python-numpy 1:1.12.1-3 / usr / lib / python2.7 / dist-packages / numpy / core / tests / test_numeric.py

from __future__ import division, absolute_import, print_function

import sys
import warnings
import itertools
import platform
from decimal import Decimal

import numpy as np
from numpy.core import umath
from numpy.random import rand, randint, randn
from numpy.testing import (
    TestCase, run_module_suite, assert_, assert_equal, assert_raises,
    assert_raises_regex, assert_array_equal, assert_almost_equal,
    assert_array_almost_equal, dec, HAS_REFCOUNT, suppress_warnings
)


class TestResize(TestCase):
    def test_copies(self):
        A = np.array([[1, 2], [3, 4]])
        Ar1 = np.array([[1, 2, 3, 4], [1, 2, 3, 4]])
        assert_equal(np.resize(A, (2, 4)), Ar1)

        Ar2 = np.array([[1, 2], [3, 4], [1, 2], [3, 4]])
        assert_equal(np.resize(A, (4, 2)), Ar2)

        Ar3 = np.array([[1, 2, 3], [4, 1, 2], [3, 4, 1], [2, 3, 4]])
        assert_equal(np.resize(A, (4, 3)), Ar3)

    def test_zeroresize(self):
        A = np.array([[1, 2], [3, 4]])
        Ar = np.resize(A, (0,))
        assert_array_equal(Ar, np.array([]))
        assert_equal(A.dtype, Ar.dtype)

    def test_reshape_from_zero(self):
        # See also gh-6740
        A = np.zeros(0, dtype=[('a', np.float32, 1)])
        Ar = np.resize(A, (2, 1))
        assert_array_equal(Ar, np.zeros((2, 1), Ar.dtype))
        assert_equal(A.dtype, Ar.dtype)


class TestNonarrayArgs(TestCase):
    # check that non-array arguments to functions wrap them in arrays
    def test_choose(self):
        choices = [[0, 1, 2],
                   [3, 4, 5],
                   [5, 6, 7]]
        tgt = [5, 1, 5]
        a = [2, 0, 1]

        out = np.choose(a, choices)
        assert_equal(out, tgt)

    def test_clip(self):
        arr = [-1, 5, 2, 3, 10, -4, -9]
        out = np.clip(arr, 2, 7)
        tgt = [2, 5, 2, 3, 7, 2, 2]
        assert_equal(out, tgt)

    def test_compress(self):
        arr = [[0, 1, 2, 3, 4],
               [5, 6, 7, 8, 9]]
        tgt = [[5, 6, 7, 8, 9]]
        out = np.compress([0, 1], arr, axis=0)
        assert_equal(out, tgt)

    def test_count_nonzero(self):
        arr = [[0, 1, 7, 0, 0],
               [3, 0, 0, 2, 19]]
        tgt = np.array([2, 3])
        out = np.count_nonzero(arr, axis=1)
        assert_equal(out, tgt)

    def test_cumproduct(self):
        A = [[1, 2, 3], [4, 5, 6]]
        assert_(np.all(np.cumproduct(A) == np.array([1, 2, 6, 24, 120, 720])))

    def test_diagonal(self):
        a = [[0, 1, 2, 3],
             [4, 5, 6, 7],
             [8, 9, 10, 11]]
        out = np.diagonal(a)
        tgt = [0, 5, 10]

        assert_equal(out, tgt)

    def test_mean(self):
        A = [[1, 2, 3], [4, 5, 6]]
        assert_(np.mean(A) == 3.5)
        assert_(np.all(np.mean(A, 0) == np.array([2.5, 3.5, 4.5])))
        assert_(np.all(np.mean(A, 1) == np.array([2., 5.])))

        with warnings.catch_warnings(record=True) as w:
            warnings.filterwarnings('always', '', RuntimeWarning)
            assert_(np.isnan(np.mean([])))
            assert_(w[0].category is RuntimeWarning)

    def test_ptp(self):
        a = [3, 4, 5, 10, -3, -5, 6.0]
        assert_equal(np.ptp(a, axis=0), 15.0)

    def test_prod(self):
        arr = [[1, 2, 3, 4],
               [5, 6, 7, 9],
               [10, 3, 4, 5]]
        tgt = [24, 1890, 600]

        assert_equal(np.prod(arr, axis=-1), tgt)

    def test_ravel(self):
        a = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
        tgt = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
        assert_equal(np.ravel(a), tgt)

    def test_repeat(self):
        a = [1, 2, 3]
        tgt = [1, 1, 2, 2, 3, 3]

        out = np.repeat(a, 2)
        assert_equal(out, tgt)

    def test_reshape(self):
        arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
        tgt = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]]
        assert_equal(np.reshape(arr, (2, 6)), tgt)

    def test_round(self):
        arr = [1.56, 72.54, 6.35, 3.25]
        tgt = [1.6, 72.5, 6.4, 3.2]
        assert_equal(np.around(arr, decimals=1), tgt)

    def test_searchsorted(self):
        arr = [-8, -5, -1, 3, 6, 10]
        out = np.searchsorted(arr, 0)
        assert_equal(out, 3)

    def test_size(self):
        A = [[1, 2, 3], [4, 5, 6]]
        assert_(np.size(A) == 6)
        assert_(np.size(A, 0) == 2)
        assert_(np.size(A, 1) == 3)

    def test_squeeze(self):
        A = [[[1, 1, 1], [2, 2, 2], [3, 3, 3]]]
        assert_(np.squeeze(A).shape == (3, 3))

    def test_std(self):
        A = [[1, 2, 3], [4, 5, 6]]
        assert_almost_equal(np.std(A), 1.707825127659933)
        assert_almost_equal(np.std(A, 0), np.array([1.5, 1.5, 1.5]))
        assert_almost_equal(np.std(A, 1), np.array([0.81649658, 0.81649658]))

        with warnings.catch_warnings(record=True) as w:
            warnings.filterwarnings('always', '', RuntimeWarning)
            assert_(np.isnan(np.std([])))
            assert_(w[0].category is RuntimeWarning)

    def test_swapaxes(self):
        tgt = [[[0, 4], [2, 6]], [[1, 5], [3, 7]]]
        a = [[[0, 1], [2, 3]], [[4, 5], [6, 7]]]
        out = np.swapaxes(a, 0, 2)
        assert_equal(out, tgt)

    def test_sum(self):
        m = [[1, 2, 3],
             [4, 5, 6],
             [7, 8, 9]]
        tgt = [[6], [15], [24]]
        out = np.sum(m, axis=1, keepdims=True)

        assert_equal(tgt, out)

    def test_take(self):
        tgt = [2, 3, 5]
        indices = [1, 2, 4]
        a = [1, 2, 3, 4, 5]

        out = np.take(a, indices)
        assert_equal(out, tgt)

    def test_trace(self):
        c = [[1, 2], [3, 4], [5, 6]]
        assert_equal(np.trace(c), 5)

    def test_transpose(self):
        arr = [[1, 2], [3, 4], [5, 6]]
        tgt = [[1, 3, 5], [2, 4, 6]]
        assert_equal(np.transpose(arr, (1, 0)), tgt)

    def test_var(self):
        A = [[1, 2, 3], [4, 5, 6]]
        assert_almost_equal(np.var(A), 2.9166666666666665)
        assert_almost_equal(np.var(A, 0), np.array([2.25, 2.25, 2.25]))
        assert_almost_equal(np.var(A, 1), np.array([0.66666667, 0.66666667]))

        with warnings.catch_warnings(record=True) as w:
            warnings.filterwarnings('always', '', RuntimeWarning)
            assert_(np.isnan(np.var([])))
            assert_(w[0].category is RuntimeWarning)


class TestBoolScalar(TestCase):
    def test_logical(self):
        f = np.False_
        t = np.True_
        s = "xyz"
        self.assertTrue((t and s) is s)
        self.assertTrue((f and s) is f)

    def test_bitwise_or(self):
        f = np.False_
        t = np.True_
        self.assertTrue((t | t) is t)
        self.assertTrue((f | t) is t)
        self.assertTrue((t | f) is t)
        self.assertTrue((f | f) is f)

    def test_bitwise_and(self):
        f = np.False_
        t = np.True_
        self.assertTrue((t & t) is t)
        self.assertTrue((f & t) is f)
        self.assertTrue((t & f) is f)
        self.assertTrue((f & f) is f)

    def test_bitwise_xor(self):
        f = np.False_
        t = np.True_
        self.assertTrue((t ^ t) is f)
        self.assertTrue((f ^ t) is t)
        self.assertTrue((t ^ f) is t)
        self.assertTrue((f ^ f) is f)


class TestBoolArray(TestCase):
    def setUp(self):
        # offset for simd tests
        self.t = np.array([True] * 41, dtype=np.bool)[1::]
        self.f = np.array([False] * 41, dtype=np.bool)[1::]
        self.o = np.array([False] * 42, dtype=np.bool)[2::]
        self.nm = self.f.copy()
        self.im = self.t.copy()
        self.nm[3] = True
        self.nm[-2] = True
        self.im[3] = False
        self.im[-2] = False

    def test_all_any(self):
        self.assertTrue(self.t.all())
        self.assertTrue(self.t.any())
        self.assertFalse(self.f.all())
        self.assertFalse(self.f.any())
        self.assertTrue(self.nm.any())
        self.assertTrue(self.im.any())
        self.assertFalse(self.nm.all())
        self.assertFalse(self.im.all())
        # check bad element in all positions
        for i in range(256 - 7):
            d = np.array([False] * 256, dtype=np.bool)[7::]
            d[i] = True
            self.assertTrue(np.any(d))
            e = np.array([True] * 256, dtype=np.bool)[7::]
            e[i] = False
            self.assertFalse(np.all(e))
            assert_array_equal(e, ~d)
        # big array test for blocked libc loops
        for i in list(range(9, 6000, 507)) + [7764, 90021, -10]:
            d = np.array([False] * 100043, dtype=np.bool)
            d[i] = True
            self.assertTrue(np.any(d), msg="%r" % i)
            e = np.array([True] * 100043, dtype=np.bool)
            e[i] = False
            self.assertFalse(np.all(e), msg="%r" % i)

    def test_logical_not_abs(self):
        assert_array_equal(~self.t, self.f)
        assert_array_equal(np.abs(~self.t), self.f)
        assert_array_equal(np.abs(~self.f), self.t)
        assert_array_equal(np.abs(self.f), self.f)
        assert_array_equal(~np.abs(self.f), self.t)
        assert_array_equal(~np.abs(self.t), self.f)
        assert_array_equal(np.abs(~self.nm), self.im)
        np.logical_not(self.t, out=self.o)
        assert_array_equal(self.o, self.f)
        np.abs(self.t, out=self.o)
        assert_array_equal(self.o, self.t)

    def test_logical_and_or_xor(self):
        assert_array_equal(self.t | self.t, self.t)
        assert_array_equal(self.f | self.f, self.f)
        assert_array_equal(self.t | self.f, self.t)
        assert_array_equal(self.f | self.t, self.t)
        np.logical_or(self.t, self.t, out=self.o)
        assert_array_equal(self.o, self.t)
        assert_array_equal(self.t & self.t, self.t)
        assert_array_equal(self.f & self.f, self.f)
        assert_array_equal(self.t & self.f, self.f)
        assert_array_equal(self.f & self.t, self.f)
        np.logical_and(self.t, self.t, out=self.o)
        assert_array_equal(self.o, self.t)
        assert_array_equal(self.t ^ self.t, self.f)
        assert_array_equal(self.f ^ self.f, self.f)
        assert_array_equal(self.t ^ self.f, self.t)
        assert_array_equal(self.f ^ self.t, self.t)
        np.logical_xor(self.t, self.t, out=self.o)
        assert_array_equal(self.o, self.f)

        assert_array_equal(self.nm & self.t, self.nm)
        assert_array_equal(self.im & self.f, False)
        assert_array_equal(self.nm & True, self.nm)
        assert_array_equal(self.im & False, self.f)
        assert_array_equal(self.nm | self.t, self.t)
        assert_array_equal(self.im | self.f, self.im)
        assert_array_equal(self.nm | True, self.t)
        assert_array_equal(self.im | False, self.im)
        assert_array_equal(self.nm ^ self.t, self.im)
        assert_array_equal(self.im ^ self.f, self.im)
        assert_array_equal(self.nm ^ True, self.im)
        assert_array_equal(self.im ^ False, self.im)


class TestBoolCmp(TestCase):
    def setUp(self):
        self.f = np.ones(256, dtype=np.float32)
        self.ef = np.ones(self.f.size, dtype=np.bool)
        self.d = np.ones(128, dtype=np.float64)
        self.ed = np.ones(self.d.size, dtype=np.bool)
        # generate values for all permutation of 256bit simd vectors
        s = 0
        for i in range(32):
            self.f[s:s+8] = [i & 2**x for x in range(8)]
            self.ef[s:s+8] = [(i & 2**x) != 0 for x in range(8)]
            s += 8
        s = 0
        for i in range(16):
            self.d[s:s+4] = [i & 2**x for x in range(4)]
            self.ed[s:s+4] = [(i & 2**x) != 0 for x in range(4)]
            s += 4

        self.nf = self.f.copy()
        self.nd = self.d.copy()
        self.nf[self.ef] = np.nan
        self.nd[self.ed] = np.nan

        self.inff = self.f.copy()
        self.infd = self.d.copy()
        self.inff[::3][self.ef[::3]] = np.inf
        self.infd[::3][self.ed[::3]] = np.inf
        self.inff[1::3][self.ef[1::3]] = -np.inf
        self.infd[1::3][self.ed[1::3]] = -np.inf
        self.inff[2::3][self.ef[2::3]] = np.nan
        self.infd[2::3][self.ed[2::3]] = np.nan
        self.efnonan = self.ef.copy()
        self.efnonan[2::3] = False
        self.ednonan = self.ed.copy()
        self.ednonan[2::3] = False

        self.signf = self.f.copy()
        self.signd = self.d.copy()
        self.signf[self.ef] *= -1.
        self.signd[self.ed] *= -1.
        self.signf[1::6][self.ef[1::6]] = -np.inf
        self.signd[1::6][self.ed[1::6]] = -np.inf
        self.signf[3::6][self.ef[3::6]] = -np.nan
        self.signd[3::6][self.ed[3::6]] = -np.nan
        self.signf[4::6][self.ef[4::6]] = -0.
        self.signd[4::6][self.ed[4::6]] = -0.

    def test_float(self):
        # offset for alignment test
        for i in range(4):
            assert_array_equal(self.f[i:] > 0, self.ef[i:])
            assert_array_equal(self.f[i:] - 1 >= 0, self.ef[i:])
            assert_array_equal(self.f[i:] == 0, ~self.ef[i:])
            assert_array_equal(-self.f[i:] < 0, self.ef[i:])
            assert_array_equal(-self.f[i:] + 1 <= 0, self.ef[i:])
            r = self.f[i:] != 0
            assert_array_equal(r, self.ef[i:])
            r2 = self.f[i:] != np.zeros_like(self.f[i:])
            r3 = 0 != self.f[i:]
            assert_array_equal(r, r2)
            assert_array_equal(r, r3)
            # check bool == 0x1
            assert_array_equal(r.view(np.int8), r.astype(np.int8))
            assert_array_equal(r2.view(np.int8), r2.astype(np.int8))
            assert_array_equal(r3.view(np.int8), r3.astype(np.int8))

            # isnan on amd64 takes the same code path
            assert_array_equal(np.isnan(self.nf[i:]), self.ef[i:])
            assert_array_equal(np.isfinite(self.nf[i:]), ~self.ef[i:])
            assert_array_equal(np.isfinite(self.inff[i:]), ~self.ef[i:])
            assert_array_equal(np.isinf(self.inff[i:]), self.efnonan[i:])
            assert_array_equal(np.signbit(self.signf[i:]), self.ef[i:])

    def test_double(self):
        # offset for alignment test
        for i in range(2):
            assert_array_equal(self.d[i:] > 0, self.ed[i:])
            assert_array_equal(self.d[i:] - 1 >= 0, self.ed[i:])
            assert_array_equal(self.d[i:] == 0, ~self.ed[i:])
            assert_array_equal(-self.d[i:] < 0, self.ed[i:])
            assert_array_equal(-self.d[i:] + 1 <= 0, self.ed[i:])
            r = self.d[i:] != 0
            assert_array_equal(r, self.ed[i:])
            r2 = self.d[i:] != np.zeros_like(self.d[i:])
            r3 = 0 != self.d[i:]
            assert_array_equal(r, r2)
            assert_array_equal(r, r3)
            # check bool == 0x1
            assert_array_equal(r.view(np.int8), r.astype(np.int8))
            assert_array_equal(r2.view(np.int8), r2.astype(np.int8))
            assert_array_equal(r3.view(np.int8), r3.astype(np.int8))

            # isnan on amd64 takes the same code path
            assert_array_equal(np.isnan(self.nd[i:]), self.ed[i:])
            assert_array_equal(np.isfinite(self.nd[i:]), ~self.ed[i:])
            assert_array_equal(np.isfinite(self.infd[i:]), ~self.ed[i:])
            assert_array_equal(np.isinf(self.infd[i:]), self.ednonan[i:])
            assert_array_equal(np.signbit(self.signd[i:]), self.ed[i:])


class TestSeterr(TestCase):
    def test_default(self):
        err = np.geterr()
        self.assertEqual(err, dict(
            divide='warn',
            invalid='warn',
            over='warn',
            under='ignore',
        ))

    def test_set(self):
        with np.errstate():
            err = np.seterr()
            old = np.seterr(divide='print')
            self.assertTrue(err == old)
            new = np.seterr()
            self.assertTrue(new['divide'] == 'print')
            np.seterr(over='raise')
            self.assertTrue(np.geterr()['over'] == 'raise')
            self.assertTrue(new['divide'] == 'print')
            np.seterr(**old)
            self.assertTrue(np.geterr() == old)

    @dec.skipif(platform.machine() == "armv5tel", "See gh-413.")
    def test_divide_err(self):
        with np.errstate(divide='raise'):
            try:
                np.array([1.]) / np.array([0.])
            except FloatingPointError:
                pass
            else:
                self.fail()
            np.seterr(divide='ignore')
            np.array([1.]) / np.array([0.])

    def test_errobj(self):
        olderrobj = np.geterrobj()
        self.called = 0
        try:
            with warnings.catch_warnings(record=True) as w:
                warnings.simplefilter("always")
                with np.errstate(divide='warn'):
                    np.seterrobj([20000, 1, None])
                    np.array([1.]) / np.array([0.])
                    self.assertEqual(len(w), 1)

            def log_err(*args):
                self.called += 1
                extobj_err = args
                assert_(len(extobj_err) == 2)
                assert_("divide" in extobj_err[0])

            with np.errstate(divide='ignore'):
                np.seterrobj([20000, 3, log_err])
                np.array([1.]) / np.array([0.])
            self.assertEqual(self.called, 1)

            np.seterrobj(olderrobj)
            with np.errstate(divide='ignore'):
                np.divide(1., 0., extobj=[20000, 3, log_err])
            self.assertEqual(self.called, 2)
        finally:
            np.seterrobj(olderrobj)
            del self.called

    def test_errobj_noerrmask(self):
        # errmask = 0 has a special code path for the default
        olderrobj = np.geterrobj()
        try:
            # set errobj to something non default
            np.seterrobj([umath.UFUNC_BUFSIZE_DEFAULT,
                         umath.ERR_DEFAULT + 1, None])
            # call a ufunc
            np.isnan(np.array([6]))
            # same with the default, lots of times to get rid of possible
            # pre-existing stack in the code
            for i in range(10000):
                np.seterrobj([umath.UFUNC_BUFSIZE_DEFAULT, umath.ERR_DEFAULT,
                             None])
            np.isnan(np.array([6]))
        finally:
            np.seterrobj(olderrobj)


class TestFloatExceptions(TestCase):
    def assert_raises_fpe(self, fpeerr, flop, x, y):
        ftype = type(x)
        try:
            flop(x, y)
            assert_(False,
                    "Type %s did not raise fpe error '%s'." % (ftype, fpeerr))
        except FloatingPointError as exc:
            assert_(str(exc).find(fpeerr) >= 0,
                    "Type %s raised wrong fpe error '%s'." % (ftype, exc))

    def assert_op_raises_fpe(self, fpeerr, flop, sc1, sc2):
        # Check that fpe exception is raised.
        #
        # Given a floating operation `flop` and two scalar values, check that
        # the operation raises the floating point exception specified by
        # `fpeerr`. Tests all variants with 0-d array scalars as well.

        self.assert_raises_fpe(fpeerr, flop, sc1, sc2)
        self.assert_raises_fpe(fpeerr, flop, sc1[()], sc2)
        self.assert_raises_fpe(fpeerr, flop, sc1, sc2[()])
        self.assert_raises_fpe(fpeerr, flop, sc1[()], sc2[()])

    @dec.knownfailureif(True, "See ticket #2350")
    def test_floating_exceptions(self):
        # Test basic arithmetic function errors
        with np.errstate(all='raise'):
            # Test for all real and complex float types
            for typecode in np.typecodes['AllFloat']:
                ftype = np.obj2sctype(typecode)
                if np.dtype(ftype).kind == 'f':
                    # Get some extreme values for the type
                    fi = np.finfo(ftype)
                    ft_tiny = fi.tiny
                    ft_max = fi.max
                    ft_eps = fi.eps
                    underflow = 'underflow'
                    divbyzero = 'divide by zero'
                else:
                    # 'c', complex, corresponding real dtype
                    rtype = type(ftype(0).real)
                    fi = np.finfo(rtype)
                    ft_tiny = ftype(fi.tiny)
                    ft_max = ftype(fi.max)
                    ft_eps = ftype(fi.eps)
                    # The complex types raise different exceptions
                    underflow = ''
                    divbyzero = ''
                overflow = 'overflow'
                invalid = 'invalid'

                self.assert_raises_fpe(underflow,
                                       lambda a, b: a/b, ft_tiny, ft_max)
                self.assert_raises_fpe(underflow,
                                       lambda a, b: a*b, ft_tiny, ft_tiny)
                self.assert_raises_fpe(overflow,
                                       lambda a, b: a*b, ft_max, ftype(2))
                self.assert_raises_fpe(overflow,
                                       lambda a, b: a/b, ft_max, ftype(0.5))
                self.assert_raises_fpe(overflow,
                                       lambda a, b: a+b, ft_max, ft_max*ft_eps)
                self.assert_raises_fpe(overflow,
                                       lambda a, b: a-b, -ft_max, ft_max*ft_eps)
                self.assert_raises_fpe(overflow,
                                       np.power, ftype(2), ftype(2**fi.nexp))
                self.assert_raises_fpe(divbyzero,
                                       lambda a, b: a/b, ftype(1), ftype(0))
                self.assert_raises_fpe(invalid,
                                       lambda a, b: a/b, ftype(np.inf), ftype(np.inf))
                self.assert_raises_fpe(invalid,
                                       lambda a, b: a/b, ftype(0), ftype(0))
                self.assert_raises_fpe(invalid,
                                       lambda a, b: a-b, ftype(np.inf), ftype(np.inf))
                self.assert_raises_fpe(invalid,
                                       lambda a, b: a+b, ftype(np.inf), ftype(-np.inf))
                self.assert_raises_fpe(invalid,
                                       lambda a, b: a*b, ftype(0), ftype(np.inf))

    def test_warnings(self):
        # test warning code path
        with warnings.catch_warnings(record=True) as w:
            warnings.simplefilter("always")
            with np.errstate(all="warn"):
                np.divide(1, 0.)
                self.assertEqual(len(w), 1)
                self.assertTrue("divide by zero" in str(w[0].message))
                np.array(1e300) * np.array(1e300)
                self.assertEqual(len(w), 2)
                self.assertTrue("overflow" in str(w[-1].message))
                np.array(np.inf) - np.array(np.inf)
                self.assertEqual(len(w), 3)
                self.assertTrue("invalid value" in str(w[-1].message))
                np.array(1e-300) * np.array(1e-300)
                self.assertEqual(len(w), 4)
                self.assertTrue("underflow" in str(w[-1].message))


class TestTypes(TestCase):
    def check_promotion_cases(self, promote_func):
        # tests that the scalars get coerced correctly.
        b = np.bool_(0)
        i8, i16, i32, i64 = np.int8(0), np.int16(0), np.int32(0), np.int64(0)
        u8, u16, u32, u64 = np.uint8(0), np.uint16(0), np.uint32(0), np.uint64(0)
        f32, f64, fld = np.float32(0), np.float64(0), np.longdouble(0)
        c64, c128, cld = np.complex64(0), np.complex128(0), np.clongdouble(0)

        # coercion within the same kind
        assert_equal(promote_func(i8, i16), np.dtype(np.int16))
        assert_equal(promote_func(i32, i8), np.dtype(np.int32))
        assert_equal(promote_func(i16, i64), np.dtype(np.int64))
        assert_equal(promote_func(u8, u32), np.dtype(np.uint32))
        assert_equal(promote_func(f32, f64), np.dtype(np.float64))
        assert_equal(promote_func(fld, f32), np.dtype(np.longdouble))
        assert_equal(promote_func(f64, fld), np.dtype(np.longdouble))
        assert_equal(promote_func(c128, c64), np.dtype(np.complex128))
        assert_equal(promote_func(cld, c128), np.dtype(np.clongdouble))
        assert_equal(promote_func(c64, fld), np.dtype(np.clongdouble))

        # coercion between kinds
        assert_equal(promote_func(b, i32), np.dtype(np.int32))
        assert_equal(promote_func(b, u8), np.dtype(np.uint8))
        assert_equal(promote_func(i8, u8), np.dtype(np.int16))
        assert_equal(promote_func(u8, i32), np.dtype(np.int32))
        assert_equal(promote_func(i64, u32), np.dtype(np.int64))
        assert_equal(promote_func(u64, i32), np.dtype(np.float64))
        assert_equal(promote_func(i32, f32), np.dtype(np.float64))
        assert_equal(promote_func(i64, f32), np.dtype(np.float64))
        assert_equal(promote_func(f32, i16), np.dtype(np.float32))
        assert_equal(promote_func(f32, u32), np.dtype(np.float64))
        assert_equal(promote_func(f32, c64), np.dtype(np.complex64))
        assert_equal(promote_func(c128, f32), np.dtype(np.complex128))
        assert_equal(promote_func(cld, f64), np.dtype(np.clongdouble))

        # coercion between scalars and 1-D arrays
        assert_equal(promote_func(np.array([b]), i8), np.dtype(np.int8))
        assert_equal(promote_func(np.array([b]), u8), np.dtype(np.uint8))
        assert_equal(promote_func(np.array([b]), i32), np.dtype(np.int32))
        assert_equal(promote_func(np.array([b]), u32), np.dtype(np.uint32))
        assert_equal(promote_func(np.array([i8]), i64), np.dtype(np.int8))
        assert_equal(promote_func(u64, np.array([i32])), np.dtype(np.int32))
        assert_equal(promote_func(i64, np.array([u32])), np.dtype(np.uint32))
        assert_equal(promote_func(np.int32(-1), np.array([u64])),
                     np.dtype(np.float64))
        assert_equal(promote_func(f64, np.array([f32])), np.dtype(np.float32))
        assert_equal(promote_func(fld, np.array([f32])), np.dtype(np.float32))
        assert_equal(promote_func(np.array([f64]), fld), np.dtype(np.float64))
        assert_equal(promote_func(fld, np.array([c64])),
                     np.dtype(np.complex64))
        assert_equal(promote_func(c64, np.array([f64])),
                     np.dtype(np.complex128))
        assert_equal(promote_func(np.complex64(3j), np.array([f64])),
                     np.dtype(np.complex128))

        # coercion between scalars and 1-D arrays, where
        # the scalar has greater kind than the array
        assert_equal(promote_func(np.array([b]), f64), np.dtype(np.float64))
        assert_equal(promote_func(np.array([b]), i64), np.dtype(np.int64))
        assert_equal(promote_func(np.array([b]), u64), np.dtype(np.uint64))
        assert_equal(promote_func(np.array([i8]), f64), np.dtype(np.float64))
        assert_equal(promote_func(np.array([u16]), f64), np.dtype(np.float64))

        # uint and int are treated as the same "kind" for
        # the purposes of array-scalar promotion.
        assert_equal(promote_func(np.array([u16]), i32), np.dtype(np.uint16))

        # float and complex are treated as the same "kind" for
        # the purposes of array-scalar promotion, so that you can do
        # (0j + float32array) to get a complex64 array instead of
        # a complex128 array.
        assert_equal(promote_func(np.array([f32]), c128),
                     np.dtype(np.complex64))

    def test_coercion(self):
        def res_type(a, b):
            return np.add(a, b).dtype

        self.check_promotion_cases(res_type)

        # Use-case: float/complex scalar * bool/int8 array
        #           shouldn't narrow the float/complex type
        for a in [np.array([True, False]), np.array([-3, 12], dtype=np.int8)]:
            b = 1.234 * a
            assert_equal(b.dtype, np.dtype('f8'), "array type %s" % a.dtype)
            b = np.longdouble(1.234) * a
            assert_equal(b.dtype, np.dtype(np.longdouble),
                         "array type %s" % a.dtype)
            b = np.float64(1.234) * a
            assert_equal(b.dtype, np.dtype('f8'), "array type %s" % a.dtype)
            b = np.float32(1.234) * a
            assert_equal(b.dtype, np.dtype('f4'), "array type %s" % a.dtype)
            b = np.float16(1.234) * a
            assert_equal(b.dtype, np.dtype('f2'), "array type %s" % a.dtype)

            b = 1.234j * a
            assert_equal(b.dtype, np.dtype('c16'), "array type %s" % a.dtype)
            b = np.clongdouble(1.234j) * a
            assert_equal(b.dtype, np.dtype(np.clongdouble),
                         "array type %s" % a.dtype)
            b = np.complex128(1.234j) * a
            assert_equal(b.dtype, np.dtype('c16'), "array type %s" % a.dtype)
            b = np.complex64(1.234j) * a
            assert_equal(b.dtype, np.dtype('c8'), "array type %s" % a.dtype)

        # The following use-case is problematic, and to resolve its
        # tricky side-effects requires more changes.
        #
        # Use-case: (1-t)*a, where 't' is a boolean array and 'a' is
        #            a float32, shouldn't promote to float64
        #
        # a = np.array([1.0, 1.5], dtype=np.float32)
        # t = np.array([True, False])
        # b = t*a
        # assert_equal(b, [1.0, 0.0])
        # assert_equal(b.dtype, np.dtype('f4'))
        # b = (1-t)*a
        # assert_equal(b, [0.0, 1.5])
        # assert_equal(b.dtype, np.dtype('f4'))
        #
        # Probably ~t (bitwise negation) is more proper to use here,
        # but this is arguably less intuitive to understand at a glance, and
        # would fail if 't' is actually an integer array instead of boolean:
        #
        # b = (~t)*a
        # assert_equal(b, [0.0, 1.5])
        # assert_equal(b.dtype, np.dtype('f4'))

    def test_result_type(self):
        self.check_promotion_cases(np.result_type)
        assert_(np.result_type(None) == np.dtype(None))

    def test_promote_types_endian(self):
        # promote_types should always return native-endian types
        assert_equal(np.promote_types('<i8', '<i8'), np.dtype('i8'))
        assert_equal(np.promote_types('>i8', '>i8'), np.dtype('i8'))

        assert_equal(np.promote_types('>i8', '>U16'), np.dtype('U21'))
        assert_equal(np.promote_types('<i8', '<U16'), np.dtype('U21'))
        assert_equal(np.promote_types('>U16', '>i8'), np.dtype('U21'))
        assert_equal(np.promote_types('<U16', '<i8'), np.dtype('U21'))

        assert_equal(np.promote_types('<S5', '<U8'), np.dtype('U8'))
        assert_equal(np.promote_types('>S5', '>U8'), np.dtype('U8'))
        assert_equal(np.promote_types('<U8', '<S5'), np.dtype('U8'))
        assert_equal(np.promote_types('>U8', '>S5'), np.dtype('U8'))
        assert_equal(np.promote_types('<U5', '<U8'), np.dtype('U8'))
        assert_equal(np.promote_types('>U8', '>U5'), np.dtype('U8'))

        assert_equal(np.promote_types('<M8', '<M8'), np.dtype('M8'))
        assert_equal(np.promote_types('>M8', '>M8'), np.dtype('M8'))
        assert_equal(np.promote_types('<m8', '<m8'), np.dtype('m8'))
        assert_equal(np.promote_types('>m8', '>m8'), np.dtype('m8'))

    def test_promote_types_strings(self):
        assert_equal(np.promote_types('bool', 'S'), np.dtype('S5'))
        assert_equal(np.promote_types('b', 'S'), np.dtype('S4'))
        assert_equal(np.promote_types('u1', 'S'), np.dtype('S3'))
        assert_equal(np.promote_types('u2', 'S'), np.dtype('S5'))
        assert_equal(np.promote_types('u4', 'S'), np.dtype('S10'))
        assert_equal(np.promote_types('u8', 'S'), np.dtype('S20'))
        assert_equal(np.promote_types('i1', 'S'), np.dtype('S4'))
        assert_equal(np.promote_types('i2', 'S'), np.dtype('S6'))
        assert_equal(np.promote_types('i4', 'S'), np.dtype('S11'))
        assert_equal(np.promote_types('i8', 'S'), np.dtype('S21'))
        assert_equal(np.promote_types('bool', 'U'), np.dtype('U5'))
        assert_equal(np.promote_types('b', 'U'), np.dtype('U4'))
        assert_equal(np.promote_types('u1', 'U'), np.dtype('U3'))
        assert_equal(np.promote_types('u2', 'U'), np.dtype('U5'))
        assert_equal(np.promote_types('u4', 'U'), np.dtype('U10'))
        assert_equal(np.promote_types('u8', 'U'), np.dtype('U20'))
        assert_equal(np.promote_types('i1', 'U'), np.dtype('U4'))
        assert_equal(np.promote_types('i2', 'U'), np.dtype('U6'))
        assert_equal(np.promote_types('i4', 'U'), np.dtype('U11'))
        assert_equal(np.promote_types('i8', 'U'), np.dtype('U21'))
        assert_equal(np.promote_types('bool', 'S1'), np.dtype('S5'))
        assert_equal(np.promote_types('bool', 'S30'), np.dtype('S30'))
        assert_equal(np.promote_types('b', 'S1'), np.dtype('S4'))
        assert_equal(np.promote_types('b', 'S30'), np.dtype('S30'))
        assert_equal(np.promote_types('u1', 'S1'), np.dtype('S3'))
        assert_equal(np.promote_types('u1', 'S30'), np.dtype('S30'))
        assert_equal(np.promote_types('u2', 'S1'), np.dtype('S5'))
        assert_equal(np.promote_types('u2', 'S30'), np.dtype('S30'))
        assert_equal(np.promote_types('u4', 'S1'), np.dtype('S10'))
        assert_equal(np.promote_types('u4', 'S30'), np.dtype('S30'))
        assert_equal(np.promote_types('u8', 'S1'), np.dtype('S20'))
        assert_equal(np.promote_types('u8', 'S30'), np.dtype('S30'))

    def test_can_cast(self):
        assert_(np.can_cast(np.int32, np.int64))
        assert_(np.can_cast(np.float64, np.complex))
        assert_(not np.can_cast(np.complex, np.float))

        assert_(np.can_cast('i8', 'f8'))
        assert_(not np.can_cast('i8', 'f4'))
        assert_(np.can_cast('i4', 'S11'))

        assert_(np.can_cast('i8', 'i8', 'no'))
        assert_(not np.can_cast('<i8', '>i8', 'no'))

        assert_(np.can_cast('<i8', '>i8', 'equiv'))
        assert_(not np.can_cast('<i4', '>i8', 'equiv'))

        assert_(np.can_cast('<i4', '>i8', 'safe'))
        assert_(not np.can_cast('<i8', '>i4', 'safe'))

        assert_(np.can_cast('<i8', '>i4', 'same_kind'))
        assert_(not np.can_cast('<i8', '>u4', 'same_kind'))

        assert_(np.can_cast('<i8', '>u4', 'unsafe'))

        assert_(np.can_cast('bool', 'S5'))
        assert_(not np.can_cast('bool', 'S4'))

        assert_(np.can_cast('b', 'S4'))
        assert_(not np.can_cast('b', 'S3'))

        assert_(np.can_cast('u1', 'S3'))
        assert_(not np.can_cast('u1', 'S2'))
        assert_(np.can_cast('u2', 'S5'))
        assert_(not np.can_cast('u2', 'S4'))
        assert_(np.can_cast('u4', 'S10'))
        assert_(not np.can_cast('u4', 'S9'))
        assert_(np.can_cast('u8', 'S20'))
        assert_(not np.can_cast('u8', 'S19'))

        assert_(np.can_cast('i1', 'S4'))
        assert_(not np.can_cast('i1', 'S3'))
        assert_(np.can_cast('i2', 'S6'))
        assert_(not np.can_cast('i2', 'S5'))
        assert_(np.can_cast('i4', 'S11'))
        assert_(not np.can_cast('i4', 'S10'))
        assert_(np.can_cast('i8', 'S21'))
        assert_(not np.can_cast('i8', 'S20'))

        assert_(np.can_cast('bool', 'S5'))
        assert_(not np.can_cast('bool', 'S4'))

        assert_(np.can_cast('b', 'U4'))
        assert_(not np.can_cast('b', 'U3'))

        assert_(np.can_cast('u1', 'U3'))
        assert_(not np.can_cast('u1', 'U2'))
        assert_(np.can_cast('u2', 'U5'))
        assert_(not np.can_cast('u2', 'U4'))
        assert_(np.can_cast('u4', 'U10'))
        assert_(not np.can_cast('u4', 'U9'))
        assert_(np.can_cast('u8', 'U20'))
        assert_(not np.can_cast('u8', 'U19'))

        assert_(np.can_cast('i1', 'U4'))
        assert_(not np.can_cast('i1', 'U3'))
        assert_(np.can_cast('i2', 'U6'))
        assert_(not np.can_cast('i2', 'U5'))
        assert_(np.can_cast('i4', 'U11'))
        assert_(not np.can_cast('i4', 'U10'))
        assert_(np.can_cast('i8', 'U21'))
        assert_(not np.can_cast('i8', 'U20'))

        assert_raises(TypeError, np.can_cast, 'i4', None)
        assert_raises(TypeError, np.can_cast, None, 'i4')


# Custom exception class to test exception propagation in fromiter
class NIterError(Exception):
    pass


class TestFromiter(TestCase):
    def makegen(self):
        for x in range(24):
            yield x**2

    def test_types(self):
        ai32 = np.fromiter(self.makegen(), np.int32)
        ai64 = np.fromiter(self.makegen(), np.int64)
        af = np.fromiter(self.makegen(), float)
        self.assertTrue(ai32.dtype == np.dtype(np.int32))
        self.assertTrue(ai64.dtype == np.dtype(np.int64))
        self.assertTrue(af.dtype == np.dtype(float))

    def test_lengths(self):
        expected = np.array(list(self.makegen()))
        a = np.fromiter(self.makegen(), int)
        a20 = np.fromiter(self.makegen(), int, 20)
        self.assertTrue(len(a) == len(expected))
        self.assertTrue(len(a20) == 20)
        self.assertRaises(ValueError, np.fromiter,
                          self.makegen(), int, len(expected) + 10)

    def test_values(self):
        expected = np.array(list(self.makegen()))
        a = np.fromiter(self.makegen(), int)
        a20 = np.fromiter(self.makegen(), int, 20)
        self.assertTrue(np.alltrue(a == expected, axis=0))
        self.assertTrue(np.alltrue(a20 == expected[:20], axis=0))

    def load_data(self, n, eindex):
        # Utility method for the issue 2592 tests.
        # Raise an exception at the desired index in the iterator.
        for e in range(n):
            if e == eindex:
                raise NIterError('error at index %s' % eindex)
            yield e

    def test_2592(self):
        # Test iteration exceptions are correctly raised.
        count, eindex = 10, 5
        self.assertRaises(NIterError, np.fromiter,
                          self.load_data(count, eindex), dtype=int, count=count)

    def test_2592_edge(self):
        # Test iter. exceptions, edge case (exception at end of iterator).
        count = 10
        eindex = count-1
        self.assertRaises(NIterError, np.fromiter,
                          self.load_data(count, eindex), dtype=int, count=count)


class TestNonzero(TestCase):
    def test_nonzero_trivial(self):
        assert_equal(np.count_nonzero(np.array([])), 0)
        assert_equal(np.count_nonzero(np.array([], dtype='?')), 0)
        assert_equal(np.nonzero(np.array([])), ([],))

        assert_equal(np.count_nonzero(np.array(0)), 0)
        assert_equal(np.count_nonzero(np.array(0, dtype='?')), 0)
        assert_equal(np.nonzero(np.array(0)), ([],))
        assert_equal(np.count_nonzero(np.array(1)), 1)
        assert_equal(np.count_nonzero(np.array(1, dtype='?')), 1)
        assert_equal(np.nonzero(np.array(1)), ([0],))

    def test_nonzero_onedim(self):
        x = np.array([1, 0, 2, -1, 0, 0, 8])
        assert_equal(np.count_nonzero(x), 4)
        assert_equal(np.count_nonzero(x), 4)
        assert_equal(np.nonzero(x), ([0, 2, 3, 6],))

        x = np.array([(1, 2), (0, 0), (1, 1), (-1, 3), (0, 7)],
                     dtype=[('a', 'i4'), ('b', 'i2')])
        assert_equal(np.count_nonzero(x['a']), 3)
        assert_equal(np.count_nonzero(x['b']), 4)
        assert_equal(np.nonzero(x['a']), ([0, 2, 3],))
        assert_equal(np.nonzero(x['b']), ([0, 2, 3, 4],))

    def test_nonzero_twodim(self):
        x = np.array([[0, 1, 0], [2, 0, 3]])
        assert_equal(np.count_nonzero(x), 3)
        assert_equal(np.nonzero(x), ([0, 1, 1], [1, 0, 2]))

        x = np.eye(3)
        assert_equal(np.count_nonzero(x), 3)
        assert_equal(np.nonzero(x), ([0, 1, 2], [0, 1, 2]))

        x = np.array([[(0, 1), (0, 0), (1, 11)],
                   [(1, 1), (1, 0), (0, 0)],
                   [(0, 0), (1, 5), (0, 1)]], dtype=[('a', 'f4'), ('b', 'u1')])
        assert_equal(np.count_nonzero(x['a']), 4)
        assert_equal(np.count_nonzero(x['b']), 5)
        assert_equal(np.nonzero(x['a']), ([0, 1, 1, 2], [2, 0, 1, 1]))
        assert_equal(np.nonzero(x['b']), ([0, 0, 1, 2, 2], [0, 2, 0, 1, 2]))

        assert_(not x['a'].T.flags.aligned)
        assert_equal(np.count_nonzero(x['a'].T), 4)
        assert_equal(np.count_nonzero(x['b'].T), 5)
        assert_equal(np.nonzero(x['a'].T), ([0, 1, 1, 2], [1, 1, 2, 0]))
        assert_equal(np.nonzero(x['b'].T), ([0, 0, 1, 2, 2], [0, 1, 2, 0, 2]))

    def test_sparse(self):
        # test special sparse condition boolean code path
        for i in range(20):
            c = np.zeros(200, dtype=np.bool)
            c[i::20] = True
            assert_equal(np.nonzero(c)[0], np.arange(i, 200 + i, 20))

            c = np.zeros(400, dtype=np.bool)
            c[10 + i:20 + i] = True
            c[20 + i*2] = True
            assert_equal(np.nonzero(c)[0],
                         np.concatenate((np.arange(10 + i, 20 + i), [20 + i*2])))

    def test_return_type(self):
        class C(np.ndarray):
            pass

        for view in (C, np.ndarray):
            for nd in range(1, 4):
                shape = tuple(range(2, 2+nd))
                x = np.arange(np.prod(shape)).reshape(shape).view(view)
                for nzx in (np.nonzero(x), x.nonzero()):
                    for nzx_i in nzx:
                        assert_(type(nzx_i) is np.ndarray)
                        assert_(nzx_i.flags.writeable)

    def test_count_nonzero_axis(self):
        # Basic check of functionality
        m = np.array([[0, 1, 7, 0, 0], [3, 0, 0, 2, 19]])

        expected = np.array([1, 1, 1, 1, 1])
        assert_equal(np.count_nonzero(m, axis=0), expected)

        expected = np.array([2, 3])
        assert_equal(np.count_nonzero(m, axis=1), expected)

        assert_raises(ValueError, np.count_nonzero, m, axis=(1, 1))
        assert_raises(TypeError, np.count_nonzero, m, axis='foo')
        assert_raises(ValueError, np.count_nonzero, m, axis=3)
        assert_raises(TypeError, np.count_nonzero,
                      m, axis=np.array([[1], [2]]))

    def test_count_nonzero_axis_all_dtypes(self):
        # More thorough test that the axis argument is respected
        # for all dtypes and responds correctly when presented with
        # either integer or tuple arguments for axis
        msg = "Mismatch for dtype: %s"

        for dt in np.typecodes['All']:
            err_msg = msg % (np.dtype(dt).name,)

            if dt != 'V':
                if dt != 'M':
                    m = np.zeros((3, 3), dtype=dt)
                    n = np.ones(1, dtype=dt)

                    m[0, 0] = n[0]
                    m[1, 0] = n[0]

                else:  # np.zeros doesn't work for np.datetime64
                    m = np.array(['1970-01-01'] * 9)
                    m = m.reshape((3, 3))

                    m[0, 0] = '1970-01-12'
                    m[1, 0] = '1970-01-12'
                    m = m.astype(dt)

                expected = np.array([2, 0, 0])
                assert_equal(np.count_nonzero(m, axis=0),
                             expected, err_msg=err_msg)

                expected = np.array([1, 1, 0])
                assert_equal(np.count_nonzero(m, axis=1),
                             expected, err_msg=err_msg)

                expected = np.array(2)
                assert_equal(np.count_nonzero(m, axis=(0, 1)),
                             expected, err_msg=err_msg)
                assert_equal(np.count_nonzero(m, axis=None),
                             expected, err_msg=err_msg)
                assert_equal(np.count_nonzero(m),
                             expected, err_msg=err_msg)

            if dt == 'V':
                # There are no 'nonzero' objects for np.void, so the testing
                # setup is slightly different for this dtype
                m = np.array([np.void(1)] * 6).reshape((2, 3))

                expected = np.array([0, 0, 0])
                assert_equal(np.count_nonzero(m, axis=0),
                             expected, err_msg=err_msg)

                expected = np.array([0, 0])
                assert_equal(np.count_nonzero(m, axis=1),
                             expected, err_msg=err_msg)

                expected = np.array(0)
                assert_equal(np.count_nonzero(m, axis=(0, 1)),
                             expected, err_msg=err_msg)
                assert_equal(np.count_nonzero(m, axis=None),
                             expected, err_msg=err_msg)
                assert_equal(np.count_nonzero(m),
                             expected, err_msg=err_msg)

    def test_count_nonzero_axis_consistent(self):
        # Check that the axis behaviour for valid axes in
        # non-special cases is consistent (and therefore
        # correct) by checking it against an integer array
        # that is then casted to the generic object dtype
        from itertools import combinations, permutations

        axis = (0, 1, 2, 3)
        size = (5, 5, 5, 5)
        msg = "Mismatch for axis: %s"

        rng = np.random.RandomState(1234)
        m = rng.randint(-100, 100, size=size)
        n = m.astype(np.object)

        for length in range(len(axis)):
            for combo in combinations(axis, length):
                for perm in permutations(combo):
                    assert_equal(
                        np.count_nonzero(m, axis=perm),
                        np.count_nonzero(n, axis=perm),
                        err_msg=msg % (perm,))

    def test_array_method(self):
        # Tests that the array method
        # call to nonzero works
        m = np.array([[1, 0, 0], [4, 0, 6]])
        tgt = [[0, 1, 1], [0, 0, 2]]

        assert_equal(m.nonzero(), tgt)


class TestIndex(TestCase):
    def test_boolean(self):
        a = rand(3, 5, 8)
        V = rand(5, 8)
        g1 = randint(0, 5, size=15)
        g2 = randint(0, 8, size=15)
        V[g1, g2] = -V[g1, g2]
        assert_((np.array([a[0][V > 0], a[1][V > 0], a[2][V > 0]]) == a[:, V > 0]).all())

    def test_boolean_edgecase(self):
        a = np.array([], dtype='int32')
        b = np.array([], dtype='bool')
        c = a[b]
        assert_equal(c, [])
        assert_equal(c.dtype, np.dtype('int32'))


class TestBinaryRepr(TestCase):
    def test_zero(self):
        assert_equal(np.binary_repr(0), '0')

    def test_positive(self):
        assert_equal(np.binary_repr(10), '1010')
        assert_equal(np.binary_repr(12522),
                     '11000011101010')
        assert_equal(np.binary_repr(10736848),
                     '101000111101010011010000')

    def test_negative(self):
        assert_equal(np.binary_repr(-1), '-1')
        assert_equal(np.binary_repr(-10), '-1010')
        assert_equal(np.binary_repr(-12522),
                     '-11000011101010')
        assert_equal(np.binary_repr(-10736848),
                     '-101000111101010011010000')

    def test_sufficient_width(self):
        assert_equal(np.binary_repr(0, width=5), '00000')
        assert_equal(np.binary_repr(10, width=7), '0001010')
        assert_equal(np.binary_repr(-5, width=7), '1111011')

    def test_neg_width_boundaries(self):
        # see gh-8670

        # Ensure that the example in the issue does not
        # break before proceeding to a more thorough test.
        assert_equal(np.binary_repr(-128, width=8), '10000000')

        for width in range(1, 11):
            num = -2**(width - 1)
            exp = '1' + (width - 1) * '0'
            assert_equal(np.binary_repr(num, width=width), exp)


class TestBaseRepr(TestCase):
    def test_base3(self):
        assert_equal(np.base_repr(3**5, 3), '100000')

    def test_positive(self):
        assert_equal(np.base_repr(12, 10), '12')
        assert_equal(np.base_repr(12, 10, 4), '000012')
        assert_equal(np.base_repr(12, 4), '30')
        assert_equal(np.base_repr(3731624803700888, 36), '10QR0ROFCEW')

    def test_negative(self):
        assert_equal(np.base_repr(-12, 10), '-12')
        assert_equal(np.base_repr(-12, 10, 4), '-000012')
        assert_equal(np.base_repr(-12, 4), '-30')

    def test_base_range(self):
        with self.assertRaises(ValueError):
            np.base_repr(1, 1)
        with self.assertRaises(ValueError):
            np.base_repr(1, 37)


class TestArrayComparisons(TestCase):
    def test_array_equal(self):
        res = np.array_equal(np.array([1, 2]), np.array([1, 2]))
        assert_(res)
        assert_(type(res) is bool)
        res = np.array_equal(np.array([1, 2]), np.array([1, 2, 3]))
        assert_(not res)
        assert_(type(res) is bool)
        res = np.array_equal(np.array([1, 2]), np.array([3, 4]))
        assert_(not res)
        assert_(type(res) is bool)
        res = np.array_equal(np.array([1, 2]), np.array([1, 3]))
        assert_(not res)
        assert_(type(res) is bool)
        res = np.array_equal(np.array(['a'], dtype='S1'), np.array(['a'], dtype='S1'))
        assert_(res)
        assert_(type(res) is bool)
        res = np.array_equal(np.array([('a', 1)], dtype='S1,u4'),
                             np.array([('a', 1)], dtype='S1,u4'))
        assert_(res)
        assert_(type(res) is bool)

    def test_array_equiv(self):
        res = np.array_equiv(np.array([1, 2]), np.array([1, 2]))
        assert_(res)
        assert_(type(res) is bool)
        res = np.array_equiv(np.array([1, 2]), np.array([1, 2, 3]))
        assert_(not res)
        assert_(type(res) is bool)
        res = np.array_equiv(np.array([1, 2]), np.array([3, 4]))
        assert_(not res)
        assert_(type(res) is bool)
        res = np.array_equiv(np.array([1, 2]), np.array([1, 3]))
        assert_(not res)
        assert_(type(res) is bool)

        res = np.array_equiv(np.array([1, 1]), np.array([1]))
        assert_(res)
        assert_(type(res) is bool)
        res = np.array_equiv(np.array([1, 1]), np.array([[1], [1]]))
        assert_(res)
        assert_(type(res) is bool)
        res = np.array_equiv(np.array([1, 2]), np.array([2]))
        assert_(not res)
        assert_(type(res) is bool)
        res = np.array_equiv(np.array([1, 2]), np.array([[1], [2]]))
        assert_(not res)
        assert_(type(res) is bool)
        res = np.array_equiv(np.array([1, 2]), np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
        assert_(not res)
        assert_(type(res) is bool)


def assert_array_strict_equal(x, y):
    assert_array_equal(x, y)
    # Check flags, 32 bit arches typically don't provide 16 byte alignment
    if ((x.dtype.alignment <= 8 or
            np.intp().dtype.itemsize != 4) and
            sys.platform != 'win32'):
        assert_(x.flags == y.flags)
    else:
        assert_(x.flags.owndata == y.flags.owndata)
        assert_(x.flags.writeable == y.flags.writeable)
        assert_(x.flags.c_contiguous == y.flags.c_contiguous)
        assert_(x.flags.f_contiguous == y.flags.f_contiguous)
        assert_(x.flags.updateifcopy == y.flags.updateifcopy)
    # check endianness
    assert_(x.dtype.isnative == y.dtype.isnative)


class TestClip(TestCase):
    def setUp(self):
        self.nr = 5
        self.nc = 3

    def fastclip(self, a, m, M, out=None):
        if out is None:
            return a.clip(m, M)
        else:
            return a.clip(m, M, out)

    def clip(self, a, m, M, out=None):
        # use slow-clip
        selector = np.less(a, m) + 2*np.greater(a, M)
        return selector.choose((a, m, M), out=out)

    # Handy functions
    def _generate_data(self, n, m):
        return randn(n, m)

    def _generate_data_complex(self, n, m):
        return randn(n, m) + 1.j * rand(n, m)

    def _generate_flt_data(self, n, m):
        return (randn(n, m)).astype(np.float32)

    def _neg_byteorder(self, a):
        a = np.asarray(a)
        if sys.byteorder == 'little':
            a = a.astype(a.dtype.newbyteorder('>'))
        else:
            a = a.astype(a.dtype.newbyteorder('<'))
        return a

    def _generate_non_native_data(self, n, m):
        data = randn(n, m)
        data = self._neg_byteorder(data)
        assert_(not data.dtype.isnative)
        return data

    def _generate_int_data(self, n, m):
        return (10 * rand(n, m)).astype(np.int64)

    def _generate_int32_data(self, n, m):
        return (10 * rand(n, m)).astype(np.int32)

    # Now the real test cases
    def test_simple_double(self):
        # Test native double input with scalar min/max.
        a = self._generate_data(self.nr, self.nc)
        m = 0.1
        M = 0.6
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

    def test_simple_int(self):
        # Test native int input with scalar min/max.
        a = self._generate_int_data(self.nr, self.nc)
        a = a.astype(int)
        m = -2
        M = 4
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

    def test_array_double(self):
        # Test native double input with array min/max.
        a = self._generate_data(self.nr, self.nc)
        m = np.zeros(a.shape)
        M = m + 0.5
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

    def test_simple_nonnative(self):
        # Test non native double input with scalar min/max.
        # Test native double input with non native double scalar min/max.
        a = self._generate_non_native_data(self.nr, self.nc)
        m = -0.5
        M = 0.6
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_equal(ac, act)

        # Test native double input with non native double scalar min/max.
        a = self._generate_data(self.nr, self.nc)
        m = -0.5
        M = self._neg_byteorder(0.6)
        assert_(not M.dtype.isnative)
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_equal(ac, act)

    def test_simple_complex(self):
        # Test native complex input with native double scalar min/max.
        # Test native input with complex double scalar min/max.
        a = 3 * self._generate_data_complex(self.nr, self.nc)
        m = -0.5
        M = 1.
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

        # Test native input with complex double scalar min/max.
        a = 3 * self._generate_data(self.nr, self.nc)
        m = -0.5 + 1.j
        M = 1. + 2.j
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

    def test_clip_complex(self):
        # Address Issue gh-5354 for clipping complex arrays
        # Test native complex input without explicit min/max
        # ie, either min=None or max=None
        a = np.ones(10, dtype=np.complex)
        m = a.min()
        M = a.max()
        am = self.fastclip(a, m, None)
        aM = self.fastclip(a, None, M)
        assert_array_strict_equal(am, a)
        assert_array_strict_equal(aM, a)

    def test_clip_non_contig(self):
        # Test clip for non contiguous native input and native scalar min/max.
        a = self._generate_data(self.nr * 2, self.nc * 3)
        a = a[::2, ::3]
        assert_(not a.flags['F_CONTIGUOUS'])
        assert_(not a.flags['C_CONTIGUOUS'])
        ac = self.fastclip(a, -1.6, 1.7)
        act = self.clip(a, -1.6, 1.7)
        assert_array_strict_equal(ac, act)

    def test_simple_out(self):
        # Test native double input with scalar min/max.
        a = self._generate_data(self.nr, self.nc)
        m = -0.5
        M = 0.6
        ac = np.zeros(a.shape)
        act = np.zeros(a.shape)
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_simple_int32_inout(self):
        # Test native int32 input with double min/max and int32 out.
        a = self._generate_int32_data(self.nr, self.nc)
        m = np.float64(0)
        M = np.float64(2)
        ac = np.zeros(a.shape, dtype=np.int32)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_simple_int64_out(self):
        # Test native int32 input with int32 scalar min/max and int64 out.
        a = self._generate_int32_data(self.nr, self.nc)
        m = np.int32(-1)
        M = np.int32(1)
        ac = np.zeros(a.shape, dtype=np.int64)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_simple_int64_inout(self):
        # Test native int32 input with double array min/max and int32 out.
        a = self._generate_int32_data(self.nr, self.nc)
        m = np.zeros(a.shape, np.float64)
        M = np.float64(1)
        ac = np.zeros(a.shape, dtype=np.int32)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_simple_int32_out(self):
        # Test native double input with scalar min/max and int out.
        a = self._generate_data(self.nr, self.nc)
        m = -1.0
        M = 2.0
        ac = np.zeros(a.shape, dtype=np.int32)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_simple_inplace_01(self):
        # Test native double input with array min/max in-place.
        a = self._generate_data(self.nr, self.nc)
        ac = a.copy()
        m = np.zeros(a.shape)
        M = 1.0
        self.fastclip(a, m, M, a)
        self.clip(a, m, M, ac)
        assert_array_strict_equal(a, ac)

    def test_simple_inplace_02(self):
        # Test native double input with scalar min/max in-place.
        a = self._generate_data(self.nr, self.nc)
        ac = a.copy()
        m = -0.5
        M = 0.6
        self.fastclip(a, m, M, a)
        self.clip(a, m, M, ac)
        assert_array_strict_equal(a, ac)

    def test_noncontig_inplace(self):
        # Test non contiguous double input with double scalar min/max in-place.
        a = self._generate_data(self.nr * 2, self.nc * 3)
        a = a[::2, ::3]
        assert_(not a.flags['F_CONTIGUOUS'])
        assert_(not a.flags['C_CONTIGUOUS'])
        ac = a.copy()
        m = -0.5
        M = 0.6
        self.fastclip(a, m, M, a)
        self.clip(a, m, M, ac)
        assert_array_equal(a, ac)

    def test_type_cast_01(self):
        # Test native double input with scalar min/max.
        a = self._generate_data(self.nr, self.nc)
        m = -0.5
        M = 0.6
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_02(self):
        # Test native int32 input with int32 scalar min/max.
        a = self._generate_int_data(self.nr, self.nc)
        a = a.astype(np.int32)
        m = -2
        M = 4
        ac = self.fastclip(a, m, M)
        act = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_03(self):
        # Test native int32 input with float64 scalar min/max.
        a = self._generate_int32_data(self.nr, self.nc)
        m = -2
        M = 4
        ac = self.fastclip(a, np.float64(m), np.float64(M))
        act = self.clip(a, np.float64(m), np.float64(M))
        assert_array_strict_equal(ac, act)

    def test_type_cast_04(self):
        # Test native int32 input with float32 scalar min/max.
        a = self._generate_int32_data(self.nr, self.nc)
        m = np.float32(-2)
        M = np.float32(4)
        act = self.fastclip(a, m, M)
        ac = self.clip(a, m, M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_05(self):
        # Test native int32 with double arrays min/max.
        a = self._generate_int_data(self.nr, self.nc)
        m = -0.5
        M = 1.
        ac = self.fastclip(a, m * np.zeros(a.shape), M)
        act = self.clip(a, m * np.zeros(a.shape), M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_06(self):
        # Test native with NON native scalar min/max.
        a = self._generate_data(self.nr, self.nc)
        m = 0.5
        m_s = self._neg_byteorder(m)
        M = 1.
        act = self.clip(a, m_s, M)
        ac = self.fastclip(a, m_s, M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_07(self):
        # Test NON native with native array min/max.
        a = self._generate_data(self.nr, self.nc)
        m = -0.5 * np.ones(a.shape)
        M = 1.
        a_s = self._neg_byteorder(a)
        assert_(not a_s.dtype.isnative)
        act = a_s.clip(m, M)
        ac = self.fastclip(a_s, m, M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_08(self):
        # Test NON native with native scalar min/max.
        a = self._generate_data(self.nr, self.nc)
        m = -0.5
        M = 1.
        a_s = self._neg_byteorder(a)
        assert_(not a_s.dtype.isnative)
        ac = self.fastclip(a_s, m, M)
        act = a_s.clip(m, M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_09(self):
        # Test native with NON native array min/max.
        a = self._generate_data(self.nr, self.nc)
        m = -0.5 * np.ones(a.shape)
        M = 1.
        m_s = self._neg_byteorder(m)
        assert_(not m_s.dtype.isnative)
        ac = self.fastclip(a, m_s, M)
        act = self.clip(a, m_s, M)
        assert_array_strict_equal(ac, act)

    def test_type_cast_10(self):
        # Test native int32 with float min/max and float out for output argument.
        a = self._generate_int_data(self.nr, self.nc)
        b = np.zeros(a.shape, dtype=np.float32)
        m = np.float32(-0.5)
        M = np.float32(1)
        act = self.clip(a, m, M, out=b)
        ac = self.fastclip(a, m, M, out=b)
        assert_array_strict_equal(ac, act)

    def test_type_cast_11(self):
        # Test non native with native scalar, min/max, out non native
        a = self._generate_non_native_data(self.nr, self.nc)
        b = a.copy()
        b = b.astype(b.dtype.newbyteorder('>'))
        bt = b.copy()
        m = -0.5
        M = 1.
        self.fastclip(a, m, M, out=b)
        self.clip(a, m, M, out=bt)
        assert_array_strict_equal(b, bt)

    def test_type_cast_12(self):
        # Test native int32 input and min/max and float out
        a = self._generate_int_data(self.nr, self.nc)
        b = np.zeros(a.shape, dtype=np.float32)
        m = np.int32(0)
        M = np.int32(1)
        act = self.clip(a, m, M, out=b)
        ac = self.fastclip(a, m, M, out=b)
        assert_array_strict_equal(ac, act)

    def test_clip_with_out_simple(self):
        # Test native double input with scalar min/max
        a = self._generate_data(self.nr, self.nc)
        m = -0.5
        M = 0.6
        ac = np.zeros(a.shape)
        act = np.zeros(a.shape)
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_clip_with_out_simple2(self):
        # Test native int32 input with double min/max and int32 out
        a = self._generate_int32_data(self.nr, self.nc)
        m = np.float64(0)
        M = np.float64(2)
        ac = np.zeros(a.shape, dtype=np.int32)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_clip_with_out_simple_int32(self):
        # Test native int32 input with int32 scalar min/max and int64 out
        a = self._generate_int32_data(self.nr, self.nc)
        m = np.int32(-1)
        M = np.int32(1)
        ac = np.zeros(a.shape, dtype=np.int64)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_clip_with_out_array_int32(self):
        # Test native int32 input with double array min/max and int32 out
        a = self._generate_int32_data(self.nr, self.nc)
        m = np.zeros(a.shape, np.float64)
        M = np.float64(1)
        ac = np.zeros(a.shape, dtype=np.int32)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_clip_with_out_array_outint32(self):
        # Test native double input with scalar min/max and int out
        a = self._generate_data(self.nr, self.nc)
        m = -1.0
        M = 2.0
        ac = np.zeros(a.shape, dtype=np.int32)
        act = ac.copy()
        self.fastclip(a, m, M, ac)
        self.clip(a, m, M, act)
        assert_array_strict_equal(ac, act)

    def test_clip_inplace_array(self):
        # Test native double input with array min/max
        a = self._generate_data(self.nr, self.nc)
        ac = a.copy()
        m = np.zeros(a.shape)
        M = 1.0
        self.fastclip(a, m, M, a)
        self.clip(a, m, M, ac)
        assert_array_strict_equal(a, ac)

    def test_clip_inplace_simple(self):
        # Test native double input with scalar min/max
        a = self._generate_data(self.nr, self.nc)
        ac = a.copy()
        m = -0.5
        M = 0.6
        self.fastclip(a, m, M, a)
        self.clip(a, m, M, ac)
        assert_array_strict_equal(a, ac)

    def test_clip_func_takes_out(self):
        # Ensure that the clip() function takes an out=argument.
        a = self._generate_data(self.nr, self.nc)
        ac = a.copy()
        m = -0.5
        M = 0.6
        a2 = np.clip(a, m, M, out=a)
        self.clip(a, m, M, ac)
        assert_array_strict_equal(a2, ac)
        self.assertTrue(a2 is a)

    def test_clip_nan(self):
        d = np.arange(7.)
        assert_equal(d.clip(min=np.nan), d)
        assert_equal(d.clip(max=np.nan), d)
        assert_equal(d.clip(min=np.nan, max=np.nan), d)
        assert_equal(d.clip(min=-2, max=np.nan), d)
        assert_equal(d.clip(min=np.nan, max=10), d)


class TestAllclose(object):
    rtol = 1e-5
    atol = 1e-8

    def setUp(self):
        self.olderr = np.seterr(invalid='ignore')

    def tearDown(self):
        np.seterr(**self.olderr)

    def tst_allclose(self, x, y):
        assert_(np.allclose(x, y), "%s and %s not close" % (x, y))

    def tst_not_allclose(self, x, y):
        assert_(not np.allclose(x, y), "%s and %s shouldn't be close" % (x, y))

    def test_ip_allclose(self):
        # Parametric test factory.
        arr = np.array([100, 1000])
        aran = np.arange(125).reshape((5, 5, 5))

        atol = self.atol
        rtol = self.rtol

        data = [([1, 0], [1, 0]),
                ([atol], [0]),
                ([1], [1+rtol+atol]),
                (arr, arr + arr*rtol),
                (arr, arr + arr*rtol + atol*2),
                (aran, aran + aran*rtol),
                (np.inf, np.inf),
                (np.inf, [np.inf])]

        for (x, y) in data:
            yield (self.tst_allclose, x, y)

    def test_ip_not_allclose(self):
        # Parametric test factory.
        aran = np.arange(125).reshape((5, 5, 5))

        atol = self.atol
        rtol = self.rtol

        data = [([np.inf, 0], [1, np.inf]),
                ([np.inf, 0], [1, 0]),
                ([np.inf, np.inf], [1, np.inf]),
                ([np.inf, np.inf], [1, 0]),
                ([-np.inf, 0], [np.inf, 0]),
                ([np.nan, 0], [np.nan, 0]),
                ([atol*2], [0]),
                ([1], [1+rtol+atol*2]),
                (aran, aran + aran*atol + atol*2),
                (np.array([np.inf, 1]), np.array([0, np.inf]))]

        for (x, y) in data:
            yield (self.tst_not_allclose, x, y)

    def test_no_parameter_modification(self):
        x = np.array([np.inf, 1])
        y = np.array([0, np.inf])
        np.allclose(x, y)
        assert_array_equal(x, np.array([np.inf, 1]))
        assert_array_equal(y, np.array([0, np.inf]))

    def test_min_int(self):
        # Could make problems because of abs(min_int) == min_int
        min_int = np.iinfo(np.int_).min
        a = np.array([min_int], dtype=np.int_)
        assert_(np.allclose(a, a))

    def test_equalnan(self):
        x = np.array([1.0, np.nan])
        assert_(np.allclose(x, x, equal_nan=True))

    def test_return_class_is_ndarray(self):
        # Issue gh-6475
        # Check that allclose does not preserve subtypes
        class Foo(np.ndarray):
            def __new__(cls, *args, **kwargs):
                return np.array(*args, **kwargs).view(cls)

        a = Foo([1])
        assert_(type(np.allclose(a, a)) is bool)


class TestIsclose(object):
    rtol = 1e-5
    atol = 1e-8

    def setup(self):
        atol = self.atol
        rtol = self.rtol
        arr = np.array([100, 1000])
        aran = np.arange(125).reshape((5, 5, 5))

        self.all_close_tests = [
                ([1, 0], [1, 0]),
                ([atol], [0]),
                ([1], [1 + rtol + atol]),
                (arr, arr + arr*rtol),
                (arr, arr + arr*rtol + atol),
                (aran, aran + aran*rtol),
                (np.inf, np.inf),
                (np.inf, [np.inf]),
                ([np.inf, -np.inf], [np.inf, -np.inf]),
                ]
        self.none_close_tests = [
                ([np.inf, 0], [1, np.inf]),
                ([np.inf, -np.inf], [1, 0]),
                ([np.inf, np.inf], [1, -np.inf]),
                ([np.inf, np.inf], [1, 0]),
                ([np.nan, 0], [np.nan, -np.inf]),
                ([atol*2], [0]),
                ([1], [1 + rtol + atol*2]),
                (aran, aran + rtol*1.1*aran + atol*1.1),
                (np.array([np.inf, 1]), np.array([0, np.inf])),
                ]
        self.some_close_tests = [
                ([np.inf, 0], [np.inf, atol*2]),
                ([atol, 1, 1e6*(1 + 2*rtol) + atol], [0, np.nan, 1e6]),
                (np.arange(3), [0, 1, 2.1]),
                (np.nan, [np.nan, np.nan, np.nan]),
                ([0], [atol, np.inf, -np.inf, np.nan]),
                (0, [atol, np.inf, -np.inf, np.nan]),
                ]
        self.some_close_results = [
                [True, False],
                [True, False, False],
                [True, True, False],
                [False, False, False],
                [True, False, False, False],
                [True, False, False, False],
                ]

    def test_ip_isclose(self):
        self.setup()
        tests = self.some_close_tests
        results = self.some_close_results
        for (x, y), result in zip(tests, results):
            yield (assert_array_equal, np.isclose(x, y), result)

    def tst_all_isclose(self, x, y):
        assert_(np.all(np.isclose(x, y)), "%s and %s not close" % (x, y))

    def tst_none_isclose(self, x, y):
        msg = "%s and %s shouldn't be close"
        assert_(not np.any(np.isclose(x, y)), msg % (x, y))

    def tst_isclose_allclose(self, x, y):
        msg = "isclose.all() and allclose aren't same for %s and %s"
        msg2 = "isclose and allclose aren't same for %s and %s"
        if np.isscalar(x) and np.isscalar(y):
            assert_(np.isclose(x, y) == np.allclose(x, y), msg=msg2 % (x, y))
        else:
            assert_array_equal(np.isclose(x, y).all(), np.allclose(x, y), msg % (x, y))

    def test_ip_all_isclose(self):
        self.setup()
        for (x, y) in self.all_close_tests:
            yield (self.tst_all_isclose, x, y)

    def test_ip_none_isclose(self):
        self.setup()
        for (x, y) in self.none_close_tests:
            yield (self.tst_none_isclose, x, y)

    def test_ip_isclose_allclose(self):
        self.setup()
        tests = (self.all_close_tests + self.none_close_tests +
                 self.some_close_tests)
        for (x, y) in tests:
            yield (self.tst_isclose_allclose, x, y)

    def test_equal_nan(self):
        assert_array_equal(np.isclose(np.nan, np.nan, equal_nan=True), [True])
        arr = np.array([1.0, np.nan])
        assert_array_equal(np.isclose(arr, arr, equal_nan=True), [True, True])

    def test_masked_arrays(self):
        # Make sure to test the output type when arguments are interchanged.

        x = np.ma.masked_where([True, True, False], np.arange(3))
        assert_(type(x) is type(np.isclose(2, x)))
        assert_(type(x) is type(np.isclose(x, 2)))

        x = np.ma.masked_where([True, True, False], [np.nan, np.inf, np.nan])
        assert_(type(x) is type(np.isclose(np.inf, x)))
        assert_(type(x) is type(np.isclose(x, np.inf)))

        x = np.ma.masked_where([True, True, False], [np.nan, np.nan, np.nan])
        y = np.isclose(np.nan, x, equal_nan=True)
        assert_(type(x) is type(y))
        # Ensure that the mask isn't modified...
        assert_array_equal([True, True, False], y.mask)
        y = np.isclose(x, np.nan, equal_nan=True)
        assert_(type(x) is type(y))
        # Ensure that the mask isn't modified...
        assert_array_equal([True, True, False], y.mask)

        x = np.ma.masked_where([True, True, False], [np.nan, np.nan, np.nan])
        y = np.isclose(x, x, equal_nan=True)
        assert_(type(x) is type(y))
        # Ensure that the mask isn't modified...
        assert_array_equal([True, True, False], y.mask)

    def test_scalar_return(self):
        assert_(np.isscalar(np.isclose(1, 1)))

    def test_no_parameter_modification(self):
        x = np.array([np.inf, 1])
        y = np.array([0, np.inf])
        np.isclose(x, y)
        assert_array_equal(x, np.array([np.inf, 1]))
        assert_array_equal(y, np.array([0, np.inf]))

    def test_non_finite_scalar(self):
        # GH7014, when two scalars are compared the output should also be a
        # scalar
        assert_(np.isclose(np.inf, -np.inf) is False)
        assert_(np.isclose(0, np.inf) is False)
        assert_(type(np.isclose(0, np.inf)) is bool)


class TestStdVar(TestCase):
    def setUp(self):
        self.A = np.array([1, -1, 1, -1])
        self.real_var = 1

    def test_basic(self):
        assert_almost_equal(np.var(self.A), self.real_var)
        assert_almost_equal(np.std(self.A)**2, self.real_var)

    def test_scalars(self):
        assert_equal(np.var(1), 0)
        assert_equal(np.std(1), 0)

    def test_ddof1(self):
        assert_almost_equal(np.var(self.A, ddof=1),
                            self.real_var*len(self.A)/float(len(self.A)-1))
        assert_almost_equal(np.std(self.A, ddof=1)**2,
                            self.real_var*len(self.A)/float(len(self.A)-1))

    def test_ddof2(self):
        assert_almost_equal(np.var(self.A, ddof=2),
                            self.real_var*len(self.A)/float(len(self.A)-2))
        assert_almost_equal(np.std(self.A, ddof=2)**2,
                            self.real_var*len(self.A)/float(len(self.A)-2))

    def test_out_scalar(self):
        d = np.arange(10)
        out = np.array(0.)
        r = np.std(d, out=out)
        assert_(r is out)
        assert_array_equal(r, out)
        r = np.var(d, out=out)
        assert_(r is out)
        assert_array_equal(r, out)
        r = np.mean(d, out=out)
        assert_(r is out)
        assert_array_equal(r, out)


class TestStdVarComplex(TestCase):
    def test_basic(self):
        A = np.array([1, 1.j, -1, -1.j])
        real_var = 1
        assert_almost_equal(np.var(A), real_var)
        assert_almost_equal(np.std(A)**2, real_var)

    def test_scalars(self):
        assert_equal(np.var(1j), 0)
        assert_equal(np.std(1j), 0)


class TestCreationFuncs(TestCase):
    # Test ones, zeros, empty and full.

    def setUp(self):
        dtypes = {np.dtype(tp) for tp in itertools.chain(*np.sctypes.values())}
        # void, bytes, str
        variable_sized = {tp for tp in dtypes if tp.str.endswith('0')}
        self.dtypes = sorted(dtypes - variable_sized |
                             {np.dtype(tp.str.replace("0", str(i)))
                              for tp in variable_sized for i in range(1, 10)},
                             key=lambda dtype: dtype.str)
        self.orders = {'C': 'c_contiguous', 'F': 'f_contiguous'}
        self.ndims = 10

    def check_function(self, func, fill_value=None):
        par = ((0, 1, 2),
               range(self.ndims),
               self.orders,
               self.dtypes)
        fill_kwarg = {}
        if fill_value is not None:
            fill_kwarg = {'fill_value': fill_value}

        for size, ndims, order, dtype in itertools.product(*par):
            shape = ndims * [size]

            # do not fill void type
            if fill_kwarg and dtype.str.startswith('|V'):
                continue

            arr = func(shape, order=order, dtype=dtype,
                       **fill_kwarg)

            assert_equal(arr.dtype, dtype)
            assert_(getattr(arr.flags, self.orders[order]))

            if fill_value is not None:
                if dtype.str.startswith('|S'):
                    val = str(fill_value)
                else:
                    val = fill_value
                assert_equal(arr, dtype.type(val))

    def test_zeros(self):
        self.check_function(np.zeros)

    def test_ones(self):
        self.check_function(np.zeros)

    def test_empty(self):
        self.check_function(np.empty)

    def test_full(self):
        self.check_function(np.full, 0)
        self.check_function(np.full, 1)

    @dec.skipif(not HAS_REFCOUNT, "python has no sys.getrefcount")
    def test_for_reference_leak(self):
        # Make sure we have an object for reference
        dim = 1
        beg = sys.getrefcount(dim)
        np.zeros([dim]*10)
        assert_(sys.getrefcount(dim) == beg)
        np.ones([dim]*10)
        assert_(sys.getrefcount(dim) == beg)
        np.empty([dim]*10)
        assert_(sys.getrefcount(dim) == beg)
        np.full([dim]*10, 0)
        assert_(sys.getrefcount(dim) == beg)


class TestLikeFuncs(TestCase):
    '''Test ones_like, zeros_like, empty_like and full_like'''

    def setUp(self):
        self.data = [
                # Array scalars
                (np.array(3.), None),
                (np.array(3), 'f8'),
                # 1D arrays
                (np.arange(6, dtype='f4'), None),
                (np.arange(6), 'c16'),
                # 2D C-layout arrays
                (np.arange(6).reshape(2, 3), None),
                (np.arange(6).reshape(3, 2), 'i1'),
                # 2D F-layout arrays
                (np.arange(6).reshape((2, 3), order='F'), None),
                (np.arange(6).reshape((3, 2), order='F'), 'i1'),
                # 3D C-layout arrays
                (np.arange(24).reshape(2, 3, 4), None),
                (np.arange(24).reshape(4, 3, 2), 'f4'),
                # 3D F-layout arrays
                (np.arange(24).reshape((2, 3, 4), order='F'), None),
                (np.arange(24).reshape((4, 3, 2), order='F'), 'f4'),
                # 3D non-C/F-layout arrays
                (np.arange(24).reshape(2, 3, 4).swapaxes(0, 1), None),
                (np.arange(24).reshape(4, 3, 2).swapaxes(0, 1), '?'),
                     ]

    def compare_array_value(self, dz, value, fill_value):
        if value is not None:
            if fill_value:
                try:
                    z = dz.dtype.type(value)
                except OverflowError:
                    pass
                else:
                    assert_(np.all(dz == z))
            else:
                assert_(np.all(dz == value))

    def check_like_function(self, like_function, value, fill_value=False):
        if fill_value:
            fill_kwarg = {'fill_value': value}
        else:
            fill_kwarg = {}
        for d, dtype in self.data:
            # default (K) order, dtype
            dz = like_function(d, dtype=dtype, **fill_kwarg)
            assert_equal(dz.shape, d.shape)
            assert_equal(np.array(dz.strides)*d.dtype.itemsize,
                         np.array(d.strides)*dz.dtype.itemsize)
            assert_equal(d.flags.c_contiguous, dz.flags.c_contiguous)
            assert_equal(d.flags.f_contiguous, dz.flags.f_contiguous)
            if dtype is None:
                assert_equal(dz.dtype, d.dtype)
            else:
                assert_equal(dz.dtype, np.dtype(dtype))
            self.compare_array_value(dz, value, fill_value)

            # C order, default dtype
            dz = like_function(d, order='C', dtype=dtype, **fill_kwarg)
            assert_equal(dz.shape, d.shape)
            assert_(dz.flags.c_contiguous)
            if dtype is None:
                assert_equal(dz.dtype, d.dtype)
            else:
                assert_equal(dz.dtype, np.dtype(dtype))
            self.compare_array_value(dz, value, fill_value)

            # F order, default dtype
            dz = like_function(d, order='F', dtype=dtype, **fill_kwarg)
            assert_equal(dz.shape, d.shape)
            assert_(dz.flags.f_contiguous)
            if dtype is None:
                assert_equal(dz.dtype, d.dtype)
            else:
                assert_equal(dz.dtype, np.dtype(dtype))
            self.compare_array_value(dz, value, fill_value)

            # A order
            dz = like_function(d, order='A', dtype=dtype, **fill_kwarg)
            assert_equal(dz.shape, d.shape)
            if d.flags.f_contiguous:
                assert_(dz.flags.f_contiguous)
            else:
                assert_(dz.flags.c_contiguous)
            if dtype is None:
                assert_equal(dz.dtype, d.dtype)
            else:
                assert_equal(dz.dtype, np.dtype(dtype))
            self.compare_array_value(dz, value, fill_value)

        # Test the 'subok' parameter
        a = np.matrix([[1, 2], [3, 4]])

        b = like_function(a, **fill_kwarg)
        assert_(type(b) is np.matrix)

        b = like_function(a, subok=False, **fill_kwarg)
        assert_(type(b) is not np.matrix)

    def test_ones_like(self):
        self.check_like_function(np.ones_like, 1)

    def test_zeros_like(self):
        self.check_like_function(np.zeros_like, 0)

    def test_empty_like(self):
        self.check_like_function(np.empty_like, None)

    def test_filled_like(self):
        self.check_like_function(np.full_like, 0, True)
        self.check_like_function(np.full_like, 1, True)
        self.check_like_function(np.full_like, 1000, True)
        self.check_like_function(np.full_like, 123.456, True)
        self.check_like_function(np.full_like, np.inf, True)


class TestCorrelate(TestCase):
    def _setup(self, dt):
        self.x = np.array([1, 2, 3, 4, 5], dtype=dt)
        self.xs = np.arange(1, 20)[::3]
        self.y = np.array([-1, -2, -3], dtype=dt)
        self.z1 = np.array([ -3.,  -8., -14., -20., -26., -14.,  -5.], dtype=dt)
        self.z1_4 = np.array([-2., -5., -8., -11., -14., -5.], dtype=dt)
        self.z1r = np.array([-15., -22., -22., -16., -10.,  -4.,  -1.], dtype=dt)
        self.z2 = np.array([-5., -14., -26., -20., -14., -8.,  -3.], dtype=dt)
        self.z2r = np.array([-1., -4., -10., -16., -22., -22., -15.], dtype=dt)
        self.zs = np.array([-3., -14., -30., -48., -66., -84.,
                           -102., -54., -19.], dtype=dt)

    def test_float(self):
        self._setup(np.float)
        z = np.correlate(self.x, self.y, 'full')
        assert_array_almost_equal(z, self.z1)
        z = np.correlate(self.x, self.y[:-1], 'full')
        assert_array_almost_equal(z, self.z1_4)
        z = np.correlate(self.y, self.x, 'full')
        assert_array_almost_equal(z, self.z2)
        z = np.correlate(self.x[::-1], self.y, 'full')
        assert_array_almost_equal(z, self.z1r)
        z = np.correlate(self.y, self.x[::-1], 'full')
        assert_array_almost_equal(z, self.z2r)
        z = np.correlate(self.xs, self.y, 'full')
        assert_array_almost_equal(z, self.zs)

    def test_object(self):
        self._setup(Decimal)
        z = np.correlate(self.x, self.y, 'full')
        assert_array_almost_equal(z, self.z1)
        z = np.correlate(self.y, self.x, 'full')
        assert_array_almost_equal(z, self.z2)

    def test_no_overwrite(self):
        d = np.ones(100)
        k = np.ones(3)
        np.correlate(d, k)
        assert_array_equal(d, np.ones(100))
        assert_array_equal(k, np.ones(3))

    def test_complex(self):
        x = np.array([1, 2, 3, 4+1j], dtype=np.complex)
        y = np.array([-1, -2j, 3+1j], dtype=np.complex)
        r_z = np.array([3-1j, 6, 8+1j, 11+5j, -5+8j, -4-1j], dtype=np.complex)
        r_z = r_z[::-1].conjugate()
        z = np.correlate(y, x, mode='full')
        assert_array_almost_equal(z, r_z)


class TestConvolve(TestCase):
    def test_object(self):
        d = [1.] * 100
        k = [1.] * 3
        assert_array_almost_equal(np.convolve(d, k)[2:-2], np.full(98, 3))

    def test_no_overwrite(self):
        d = np.ones(100)
        k = np.ones(3)
        np.convolve(d, k)
        assert_array_equal(d, np.ones(100))
        assert_array_equal(k, np.ones(3))


class TestArgwhere(object):
    def test_2D(self):
        x = np.arange(6).reshape((2, 3))
        assert_array_equal(np.argwhere(x > 1),
                           [[0, 2],
                            [1, 0],
                            [1, 1],
                            [1, 2]])

    def test_list(self):
        assert_equal(np.argwhere([4, 0, 2, 1, 3]), [[0], [2], [3], [4]])


class TestStringFunction(object):

    def test_set_string_function(self):
        a = np.array([1])
        np.set_string_function(lambda x: "FOO", repr=True)
        assert_equal(repr(a), "FOO")
        np.set_string_function(None, repr=True)
        assert_equal(repr(a), "array([1])")

        np.set_string_function(lambda x: "FOO", repr=False)
        assert_equal(str(a), "FOO")
        np.set_string_function(None, repr=False)
        assert_equal(str(a), "[1]")


class TestRoll(TestCase):
    def test_roll1d(self):
        x = np.arange(10)
        xr = np.roll(x, 2)
        assert_equal(xr, np.array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]))

    def test_roll2d(self):
        x2 = np.reshape(np.arange(10), (2, 5))
        x2r = np.roll(x2, 1)
        assert_equal(x2r, np.array([[9, 0, 1, 2, 3], [4, 5, 6, 7, 8]]))

        x2r = np.roll(x2, 1, axis=0)
        assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]))

        x2r = np.roll(x2, 1, axis=1)
        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))

        # Roll multiple axes at once.
        x2r = np.roll(x2, 1, axis=(0, 1))
        assert_equal(x2r, np.array([[9, 5, 6, 7, 8], [4, 0, 1, 2, 3]]))

        x2r = np.roll(x2, (1, 0), axis=(0, 1))
        assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]))

        x2r = np.roll(x2, (-1, 0), axis=(0, 1))
        assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]))

        x2r = np.roll(x2, (0, 1), axis=(0, 1))
        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))

        x2r = np.roll(x2, (0, -1), axis=(0, 1))
        assert_equal(x2r, np.array([[1, 2, 3, 4, 0], [6, 7, 8, 9, 5]]))

        x2r = np.roll(x2, (1, 1), axis=(0, 1))
        assert_equal(x2r, np.array([[9, 5, 6, 7, 8], [4, 0, 1, 2, 3]]))

        x2r = np.roll(x2, (-1, -1), axis=(0, 1))
        assert_equal(x2r, np.array([[6, 7, 8, 9, 5], [1, 2, 3, 4, 0]]))

        # Roll the same axis multiple times.
        x2r = np.roll(x2, 1, axis=(0, 0))
        assert_equal(x2r, np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]))

        x2r = np.roll(x2, 1, axis=(1, 1))
        assert_equal(x2r, np.array([[3, 4, 0, 1, 2], [8, 9, 5, 6, 7]]))

        # Roll more than one turn in either direction.
        x2r = np.roll(x2, 6, axis=1)
        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))

        x2r = np.roll(x2, -4, axis=1)
        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))

    def test_roll_empty(self):
        x = np.array([])
        assert_equal(np.roll(x, 1), np.array([]))


class TestRollaxis(TestCase):

    # expected shape indexed by (axis, start) for array of
    # shape (1, 2, 3, 4)
    tgtshape = {(0, 0): (1, 2, 3, 4), (0, 1): (1, 2, 3, 4),
                (0, 2): (2, 1, 3, 4), (0, 3): (2, 3, 1, 4),
                (0, 4): (2, 3, 4, 1),
                (1, 0): (2, 1, 3, 4), (1, 1): (1, 2, 3, 4),
                (1, 2): (1, 2, 3, 4), (1, 3): (1, 3, 2, 4),
                (1, 4): (1, 3, 4, 2),
                (2, 0): (3, 1, 2, 4), (2, 1): (1, 3, 2, 4),
                (2, 2): (1, 2, 3, 4), (2, 3): (1, 2, 3, 4),
                (2, 4): (1, 2, 4, 3),
                (3, 0): (4, 1, 2, 3), (3, 1): (1, 4, 2, 3),
                (3, 2): (1, 2, 4, 3), (3, 3): (1, 2, 3, 4),
                (3, 4): (1, 2, 3, 4)}

    def test_exceptions(self):
        a = np.arange(1*2*3*4).reshape(1, 2, 3, 4)
        assert_raises(ValueError, np.rollaxis, a, -5, 0)
        assert_raises(ValueError, np.rollaxis, a, 0, -5)
        assert_raises(ValueError, np.rollaxis, a, 4, 0)
        assert_raises(ValueError, np.rollaxis, a, 0, 5)

    def test_results(self):
        a = np.arange(1*2*3*4).reshape(1, 2, 3, 4).copy()
        aind = np.indices(a.shape)
        assert_(a.flags['OWNDATA'])
        for (i, j) in self.tgtshape:
            # positive axis, positive start
            res = np.rollaxis(a, axis=i, start=j)
            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
            assert_(np.all(res[i0, i1, i2, i3] == a))
            assert_(res.shape == self.tgtshape[(i, j)], str((i,j)))
            assert_(not res.flags['OWNDATA'])

            # negative axis, positive start
            ip = i + 1
            res = np.rollaxis(a, axis=-ip, start=j)
            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
            assert_(np.all(res[i0, i1, i2, i3] == a))
            assert_(res.shape == self.tgtshape[(4 - ip, j)])
            assert_(not res.flags['OWNDATA'])

            # positive axis, negative start
            jp = j + 1 if j < 4 else j
            res = np.rollaxis(a, axis=i, start=-jp)
            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
            assert_(np.all(res[i0, i1, i2, i3] == a))
            assert_(res.shape == self.tgtshape[(i, 4 - jp)])
            assert_(not res.flags['OWNDATA'])

            # negative axis, negative start
            ip = i + 1
            jp = j + 1 if j < 4 else j
            res = np.rollaxis(a, axis=-ip, start=-jp)
            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
            assert_(np.all(res[i0, i1, i2, i3] == a))
            assert_(res.shape == self.tgtshape[(4 - ip, 4 - jp)])
            assert_(not res.flags['OWNDATA'])


class TestMoveaxis(TestCase):
    def test_move_to_end(self):
        x = np.random.randn(5, 6, 7)
        for source, expected in [(0, (6, 7, 5)),
                                 (1, (5, 7, 6)),
                                 (2, (5, 6, 7)),
                                 (-1, (5, 6, 7))]:
            actual = np.moveaxis(x, source, -1).shape
            assert_(actual, expected)

    def test_move_new_position(self):
        x = np.random.randn(1, 2, 3, 4)
        for source, destination, expected in [
                (0, 1, (2, 1, 3, 4)),
                (1, 2, (1, 3, 2, 4)),
                (1, -1, (1, 3, 4, 2)),
                ]:
            actual = np.moveaxis(x, source, destination).shape
            assert_(actual, expected)

    def test_preserve_order(self):
        x = np.zeros((1, 2, 3, 4))
        for source, destination in [
                (0, 0),
                (3, -1),
                (-1, 3),
                ([0, -1], [0, -1]),
                ([2, 0], [2, 0]),
                (range(4), range(4)),
                ]:
            actual = np.moveaxis(x, source, destination).shape
            assert_(actual, (1, 2, 3, 4))

    def test_move_multiples(self):
        x = np.zeros((0, 1, 2, 3))
        for source, destination, expected in [
                ([0, 1], [2, 3], (2, 3, 0, 1)),
                ([2, 3], [0, 1], (2, 3, 0, 1)),
                ([0, 1, 2], [2, 3, 0], (2, 3, 0, 1)),
                ([3, 0], [1, 0], (0, 3, 1, 2)),
                ([0, 3], [0, 1], (0, 3, 1, 2)),
                ]:
            actual = np.moveaxis(x, source, destination).shape
            assert_(actual, expected)

    def test_errors(self):
        x = np.random.randn(1, 2, 3)
        assert_raises_regex(ValueError, 'invalid axis .* `source`',
                            np.moveaxis, x, 3, 0)
        assert_raises_regex(ValueError, 'invalid axis .* `source`',
                            np.moveaxis, x, -4, 0)
        assert_raises_regex(ValueError, 'invalid axis .* `destination`',
                            np.moveaxis, x, 0, 5)
        assert_raises_regex(ValueError, 'repeated axis in `source`',
                            np.moveaxis, x, [0, 0], [0, 1])
        assert_raises_regex(ValueError, 'repeated axis in `destination`',
                            np.moveaxis, x, [0, 1], [1, 1])
        assert_raises_regex(ValueError, 'must have the same number',
                            np.moveaxis, x, 0, [0, 1])
        assert_raises_regex(ValueError, 'must have the same number',
                            np.moveaxis, x, [0, 1], [0])

    def test_array_likes(self):
        x = np.ma.zeros((1, 2, 3))
        result = np.moveaxis(x, 0, 0)
        assert_(x.shape, result.shape)
        assert_(isinstance(result, np.ma.MaskedArray))

        x = [1, 2, 3]
        result = np.moveaxis(x, 0, 0)
        assert_(x, list(result))
        assert_(isinstance(result, np.ndarray))


class TestCross(TestCase):
    def test_2x2(self):
        u = [1, 2]
        v = [3, 4]
        z = -2
        cp = np.cross(u, v)
        assert_equal(cp, z)
        cp = np.cross(v, u)
        assert_equal(cp, -z)

    def test_2x3(self):
        u = [1, 2]
        v = [3, 4, 5]
        z = np.array([10, -5, -2])
        cp = np.cross(u, v)
        assert_equal(cp, z)
        cp = np.cross(v, u)
        assert_equal(cp, -z)

    def test_3x3(self):
        u = [1, 2, 3]
        v = [4, 5, 6]
        z = np.array([-3, 6, -3])
        cp = np.cross(u, v)
        assert_equal(cp, z)
        cp = np.cross(v, u)
        assert_equal(cp, -z)

    def test_broadcasting(self):
        # Ticket #2624 (Trac #2032)
        u = np.tile([1, 2], (11, 1))
        v = np.tile([3, 4], (11, 1))
        z = -2
        assert_equal(np.cross(u, v), z)
        assert_equal(np.cross(v, u), -z)
        assert_equal(np.cross(u, u), 0)

        u = np.tile([1, 2], (11, 1)).T
        v = np.tile([3, 4, 5], (11, 1))
        z = np.tile([10, -5, -2], (11, 1))
        assert_equal(np.cross(u, v, axisa=0), z)
        assert_equal(np.cross(v, u.T), -z)
        assert_equal(np.cross(v, v), 0)

        u = np.tile([1, 2, 3], (11, 1)).T
        v = np.tile([3, 4], (11, 1)).T
        z = np.tile([-12, 9, -2], (11, 1))
        assert_equal(np.cross(u, v, axisa=0, axisb=0), z)
        assert_equal(np.cross(v.T, u.T), -z)
        assert_equal(np.cross(u.T, u.T), 0)

        u = np.tile([1, 2, 3], (5, 1))
        v = np.tile([4, 5, 6], (5, 1)).T
        z = np.tile([-3, 6, -3], (5, 1))
        assert_equal(np.cross(u, v, axisb=0), z)
        assert_equal(np.cross(v.T, u), -z)
        assert_equal(np.cross(u, u), 0)

    def test_broadcasting_shapes(self):
        u = np.ones((2, 1, 3))
        v = np.ones((5, 3))
        assert_equal(np.cross(u, v).shape, (2, 5, 3))
        u = np.ones((10, 3, 5))
        v = np.ones((2, 5))
        assert_equal(np.cross(u, v, axisa=1, axisb=0).shape, (10, 5, 3))
        assert_raises(ValueError, np.cross, u, v, axisa=1, axisb=2)
        assert_raises(ValueError, np.cross, u, v, axisa=3, axisb=0)
        u = np.ones((10, 3, 5, 7))
        v = np.ones((5, 7, 2))
        assert_equal(np.cross(u, v, axisa=1, axisc=2).shape, (10, 5, 3, 7))
        assert_raises(ValueError, np.cross, u, v, axisa=-5, axisb=2)
        assert_raises(ValueError, np.cross, u, v, axisa=1, axisb=-4)
        # gh-5885
        u = np.ones((3, 4, 2))
        for axisc in range(-2, 2):
            assert_equal(np.cross(u, u, axisc=axisc).shape, (3, 4))


def test_outer_out_param():
    arr1 = np.ones((5,))
    arr2 = np.ones((2,))
    arr3 = np.linspace(-2, 2, 5)
    out1 = np.ndarray(shape=(5,5))
    out2 = np.ndarray(shape=(2, 5))
    res1 = np.outer(arr1, arr3, out1)
    assert_equal(res1, out1)
    assert_equal(np.outer(arr2, arr3, out2), out2)


class TestRequire(object):
    flag_names = ['C', 'C_CONTIGUOUS', 'CONTIGUOUS',
                  'F', 'F_CONTIGUOUS', 'FORTRAN',
                  'A', 'ALIGNED',
                  'W', 'WRITEABLE',
                  'O', 'OWNDATA']

    def generate_all_false(self, dtype):
        arr = np.zeros((2, 2), [('junk', 'i1'), ('a', dtype)])
        arr.setflags(write=False)
        a = arr['a']
        assert_(not a.flags['C'])
        assert_(not a.flags['F'])
        assert_(not a.flags['O'])
        assert_(not a.flags['W'])
        assert_(not a.flags['A'])
        return a

    def set_and_check_flag(self, flag, dtype, arr):
        if dtype is None:
            dtype = arr.dtype
        b = np.require(arr, dtype, [flag])
        assert_(b.flags[flag])
        assert_(b.dtype == dtype)

        # a further call to np.require ought to return the same array
        # unless OWNDATA is specified.
        c = np.require(b, None, [flag])
        if flag[0] != 'O':
            assert_(c is b)
        else:
            assert_(c.flags[flag])

    def test_require_each(self):

        id = ['f8', 'i4']
        fd = [None, 'f8', 'c16']
        for idtype, fdtype, flag in itertools.product(id, fd, self.flag_names):
            a = self.generate_all_false(idtype)
            yield self.set_and_check_flag, flag, fdtype,  a

    def test_unknown_requirement(self):
        a = self.generate_all_false('f8')
        assert_raises(KeyError, np.require, a, None, 'Q')

    def test_non_array_input(self):
        a = np.require([1, 2, 3, 4], 'i4', ['C', 'A', 'O'])
        assert_(a.flags['O'])
        assert_(a.flags['C'])
        assert_(a.flags['A'])
        assert_(a.dtype == 'i4')
        assert_equal(a, [1, 2, 3, 4])

    def test_C_and_F_simul(self):
        a = self.generate_all_false('f8')
        assert_raises(ValueError, np.require, a, None, ['C', 'F'])

    def test_ensure_array(self):
        class ArraySubclass(np.ndarray):
            pass

        a = ArraySubclass((2, 2))
        b = np.require(a, None, ['E'])
        assert_(type(b) is np.ndarray)

    def test_preserve_subtype(self):
        class ArraySubclass(np.ndarray):
            pass

        for flag in self.flag_names:
            a = ArraySubclass((2, 2))
            yield self.set_and_check_flag, flag, None, a


class TestBroadcast(TestCase):
    def test_broadcast_in_args(self):
        # gh-5881
        arrs = [np.empty((6, 7)), np.empty((5, 6, 1)), np.empty((7,)),
                np.empty((5, 1, 7))]
        mits = [np.broadcast(*arrs),
                np.broadcast(np.broadcast(*arrs[:2]), np.broadcast(*arrs[2:])),
                np.broadcast(arrs[0], np.broadcast(*arrs[1:-1]), arrs[-1])]
        for mit in mits:
            assert_equal(mit.shape, (5, 6, 7))
            assert_equal(mit.ndim, 3)
            assert_equal(mit.nd, 3)
            assert_equal(mit.numiter, 4)
            for a, ia in zip(arrs, mit.iters):
                assert_(a is ia.base)

    def test_broadcast_single_arg(self):
        # gh-6899
        arrs = [np.empty((5, 6, 7))]
        mit = np.broadcast(*arrs)
        assert_equal(mit.shape, (5, 6, 7))
        assert_equal(mit.ndim, 3)
        assert_equal(mit.nd, 3)
        assert_equal(mit.numiter, 1)
        assert_(arrs[0] is mit.iters[0].base)

    def test_number_of_arguments(self):
        arr = np.empty((5,))
        for j in range(35):
            arrs = [arr] * j
            if j < 1 or j > 32:
                assert_raises(ValueError, np.broadcast, *arrs)
            else:
                mit = np.broadcast(*arrs)
                assert_equal(mit.numiter, j)


class TestKeepdims(TestCase):

    class sub_array(np.ndarray):
        def sum(self, axis=None, dtype=None, out=None):
            return np.ndarray.sum(self, axis, dtype, out, keepdims=True)

    def test_raise(self):
        sub_class = self.sub_array
        x = np.arange(30).view(sub_class)
        assert_raises(TypeError, np.sum, x, keepdims=True)


if __name__ == "__main__":
    run_module_suite()