 3.0j, 2.1 + 0.5j, 1.6 + 2.3j], dtype='D')
        assert_raises(TypeError, np.quantile, arr_c, 0.5)
        arr_c = np.array([0.5 + 3.0j, 2.1 + 0.5j, 1.6 + 2.3j], dtype='F')
        assert_raises(TypeError, np.quantile, arr_c, 0.5)

    def test_no_p_overwrite(self):
        # this is worth retesting, because quantile does not make a copy
        p0 = np.array([0, 0.75, 0.25, 0.5, 1.0])
        p = p0.copy()
        np.quantile(np.arange(100.), p, method="midpoint")
        assert_array_equal(p, p0)

        p0 = p0.tolist()
        p = p.tolist()
        np.quantile(np.arange(100.), p, method="midpoint")
        assert_array_equal(p, p0)

    @pytest.mark.parametrize("dtype", np.typecodes["AllInteger"])
    def test_quantile_preserve_int_type(self, dtype):
        res = np.quantile(np.array([1, 2], dtype=dtype), [0.5],
                          method="nearest")
        assert res.dtype == dtype

    @pytest.mark.parametrize("method", quantile_methods)
    def test_q_zero_one(self, method):
        # gh-24710
        arr = [10, 11, 12]
        quantile = np.quantile(arr, q=[0, 1], method=method)
        assert_equal(quantile, np.array([10, 12]))

    @pytest.mark.parametrize("method", quantile_methods)
    def test_quantile_monotonic(self, method):
        # GH 14685
        # test that the return value of quantile is monotonic if p0 is ordered
        # Also tests that the boundary values are not mishandled.
        p0 = np.linspace(0, 1, 101)
        quantile = np.quantile(np.array([0, 1, 1, 2, 2, 3, 3, 4, 5, 5, 1, 1, 9, 9, 9,
                                         8, 8, 7]) * 0.1, p0, method=method)
        assert_equal(np.sort(quantile), quantile)

        # Also test one where the number of data points is clearly divisible:
        quantile = np.quantile([0., 1., 2., 3.], p0, method=method)
        assert_equal(np.sort(quantile), quantile)

    @hypothesis.given(
            arr=arrays(dtype=np.float64,
                       shape=st.integers(min_value=3, max_value=1000),
                       elements=st.floats(allow_infinity=False, allow_nan=False,
                                          min_value=-1e300, max_value=1e300)))
    def test_quantile_monotonic_hypo(self, arr):
        p0 = np.arange(0, 1, 0.01)
        quantile = np.quantile(arr, p0)
        assert_equal(np.sort(quantile), quantile)

    def test_quantile_scalar_nan(self):
        a = np.array([[10., 7., 4.], [3., 2., 1.]])
        a[0][1] = np.nan
        actual = np.quantile(a, 0.5)
        assert np.isscalar(actual)
        assert_equal(np.quantile(a, 0.5), np.nan)

    @pytest.mark.parametrize("weights", [False, True])
    @pytest.mark.parametrize("method", quantile_methods)
    @pytest.mark.parametrize("alpha", [0.2, 0.5, 0.9])
    def test_quantile_identification_equation(self, weights, method, alpha):
        # Test that the identification equation holds for the empirical
        # CDF:
        #   E[V(x, Y)] = 0  <=>  x is quantile
        # with Y the random variable for which we have observed values and
        # V(x, y) the canonical identification function for the quantile (at
        # level alpha), see
        # https://doi.org/10.48550/arXiv.0912.0902
        if weights and method not in methods_supporting_weights:
            pytest.skip("Weights not supported by method.")
        rng = np.random.default_rng(4321)
        # We choose n and alpha such that we cover 3 cases:
        #  - n * alpha is an integer
        #  - n * alpha is a float that gets rounded down
        #  - n * alpha is a float that gest rounded up
        n = 102  # n * alpha = 20.4, 51. , 91.8
        y = rng.random(n)
        w = rng.integers(low=0, high=10, size=n) if weights else None
        x = np.quantile(y, alpha, method=method, weights=w)

        if method in ("higher",):
            # These methods do not fulfill the identification equation.
            assert np.abs(np.mean(self.V(x, y, alpha))) > 0.1 / n
        elif int(n * alpha) == n * alpha and not weights:
            # We can expect exact results, up to machine precision.
            assert_allclose(
                np.average(self.V(x, y, alpha), weights=w), 0, atol=1e-14,
            )
        else:
            # V = (x >= y) - alpha cannot sum to zero exactly but within
            # "sample precision".
            assert_allclose(np.average(self.V(x, y, alpha), weights=w), 0,
                atol=1 / n / np.amin([alpha, 1 - alpha]))

    @pytest.mark.parametrize("weights", [False, True])
    @pytest.mark.parametrize("method", quantile_methods)
    @pytest.mark.parametrize("alpha", [0.2, 0.5, 0.9])
    def test_quantile_add_and_multiply_constant(self, weights, method, alpha):
        # Test that
        #  1. quantile(c + x) = c + quantile(x)
        #  2. quantile(c * x) = c * quantile(x)
        #  3. quantile(-x) = -quantile(x, 1 - alpha)
        #     On empirical quantiles, this equation does not hold exactly.
        # Koenker (2005) "Quantile Regression" Chapter 2.2.3 calls these
        # properties equivariance.
        if weights and method not in methods_supporting_weights:
            pytest.skip("Weights not supported by method.")
        rng = np.random.default_rng(4321)
        # We choose n and alpha such that we have cases for
        #  - n * alpha is an integer
        #  - n * alpha is a float that gets rounded down
        #  - n * alpha is a float that gest rounded up
        n = 102  # n * alpha = 20.4, 51. , 91.8
        y = rng.random(n)
        w = rng.integers(low=0, high=10, size=n) if weights else None
        q = np.quantile(y, alpha, method=method, weights=w)
        c = 13.5

        # 1
        assert_allclose(np.quantile(c + y, alpha, method=method, weights=w),
                        c + q)
        # 2
        assert_allclose(np.quantile(c * y, alpha, method=method, weights=w),
                        c * q)
        # 3
        if weights:
            # From here on, we would need more methods to support weights.
            return
        q = -np.quantile(-y, 1 - alpha, method=method)
        if method == "inverted_cdf":
            if (
                n * alpha == int(n * alpha)
                or np.round(n * alpha) == int(n * alpha) + 1
            ):
                assert_allclose(q, np.quantile(y, alpha, method="higher"))
            else:
                assert_allclose(q, np.quantile(y, alpha, method="lower"))
        elif method == "closest_observation":
            if n * alpha == int(n * alpha):
                assert_allclose(q, np.quantile(y, alpha, method="higher"))
            elif np.round(n * alpha) == int(n * alpha) + 1:
                assert_allclose(
                    q, np.quantile(y, alpha + 1 / n, method="higher"))
            else:
                assert_allclose(q, np.quantile(y, alpha, method="lower"))
        elif method == "interpolated_inverted_cdf":
            assert_allclose(q, np.quantile(y, alpha + 1 / n, method=method))
        elif method == "nearest":
            if n * alpha == int(n * alpha):
                assert_allclose(q, np.quantile(y, alpha + 1 / n, method=method))
            else:
                assert_allclose(q, np.quantile(y, alpha, method=method))
        elif method == "lower":
            assert_allclose(q, np.quantile(y, alpha, method="higher"))
        elif method == "higher":
            assert_allclose(q, np.quantile(y, alpha, method="lower"))
        else:
            # "averaged_inverted_cdf", "hazen", "weibull", "linear",
            # "median_unbiased", "normal_unbiased", "midpoint"
            assert_allclose(q, np.quantile(y, alpha, method=method))

    @pytest.mark.parametrize("method", methods_supporting_weights)
    @pytest.mark.parametrize("alpha", [0.2, 0.5, 0.9])
    def test_quantile_constant_weights(self, method, alpha):
        rng = np.random.default_rng(4321)
        # We choose n and alpha such that we have cases for
        #  - n * alpha is an integer
        #  - n * alpha is a float that gets rounded down
        #  - n * alpha is a float that gest rounded up
        n = 102  # n * alpha = 20.4, 51. , 91.8
        y = rng.random(n)
        q = np.quantile(y, alpha, method=method)

        w = np.ones_like(y)
        qw = np.quantile(y, alpha, method=method, weights=w)
        assert_allclose(qw, q)

        w = 8.125 * np.ones_like(y)
        qw = np.quantile(y, alpha, method=method, weights=w)
        assert_allclose(qw, q)

    @pytest.mark.parametrize("method", methods_supporting_weights)
    @pytest.mark.parametrize("alpha", [0, 0.2, 0.5, 0.9, 1])
    def test_quantile_with_integer_weights(self, method, alpha):
        # Integer weights can be interpreted as repeated observations.
        rng = np.random.default_rng(4321)
        # We choose n and alpha such that we have cases for
        #  - n * alpha is an integer
        #  - n * alpha is a float that gets rounded down
        #  - n * alpha is a float that gest rounded up
        n = 102  # n * alpha = 20.4, 51. , 91.8
        y = rng.random(n)
        w = rng.integers(low=0, high=10, size=n, dtype=np.int32)

        qw = np.quantile(y, alpha, method=method, weights=w)
        q = np.quantile(np.repeat(y, w), alpha, method=method)
        assert_allclose(qw, q)

    @pytest.mark.parametrize("method", methods_supporting_weights)
    def test_quantile_with_weights_and_axis(self, method):
        rng = np.random.default_rng(4321)

        # 1d weight and single alpha
        y = rng.random((2, 10, 3))
        w = np.abs(rng.random(10))
        alpha = 0.5
        q = np.quantile(y, alpha, weights=w, method=method, axis=1)
        q_res = np.zeros(shape=(2, 3))
        for i in range(2):
            for j in range(3):
                q_res[i, j] = np.quantile(
                    y[i, :, j], alpha, method=method, weights=w
                )
        assert_allclose(q, q_res)

        # 1d weight and 1d alpha
        alpha = [0, 0.2, 0.4, 0.6, 0.8, 1]  # shape (6,)
        q = np.quantile(y, alpha, weights=w, method=method, axis=1)
        q_res = np.zeros(shape=(6, 2, 3))
        for i in range(2):
            for j in range(3):
                q_res[:, i, j] = np.quantile(
                    y[i, :, j], alpha, method=method, weights=w
                )
        assert_allclose(q, q_res)

        # 1d weight and 2d alpha
        alpha = [[0, 0.2], [0.4, 0.6], [0.8, 1]]  # shape (3, 2)
        q = np.quantile(y, alpha, weights=w, method=method, axis=1)
        q_res = q_res.reshape((3, 2, 2, 3))
        assert_allclose(q, q_res)

        # shape of weights equals shape of y
        w = np.abs(rng.random((2, 10, 3)))
        alpha = 0.5
        q = np.quantile(y, alpha, weights=w, method=method, axis=1)
        q_res = np.zeros(shape=(2, 3))
        for i in range(2):
            for j in range(3):
                q_res[i, j] = np.quantile(
                    y[i, :, j], alpha, method=method, weights=w[i, :, j]
                )
        assert_allclose(q, q_res)

        # axis is a tuple of all axes
        q = np.quantile(y, alpha, weights=w, method=method, axis=(0, 1, 2))
        q_res = np.quantile(y, alpha, weights=w, method=method, axis=None)
        assert_allclose(q, q_res)

        q = np.quantile(y, alpha, weights=w, method=method, axis=(1, 2))
        q_res = np.zeros(shape=(2,))
        for i in range(2):
            q_res[i] = np.quantile(y[i], alpha, weights=w[i], method=method)
        assert_allclose(q, q_res)

    @pytest.mark.parametrize("method", methods_supporting_weights)
    def test_quantile_weights_min_max(self, method):
        # Test weighted quantile at 0 and 1 with leading and trailing zero
        # weights.
        w = [0, 0, 1, 2, 3, 0]
        y = np.arange(6)
        y_min = np.quantile(y, 0, weights=w, method="inverted_cdf")
        y_max = np.quantile(y, 1, weights=w, method="inverted_cdf")
        assert y_min == y[2]  # == 2
        assert y_max == y[4]  # == 4

    def test_quantile_weights_raises_negative_weights(self):
        y = [1, 2]
        w = [-0.5, 1]
        with pytest.raises(ValueError, match="Weights must be non-negative"):
            np.quantile(y, 0.5, weights=w, method="inverted_cdf")

    @pytest.mark.parametrize(
            "method",
            sorted(set(quantile_methods) - set(methods_supporting_weights)),
    )
    def test_quantile_weights_raises_unsupported_methods(self, method):
        y = [1, 2]
        w = [0.5, 1]
        msg = "Only method 'inverted_cdf' supports weights"
        with pytest.raises(ValueError, match=msg):
            np.quantile(y, 0.5, weights=w, method=method)

    def test_weibull_fraction(self):
        arr = [Fraction(0, 1), Fraction(1, 10)]
        quantile = np.quantile(arr, [0, ], method='weibull')
        assert_equal(quantile, np.array(Fraction(0, 1)))
        quantile = np.quantile(arr, [Fraction(1, 2)], method='weibull')
        assert_equal(quantile, np.array(Fraction(1, 20)))

    def test_closest_observation(self):
        # Round ties to nearest even order statistic (see #26656)
        m = 'closest_observation'
        q = 0.5
        arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
        assert_equal(2, np.quantile(arr[0:3], q, method=m))
        assert_equal(2, np.quantile(arr[0:4], q, method=m))
        assert_equal(2, np.quantile(arr[0:5], q, method=m))
        assert_equal(3, np.quantile(arr[0:6], q, method=m))
        assert_equal(4, np.quantile(arr[0:7], q, method=m))
        assert_equal(4, np.quantile(arr[0:8], q, method=m))
        assert_equal(4, np.quantile(arr[0:9], q, method=m))
        assert_equal(5, np.quantile(arr, q, method=m))

    @pytest.mark.parametrize("weights",
            [[1, np.inf, 1, 1], [1, np.inf, 1, np.inf], [0, 0, 0, 0],
             [np.finfo("float64").max] * 4])
    @pytest.mark.parametrize("dty", ["f8", "O"])
    def test_inf_zeroes_err(self, weights, dty):
        m = "inverted_cdf"
        q = 0.5
        arr = np.array([[1, 2, 3, 4]] * 2)
        # Make one entry have bad weights and another good ones.
        wgts = np.array([weights, [0.5] * 4], dtype=dty)
        with pytest.raises(ValueError,
                match=r"Weights included NaN, inf or were all zero"):
            # We (currently) don't bother to check ahead so 0/0 or
            # overflow to `inf` while summing weights, or `inf / inf`
            # will all warn before the error is raised.
            with np.errstate(all="ignore"):
                a = np.quantile(arr, q, weights=wgts, method=m, axis=1)

    @pytest.mark.parametrize("weights",
            [[1, np.nan, 1, 1], [1, np.nan, np.nan, 1]])
    @pytest.mark.parametrize(["err", "dty"],
            [(ValueError, "f8"), ((RuntimeWarning, ValueError), "O")])
    def test_nan_err(self, err, dty, weights):
        m = "inverted_cdf"
        q = 0.5
        arr = np.array([[1, 2, 3, 4]] * 2)
        # Make one entry have bad weights and another good ones.
        wgts = np.array([weights, [0.5] * 4], dtype=dty)
        with pytest.raises(err):
            a = np.quantile(arr, q, weights=wgts, method=m)

    def test_quantile_gh_29003_Fraction(self):
        r = np.quantile([1, 2], q=Fraction(1))
        assert r == Fraction(2)
        assert isinstance(r, Fraction)

        r = np.quantile([1, 2], q=Fraction(.5))
        assert r == Fraction(3, 2)
        assert isinstance(r, Fraction)

    def test_float16_gh_29003(self):
        a = np.arange(50_001, dtype=np.float16)
        q = .999
        value = np.quantile(a, q)
        assert value == q * 50_000
        assert value.dtype == np.float16

    @pytest.mark.parametrize("method", interpolating_quantile_methods)
    @pytest.mark.parametrize("q", [0.5, 1])
    def test_q_weak_promotion(self, method, q):
        a = np.array([1, 2, 3, 4, 5], dtype=np.float32)
        value = np.quantile(a, q, method=method)
        assert value.dtype == np.float32

    @pytest.mark.parametrize("method", interpolating_quantile_methods)
    def test_q_strong_promotion(self, method):
        # For interpolating methods, the dtype should be float64, for
        # discrete ones the original int8.  (technically, mid-point has no
        # reason to take into account `q`, but does so anyway.)
        a = np.array([1, 2, 3, 4, 5], dtype=np.float32)
        value = np.quantile(a, np.float64(0.5), method=method)
        assert value.dtype == np.float64
        # Check that we don't do accidental promotion either:
        value = np.quantile(a, np.float32(0.5), method=method)
        assert value.dtype == np.float32


class TestLerp:
    @hypothesis.given(t0=st.floats(allow_nan=False, allow_infinity=False,
                                   min_value=0, max_value=1),
                      t1=st.floats(allow_nan=False, allow_infinity=False,
                                   min_value=0, max_value=1),
                      a=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=-1e300, max_value=1e300),
                      b=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=-1e300, max_value=1e300))
    def test_linear_interpolation_formula_monotonic(self, t0, t1, a, b):
        l0 = nfb._lerp(a, b, t0)
        l1 = nfb._lerp(a, b, t1)
        if t0 == t1 or a == b:
            assert l0 == l1  # uninteresting
        elif (t0 < t1) == (a < b):
            assert l0 <= l1
        else:
            assert l0 >= l1

    @hypothesis.given(t=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=0, max_value=1),
                      a=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=-1e300, max_value=1e300),
                      b=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=-1e300, max_value=1e300))
    def test_linear_interpolation_formula_bounded(self, t, a, b):
        if a <= b:
            assert a <= nfb._lerp(a, b, t) <= b
        else:
            assert b <= nfb._lerp(a, b, t) <= a

    @hypothesis.given(t=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=0, max_value=1),
                      a=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=-1e300, max_value=1e300),
                      b=st.floats(allow_nan=False, allow_infinity=False,
                                  min_value=-1e300, max_value=1e300))
    def test_linear_interpolation_formula_symmetric(self, t, a, b):
        # double subtraction is needed to remove the extra precision of t < 0.5
        left = nfb._lerp(a, b, 1 - (1 - t))
        right = nfb._lerp(b, a, 1 - t)
        assert_allclose(left, right)

    def test_linear_interpolation_formula_0d_inputs(self):
        a = np.array(2)
        b = np.array(5)
        t = np.array(0.2)
        assert nfb._lerp(a, b, t) == 2.6


class TestMedian:

    def test_basic(self):
        a0 = np.array(1)
        a1 = np.arange(2)
        a2 = np.arange(6).reshape(2, 3)
        assert_equal(np.median(a0), 1)
        assert_allclose(np.median(a1), 0.5)
        assert_allclose(np.median(a2), 2.5)
        assert_allclose(np.median(a2, axis=0), [1.5, 2.5, 3.5])
        assert_equal(np.median(a2, axis=1), [1, 4])
        assert_allclose(np.median(a2, axis=None), 2.5)

        a = np.array([0.0444502, 0.0463301, 0.141249, 0.0606775])
        assert_almost_equal((a[1] + a[3]) / 2., np.median(a))
        a = np.array([0.0463301, 0.0444502, 0.141249])
        assert_equal(a[0], np.median(a))
        a = np.array([0.0444502, 0.141249, 0.0463301])
        assert_equal(a[-1], np.median(a))
        # check array scalar result
        assert_equal(np.median(a).ndim, 0)
        a[1] = np.nan
        assert_equal(np.median(a).ndim, 0)

    def test_axis_keyword(self):
        a3 = np.array([[2, 3],
                       [0, 1],
                       [6, 7],
                       [4, 5]])
        for a in [a3, np.random.randint(0, 100, size=(2, 3, 4))]:
            orig = a.copy()
            np.median(a, axis=None)
            for ax in range(a.ndim):
                np.median(a, axis=ax)
            assert_array_equal(a, orig)

        assert_allclose(np.median(a3, axis=0), [3, 4])
        assert_allclose(np.median(a3.T, axis=1), [3, 4])
        assert_allclose(np.median(a3), 3.5)
        assert_allclose(np.median(a3, axis=None), 3.5)
        assert_allclose(np.median(a3.T), 3.5)

    def test_overwrite_keyword(self):
        a3 = np.array([[2, 3],
                       [0, 1],
                       [6, 7],
                       [4, 5]])
        a0 = np.array(1)
        a1 = np.arange(2)
        a2 = np.arange(6).reshape(2, 3)
        assert_allclose(np.median(a0.copy(), overwrite_input=True), 1)
        assert_allclose(np.median(a1.copy(), overwrite_input=True), 0.5)
        assert_allclose(np.median(a2.copy(), overwrite_input=True), 2.5)
        assert_allclose(
            np.median(a2.copy(), overwrite_input=True, axis=0), [1.5, 2.5, 3.5])
        assert_allclose(
            np.median(a2.copy(), overwrite_input=True, axis=1), [1, 4])
        assert_allclose(
            np.median(a2.copy(), overwrite_input=True, axis=None), 2.5)
        assert_allclose(
            np.median(a3.copy(), overwrite_input=True, axis=0), [3, 4])
        assert_allclose(
            np.median(a3.T.copy(), overwrite_input=True, axis=1), [3, 4])

        a4 = np.arange(3 * 4 * 5, dtype=np.float32).reshape((3, 4, 5))
        np.random.shuffle(a4.ravel())
        assert_allclose(np.median(a4, axis=None),
                        np.median(a4.copy(), axis=None, overwrite_input=True))
        assert_allclose(np.median(a4, axis=0),
                        np.median(a4.copy(), axis=0, overwrite_input=True))
        assert_allclose(np.median(a4, axis=1),
                        np.median(a4.copy(), axis=1, overwrite_input=True))
        assert_allclose(np.median(a4, axis=2),
                        np.median(a4.copy(), axis=2, overwrite_input=True))

    def test_array_like(self):
        x = [1, 2, 3]
        assert_almost_equal(np.median(x), 2)
        x2 = [x]
        assert_almost_equal(np.median(x2), 2)
        assert_allclose(np.median(x2, axis=0), x)

    def test_subclass(self):
        # gh-3846
        class MySubClass(np.ndarray):

            def __new__(cls, input_array, info=None):
                obj = np.asarray(input_array).view(cls)
                obj.info = info
                return obj

            def mean(self, axis=None, dtype=None, out=None):
                return -7

        a = MySubClass([1, 2, 3])
        assert_equal(np.median(a), -7)

    @pytest.mark.parametrize('arr',
                             ([1., 2., 3.], [1., np.nan, 3.], np.nan, 0.))
    def test_subclass2(self, arr):
        """Check that we return subclasses, even if a NaN scalar."""
        class MySubclass(np.ndarray):
            pass

        m = np.median(np.array(arr).view(MySubclass))
        assert isinstance(m, MySubclass)

    def test_out(self):
        o = np.zeros((4,))
        d = np.ones((3, 4))
        assert_equal(np.median(d, 0, out=o), o)
        o = np.zeros((3,))
        assert_equal(np.median(d, 1, out=o), o)
        o = np.zeros(())
        assert_equal(np.median(d, out=o), o)

    def test_out_nan(self):
        with warnings.catch_warnings(record=True):
            warnings.filterwarnings('always', '', RuntimeWarning)
            o = np.zeros((4,))
            d = np.ones((3, 4))
            d[2, 1] = np.nan
            assert_equal(np.median(d, 0, out=o), o)
            o = np.zeros((3,))
            assert_equal(np.median(d, 1, out=o), o)
            o = np.zeros(())
            assert_equal(np.median(d, out=o), o)

    def test_nan_behavior(self):
        a = np.arange(24, dtype=float)
        a[2] = np.nan
        assert_equal(np.median(a), np.nan)
        assert_equal(np.median(a, axis=0), np.nan)

        a = np.arange(24, dtype=float).reshape(2, 3, 4)
        a[1, 2, 3] = np.nan
        a[1, 1, 2] = np.nan

        # no axis
        assert_equal(np.median(a), np.nan)
        assert_equal(np.median(a).ndim, 0)

        # axis0
        b = np.median(np.arange(24, dtype=float).reshape(2, 3, 4), 0)
        b[2, 3] = np.nan
        b[1, 2] = np.nan
        assert_equal(np.median(a, 0), b)

        # axis1
        b = np.median(np.arange(24, dtype=float).reshape(2, 3, 4), 1)
        b[1, 3] = np.nan
        b[1, 2] = np.nan
        assert_equal(np.median(a, 1), b)

        # axis02
        b = np.median(np.arange(24, dtype=float).reshape(2, 3, 4), (0, 2))
        b[1] = np.nan
        b[2] = np.nan
        assert_equal(np.median(a, (0, 2)), b)

    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work correctly")
    def test_empty(self):
        # mean(empty array) emits two warnings: empty slice and divide by 0
        a = np.array([], dtype=float)
        with warnings.catch_warnings(record=True) as w:
            warnings.filterwarnings('always', '', RuntimeWarning)
            assert_equal(np.median(a), np.nan)
            assert_(w[0].category is RuntimeWarning)
            assert_equal(len(w), 2)

        # multiple dimensions
        a = np.array([], dtype=float, ndmin=3)
        # no axis
        with warnings.catch_warnings(record=True) as w:
            warnings.filterwarnings('always', '', RuntimeWarning)
            assert_equal(np.median(a), np.nan)
            assert_(w[0].category is RuntimeWarning)

        # axis 0 and 1
        b = np.array([], dtype=float, ndmin=2)
        assert_equal(np.median(a, axis=0), b)
        assert_equal(np.median(a, axis=1), b)

        # axis 2
        b = np.array(np.nan, dtype=float, ndmin=2)
        with warnings.catch_warnings(record=True) as w:
            warnings.filterwarnings('always', '', RuntimeWarning)
            assert_equal(np.median(a, axis=2), b)
            assert_(w[0].category is RuntimeWarning)

    def test_object(self):
        o = np.arange(7.)
        assert_(type(np.median(o.astype(object))), float)
        o[2] = np.nan
        assert_(type(np.median(o.astype(object))), float)

    def test_extended_axis(self):
        o = np.random.normal(size=(71, 23))
        x = np.dstack([o] * 10)
        assert_equal(np.median(x, axis=(0, 1)), np.median(o))
        x = np.moveaxis(x, -1, 0)
        assert_equal(np.median(x, axis=(-2, -1)), np.median(o))
        x = x.swapaxes(0, 1).copy()
        assert_equal(np.median(x, axis=(0, -1)), np.median(o))

        assert_equal(np.median(x, axis=(0, 1, 2)), np.median(x, axis=None))
        assert_equal(np.median(x, axis=(0, )), np.median(x, axis=0))
        assert_equal(np.median(x, axis=(-1, )), np.median(x, axis=-1))

        d = np.arange(3 * 5 * 7 * 11).reshape((3, 5, 7, 11))
        np.random.shuffle(d.ravel())
        assert_equal(np.median(d, axis=(0, 1, 2))[0],
                     np.median(d[:, :, :, 0].flatten()))
        assert_equal(np.median(d, axis=(0, 1, 3))[1],
                     np.median(d[:, :, 1, :].flatten()))
        assert_equal(np.median(d, axis=(3, 1, -4))[2],
                     np.median(d[:, :, 2, :].flatten()))
        assert_equal(np.median(d, axis=(3, 1, 2))[2],
                     np.median(d[2, :, :, :].flatten()))
        assert_equal(np.median(d, axis=(3, 2))[2, 1],
                     np.median(d[2, 1, :, :].flatten()))
        assert_equal(np.median(d, axis=(1, -2))[2, 1],
                     np.median(d[2, :, :, 1].flatten()))
        assert_equal(np.median(d, axis=(1, 3))[2, 2],
                     np.median(d[2, :, 2, :].flatten()))

    def test_extended_axis_invalid(self):
        d = np.ones((3, 5, 7, 11))
        assert_raises(AxisError, np.median, d, axis=-5)
        assert_raises(AxisError, np.median, d, axis=(0, -5))
        assert_raises(AxisError, np.median, d, axis=4)
        assert_raises(AxisError, np.median, d, axis=(0, 4))
        assert_raises(ValueError, np.median, d, axis=(1, 1))

    def test_keepdims(self):
        d = np.ones((3, 5, 7, 11))
        assert_equal(np.median(d, axis=None, keepdims=True).shape,
                     (1, 1, 1, 1))
        assert_equal(np.median(d, axis=(0, 1), keepdims=True).shape,
                     (1, 1, 7, 11))
        assert_equal(np.median(d, axis=(0, 3), keepdims=True).shape,
                     (1, 5, 7, 1))
        assert_equal(np.median(d, axis=(1,), keepdims=True).shape,
                     (3, 1, 7, 11))
        assert_equal(np.median(d, axis=(0, 1, 2, 3), keepdims=True).shape,
                     (1, 1, 1, 1))
        assert_equal(np.median(d, axis=(0, 1, 3), keepdims=True).shape,
                     (1, 1, 7, 1))

    @pytest.mark.parametrize(
        argnames='axis',
        argvalues=[
            None,
            1,
            (1, ),
            (0, 1),
            (-3, -1),
        ]
    )
    def test_keepdims_out(self, axis):
        d = np.ones((3, 5, 7, 11))
        if axis is None:
            shape_out = (1,) * d.ndim
        else:
            axis_norm = normalize_axis_tuple(axis, d.ndim)
            shape_out = tuple(
                1 if i in axis_norm else d.shape[i] for i in range(d.ndim))
        out = np.empty(shape_out)
        result = np.median(d, axis=axis, keepdims=True, out=out)
        assert result is out
        assert_equal(result.shape, shape_out)

    @pytest.mark.parametrize("dtype", ["m8[s]"])
    @pytest.mark.parametrize("pos", [0, 23, 10])
    def test_nat_behavior(self, dtype, pos):
        # TODO: Median does not support Datetime, due to `mean`.
        # NaT and NaN should behave the same, do basic tests for NaT.
        a = np.arange(0, 24, dtype=dtype)
        a[pos] = "NaT"
        res = np.median(a)
        assert res.dtype == dtype
        assert np.isnat(res)
        res = np.percentile(a, [30, 60])
        assert res.dtype == dtype
        assert np.isnat(res).all()

        a = np.arange(0, 24 * 3, dtype=dtype).reshape(-1, 3)
        a[pos, 1] = "NaT"
        res = np.median(a, axis=0)
        assert_array_equal(np.isnat(res), [False, True, False])


class TestSortComplex:

    @pytest.mark.parametrize("type_in, type_out", [
        ('l', 'D'),
        ('h', 'F'),
        ('H', 'F'),
        ('b', 'F'),
        ('B', 'F'),
        ('g', 'G'),
        ])
    def test_sort_real(self, type_in, type_out):
        # sort_complex() type casting for real input types
        a = np.array([5, 3, 6, 2, 1], dtype=type_in)
        actual = np.sort_complex(a)
        expected = np.sort(a).astype(type_out)
        assert_equal(actual, expected)
        assert_equal(actual.dtype, expected.dtype)

    def test_sort_complex(self):
        # sort_complex() handling of complex input
        a = np.array([2 + 3j, 1 - 2j, 1 - 3j, 2 + 1j], dtype='D')
        expected = np.array([1 - 3j, 1 - 2j, 2 + 1j, 2 + 3j], dtype='D')
        actual = np.sort_complex(a)
        assert_equal(actual, expected)
        assert_equal(actual.dtype, expected.dtype)
