path: root/numpy/lib/tests/test_nanfunctions.py

import warnings
import pytest
import inspect

import numpy as np
from numpy.core.numeric import normalize_axis_tuple
from numpy.lib.nanfunctions import _nan_mask, _replace_nan
from numpy.testing import (
    assert_, assert_equal, assert_almost_equal, assert_raises,
    assert_array_equal, suppress_warnings
    )


# Test data
_ndat = np.array([[0.6244, np.nan, 0.2692, 0.0116, np.nan, 0.1170],
                  [0.5351, -0.9403, np.nan, 0.2100, 0.4759, 0.2833],
                  [np.nan, np.nan, np.nan, 0.1042, np.nan, -0.5954],
                  [0.1610, np.nan, np.nan, 0.1859, 0.3146, np.nan]])


# Rows of _ndat with nans removed
_rdat = [np.array([0.6244, 0.2692, 0.0116, 0.1170]),
         np.array([0.5351, -0.9403, 0.2100, 0.4759, 0.2833]),
         np.array([0.1042, -0.5954]),
         np.array([0.1610, 0.1859, 0.3146])]

# Rows of _ndat with nans converted to ones
_ndat_ones = np.array([[0.6244, 1.0, 0.2692, 0.0116, 1.0, 0.1170],
                       [0.5351, -0.9403, 1.0, 0.2100, 0.4759, 0.2833],
                       [1.0, 1.0, 1.0, 0.1042, 1.0, -0.5954],
                       [0.1610, 1.0, 1.0, 0.1859, 0.3146, 1.0]])

# Rows of _ndat with nans converted to zeros
_ndat_zeros = np.array([[0.6244, 0.0, 0.2692, 0.0116, 0.0, 0.1170],
                        [0.5351, -0.9403, 0.0, 0.2100, 0.4759, 0.2833],
                        [0.0, 0.0, 0.0, 0.1042, 0.0, -0.5954],
                        [0.1610, 0.0, 0.0, 0.1859, 0.3146, 0.0]])


class TestSignatureMatch:
    NANFUNCS = {
        np.nanmin: np.amin,
        np.nanmax: np.amax,
        np.nanargmin: np.argmin,
        np.nanargmax: np.argmax,
        np.nansum: np.sum,
        np.nanprod: np.prod,
        np.nancumsum: np.cumsum,
        np.nancumprod: np.cumprod,
        np.nanmean: np.mean,
        np.nanmedian: np.median,
        np.nanpercentile: np.percentile,
        np.nanquantile: np.quantile,
        np.nanvar: np.var,
        np.nanstd: np.std,
    }
    IDS = [k.__name__ for k in NANFUNCS]

    @staticmethod
    def get_signature(func, default="..."):
        """Construct a signature and replace all default parameter-values."""
        prm_list = []
        signature = inspect.signature(func)
        for prm in signature.parameters.values():
            if prm.default is inspect.Parameter.empty:
                prm_list.append(prm)
            else:
                prm_list.append(prm.replace(default=default))
        return inspect.Signature(prm_list)

    @pytest.mark.parametrize("nan_func,func", NANFUNCS.items(), ids=IDS)
    def test_signature_match(self, nan_func, func):
        # Ignore the default parameter-values as they can sometimes differ
        # between the two functions (*e.g.* one has `False` while the other
        # has `np._NoValue`)
        signature = self.get_signature(func)
        nan_signature = self.get_signature(nan_func)
        np.testing.assert_equal(signature, nan_signature)

    def test_exhaustiveness(self):
        """Validate that all nan functions are actually tested."""
        np.testing.assert_equal(
            set(self.IDS), set(np.lib.nanfunctions.__all__)
        )


class TestNanFunctions_MinMax:

    nanfuncs = [np.nanmin, np.nanmax]
    stdfuncs = [np.min, np.max]

    def test_mutation(self):
        # Check that passed array is not modified.
        ndat = _ndat.copy()
        for f in self.nanfuncs:
            f(ndat)
            assert_equal(ndat, _ndat)

    def test_keepdims(self):
        mat = np.eye(3)
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            for axis in [None, 0, 1]:
                tgt = rf(mat, axis=axis, keepdims=True)
                res = nf(mat, axis=axis, keepdims=True)
                assert_(res.ndim == tgt.ndim)

    def test_out(self):
        mat = np.eye(3)
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            resout = np.zeros(3)
            tgt = rf(mat, axis=1)
            res = nf(mat, axis=1, out=resout)
            assert_almost_equal(res, resout)
            assert_almost_equal(res, tgt)

    def test_dtype_from_input(self):
        codes = 'efdgFDG'
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            for c in codes:
                mat = np.eye(3, dtype=c)
                tgt = rf(mat, axis=1).dtype.type
                res = nf(mat, axis=1).dtype.type
                assert_(res is tgt)
                # scalar case
                tgt = rf(mat, axis=None).dtype.type
                res = nf(mat, axis=None).dtype.type
                assert_(res is tgt)

    def test_result_values(self):
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            tgt = [rf(d) for d in _rdat]
            res = nf(_ndat, axis=1)
            assert_almost_equal(res, tgt)

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    @pytest.mark.parametrize("array", [
        np.array(np.nan),
        np.full((3, 3), np.nan),
    ], ids=["0d", "2d"])
    def test_allnans(self, axis, dtype, array):
        if axis is not None and array.ndim == 0:
            pytest.skip(f"`axis != None` not supported for 0d arrays")

        array = array.astype(dtype)
        match = "All-NaN slice encountered"
        for func in self.nanfuncs:
            with pytest.warns(RuntimeWarning, match=match):
                out = func(array, axis=axis)
            assert np.isnan(out).all()
            assert out.dtype == array.dtype

    def test_masked(self):
        mat = np.ma.fix_invalid(_ndat)
        msk = mat._mask.copy()
        for f in [np.nanmin]:
            res = f(mat, axis=1)
            tgt = f(_ndat, axis=1)
            assert_equal(res, tgt)
            assert_equal(mat._mask, msk)
            assert_(not np.isinf(mat).any())

    def test_scalar(self):
        for f in self.nanfuncs:
            assert_(f(0.) == 0.)

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

        # Check that it works and that type and
        # shape are preserved
        mine = np.eye(3).view(MyNDArray)
        for f in self.nanfuncs:
            res = f(mine, axis=0)
            assert_(isinstance(res, MyNDArray))
            assert_(res.shape == (3,))
            res = f(mine, axis=1)
            assert_(isinstance(res, MyNDArray))
            assert_(res.shape == (3,))
            res = f(mine)
            assert_(res.shape == ())

        # check that rows of nan are dealt with for subclasses (#4628)
        mine[1] = np.nan
        for f in self.nanfuncs:
            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter('always')
                res = f(mine, axis=0)
                assert_(isinstance(res, MyNDArray))
                assert_(not np.any(np.isnan(res)))
                assert_(len(w) == 0)

            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter('always')
                res = f(mine, axis=1)
                assert_(isinstance(res, MyNDArray))
                assert_(np.isnan(res[1]) and not np.isnan(res[0])
                        and not np.isnan(res[2]))
                assert_(len(w) == 1, 'no warning raised')
                assert_(issubclass(w[0].category, RuntimeWarning))

            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter('always')
                res = f(mine)
                assert_(res.shape == ())
                assert_(res != np.nan)
                assert_(len(w) == 0)

    def test_object_array(self):
        arr = np.array([[1.0, 2.0], [np.nan, 4.0], [np.nan, np.nan]], dtype=object)
        assert_equal(np.nanmin(arr), 1.0)
        assert_equal(np.nanmin(arr, axis=0), [1.0, 2.0])

        with warnings.catch_warnings(record=True) as w:
            warnings.simplefilter('always')
            # assert_equal does not work on object arrays of nan
            assert_equal(list(np.nanmin(arr, axis=1)), [1.0, 4.0, np.nan])
            assert_(len(w) == 1, 'no warning raised')
            assert_(issubclass(w[0].category, RuntimeWarning))

    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    def test_initial(self, dtype):
        class MyNDArray(np.ndarray):
            pass

        ar = np.arange(9).astype(dtype)
        ar[:5] = np.nan

        for f in self.nanfuncs:
            initial = 100 if f is np.nanmax else 0

            ret1 = f(ar, initial=initial)
            assert ret1.dtype == dtype
            assert ret1 == initial

            ret2 = f(ar.view(MyNDArray), initial=initial)
            assert ret2.dtype == dtype
            assert ret2 == initial

    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    def test_where(self, dtype):
        class MyNDArray(np.ndarray):
            pass

        ar = np.arange(9).reshape(3, 3).astype(dtype)
        ar[0, :] = np.nan
        where = np.ones_like(ar, dtype=np.bool_)
        where[:, 0] = False

        for f in self.nanfuncs:
            reference = 4 if f is np.nanmin else 8

            ret1 = f(ar, where=where, initial=5)
            assert ret1.dtype == dtype
            assert ret1 == reference

            ret2 = f(ar.view(MyNDArray), where=where, initial=5)
            assert ret2.dtype == dtype
            assert ret2 == reference


class TestNanFunctions_ArgminArgmax:

    nanfuncs = [np.nanargmin, np.nanargmax]

    def test_mutation(self):
        # Check that passed array is not modified.
        ndat = _ndat.copy()
        for f in self.nanfuncs:
            f(ndat)
            assert_equal(ndat, _ndat)

    def test_result_values(self):
        for f, fcmp in zip(self.nanfuncs, [np.greater, np.less]):
            for row in _ndat:
                with suppress_warnings() as sup:
                    sup.filter(RuntimeWarning, "invalid value encountered in")
                    ind = f(row)
                    val = row[ind]
                    # comparing with NaN is tricky as the result
                    # is always false except for NaN != NaN
                    assert_(not np.isnan(val))
                    assert_(not fcmp(val, row).any())
                    assert_(not np.equal(val, row[:ind]).any())

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    @pytest.mark.parametrize("array", [
        np.array(np.nan),
        np.full((3, 3), np.nan),
    ], ids=["0d", "2d"])
    def test_allnans(self, axis, dtype, array):
        if axis is not None and array.ndim == 0:
            pytest.skip(f"`axis != None` not supported for 0d arrays")

        array = array.astype(dtype)
        for func in self.nanfuncs:
            with pytest.raises(ValueError, match="All-NaN slice encountered"):
                func(array, axis=axis)

    def test_empty(self):
        mat = np.zeros((0, 3))
        for f in self.nanfuncs:
            for axis in [0, None]:
                assert_raises(ValueError, f, mat, axis=axis)
            for axis in [1]:
                res = f(mat, axis=axis)
                assert_equal(res, np.zeros(0))

    def test_scalar(self):
        for f in self.nanfuncs:
            assert_(f(0.) == 0.)

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

        # Check that it works and that type and
        # shape are preserved
        mine = np.eye(3).view(MyNDArray)
        for f in self.nanfuncs:
            res = f(mine, axis=0)
            assert_(isinstance(res, MyNDArray))
            assert_(res.shape == (3,))
            res = f(mine, axis=1)
            assert_(isinstance(res, MyNDArray))
            assert_(res.shape == (3,))
            res = f(mine)
            assert_(res.shape == ())

    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    def test_keepdims(self, dtype):
        ar = np.arange(9).astype(dtype)
        ar[:5] = np.nan

        for f in self.nanfuncs:
            reference = 5 if f is np.nanargmin else 8
            ret = f(ar, keepdims=True)
            assert ret.ndim == ar.ndim
            assert ret == reference

    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    def test_out(self, dtype):
        ar = np.arange(9).astype(dtype)
        ar[:5] = np.nan

        for f in self.nanfuncs:
            out = np.zeros((), dtype=np.intp)
            reference = 5 if f is np.nanargmin else 8
            ret = f(ar, out=out)
            assert ret is out
            assert ret == reference



_TEST_ARRAYS = {
    "0d": np.array(5),
    "1d": np.array([127, 39, 93, 87, 46])
}
for _v in _TEST_ARRAYS.values():
    _v.setflags(write=False)


@pytest.mark.parametrize(
    "dtype",
    np.typecodes["AllInteger"] + np.typecodes["AllFloat"] + "O",
)
@pytest.mark.parametrize("mat", _TEST_ARRAYS.values(), ids=_TEST_ARRAYS.keys())
class TestNanFunctions_NumberTypes:
    nanfuncs = {
        np.nanmin: np.min,
        np.nanmax: np.max,
        np.nanargmin: np.argmin,
        np.nanargmax: np.argmax,
        np.nansum: np.sum,
        np.nanprod: np.prod,
        np.nancumsum: np.cumsum,
        np.nancumprod: np.cumprod,
        np.nanmean: np.mean,
        np.nanmedian: np.median,
        np.nanvar: np.var,
        np.nanstd: np.std,
    }
    nanfunc_ids = [i.__name__ for i in nanfuncs]

    @pytest.mark.parametrize("nanfunc,func", nanfuncs.items(), ids=nanfunc_ids)
    @np.errstate(over="ignore")
    def test_nanfunc(self, mat, dtype, nanfunc, func):
        mat = mat.astype(dtype)
        tgt = func(mat)
        out = nanfunc(mat)

        assert_almost_equal(out, tgt)
        if dtype == "O":
            assert type(out) is type(tgt)
        else:
            assert out.dtype == tgt.dtype

    @pytest.mark.parametrize(
        "nanfunc,func",
        [(np.nanquantile, np.quantile), (np.nanpercentile, np.percentile)],
        ids=["nanquantile", "nanpercentile"],
    )
    def test_nanfunc_q(self, mat, dtype, nanfunc, func):
        mat = mat.astype(dtype)
        if mat.dtype.kind == "c":
            assert_raises(TypeError, func, mat, q=1)
            assert_raises(TypeError, nanfunc, mat, q=1)

        else:
            tgt = func(mat, q=1)
            out = nanfunc(mat, q=1)

            assert_almost_equal(out, tgt)

            if dtype == "O":
                assert type(out) is type(tgt)
            else:
                assert out.dtype == tgt.dtype

    @pytest.mark.parametrize(
        "nanfunc,func",
        [(np.nanvar, np.var), (np.nanstd, np.std)],
        ids=["nanvar", "nanstd"],
    )
    def test_nanfunc_ddof(self, mat, dtype, nanfunc, func):
        mat = mat.astype(dtype)
        tgt = func(mat, ddof=0.5)
        out = nanfunc(mat, ddof=0.5)

        assert_almost_equal(out, tgt)
        if dtype == "O":
            assert type(out) is type(tgt)
        else:
            assert out.dtype == tgt.dtype


class SharedNanFunctionsTestsMixin:
    def test_mutation(self):
        # Check that passed array is not modified.
        ndat = _ndat.copy()
        for f in self.nanfuncs:
            f(ndat)
            assert_equal(ndat, _ndat)

    def test_keepdims(self):
        mat = np.eye(3)
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            for axis in [None, 0, 1]:
                tgt = rf(mat, axis=axis, keepdims=True)
                res = nf(mat, axis=axis, keepdims=True)
                assert_(res.ndim == tgt.ndim)

    def test_out(self):
        mat = np.eye(3)
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            resout = np.zeros(3)
            tgt = rf(mat, axis=1)
            res = nf(mat, axis=1, out=resout)
            assert_almost_equal(res, resout)
            assert_almost_equal(res, tgt)

    def test_dtype_from_dtype(self):
        mat = np.eye(3)
        codes = 'efdgFDG'
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            for c in codes:
                with suppress_warnings() as sup:
                    if nf in {np.nanstd, np.nanvar} and c in 'FDG':
                        # Giving the warning is a small bug, see gh-8000
                        sup.filter(np.ComplexWarning)
                    tgt = rf(mat, dtype=np.dtype(c), axis=1).dtype.type
                    res = nf(mat, dtype=np.dtype(c), axis=1).dtype.type
                    assert_(res is tgt)
                    # scalar case
                    tgt = rf(mat, dtype=np.dtype(c), axis=None).dtype.type
                    res = nf(mat, dtype=np.dtype(c), axis=None).dtype.type
                    assert_(res is tgt)

    def test_dtype_from_char(self):
        mat = np.eye(3)
        codes = 'efdgFDG'
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            for c in codes:
                with suppress_warnings() as sup:
                    if nf in {np.nanstd, np.nanvar} and c in 'FDG':
                        # Giving the warning is a small bug, see gh-8000
                        sup.filter(np.ComplexWarning)
                    tgt = rf(mat, dtype=c, axis=1).dtype.type
                    res = nf(mat, dtype=c, axis=1).dtype.type
                    assert_(res is tgt)
                    # scalar case
                    tgt = rf(mat, dtype=c, axis=None).dtype.type
                    res = nf(mat, dtype=c, axis=None).dtype.type
                    assert_(res is tgt)

    def test_dtype_from_input(self):
        codes = 'efdgFDG'
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            for c in codes:
                mat = np.eye(3, dtype=c)
                tgt = rf(mat, axis=1).dtype.type
                res = nf(mat, axis=1).dtype.type
                assert_(res is tgt, "res %s, tgt %s" % (res, tgt))
                # scalar case
                tgt = rf(mat, axis=None).dtype.type
                res = nf(mat, axis=None).dtype.type
                assert_(res is tgt)

    def test_result_values(self):
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            tgt = [rf(d) for d in _rdat]
            res = nf(_ndat, axis=1)
            assert_almost_equal(res, tgt)

    def test_scalar(self):
        for f in self.nanfuncs:
            assert_(f(0.) == 0.)

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

        # Check that it works and that type and
        # shape are preserved
        array = np.eye(3)
        mine = array.view(MyNDArray)
        for f in self.nanfuncs:
            expected_shape = f(array, axis=0).shape
            res = f(mine, axis=0)
            assert_(isinstance(res, MyNDArray))
            assert_(res.shape == expected_shape)
            expected_shape = f(array, axis=1).shape
            res = f(mine, axis=1)
            assert_(isinstance(res, MyNDArray))
            assert_(res.shape == expected_shape)
            expected_shape = f(array).shape
            res = f(mine)
            assert_(isinstance(res, MyNDArray))
            assert_(res.shape == expected_shape)


class TestNanFunctions_SumProd(SharedNanFunctionsTestsMixin):

    nanfuncs = [np.nansum, np.nanprod]
    stdfuncs = [np.sum, np.prod]

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    @pytest.mark.parametrize("array", [
        np.array(np.nan),
        np.full((3, 3), np.nan),
    ], ids=["0d", "2d"])
    def test_allnans(self, axis, dtype, array):
        if axis is not None and array.ndim == 0:
            pytest.skip(f"`axis != None` not supported for 0d arrays")

        array = array.astype(dtype)
        for func, identity in zip(self.nanfuncs, [0, 1]):
            out = func(array, axis=axis)
            assert np.all(out == identity)
            assert out.dtype == array.dtype

    def test_empty(self):
        for f, tgt_value in zip([np.nansum, np.nanprod], [0, 1]):
            mat = np.zeros((0, 3))
            tgt = [tgt_value]*3
            res = f(mat, axis=0)
            assert_equal(res, tgt)
            tgt = []
            res = f(mat, axis=1)
            assert_equal(res, tgt)
            tgt = tgt_value
            res = f(mat, axis=None)
            assert_equal(res, tgt)

    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    def test_initial(self, dtype):
        ar = np.arange(9).astype(dtype)
        ar[:5] = np.nan

        for f in self.nanfuncs:
            reference = 28 if f is np.nansum else 3360
            ret = f(ar, initial=2)
            assert ret.dtype == dtype
            assert ret == reference

    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    def test_where(self, dtype):
        ar = np.arange(9).reshape(3, 3).astype(dtype)
        ar[0, :] = np.nan
        where = np.ones_like(ar, dtype=np.bool_)
        where[:, 0] = False

        for f in self.nanfuncs:
            reference = 26 if f is np.nansum else 2240
            ret = f(ar, where=where, initial=2)
            assert ret.dtype == dtype
            assert ret == reference


class TestNanFunctions_CumSumProd(SharedNanFunctionsTestsMixin):

    nanfuncs = [np.nancumsum, np.nancumprod]
    stdfuncs = [np.cumsum, np.cumprod]

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    @pytest.mark.parametrize("array", [
        np.array(np.nan),
        np.full((3, 3), np.nan)
    ], ids=["0d", "2d"])
    def test_allnans(self, axis, dtype, array):
        if axis is not None and array.ndim == 0:
            pytest.skip(f"`axis != None` not supported for 0d arrays")

        array = array.astype(dtype)
        for func, identity in zip(self.nanfuncs, [0, 1]):
            out = func(array)
            assert np.all(out == identity)
            assert out.dtype == array.dtype

    def test_empty(self):
        for f, tgt_value in zip(self.nanfuncs, [0, 1]):
            mat = np.zeros((0, 3))
            tgt = tgt_value*np.ones((0, 3))
            res = f(mat, axis=0)
            assert_equal(res, tgt)
            tgt = mat
            res = f(mat, axis=1)
            assert_equal(res, tgt)
            tgt = np.zeros((0))
            res = f(mat, axis=None)
            assert_equal(res, tgt)

    def test_keepdims(self):
        for f, g in zip(self.nanfuncs, self.stdfuncs):
            mat = np.eye(3)
            for axis in [None, 0, 1]:
                tgt = f(mat, axis=axis, out=None)
                res = g(mat, axis=axis, out=None)
                assert_(res.ndim == tgt.ndim)

        for f in self.nanfuncs:
            d = np.ones((3, 5, 7, 11))
            # Randomly set some elements to NaN:
            rs = np.random.RandomState(0)
            d[rs.rand(*d.shape) < 0.5] = np.nan
            res = f(d, axis=None)
            assert_equal(res.shape, (1155,))
            for axis in np.arange(4):
                res = f(d, axis=axis)
                assert_equal(res.shape, (3, 5, 7, 11))

    def test_result_values(self):
        for axis in (-2, -1, 0, 1, None):
            tgt = np.cumprod(_ndat_ones, axis=axis)
            res = np.nancumprod(_ndat, axis=axis)
            assert_almost_equal(res, tgt)
            tgt = np.cumsum(_ndat_zeros,axis=axis)
            res = np.nancumsum(_ndat, axis=axis)
            assert_almost_equal(res, tgt)

    def test_out(self):
        mat = np.eye(3)
        for nf, rf in zip(self.nanfuncs, self.stdfuncs):
            resout = np.eye(3)
            for axis in (-2, -1, 0, 1):
                tgt = rf(mat, axis=axis)
                res = nf(mat, axis=axis, out=resout)
                assert_almost_equal(res, resout)
                assert_almost_equal(res, tgt)


class TestNanFunctions_MeanVarStd(SharedNanFunctionsTestsMixin):

    nanfuncs = [np.nanmean, np.nanvar, np.nanstd]
    stdfuncs = [np.mean, np.var, np.std]

    def test_dtype_error(self):
        for f in self.nanfuncs:
            for dtype in [np.bool_, np.int_, np.object_]:
                assert_raises(TypeError, f, _ndat, axis=1, dtype=dtype)

    def test_out_dtype_error(self):
        for f in self.nanfuncs:
            for dtype in [np.bool_, np.int_, np.object_]:
                out = np.empty(_ndat.shape[0], dtype=dtype)
                assert_raises(TypeError, f, _ndat, axis=1, out=out)

    def test_ddof(self):
        nanfuncs = [np.nanvar, np.nanstd]
        stdfuncs = [np.var, np.std]
        for nf, rf in zip(nanfuncs, stdfuncs):
            for ddof in [0, 1]:
                tgt = [rf(d, ddof=ddof) for d in _rdat]
                res = nf(_ndat, axis=1, ddof=ddof)
                assert_almost_equal(res, tgt)

    def test_ddof_too_big(self):
        nanfuncs = [np.nanvar, np.nanstd]
        stdfuncs = [np.var, np.std]
        dsize = [len(d) for d in _rdat]
        for nf, rf in zip(nanfuncs, stdfuncs):
            for ddof in range(5):
                with suppress_warnings() as sup:
                    sup.record(RuntimeWarning)
                    sup.filter(np.ComplexWarning)
                    tgt = [ddof >= d for d in dsize]
                    res = nf(_ndat, axis=1, ddof=ddof)
                    assert_equal(np.isnan(res), tgt)
                    if any(tgt):
                        assert_(len(sup.log) == 1)
                    else:
                        assert_(len(sup.log) == 0)

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    @pytest.mark.parametrize("array", [
        np.array(np.nan),
        np.full((3, 3), np.nan),
    ], ids=["0d", "2d"])
    def test_allnans(self, axis, dtype, array):
        if axis is not None and array.ndim == 0:
            pytest.skip(f"`axis != None` not supported for 0d arrays")

        array = array.astype(dtype)
        match = "(Degrees of freedom <= 0 for slice.)|(Mean of empty slice)"
        for func in self.nanfuncs:
            with pytest.warns(RuntimeWarning, match=match):
                out = func(array, axis=axis)
            assert np.isnan(out).all()

            # `nanvar` and `nanstd` convert complex inputs to their
            # corresponding floating dtype
            if func is np.nanmean:
                assert out.dtype == array.dtype
            else:
                assert out.dtype == np.abs(array).dtype

    def test_empty(self):
        mat = np.zeros((0, 3))
        for f in self.nanfuncs:
            for axis in [0, None]:
                with warnings.catch_warnings(record=True) as w:
                    warnings.simplefilter('always')
                    assert_(np.isnan(f(mat, axis=axis)).all())
                    assert_(len(w) == 1)
                    assert_(issubclass(w[0].category, RuntimeWarning))
            for axis in [1]:
                with warnings.catch_warnings(record=True) as w:
                    warnings.simplefilter('always')
                    assert_equal(f(mat, axis=axis), np.zeros([]))
                    assert_(len(w) == 0)

    @pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
    def test_where(self, dtype):
        ar = np.arange(9).reshape(3, 3).astype(dtype)
        ar[0, :] = np.nan
        where = np.ones_like(ar, dtype=np.bool_)
        where[:, 0] = False

        for f, f_std in zip(self.nanfuncs, self.stdfuncs):
            reference = f_std(ar[where][2:])
            dtype_reference = dtype if f is np.nanmean else ar.real.dtype

            ret = f(ar, where=where)
            assert ret.dtype == dtype_reference
            np.testing.assert_allclose(ret, reference)


_TIME_UNITS = (
    "Y", "M", "W", "D", "h", "m", "s", "ms", "us", "ns", "ps", "fs", "as"
)

# All `inexact` + `timdelta64` type codes
_TYPE_CODES = list(np.typecodes["AllFloat"])
_TYPE_CODES += [f"m8[{unit}]" for unit in _TIME_UNITS]


class TestNanFunctions_Median:

    def test_mutation(self):
        # Check that passed array is not modified.
        ndat = _ndat.copy()
        np.nanmedian(ndat)
        assert_equal(ndat, _ndat)

    def test_keepdims(self):
        mat = np.eye(3)
        for axis in [None, 0, 1]:
            tgt = np.median(mat, axis=axis, out=None, overwrite_input=False)
            res = np.nanmedian(mat, axis=axis, out=None, overwrite_input=False)
            assert_(res.ndim == tgt.ndim)

        d = np.ones((3, 5, 7, 11))
        # Randomly set some elements to NaN:
        w = np.random.random((4, 200)) * np.array(d.shape)[:, None]
        w = w.astype(np.intp)
        d[tuple(w)] = np.nan
        with suppress_warnings() as sup:
            sup.filter(RuntimeWarning)
            res = np.nanmedian(d, axis=None, keepdims=True)
            assert_equal(res.shape, (1, 1, 1, 1))
            res = np.nanmedian(d, axis=(0, 1), keepdims=True)
            assert_equal(res.shape, (1, 1, 7, 11))
            res = np.nanmedian(d, axis=(0, 3), keepdims=True)
            assert_equal(res.shape, (1, 5, 7, 1))
            res = np.nanmedian(d, axis=(1,), keepdims=True)
            assert_equal(res.shape, (3, 1, 7, 11))
            res = np.nanmedian(d, axis=(0, 1, 2, 3), keepdims=True)
            assert_equal(res.shape, (1, 1, 1, 1))
            res = np.nanmedian(d, axis=(0, 1, 3), keepdims=True)
            assert_equal(res.shape, (1, 1, 7, 1))

    @pytest.mark.parametrize(
        argnames='axis',
        argvalues=[
            None,
            1,
            (1, ),
            (0, 1),
            (-3, -1),
        ]
    )
    @pytest.mark.filterwarnings("ignore:All-NaN slice:RuntimeWarning")
    def test_keepdims_out(self, axis):
        d = np.ones((3, 5, 7, 11))
        # Randomly set some elements to NaN:
        w = np.random.random((4, 200)) * np.array(d.shape)[:, None]
        w = w.astype(np.intp)
        d[tuple(w)] = np.nan
        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.nanmedian(d, axis=axis, keepdims=True, out=out)
        assert result is out
        assert_equal(result.shape, shape_out)

    def test_out(self):
        mat = np.random.rand(3, 3)
        nan_mat = np.insert(mat, [0, 2], np.nan, axis=1)
        resout = np.zeros(3)
        tgt = np.median(mat, axis=1)
        res = np.nanmedian(nan_mat, axis=1, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        # 0-d output:
        resout = np.zeros(())
        tgt = np.median(mat, axis=None)
        res = np.nanmedian(nan_mat, axis=None, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        res = np.nanmedian(nan_mat, axis=(0, 1), out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)

    def test_small_large(self):
        # test the small and large code paths, current cutoff 400 elements
        for s in [5, 20, 51, 200, 1000]:
            d = np.random.randn(4, s)
            # Randomly set some elements to NaN:
            w = np.random.randint(0, d.size, size=d.size // 5)
            d.ravel()[w] = np.nan
            d[:,0] = 1.  # ensure at least one good value
            # use normal median without nans to compare
            tgt = []
            for x in d:
                nonan = np.compress(~np.isnan(x), x)
                tgt.append(np.median(nonan, overwrite_input=True))

            assert_array_equal(np.nanmedian(d, axis=-1), tgt)

    def test_result_values(self):
            tgt = [np.median(d) for d in _rdat]
            res = np.nanmedian(_ndat, axis=1)
            assert_almost_equal(res, tgt)

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", _TYPE_CODES)
    def test_allnans(self, dtype, axis):
        mat = np.full((3, 3), np.nan).astype(dtype)
        with suppress_warnings() as sup:
            sup.record(RuntimeWarning)

            output = np.nanmedian(mat, axis=axis)
            assert output.dtype == mat.dtype
            assert np.isnan(output).all()

            if axis is None:
                assert_(len(sup.log) == 1)
            else:
                assert_(len(sup.log) == 3)

            # Check scalar
            scalar = np.array(np.nan).astype(dtype)[()]
            output_scalar = np.nanmedian(scalar)
            assert output_scalar.dtype == scalar.dtype
            assert np.isnan(output_scalar)

            if axis is None:
                assert_(len(sup.log) == 2)
            else:
                assert_(len(sup.log) == 4)

    def test_empty(self):
        mat = np.zeros((0, 3))
        for axis in [0, None]:
            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter('always')
                assert_(np.isnan(np.nanmedian(mat, axis=axis)).all())
                assert_(len(w) == 1)
                assert_(issubclass(w[0].category, RuntimeWarning))
        for axis in [1]:
            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter('always')
                assert_equal(np.nanmedian(mat, axis=axis), np.zeros([]))
                assert_(len(w) == 0)

    def test_scalar(self):
        assert_(np.nanmedian(0.) == 0.)

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

    def test_float_special(self):
        with suppress_warnings() as sup:
            sup.filter(RuntimeWarning)
            for inf in [np.inf, -np.inf]:
                a = np.array([[inf,  np.nan], [np.nan, np.nan]])
                assert_equal(np.nanmedian(a, axis=0), [inf,  np.nan])
                assert_equal(np.nanmedian(a, axis=1), [inf,  np.nan])
                assert_equal(np.nanmedian(a), inf)

                # minimum fill value check
                a = np.array([[np.nan, np.nan, inf],
                             [np.nan, np.nan, inf]])
                assert_equal(np.nanmedian(a), inf)
                assert_equal(np.nanmedian(a, axis=0), [np.nan, np.nan, inf])
                assert_equal(np.nanmedian(a, axis=1), inf)

                # no mask path
                a = np.array([[inf, inf], [inf, inf]])
                assert_equal(np.nanmedian(a, axis=1), inf)

                a = np.array([[inf, 7, -inf, -9],
                              [-10, np.nan, np.nan, 5],
                              [4, np.nan, np.nan, inf]],
                              dtype=np.float32)
                if inf > 0:
                    assert_equal(np.nanmedian(a, axis=0), [4., 7., -inf, 5.])
                    assert_equal(np.nanmedian(a), 4.5)
                else:
                    assert_equal(np.nanmedian(a, axis=0), [-10., 7., -inf, -9.])
                    assert_equal(np.nanmedian(a), -2.5)
                assert_equal(np.nanmedian(a, axis=-1), [-1., -2.5, inf])

                for i in range(0, 10):
                    for j in range(1, 10):
                        a = np.array([([np.nan] * i) + ([inf] * j)] * 2)
                        assert_equal(np.nanmedian(a), inf)
                        assert_equal(np.nanmedian(a, axis=1), inf)
                        assert_equal(np.nanmedian(a, axis=0),
                                     ([np.nan] * i) + [inf] * j)

                        a = np.array([([np.nan] * i) + ([-inf] * j)] * 2)
                        assert_equal(np.nanmedian(a), -inf)
                        assert_equal(np.nanmedian(a, axis=1), -inf)
                        assert_equal(np.nanmedian(a, axis=0),
                                     ([np.nan] * i) + [-inf] * j)


class TestNanFunctions_Percentile:

    def test_mutation(self):
        # Check that passed array is not modified.
        ndat = _ndat.copy()
        np.nanpercentile(ndat, 30)
        assert_equal(ndat, _ndat)

    def test_keepdims(self):
        mat = np.eye(3)
        for axis in [None, 0, 1]:
            tgt = np.percentile(mat, 70, axis=axis, out=None,
                                overwrite_input=False)
            res = np.nanpercentile(mat, 70, axis=axis, out=None,
                                   overwrite_input=False)
            assert_(res.ndim == tgt.ndim)

        d = np.ones((3, 5, 7, 11))
        # Randomly set some elements to NaN:
        w = np.random.random((4, 200)) * np.array(d.shape)[:, None]
        w = w.astype(np.intp)
        d[tuple(w)] = np.nan
        with suppress_warnings() as sup:
            sup.filter(RuntimeWarning)
            res = np.nanpercentile(d, 90, axis=None, keepdims=True)
            assert_equal(res.shape, (1, 1, 1, 1))
            res = np.nanpercentile(d, 90, axis=(0, 1), keepdims=True)
            assert_equal(res.shape, (1, 1, 7, 11))
            res = np.nanpercentile(d, 90, axis=(0, 3), keepdims=True)
            assert_equal(res.shape, (1, 5, 7, 1))
            res = np.nanpercentile(d, 90, axis=(1,), keepdims=True)
            assert_equal(res.shape, (3, 1, 7, 11))
            res = np.nanpercentile(d, 90, axis=(0, 1, 2, 3), keepdims=True)
            assert_equal(res.shape, (1, 1, 1, 1))
            res = np.nanpercentile(d, 90, axis=(0, 1, 3), keepdims=True)
            assert_equal(res.shape, (1, 1, 7, 1))

    @pytest.mark.parametrize('q', [7, [1, 7]])
    @pytest.mark.parametrize(
        argnames='axis',
        argvalues=[
            None,
            1,
            (1,),
            (0, 1),
            (-3, -1),
        ]
    )
    @pytest.mark.filterwarnings("ignore:All-NaN slice:RuntimeWarning")
    def test_keepdims_out(self, q, axis):
        d = np.ones((3, 5, 7, 11))
        # Randomly set some elements to NaN:
        w = np.random.random((4, 200)) * np.array(d.shape)[:, None]
        w = w.astype(np.intp)
        d[tuple(w)] = np.nan
        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.nanpercentile(d, q, axis=axis, keepdims=True, out=out)
        assert result is out
        assert_equal(result.shape, shape_out)

    def test_out(self):
        mat = np.random.rand(3, 3)
        nan_mat = np.insert(mat, [0, 2], np.nan, axis=1)
        resout = np.zeros(3)
        tgt = np.percentile(mat, 42, axis=1)
        res = np.nanpercentile(nan_mat, 42, axis=1, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        # 0-d output:
        resout = np.zeros(())
        tgt = np.percentile(mat, 42, axis=None)
        res = np.nanpercentile(nan_mat, 42, axis=None, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        res = np.nanpercentile(nan_mat, 42, axis=(0, 1), out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)

    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.nanpercentile, 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.nanpercentile, 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.nanpercentile, arr_c, 0.5)

    def test_result_values(self):
        tgt = [np.percentile(d, 28) for d in _rdat]
        res = np.nanpercentile(_ndat, 28, axis=1)
        assert_almost_equal(res, tgt)
        # Transpose the array to fit the output convention of numpy.percentile
        tgt = np.transpose([np.percentile(d, (28, 98)) for d in _rdat])
        res = np.nanpercentile(_ndat, (28, 98), axis=1)
        assert_almost_equal(res, tgt)

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", np.typecodes["Float"])
    @pytest.mark.parametrize("array", [
        np.array(np.nan),
        np.full((3, 3), np.nan),
    ], ids=["0d", "2d"])
    def test_allnans(self, axis, dtype, array):
        if axis is not None and array.ndim == 0:
            pytest.skip(f"`axis != None` not supported for 0d arrays")

        array = array.astype(dtype)
        with pytest.warns(RuntimeWarning, match="All-NaN slice encountered"):
            out = np.nanpercentile(array, 60, axis=axis)
        assert np.isnan(out).all()
        assert out.dtype == array.dtype

    def test_empty(self):
        mat = np.zeros((0, 3))
        for axis in [0, None]:
            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter('always')
                assert_(np.isnan(np.nanpercentile(mat, 40, axis=axis)).all())
                assert_(len(w) == 1)
                assert_(issubclass(w[0].category, RuntimeWarning))
        for axis in [1]:
            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter('always')
                assert_equal(np.nanpercentile(mat, 40, axis=axis), np.zeros([]))
                assert_(len(w) == 0)

    def test_scalar(self):
        assert_equal(np.nanpercentile(0., 100), 0.)
        a = np.arange(6)
        r = np.nanpercentile(a, 50, axis=0)
        assert_equal(r, 2.5)
        assert_(np.isscalar(r))

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

    def test_multiple_percentiles(self):
        perc = [50, 100]
        mat = np.ones((4, 3))
        nan_mat = np.nan * mat
        # For checking consistency in higher dimensional case
        large_mat = np.ones((3, 4, 5))
        large_mat[:, 0:2:4, :] = 0
        large_mat[:, :, 3:] *= 2
        for axis in [None, 0, 1]:
            for keepdim in [False, True]:
                with suppress_warnings() as sup:
                    sup.filter(RuntimeWarning, "All-NaN slice encountered")
                    val = np.percentile(mat, perc, axis=axis, keepdims=keepdim)
                    nan_val = np.nanpercentile(nan_mat, perc, axis=axis,
                                               keepdims=keepdim)
                    assert_equal(nan_val.shape, val.shape)

                    val = np.percentile(large_mat, perc, axis=axis,
                                        keepdims=keepdim)
                    nan_val = np.nanpercentile(large_mat, perc, axis=axis,
                                               keepdims=keepdim)
                    assert_equal(nan_val, val)

        megamat = np.ones((3, 4, 5, 6))
        assert_equal(np.nanpercentile(megamat, perc, axis=(1, 2)).shape, (2, 3, 6))


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

    def test_regression(self):
        ar = np.arange(24).reshape(2, 3, 4).astype(float)
        ar[0][1] = np.nan

        assert_equal(np.nanquantile(ar, q=0.5), np.nanpercentile(ar, q=50))
        assert_equal(np.nanquantile(ar, q=0.5, axis=0),
                     np.nanpercentile(ar, q=50, axis=0))
        assert_equal(np.nanquantile(ar, q=0.5, axis=1),
                     np.nanpercentile(ar, q=50, axis=1))
        assert_equal(np.nanquantile(ar, q=[0.5], axis=1),
                     np.nanpercentile(ar, q=[50], axis=1))
        assert_equal(np.nanquantile(ar, q=[0.25, 0.5, 0.75], axis=1),
                     np.nanpercentile(ar, q=[25, 50, 75], axis=1))

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

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

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

    @pytest.mark.parametrize("axis", [None, 0, 1])
    @pytest.mark.parametrize("dtype", np.typecodes["Float"])
    @pytest.mark.parametrize("array", [
        np.array(np.nan),
        np.full((3, 3), np.nan),
    ], ids=["0d", "2d"])
    def test_allnans(self, axis, dtype, array):
        if axis is not None and array.ndim == 0:
            pytest.skip(f"`axis != None` not supported for 0d arrays")

        array = array.astype(dtype)
        with pytest.warns(RuntimeWarning, match="All-NaN slice encountered"):
            out = np.nanquantile(array, 1, axis=axis)
        assert np.isnan(out).all()
        assert out.dtype == array.dtype

@pytest.mark.parametrize("arr, expected", [
    # array of floats with some nans
    (np.array([np.nan, 5.0, np.nan, np.inf]),
     np.array([False, True, False, True])),
    # int64 array that can't possibly have nans
    (np.array([1, 5, 7, 9], dtype=np.int64),
     True),
    # bool array that can't possibly have nans
    (np.array([False, True, False, True]),
     True),
    # 2-D complex array with nans
    (np.array([[np.nan, 5.0],
               [np.nan, np.inf]], dtype=np.complex64),
     np.array([[False, True],
               [False, True]])),
    ])
def test__nan_mask(arr, expected):
    for out in [None, np.empty(arr.shape, dtype=np.bool_)]:
        actual = _nan_mask(arr, out=out)
        assert_equal(actual, expected)
        # the above won't distinguish between True proper
        # and an array of True values; we want True proper
        # for types that can't possibly contain NaN
        if type(expected) is not np.ndarray:
            assert actual is True


def test__replace_nan():
    """ Test that _replace_nan returns the original array if there are no
    NaNs, not a copy.
    """
    for dtype in [np.bool_, np.int32, np.int64]:
        arr = np.array([0, 1], dtype=dtype)
        result, mask = _replace_nan(arr, 0)
        assert mask is None
        # do not make a copy if there are no nans
        assert result is arr

    for dtype in [np.float32, np.float64]:
        arr = np.array([0, 1], dtype=dtype)
        result, mask = _replace_nan(arr, 2)
        assert (mask == False).all()
        # mask is not None, so we make a copy
        assert result is not arr
        assert_equal(result, arr)

        arr_nan = np.array([0, 1, np.nan], dtype=dtype)
        result_nan, mask_nan = _replace_nan(arr_nan, 2)
        assert_equal(mask_nan, np.array([False, False, True]))
        assert result_nan is not arr_nan
        assert_equal(result_nan, np.array([0, 1, 2]))
        assert np.isnan(arr_nan[-1])