text: import collections.abc
  import tempfile
  import sys
  import shutil
  import warnings
  import operator
  import io
  import itertools
  import functools
  import ctypes
  import os
  import gc
  import weakref
  import pytest
  from contextlib import contextmanager
  
  from numpy.compat import pickle
  
  import pathlib
  import builtins
  from decimal import Decimal
  
  import numpy as np
  from numpy.compat import strchar
  import numpy.core._multiarray_tests as _multiarray_tests
  from numpy.testing import (
      assert_, assert_raises, assert_warns, assert_equal, assert_almost_equal,
      assert_array_equal, assert_raises_regex, assert_array_almost_equal,
      assert_allclose, IS_PYPY, HAS_REFCOUNT, assert_array_less, runstring,
      temppath, suppress_warnings, break_cycles,
      )
  from numpy.testing._private.utils import _no_tracing
  from numpy.core.tests._locales import CommaDecimalPointLocale
  
  # Need to test an object that does not fully implement math interface
  from datetime import timedelta, datetime
  
  
  def _aligned_zeros(shape, dtype=float, order="C", align=None):
      """
      Allocate a new ndarray with aligned memory.
  
      The ndarray is guaranteed *not* aligned to twice the requested alignment.
      Eg, if align=4, guarantees it is not aligned to 8. If align=None uses
      dtype.alignment."""
      dtype = np.dtype(dtype)
      if dtype == np.dtype(object):
          # Can't do this, fall back to standard allocation (which
          # should always be sufficiently aligned)
          if align is not None:
              raise ValueError("object array alignment not supported")
          return np.zeros(shape, dtype=dtype, order=order)
      if align is None:
          align = dtype.alignment
      if not hasattr(shape, '__len__'):
          shape = (shape,)
      size = functools.reduce(operator.mul, shape) * dtype.itemsize
      buf = np.empty(size + 2*align + 1, np.uint8)
  
      ptr = buf.__array_interface__['data'][0]
      offset = ptr % align
      if offset != 0:
          offset = align - offset
      if (ptr % (2*align)) == 0:
          offset += align
  
      # Note: slices producing 0-size arrays do not necessarily change
      # data pointer --- so we use and allocate size+1
      buf = buf[offset:offset+size+1][:-1]
      data = np.ndarray(shape, dtype, buf, order=order)
      data.fill(0)
      return data
  
  
  class TestFlags:
      def setup(self):
          self.a = np.arange(10)
  
      def test_writeable(self):
          mydict = locals()
          self.a.flags.writeable = False
          assert_raises(ValueError, runstring, 'self.a[0] = 3', mydict)
          assert_raises(ValueError, runstring, 'self.a[0:1].itemset(3)', mydict)
          self.a.flags.writeable = True
          self.a[0] = 5
          self.a[0] = 0
  
      def test_writeable_any_base(self):
          # Ensure that any base being writeable is sufficient to change flag;
          # this is especially interesting for arrays from an array interface.
          arr = np.arange(10)
  
          class subclass(np.ndarray):
              pass
  
          # Create subclass so base will not be collapsed, this is OK to change
          view1 = arr.view(subclass)
          view2 = view1[...]
          arr.flags.writeable = False
          view2.flags.writeable = False
          view2.flags.writeable = True  # Can be set to True again.
  
          arr = np.arange(10)
  
          class frominterface:
              def __init__(self, arr):
                  self.arr = arr
                  self.__array_interface__ = arr.__array_interface__
  
          view1 = np.asarray(frominterface)
          view2 = view1[...]
          view2.flags.writeable = False
          view2.flags.writeable = True
  
          view1.flags.writeable = False
          view2.flags.writeable = False
          with assert_raises(ValueError):
              # Must assume not writeable, since only base is not:
              view2.flags.writeable = True
  
      def test_writeable_from_readonly(self):
          # gh-9440 - make sure fromstring, from buffer on readonly buffers
          # set writeable False
          data = b'\x00' * 100
          vals = np.frombuffer(data, 'B')
          assert_raises(ValueError, vals.setflags, write=True)
          types = np.dtype( [('vals', 'u1'), ('res3', 'S4')] )
          values = np.core.records.fromstring(data, types)
          vals = values['vals']
          assert_raises(ValueError, vals.setflags, write=True)
  
      def test_writeable_from_buffer(self):
          data = bytearray(b'\x00' * 100)
          vals = np.frombuffer(data, 'B')
          assert_(vals.flags.writeable)
          vals.setflags(write=False)
          assert_(vals.flags.writeable is False)
          vals.setflags(write=True)
          assert_(vals.flags.writeable)
          types = np.dtype( [('vals', 'u1'), ('res3', 'S4')] )
          values = np.core.records.fromstring(data, types)
          vals = values['vals']
          assert_(vals.flags.writeable)
          vals.setflags(write=False)
          assert_(vals.flags.writeable is False)
          vals.setflags(write=True)
          assert_(vals.flags.writeable)
  
      @pytest.mark.skipif(IS_PYPY, reason="PyPy always copies")
      def test_writeable_pickle(self):
          import pickle
          # Small arrays will be copied without setting base.
          # See condition for using PyArray_SetBaseObject in
          # array_setstate.
          a = np.arange(1000)
          for v in range(pickle.HIGHEST_PROTOCOL):
              vals = pickle.loads(pickle.dumps(a, v))
              assert_(vals.flags.writeable)
              assert_(isinstance(vals.base, bytes))
  
      def test_writeable_from_c_data(self):
          # Test that the writeable flag can be changed for an array wrapping
          # low level C-data, but not owning its data.
          # Also see that this is deprecated to change from python.
          from numpy.core._multiarray_tests import get_c_wrapping_array
  
          arr_writeable = get_c_wrapping_array(True)
          assert not arr_writeable.flags.owndata
          assert arr_writeable.flags.writeable
          view = arr_writeable[...]
  
          # Toggling the writeable flag works on the view:
          view.flags.writeable = False
          assert not view.flags.writeable
          view.flags.writeable = True
          assert view.flags.writeable
          # Flag can be unset on the arr_writeable:
          arr_writeable.flags.writeable = False
  
          arr_readonly = get_c_wrapping_array(False)
          assert not arr_readonly.flags.owndata
          assert not arr_readonly.flags.writeable
  
          for arr in [arr_writeable, arr_readonly]:
              view = arr[...]
              view.flags.writeable = False  # make sure it is readonly
              arr.flags.writeable = False
              assert not arr.flags.writeable
  
              with assert_raises(ValueError):
                  view.flags.writeable = True
  
              with warnings.catch_warnings():
                  warnings.simplefilter("error", DeprecationWarning)
                  with assert_raises(DeprecationWarning):
                      arr.flags.writeable = True
  
              with assert_warns(DeprecationWarning):
                  arr.flags.writeable = True
  
      def test_warnonwrite(self):
          a = np.arange(10)
          a.flags._warn_on_write = True
          with warnings.catch_warnings(record=True) as w:
              warnings.filterwarnings('always')
              a[1] = 10
              a[2] = 10
              # only warn once
              assert_(len(w) == 1)
  
      def test_otherflags(self):
          assert_equal(self.a.flags.carray, True)
          assert_equal(self.a.flags['C'], True)
          assert_equal(self.a.flags.farray, False)
          assert_equal(self.a.flags.behaved, True)
          assert_equal(self.a.flags.fnc, False)
          assert_equal(self.a.flags.forc, True)
          assert_equal(self.a.flags.owndata, True)
          assert_equal(self.a.flags.writeable, True)
          assert_equal(self.a.flags.aligned, True)
          with assert_warns(DeprecationWarning):
              assert_equal(self.a.flags.updateifcopy, False)
          with assert_warns(DeprecationWarning):
              assert_equal(self.a.flags['U'], False)
              assert_equal(self.a.flags['UPDATEIFCOPY'], False)
          assert_equal(self.a.flags.writebackifcopy, False)
          assert_equal(self.a.flags['X'], False)
          assert_equal(self.a.flags['WRITEBACKIFCOPY'], False)
  
      def test_string_align(self):
          a = np.zeros(4, dtype=np.dtype('|S4'))
          assert_(a.flags.aligned)
          # not power of two are accessed byte-wise and thus considered aligned
          a = np.zeros(5, dtype=np.dtype('|S4'))
          assert_(a.flags.aligned)
  
      def test_void_align(self):
          a = np.zeros(4, dtype=np.dtype([("a", "i4"), ("b", "i4")]))
          assert_(a.flags.aligned)
  
  
  class TestHash:
      # see #3793
      def test_int(self):
          for st, ut, s in [(np.int8, np.uint8, 8),
                            (np.int16, np.uint16, 16),
                            (np.int32, np.uint32, 32),
                            (np.int64, np.uint64, 64)]:
              for i in range(1, s):
                  assert_equal(hash(st(-2**i)), hash(-2**i),
                               err_msg="%r: -2**%d" % (st, i))
                  assert_equal(hash(st(2**(i - 1))), hash(2**(i - 1)),
                               err_msg="%r: 2**%d" % (st, i - 1))
                  assert_equal(hash(st(2**i - 1)), hash(2**i - 1),
                               err_msg="%r: 2**%d - 1" % (st, i))
  
                  i = max(i - 1, 1)
                  assert_equal(hash(ut(2**(i - 1))), hash(2**(i - 1)),
                               err_msg="%r: 2**%d" % (ut, i - 1))
                  assert_equal(hash(ut(2**i - 1)), hash(2**i - 1),
                               err_msg="%r: 2**%d - 1" % (ut, i))
  
  
  class TestAttributes:
      def setup(self):
          self.one = np.arange(10)
          self.two = np.arange(20).reshape(4, 5)
          self.three = np.arange(60, dtype=np.float64).reshape(2, 5, 6)
  
      def test_attributes(self):
          assert_equal(self.one.shape, (10,))
          assert_equal(self.two.shape, (4, 5))
          assert_equal(self.three.shape, (2, 5, 6))
          self.three.shape = (10, 3, 2)
          assert_equal(self.three.shape, (10, 3, 2))
          self.three.shape = (2, 5, 6)
          assert_equal(self.one.strides, (self.one.itemsize,))
          num = self.two.itemsize
          assert_equal(self.two.strides, (5*num, num))
          num = self.three.itemsize
          assert_equal(self.three.strides, (30*num, 6*num, num))
          assert_equal(self.one.ndim, 1)
          assert_equal(self.two.ndim, 2)
          assert_equal(self.three.ndim, 3)
          num = self.two.itemsize
          assert_equal(self.two.size, 20)
          assert_equal(self.two.nbytes, 20*num)
          assert_equal(self.two.itemsize, self.two.dtype.itemsize)
          assert_equal(self.two.base, np.arange(20))
  
      def test_dtypeattr(self):
          assert_equal(self.one.dtype, np.dtype(np.int_))
          assert_equal(self.three.dtype, np.dtype(np.float_))
          assert_equal(self.one.dtype.char, 'l')
          assert_equal(self.three.dtype.char, 'd')
          assert_(self.three.dtype.str[0] in '<>')
          assert_equal(self.one.dtype.str[1], 'i')
          assert_equal(self.three.dtype.str[1], 'f')
  
      def test_int_subclassing(self):
          # Regression test for https://github.com/numpy/numpy/pull/3526
  
          numpy_int = np.int_(0)
  
          # int_ doesn't inherit from Python int, because it's not fixed-width
          assert_(not isinstance(numpy_int, int))
  
      def test_stridesattr(self):
          x = self.one
  
          def make_array(size, offset, strides):
              return np.ndarray(size, buffer=x, dtype=int,
                                offset=offset*x.itemsize,
                                strides=strides*x.itemsize)
  
          assert_equal(make_array(4, 4, -1), np.array([4, 3, 2, 1]))
          assert_raises(ValueError, make_array, 4, 4, -2)
          assert_raises(ValueError, make_array, 4, 2, -1)
          assert_raises(ValueError, make_array, 8, 3, 1)
          assert_equal(make_array(8, 3, 0), np.array([3]*8))
          # Check behavior reported in gh-2503:
          assert_raises(ValueError, make_array, (2, 3), 5, np.array([-2, -3]))
          make_array(0, 0, 10)
  
      def test_set_stridesattr(self):
          x = self.one
  
          def make_array(size, offset, strides):
              try:
                  r = np.ndarray([size], dtype=int, buffer=x,
                                 offset=offset*x.itemsize)
              except Exception as e:
                  raise RuntimeError(e)
              r.strides = strides = strides*x.itemsize
              return r
  
          assert_equal(make_array(4, 4, -1), np.array([4, 3, 2, 1]))
          assert_equal(make_array(7, 3, 1), np.array([3, 4, 5, 6, 7, 8, 9]))
          assert_raises(ValueError, make_array, 4, 4, -2)
          assert_raises(ValueError, make_array, 4, 2, -1)
          assert_raises(RuntimeError, make_array, 8, 3, 1)
          # Check that the true extent of the array is used.
          # Test relies on as_strided base not exposing a buffer.
          x = np.lib.stride_tricks.as_strided(np.arange(1), (10, 10), (0, 0))
  
          def set_strides(arr, strides):
              arr.strides = strides
  
          assert_raises(ValueError, set_strides, x, (10*x.itemsize, x.itemsize))
  
          # Test for offset calculations:
          x = np.lib.stride_tricks.as_strided(np.arange(10, dtype=np.int8)[-1],
                                                      shape=(10,), strides=(-1,))
          assert_raises(ValueError, set_strides, x[::-1], -1)
          a = x[::-1]
          a.strides = 1
          a[::2].strides = 2
  
          # test 0d
          arr_0d = np.array(0)
          arr_0d.strides = ()
          assert_raises(TypeError, set_strides, arr_0d, None)
  
      def test_fill(self):
          for t in "?bhilqpBHILQPfdgFDGO":
              x = np.empty((3, 2, 1), t)
              y = np.empty((3, 2, 1), t)
              x.fill(1)
              y[...] = 1
              assert_equal(x, y)
  
      def test_fill_max_uint64(self):
          x = np.empty((3, 2, 1), dtype=np.uint64)
          y = np.empty((3, 2, 1), dtype=np.uint64)
          value = 2**64 - 1
          y[...] = value
          x.fill(value)
          assert_array_equal(x, y)
  
      def test_fill_struct_array(self):
          # Filling from a scalar
          x = np.array([(0, 0.0), (1, 1.0)], dtype='i4,f8')
          x.fill(x[0])
          assert_equal(x['f1'][1], x['f1'][0])
          # Filling from a tuple that can be converted
          # to a scalar
          x = np.zeros(2, dtype=[('a', 'f8'), ('b', 'i4')])
          x.fill((3.5, -2))
          assert_array_equal(x['a'], [3.5, 3.5])
          assert_array_equal(x['b'], [-2, -2])
  
  
  class TestArrayConstruction:
      def test_array(self):
          d = np.ones(6)
          r = np.array([d, d])
          assert_equal(r, np.ones((2, 6)))
  
          d = np.ones(6)
          tgt = np.ones((2, 6))
          r = np.array([d, d])
          assert_equal(r, tgt)
          tgt[1] = 2
          r = np.array([d, d + 1])
          assert_equal(r, tgt)
  
          d = np.ones(6)
          r = np.array([[d, d]])
          assert_equal(r, np.ones((1, 2, 6)))
  
          d = np.ones(6)
          r = np.array([[d, d], [d, d]])
          assert_equal(r, np.ones((2, 2, 6)))
  
          d = np.ones((6, 6))
          r = np.array([d, d])
          assert_equal(r, np.ones((2, 6, 6)))
  
          d = np.ones((6, ))
          r = np.array([[d, d + 1], d + 2], dtype=object)
          assert_equal(len(r), 2)
          assert_equal(r[0], [d, d + 1])
          assert_equal(r[1], d + 2)
  
          tgt = np.ones((2, 3), dtype=bool)
          tgt[0, 2] = False
          tgt[1, 0:2] = False
          r = np.array([[True, True, False], [False, False, True]])
          assert_equal(r, tgt)
          r = np.array([[True, False], [True, False], [False, True]])
          assert_equal(r, tgt.T)
  
      def test_array_empty(self):
          assert_raises(TypeError, np.array)
  
      def test_array_copy_false(self):
          d = np.array([1, 2, 3])
          e = np.array(d, copy=False)
          d[1] = 3
          assert_array_equal(e, [1, 3, 3])
          e = np.array(d, copy=False, order='F')
          d[1] = 4
          assert_array_equal(e, [1, 4, 3])
          e[2] = 7
          assert_array_equal(d, [1, 4, 7])
  
      def test_array_copy_true(self):
          d = np.array([[1,2,3], [1, 2, 3]])
          e = np.array(d, copy=True)
          d[0, 1] = 3
          e[0, 2] = -7
          assert_array_equal(e, [[1, 2, -7], [1, 2, 3]])
          assert_array_equal(d, [[1, 3, 3], [1, 2, 3]])
          e = np.array(d, copy=True, order='F')
          d[0, 1] = 5
          e[0, 2] = 7
          assert_array_equal(e, [[1, 3, 7], [1, 2, 3]])
          assert_array_equal(d, [[1, 5, 3], [1,2,3]])
  
      def test_array_cont(self):
          d = np.ones(10)[::2]
          assert_(np.ascontiguousarray(d).flags.c_contiguous)
          assert_(np.ascontiguousarray(d).flags.f_contiguous)
          assert_(np.asfortranarray(d).flags.c_contiguous)
          assert_(np.asfortranarray(d).flags.f_contiguous)
          d = np.ones((10, 10))[::2,::2]
          assert_(np.ascontiguousarray(d).flags.c_contiguous)
          assert_(np.asfortranarray(d).flags.f_contiguous)
  
  
  class TestAssignment:
      def test_assignment_broadcasting(self):
          a = np.arange(6).reshape(2, 3)
  
          # Broadcasting the input to the output
          a[...] = np.arange(3)
          assert_equal(a, [[0, 1, 2], [0, 1, 2]])
          a[...] = np.arange(2).reshape(2, 1)
          assert_equal(a, [[0, 0, 0], [1, 1, 1]])
  
          # For compatibility with <= 1.5, a limited version of broadcasting
          # the output to the input.
          #
          # This behavior is inconsistent with NumPy broadcasting
          # in general, because it only uses one of the two broadcasting
          # rules (adding a new "1" dimension to the left of the shape),
          # applied to the output instead of an input. In NumPy 2.0, this kind
          # of broadcasting assignment will likely be disallowed.
          a[...] = np.arange(6)[::-1].reshape(1, 2, 3)
          assert_equal(a, [[5, 4, 3], [2, 1, 0]])
          # The other type of broadcasting would require a reduction operation.
  
          def assign(a, b):
              a[...] = b
  
          assert_raises(ValueError, assign, a, np.arange(12).reshape(2, 2, 3))
  
      def test_assignment_errors(self):
          # Address issue #2276
          class C:
              pass
          a = np.zeros(1)
  
          def assign(v):
              a[0] = v
  
          assert_raises((AttributeError, TypeError), assign, C())
          assert_raises(ValueError, assign, [1])
  
      def test_unicode_assignment(self):
          # gh-5049
          from numpy.core.numeric import set_string_function
  
          @contextmanager
          def inject_str(s):
              """ replace ndarray.__str__ temporarily """
              set_string_function(lambda x: s, repr=False)
              try:
                  yield
              finally:
                  set_string_function(None, repr=False)
  
          a1d = np.array([u'test'])
          a0d = np.array(u'done')
          with inject_str(u'bad'):
              a1d[0] = a0d  # previously this would invoke __str__
          assert_equal(a1d[0], u'done')
  
          # this would crash for the same reason
          np.array([np.array(u'\xe5\xe4\xf6')])
  
      def test_stringlike_empty_list(self):
          # gh-8902
          u = np.array([u'done'])
          b = np.array([b'done'])
  
          class bad_sequence:
              def __getitem__(self): pass
              def __len__(self): raise RuntimeError
  
          assert_raises(ValueError, operator.setitem, u, 0, [])
          assert_raises(ValueError, operator.setitem, b, 0, [])
  
          assert_raises(ValueError, operator.setitem, u, 0, bad_sequence())
          assert_raises(ValueError, operator.setitem, b, 0, bad_sequence())
  
      def test_longdouble_assignment(self):
          # only relevant if longdouble is larger than float
          # we're looking for loss of precision
  
          for dtype in (np.longdouble, np.longcomplex):
              # gh-8902
              tinyb = np.nextafter(np.longdouble(0), 1).astype(dtype)
              tinya = np.nextafter(np.longdouble(0), -1).astype(dtype)
  
              # construction
              tiny1d = np.array([tinya])
              assert_equal(tiny1d[0], tinya)
  
              # scalar = scalar
              tiny1d[0] = tinyb
              assert_equal(tiny1d[0], tinyb)
  
              # 0d = scalar
              tiny1d[0, ...] = tinya
              assert_equal(tiny1d[0], tinya)
  
              # 0d = 0d
              tiny1d[0, ...] = tinyb[...]
              assert_equal(tiny1d[0], tinyb)
  
              # scalar = 0d
              tiny1d[0] = tinyb[...]
              assert_equal(tiny1d[0], tinyb)
  
              arr = np.array([np.array(tinya)])
              assert_equal(arr[0], tinya)
  
      def test_cast_to_string(self):
          # cast to str should do "str(scalar)", not "str(scalar.item())"
          # Example: In python2, str(float) is truncated, so we want to avoid
          # str(np.float64(...).item()) as this would incorrectly truncate.
          a = np.zeros(1, dtype='S20')
          a[:] = np.array(['1.12345678901234567890'], dtype='f8')
          assert_equal(a[0], b"1.1234567890123457")
  
  
  class TestDtypedescr:
      def test_construction(self):
          d1 = np.dtype('i4')
          assert_equal(d1, np.dtype(np.int32))
          d2 = np.dtype('f8')
          assert_equal(d2, np.dtype(np.float64))
  
      def test_byteorders(self):
          assert_(np.dtype('<i4') != np.dtype('>i4'))
          assert_(np.dtype([('a', '<i4')]) != np.dtype([('a', '>i4')]))
  
      def test_structured_non_void(self):
          fields = [('a', '<i2'), ('b', '<i2')]
          dt_int = np.dtype(('i4', fields))
          assert_equal(str(dt_int), "(numpy.int32, [('a', '<i2'), ('b', '<i2')])")
  
          # gh-9821
          arr_int = np.zeros(4, dt_int)
          assert_equal(repr(arr_int),
              "array([0, 0, 0, 0], dtype=(numpy.int32, [('a', '<i2'), ('b', '<i2')]))")
  
  
  class TestZeroRank:
      def setup(self):
          self.d = np.array(0), np.array('x', object)
  
      def test_ellipsis_subscript(self):
          a, b = self.d
          assert_equal(a[...], 0)
          assert_equal(b[...], 'x')
          assert_(a[...].base is a)  # `a[...] is a` in numpy <1.9.
          assert_(b[...].base is b)  # `b[...] is b` in numpy <1.9.
  
      def test_empty_subscript(self):
          a, b = self.d
          assert_equal(a[()], 0)
          assert_equal(b[()], 'x')
          assert_(type(a[()]) is a.dtype.type)
          assert_(type(b[()]) is str)
  
      def test_invalid_subscript(self):
          a, b = self.d
          assert_raises(IndexError, lambda x: x[0], a)
          assert_raises(IndexError, lambda x: x[0], b)
          assert_raises(IndexError, lambda x: x[np.array([], int)], a)
          assert_raises(IndexError, lambda x: x[np.array([], int)], b)
  
      def test_ellipsis_subscript_assignment(self):
          a, b = self.d
          a[...] = 42
          assert_equal(a, 42)
          b[...] = ''
          assert_equal(b.item(), '')
  
      def test_empty_subscript_assignment(self):
          a, b = self.d
          a[()] = 42
          assert_equal(a, 42)
          b[()] = ''
          assert_equal(b.item(), '')
  
      def test_invalid_subscript_assignment(self):
          a, b = self.d
  
          def assign(x, i, v):
              x[i] = v
  
          assert_raises(IndexError, assign, a, 0, 42)
          assert_raises(IndexError, assign, b, 0, '')
          assert_raises(ValueError, assign, a, (), '')
  
      def test_newaxis(self):
          a, b = self.d
          assert_equal(a[np.newaxis].shape, (1,))
          assert_equal(a[..., np.newaxis].shape, (1,))
          assert_equal(a[np.newaxis, ...].shape, (1,))
          assert_equal(a[..., np.newaxis].shape, (1,))
          assert_equal(a[np.newaxis, ..., np.newaxis].shape, (1, 1))
          assert_equal(a[..., np.newaxis, np.newaxis].shape, (1, 1))
          assert_equal(a[np.newaxis, np.newaxis, ...].shape, (1, 1))
          assert_equal(a[(np.newaxis,)*10].shape, (1,)*10)
  
      def test_invalid_newaxis(self):
          a, b = self.d
  
          def subscript(x, i):
              x[i]
  
          assert_raises(IndexError, subscript, a, (np.newaxis, 0))
          assert_raises(IndexError, subscript, a, (np.newaxis,)*50)
  
      def test_constructor(self):
          x = np.ndarray(())
          x[()] = 5
          assert_equal(x[()], 5)
          y = np.ndarray((), buffer=x)
          y[()] = 6
          assert_equal(x[()], 6)
  
          # strides and shape must be the same length
          with pytest.raises(ValueError):
              np.ndarray((2,), strides=())
          with pytest.raises(ValueError):
              np.ndarray((), strides=(2,))
  
      def test_output(self):
          x = np.array(2)
          assert_raises(ValueError, np.add, x, [1], x)
  
      def test_real_imag(self):
          # contiguity checks are for gh-11245
          x = np.array(1j)
          xr = x.real
          xi = x.imag
  
          assert_equal(xr, np.array(0))
          assert_(type(xr) is np.ndarray)
          assert_equal(xr.flags.contiguous, True)
          assert_equal(xr.flags.f_contiguous, True)
  
          assert_equal(xi, np.array(1))
          assert_(type(xi) is np.ndarray)
          assert_equal(xi.flags.contiguous, True)
          assert_equal(xi.flags.f_contiguous, True)
  
  
  class TestScalarIndexing:
      def setup(self):
          self.d = np.array([0, 1])[0]
  
      def test_ellipsis_subscript(self):
          a = self.d
          assert_equal(a[...], 0)
          assert_equal(a[...].shape, ())
  
      def test_empty_subscript(self):
          a = self.d
          assert_equal(a[()], 0)
          assert_equal(a[()].shape, ())
  
      def test_invalid_subscript(self):
          a = self.d
          assert_raises(IndexError, lambda x: x[0], a)
          assert_raises(IndexError, lambda x: x[np.array([], int)], a)
  
      def test_invalid_subscript_assignment(self):
          a = self.d
  
          def assign(x, i, v):
              x[i] = v
  
          assert_raises(TypeError, assign, a, 0, 42)
  
      def test_newaxis(self):
          a = self.d
          assert_equal(a[np.newaxis].shape, (1,))
          assert_equal(a[..., np.newaxis].shape, (1,))
          assert_equal(a[np.newaxis, ...].shape, (1,))
          assert_equal(a[..., np.newaxis].shape, (1,))
          assert_equal(a[np.newaxis, ..., np.newaxis].shape, (1, 1))
          assert_equal(a[..., np.newaxis, np.newaxis].shape, (1, 1))
          assert_equal(a[np.newaxis, np.newaxis, ...].shape, (1, 1))
          assert_equal(a[(np.newaxis,)*10].shape, (1,)*10)
  
      def test_invalid_newaxis(self):
          a = self.d
  
          def subscript(x, i):
              x[i]
  
          assert_raises(IndexError, subscript, a, (np.newaxis, 0))
          assert_raises(IndexError, subscript, a, (np.newaxis,)*50)
  
      def test_overlapping_assignment(self):
          # With positive strides
          a = np.arange(4)
          a[:-1] = a[1:]
          assert_equal(a, [1, 2, 3, 3])
  
          a = np.arange(4)
          a[1:] = a[:-1]
          assert_equal(a, [0, 0, 1, 2])
  
          # With positive and negative strides
          a = np.arange(4)
          a[:] = a[::-1]
          assert_equal(a, [3, 2, 1, 0])
  
          a = np.arange(6).reshape(2, 3)
          a[::-1,:] = a[:, ::-1]
          assert_equal(a, [[5, 4, 3], [2, 1, 0]])
  
          a = np.arange(6).reshape(2, 3)
          a[::-1, ::-1] = a[:, ::-1]
          assert_equal(a, [[3, 4, 5], [0, 1, 2]])
  
          # With just one element overlapping
          a = np.arange(5)
          a[:3] = a[2:]
          assert_equal(a, [2, 3, 4, 3, 4])
  
          a = np.arange(5)
          a[2:] = a[:3]
          assert_equal(a, [0, 1, 0, 1, 2])
  
          a = np.arange(5)
          a[2::-1] = a[2:]
          assert_equal(a, [4, 3, 2, 3, 4])
  
          a = np.arange(5)
          a[2:] = a[2::-1]
          assert_equal(a, [0, 1, 2, 1, 0])
  
          a = np.arange(5)
          a[2::-1] = a[:1:-1]
          assert_equal(a, [2, 3, 4, 3, 4])
  
          a = np.arange(5)
          a[:1:-1] = a[2::-1]
          assert_equal(a, [0, 1, 0, 1, 2])
  
  
  class TestCreation:
      """
      Test the np.array constructor
      """
      def test_from_attribute(self):
          class x:
              def __array__(self, dtype=None):
                  pass
  
          assert_raises(ValueError, np.array, x())
  
      def test_from_string(self):
          types = np.typecodes['AllInteger'] + np.typecodes['Float']
          nstr = ['123', '123']
          result = np.array([123, 123], dtype=int)
          for type in types:
              msg = 'String conversion for %s' % type
              assert_equal(np.array(nstr, dtype=type), result, err_msg=msg)
  
      def test_void(self):
          arr = np.array([], dtype='V')
          assert_equal(arr.dtype.kind, 'V')
  
      def test_too_big_error(self):
          # 45341 is the smallest integer greater than sqrt(2**31 - 1).
          # 3037000500 is the smallest integer greater than sqrt(2**63 - 1).
          # We want to make sure that the square byte array with those dimensions
          # is too big on 32 or 64 bit systems respectively.
          if np.iinfo('intp').max == 2**31 - 1:
              shape = (46341, 46341)
          elif np.iinfo('intp').max == 2**63 - 1:
              shape = (3037000500, 3037000500)
          else:
              return
          assert_raises(ValueError, np.empty, shape, dtype=np.int8)
          assert_raises(ValueError, np.zeros, shape, dtype=np.int8)
          assert_raises(ValueError, np.ones, shape, dtype=np.int8)
  
      def test_zeros(self):
          types = np.typecodes['AllInteger'] + np.typecodes['AllFloat']
          for dt in types:
              d = np.zeros((13,), dtype=dt)
              assert_equal(np.count_nonzero(d), 0)
              # true for ieee floats
              assert_equal(d.sum(), 0)
              assert_(not d.any())
  
              d = np.zeros(2, dtype='(2,4)i4')
              assert_equal(np.count_nonzero(d), 0)
              assert_equal(d.sum(), 0)
              assert_(not d.any())
  
              d = np.zeros(2, dtype='4i4')
              assert_equal(np.count_nonzero(d), 0)
              assert_equal(d.sum(), 0)
              assert_(not d.any())
  
              d = np.zeros(2, dtype='(2,4)i4, (2,4)i4')
              assert_equal(np.count_nonzero(d), 0)
  
      @pytest.mark.slow
      def test_zeros_big(self):
          # test big array as they might be allocated different by the system
          types = np.typecodes['AllInteger'] + np.typecodes['AllFloat']
          for dt in types:
              d = np.zeros((30 * 1024**2,), dtype=dt)
              assert_(not d.any())
              # This test can fail on 32-bit systems due to insufficient
              # contiguous memory. Deallocating the previous array increases the
              # chance of success.
              del(d)
  
      def test_zeros_obj(self):
          # test initialization from PyLong(0)
          d = np.zeros((13,), dtype=object)
          assert_array_equal(d, [0] * 13)
          assert_equal(np.count_nonzero(d), 0)
  
      def test_zeros_obj_obj(self):
          d = np.zeros(10, dtype=[('k', object, 2)])
          assert_array_equal(d['k'], 0)
  
      def test_zeros_like_like_zeros(self):
          # test zeros_like returns the same as zeros
          for c in np.typecodes['All']:
              if c == 'V':
                  continue
              d = np.zeros((3,3), dtype=c)
              assert_array_equal(np.zeros_like(d), d)
              assert_equal(np.zeros_like(d).dtype, d.dtype)
          # explicitly check some special cases
          d = np.zeros((3,3), dtype='S5')
          assert_array_equal(np.zeros_like(d), d)
          assert_equal(np.zeros_like(d).dtype, d.dtype)
          d = np.zeros((3,3), dtype='U5')
          assert_array_equal(np.zeros_like(d), d)
          assert_equal(np.zeros_like(d).dtype, d.dtype)
  
          d = np.zeros((3,3), dtype='<i4')
          assert_array_equal(np.zeros_like(d), d)
          assert_equal(np.zeros_like(d).dtype, d.dtype)
          d = np.zeros((3,3), dtype='>i4')
          assert_array_equal(np.zeros_like(d), d)
          assert_equal(np.zeros_like(d).dtype, d.dtype)
  
          d = np.zeros((3,3), dtype='<M8[s]')
          assert_array_equal(np.zeros_like(d), d)
          assert_equal(np.zeros_like(d).dtype, d.dtype)
          d = np.zeros((3,3), dtype='>M8[s]')
          assert_array_equal(np.zeros_like(d), d)
          assert_equal(np.zeros_like(d).dtype, d.dtype)
  
          d = np.zeros((3,3), dtype='f4,f4')
          assert_array_equal(np.zeros_like(d), d)
          assert_equal(np.zeros_like(d).dtype, d.dtype)
  
      def test_empty_unicode(self):
          # don't throw decode errors on garbage memory
          for i in range(5, 100, 5):
              d = np.empty(i, dtype='U')
              str(d)
  
      def test_sequence_non_homogeneous(self):
          assert_equal(np.array([4, 2**80]).dtype, object)
          assert_equal(np.array([4, 2**80, 4]).dtype, object)
          assert_equal(np.array([2**80, 4]).dtype, object)
          assert_equal(np.array([2**80] * 3).dtype, object)
          assert_equal(np.array([[1, 1],[1j, 1j]]).dtype, complex)
          assert_equal(np.array([[1j, 1j],[1, 1]]).dtype, complex)
          assert_equal(np.array([[1, 1, 1],[1, 1j, 1.], [1, 1, 1]]).dtype, complex)
  
      def test_non_sequence_sequence(self):
          """Should not segfault.
  
          Class Fail breaks the sequence protocol for new style classes, i.e.,
          those derived from object. Class Map is a mapping type indicated by
          raising a ValueError. At some point we may raise a warning instead
          of an error in the Fail case.
  
          """
          class Fail:
              def __len__(self):
                  return 1
  
              def __getitem__(self, index):
                  raise ValueError()
  
          class Map:
              def __len__(self):
                  return 1
  
              def __getitem__(self, index):
                  raise KeyError()
  
          a = np.array([Map()])
          assert_(a.shape == (1,))
          assert_(a.dtype == np.dtype(object))
          assert_raises(ValueError, np.array, [Fail()])
  
      def test_no_len_object_type(self):
          # gh-5100, want object array from iterable object without len()
          class Point2:
              def __init__(self):
                  pass
  
              def __getitem__(self, ind):
                  if ind in [0, 1]:
                      return ind
                  else:
                      raise IndexError()
          d = np.array([Point2(), Point2(), Point2()])
          assert_equal(d.dtype, np.dtype(object))
  
      def test_false_len_sequence(self):
          # gh-7264, segfault for this example
          class C:
              def __getitem__(self, i):
                  raise IndexError
              def __len__(self):
                  return 42
  
          a = np.array(C()) # segfault?
          assert_equal(len(a), 0)
  
      def test_false_len_iterable(self):
          # Special case where a bad __getitem__ makes us fall back on __iter__:
          class C:
              def __getitem__(self, x):
                  raise Exception
              def __iter__(self):
                  return iter(())
              def __len__(self):
                  return 2
  
          a = np.empty(2)
          with assert_raises(ValueError):
              a[:] = C()  # Segfault!
  
      def test_failed_len_sequence(self):
          # gh-7393
          class A:
              def __init__(self, data):
                  self._data = data
              def __getitem__(self, item):
                  return type(self)(self._data[item])
              def __len__(self):
                  return len(self._data)
  
          # len(d) should give 3, but len(d[0]) will fail
          d = A([1,2,3])
          assert_equal(len(np.array(d)), 3)
  
      def test_array_too_big(self):
          # Test that array creation succeeds for arrays addressable by intp
          # on the byte level and fails for too large arrays.
          buf = np.zeros(100)
  
          max_bytes = np.iinfo(np.intp).max
          for dtype in ["intp", "S20", "b"]:
              dtype = np.dtype(dtype)
              itemsize = dtype.itemsize
  
              np.ndarray(buffer=buf, strides=(0,),
                         shape=(max_bytes//itemsize,), dtype=dtype)
              assert_raises(ValueError, np.ndarray, buffer=buf, strides=(0,),
                            shape=(max_bytes//itemsize + 1,), dtype=dtype)
  
      def _ragged_creation(self, seq):
          # without dtype=object, the ragged object should raise
          with assert_warns(np.VisibleDeprecationWarning):
              a = np.array(seq)
          b = np.array(seq, dtype=object)
          assert_equal(a, b)
          return b
  
      def test_ragged_ndim_object(self):
          # Lists of mismatching depths are treated as object arrays
          a = self._ragged_creation([[1], 2, 3])
          assert_equal(a.shape, (3,))
          assert_equal(a.dtype, object)
  
          a = self._ragged_creation([1, [2], 3])
          assert_equal(a.shape, (3,))
          assert_equal(a.dtype, object)
  
          a = self._ragged_creation([1, 2, [3]])
          assert_equal(a.shape, (3,))
          assert_equal(a.dtype, object)
  
      def test_ragged_shape_object(self):
          # The ragged dimension of a list is turned into an object array
          a = self._ragged_creation([[1, 1], [2], [3]])
          assert_equal(a.shape, (3,))
          assert_equal(a.dtype, object)
  
          a = self._ragged_creation([[1], [2, 2], [3]])
          assert_equal(a.shape, (3,))
          assert_equal(a.dtype, object)
  
          a = self._ragged_creation([[1], [2], [3, 3]])
          assert a.shape == (3,)
          assert a.dtype == object
  
      def test_array_of_ragged_array(self):
          outer = np.array([None, None])
          outer[0] = outer[1] = np.array([1, 2, 3])
          assert np.array(outer).shape == (2,)
          assert np.array([outer]).shape == (1, 2)
  
          outer_ragged = np.array([None, None])
          outer_ragged[0] = np.array([1, 2, 3])
          outer_ragged[1] = np.array([1, 2, 3, 4])
          # should both of these emit deprecation warnings?
          assert np.array(outer_ragged).shape == (2,)
          assert np.array([outer_ragged]).shape == (1, 2,)
  
      def test_deep_nonragged_object(self):
          # None of these should raise, even though they are missing dtype=object
          a = np.array([[[Decimal(1)]]])
          a = np.array([1, Decimal(1)])
          a = np.array([[1], [Decimal(1)]])
  
  class TestStructured:
      def test_subarray_field_access(self):
          a = np.zeros((3, 5), dtype=[('a', ('i4', (2, 2)))])
          a['a'] = np.arange(60).reshape(3, 5, 2, 2)
  
          # Since the subarray is always in C-order, a transpose
          # does not swap the subarray:
          assert_array_equal(a.T['a'], a['a'].transpose(1, 0, 2, 3))
  
          # In Fortran order, the subarray gets appended
          # like in all other cases, not prepended as a special case
          b = a.copy(order='F')
          assert_equal(a['a'].shape, b['a'].shape)
          assert_equal(a.T['a'].shape, a.T.copy()['a'].shape)
  
      def test_subarray_comparison(self):
          # Check that comparisons between record arrays with
          # multi-dimensional field types work properly
          a = np.rec.fromrecords(
              [([1, 2, 3], 'a', [[1, 2], [3, 4]]), ([3, 3, 3], 'b', [[0, 0], [0, 0]])],
              dtype=[('a', ('f4', 3)), ('b', object), ('c', ('i4', (2, 2)))])
          b = a.copy()
          assert_equal(a == b, [True, True])
          assert_equal(a != b, [False, False])
          b[1].b = 'c'
          assert_equal(a == b, [True, False])
          assert_equal(a != b, [False, True])
          for i in range(3):
              b[0].a = a[0].a
              b[0].a[i] = 5
              assert_equal(a == b, [False, False])
              assert_equal(a != b, [True, True])
          for i in range(2):
              for j in range(2):
                  b = a.copy()
                  b[0].c[i, j] = 10
                  assert_equal(a == b, [False, True])
                  assert_equal(a != b, [True, False])
  
          # Check that broadcasting with a subarray works
          a = np.array([[(0,)], [(1,)]], dtype=[('a', 'f8')])
          b = np.array([(0,), (0,), (1,)], dtype=[('a', 'f8')])
          assert_equal(a == b, [[True, True, False], [False, False, True]])
          assert_equal(b == a, [[True, True, False], [False, False, True]])
          a = np.array([[(0,)], [(1,)]], dtype=[('a', 'f8', (1,))])
          b = np.array([(0,), (0,), (1,)], dtype=[('a', 'f8', (1,))])
          assert_equal(a == b, [[True, True, False], [False, False, True]])
          assert_equal(b == a, [[True, True, False], [False, False, True]])
          a = np.array([[([0, 0],)], [([1, 1],)]], dtype=[('a', 'f8', (2,))])
          b = np.array([([0, 0],), ([0, 1],), ([1, 1],)], dtype=[('a', 'f8', (2,))])
          assert_equal(a == b, [[True, False, False], [False, False, True]])
          assert_equal(b == a, [[True, False, False], [False, False, True]])
  
          # Check that broadcasting Fortran-style arrays with a subarray work
          a = np.array([[([0, 0],)], [([1, 1],)]], dtype=[('a', 'f8', (2,))], order='F')
          b = np.array([([0, 0],), ([0, 1],), ([1, 1],)], dtype=[('a', 'f8', (2,))])
          assert_equal(a == b, [[True, False, False], [False, False, True]])
          assert_equal(b == a, [[True, False, False], [False, False, True]])
  
          # Check that incompatible sub-array shapes don't result to broadcasting
          x = np.zeros((1,), dtype=[('a', ('f4', (1, 2))), ('b', 'i1')])
          y = np.zeros((1,), dtype=[('a', ('f4', (2,))), ('b', 'i1')])
          # This comparison invokes deprecated behaviour, and will probably
          # start raising an error eventually. What we really care about in this
          # test is just that it doesn't return True.
          with suppress_warnings() as sup:
              sup.filter(FutureWarning, "elementwise == comparison failed")
              assert_equal(x == y, False)
  
          x = np.zeros((1,), dtype=[('a', ('f4', (2, 1))), ('b', 'i1')])
          y = np.zeros((1,), dtype=[('a', ('f4', (2,))), ('b', 'i1')])
          # This comparison invokes deprecated behaviour, and will probably
          # start raising an error eventually. What we really care about in this
          # test is just that it doesn't return True.
          with suppress_warnings() as sup:
              sup.filter(FutureWarning, "elementwise == comparison failed")
              assert_equal(x == y, False)
  
          # Check that structured arrays that are different only in
          # byte-order work
          a = np.array([(5, 42), (10, 1)], dtype=[('a', '>i8'), ('b', '<f8')])
          b = np.array([(5, 43), (10, 1)], dtype=[('a', '<i8'), ('b', '>f8')])
          assert_equal(a == b, [False, True])
  
      def test_casting(self):
          # Check that casting a structured array to change its byte order
          # works
          a = np.array([(1,)], dtype=[('a', '<i4')])
          assert_(np.can_cast(a.dtype, [('a', '>i4')], casting='unsafe'))
          b = a.astype([('a', '>i4')])
          assert_equal(b, a.byteswap().newbyteorder())
          assert_equal(a['a'][0], b['a'][0])
  
          # Check that equality comparison works on structured arrays if
          # they are 'equiv'-castable
          a = np.array([(5, 42), (10, 1)], dtype=[('a', '>i4'), ('b', '<f8')])
          b = np.array([(5, 42), (10, 1)], dtype=[('a', '<i4'), ('b', '>f8')])
          assert_(np.can_cast(a.dtype, b.dtype, casting='equiv'))
          assert_equal(a == b, [True, True])
  
          # Check that 'equiv' casting can change byte order
          assert_(np.can_cast(a.dtype, b.dtype, casting='equiv'))
          c = a.astype(b.dtype, casting='equiv')
          assert_equal(a == c, [True, True])
  
          # Check that 'safe' casting can change byte order and up-cast
          # fields
          t = [('a', '<i8'), ('b', '>f8')]
          assert_(np.can_cast(a.dtype, t, casting='safe'))
          c = a.astype(t, casting='safe')
          assert_equal((c == np.array([(5, 42), (10, 1)], dtype=t)),
                       [True, True])
  
          # Check that 'same_kind' casting can change byte order and
          # change field widths within a "kind"
          t = [('a', '<i4'), ('b', '>f4')]
          assert_(np.can_cast(a.dtype, t, casting='same_kind'))
          c = a.astype(t, casting='same_kind')
          assert_equal((c == np.array([(5, 42), (10, 1)], dtype=t)),
                       [True, True])
  
          # Check that casting fails if the casting rule should fail on
          # any of the fields
          t = [('a', '>i8'), ('b', '<f4')]
          assert_(not np.can_cast(a.dtype, t, casting='safe'))
          assert_raises(TypeError, a.astype, t, casting='safe')
          t = [('a', '>i2'), ('b', '<f8')]
          assert_(not np.can_cast(a.dtype, t, casting='equiv'))
          assert_raises(TypeError, a.astype, t, casting='equiv')
          t = [('a', '>i8'), ('b', '<i2')]
          assert_(not np.can_cast(a.dtype, t, casting='same_kind'))
          assert_raises(TypeError, a.astype, t, casting='same_kind')
          assert_(not np.can_cast(a.dtype, b.dtype, casting='no'))
          assert_raises(TypeError, a.astype, b.dtype, casting='no')
  
          # Check that non-'unsafe' casting can't change the set of field names
          for casting in ['no', 'safe', 'equiv', 'same_kind']:
              t = [('a', '>i4')]
              assert_(not np.can_cast(a.dtype, t, casting=casting))
              t = [('a', '>i4'), ('b', '<f8'), ('c', 'i4')]
              assert_(not np.can_cast(a.dtype, t, casting=casting))
  
      def test_objview(self):
          # https://github.com/numpy/numpy/issues/3286
          a = np.array([], dtype=[('a', 'f'), ('b', 'f'), ('c', 'O')])
          a[['a', 'b']]  # TypeError?
  
          # https://github.com/numpy/numpy/issues/3253
          dat2 = np.zeros(3, [('A', 'i'), ('B', '|O')])
          dat2[['B', 'A']]  # TypeError?
  
      def test_setfield(self):
          # https://github.com/numpy/numpy/issues/3126
          struct_dt = np.dtype([('elem', 'i4', 5),])
          dt = np.dtype([('field', 'i4', 10),('struct', struct_dt)])
          x = np.zeros(1, dt)
          x[0]['field'] = np.ones(10, dtype='i4')
          x[0]['struct'] = np.ones(1, dtype=struct_dt)
          assert_equal(x[0]['field'], np.ones(10, dtype='i4'))
  
      def test_setfield_object(self):
          # make sure object field assignment with ndarray value
          # on void scalar mimics setitem behavior
          b = np.zeros(1, dtype=[('x', 'O')])
          # next line should work identically to b['x'][0] = np.arange(3)
          b[0]['x'] = np.arange(3)
          assert_equal(b[0]['x'], np.arange(3))
  
          # check that broadcasting check still works
          c = np.zeros(1, dtype=[('x', 'O', 5)])
  
          def testassign():
              c[0]['x'] = np.arange(3)
  
          assert_raises(ValueError, testassign)
  
      def test_zero_width_string(self):
          # Test for PR #6430 / issues #473, #4955, #2585
  
          dt = np.dtype([('I', int), ('S', 'S0')])
  
          x = np.zeros(4, dtype=dt)
  
          assert_equal(x['S'], [b'', b'', b'', b''])
          assert_equal(x['S'].itemsize, 0)
  
          x['S'] = ['a', 'b', 'c', 'd']
          assert_equal(x['S'], [b'', b'', b'', b''])
          assert_equal(x['I'], [0, 0, 0, 0])
  
          # Variation on test case from #4955
          x['S'][x['I'] == 0] = 'hello'
          assert_equal(x['S'], [b'', b'', b'', b''])
          assert_equal(x['I'], [0, 0, 0, 0])
  
          # Variation on test case from #2585
          x['S'] = 'A'
          assert_equal(x['S'], [b'', b'', b'', b''])
          assert_equal(x['I'], [0, 0, 0, 0])
  
          # Allow zero-width dtypes in ndarray constructor
          y = np.ndarray(4, dtype=x['S'].dtype)
          assert_equal(y.itemsize, 0)
          assert_equal(x['S'], y)
  
          # More tests for indexing an array with zero-width fields
          assert_equal(np.zeros(4, dtype=[('a', 'S0,S0'),
                                          ('b', 'u1')])['a'].itemsize, 0)
          assert_equal(np.empty(3, dtype='S0,S0').itemsize, 0)
          assert_equal(np.zeros(4, dtype='S0,u1')['f0'].itemsize, 0)
  
          xx = x['S'].reshape((2, 2))
          assert_equal(xx.itemsize, 0)
          assert_equal(xx, [[b'', b''], [b'', b'']])
          # check for no uninitialized memory due to viewing S0 array
          assert_equal(xx[:].dtype, xx.dtype)
          assert_array_equal(eval(repr(xx), dict(array=np.array)), xx)
  
          b = io.BytesIO()
          np.save(b, xx)
  
          b.seek(0)
          yy = np.load(b)
          assert_equal(yy.itemsize, 0)
          assert_equal(xx, yy)
  
          with temppath(suffix='.npy') as tmp:
              np.save(tmp, xx)
              yy = np.load(tmp)
              assert_equal(yy.itemsize, 0)
              assert_equal(xx, yy)
  
      def test_base_attr(self):
          a = np.zeros(3, dtype='i4,f4')
          b = a[0]
          assert_(b.base is a)
  
      def test_assignment(self):
          def testassign(arr, v):
              c = arr.copy()
              c[0] = v  # assign using setitem
              c[1:] = v # assign using "dtype_transfer" code paths
              return c
  
          dt = np.dtype([('foo', 'i8'), ('bar', 'i8')])
          arr = np.ones(2, dt)
          v1 = np.array([(2,3)], dtype=[('foo', 'i8'), ('bar', 'i8')])
          v2 = np.array([(2,3)], dtype=[('bar', 'i8'), ('foo', 'i8')])
          v3 = np.array([(2,3)], dtype=[('bar', 'i8'), ('baz', 'i8')])
          v4 = np.array([(2,)],  dtype=[('bar', 'i8')])
          v5 = np.array([(2,3)], dtype=[('foo', 'f8'), ('bar', 'f8')])
          w = arr.view({'names': ['bar'], 'formats': ['i8'], 'offsets': [8]})
  
          ans = np.array([(2,3),(2,3)], dtype=dt)
          assert_equal(testassign(arr, v1), ans)
          assert_equal(testassign(arr, v2), ans)
          assert_equal(testassign(arr, v3), ans)
          assert_raises(ValueError, lambda: testassign(arr, v4))
          assert_equal(testassign(arr, v5), ans)
          w[:] = 4
          assert_equal(arr, np.array([(1,4),(1,4)], dtype=dt))
  
          # test field-reordering, assignment by position, and self-assignment
          a = np.array([(1,2,3)],
                       dtype=[('foo', 'i8'), ('bar', 'i8'), ('baz', 'f4')])
          a[['foo', 'bar']] = a[['bar', 'foo']]
          assert_equal(a[0].item(), (2,1,3))
  
          # test that this works even for 'simple_unaligned' structs
          # (ie, that PyArray_EquivTypes cares about field order too)
          a = np.array([(1,2)], dtype=[('a', 'i4'), ('b', 'i4')])
          a[['a', 'b']] = a[['b', 'a']]
          assert_equal(a[0].item(), (2,1))
  
      def test_structuredscalar_indexing(self):
          # test gh-7262
          x = np.empty(shape=1, dtype="(2)3S,(2)3U")
          assert_equal(x[["f0","f1"]][0], x[0][["f0","f1"]])
          assert_equal(x[0], x[0][()])
  
      def test_multiindex_titles(self):
          a = np.zeros(4, dtype=[(('a', 'b'), 'i'), ('c', 'i'), ('d', 'i')])
          assert_raises(KeyError, lambda : a[['a','c']])
          assert_raises(KeyError, lambda : a[['a','a']])
          assert_raises(ValueError, lambda : a[['b','b']])  # field exists, but repeated
          a[['b','c']]  # no exception
  
  
  class TestBool:
      def test_test_interning(self):
          a0 = np.bool_(0)
          b0 = np.bool_(False)
          assert_(a0 is b0)
          a1 = np.bool_(1)
          b1 = np.bool_(True)
          assert_(a1 is b1)
          assert_(np.array([True])[0] is a1)
          assert_(np.array(True)[()] is a1)
  
      def test_sum(self):
          d = np.ones(101, dtype=bool)
          assert_equal(d.sum(), d.size)
          assert_equal(d[::2].sum(), d[::2].size)
          assert_equal(d[::-2].sum(), d[::-2].size)
  
          d = np.frombuffer(b'\xff\xff' * 100, dtype=bool)
          assert_equal(d.sum(), d.size)
          assert_equal(d[::2].sum(), d[::2].size)
          assert_equal(d[::-2].sum(), d[::-2].size)
  
      def check_count_nonzero(self, power, length):
          powers = [2 ** i for i in range(length)]
          for i in range(2**power):
              l = [(i & x) != 0 for x in powers]
              a = np.array(l, dtype=bool)
              c = builtins.sum(l)
              assert_equal(np.count_nonzero(a), c)
              av = a.view(np.uint8)
              av *= 3
              assert_equal(np.count_nonzero(a), c)
              av *= 4
              assert_equal(np.count_nonzero(a), c)
              av[av != 0] = 0xFF
              assert_equal(np.count_nonzero(a), c)
  
      def test_count_nonzero(self):
          # check all 12 bit combinations in a length 17 array
          # covers most cases of the 16 byte unrolled code
          self.check_count_nonzero(12, 17)
  
      @pytest.mark.slow
      def test_count_nonzero_all(self):
          # check all combinations in a length 17 array
          # covers all cases of the 16 byte unrolled code
          self.check_count_nonzero(17, 17)
  
      def test_count_nonzero_unaligned(self):
          # prevent mistakes as e.g. gh-4060
          for o in range(7):
              a = np.zeros((18,), dtype=bool)[o+1:]
              a[:o] = True
              assert_equal(np.count_nonzero(a), builtins.sum(a.tolist()))
              a = np.ones((18,), dtype=bool)[o+1:]
              a[:o] = False
              assert_equal(np.count_nonzero(a), builtins.sum(a.tolist()))
  
      def _test_cast_from_flexible(self, dtype):
          # empty string -> false
          for n in range(3):
              v = np.array(b'', (dtype, n))
              assert_equal(bool(v), False)
              assert_equal(bool(v[()]), False)
              assert_equal(v.astype(bool), False)
              assert_(isinstance(v.astype(bool), np.ndarray))
              assert_(v[()].astype(bool) is np.False_)
  
          # anything else -> true
          for n in range(1, 4):
              for val in [b'a', b'0', b' ']:
                  v = np.array(val, (dtype, n))
                  assert_equal(bool(v), True)
                  assert_equal(bool(v[()]), True)
                  assert_equal(v.astype(bool), True)
                  assert_(isinstance(v.astype(bool), np.ndarray))
                  assert_(v[()].astype(bool) is np.True_)
  
      def test_cast_from_void(self):
          self._test_cast_from_flexible(np.void)
  
      @pytest.mark.xfail(reason="See gh-9847")
      def test_cast_from_unicode(self):
          self._test_cast_from_flexible(np.unicode_)
  
      @pytest.mark.xfail(reason="See gh-9847")
      def test_cast_from_bytes(self):
          self._test_cast_from_flexible(np.bytes_)
  
  
  class TestZeroSizeFlexible:
      @staticmethod
      def _zeros(shape, dtype=str):
          dtype = np.dtype(dtype)
          if dtype == np.void:
              return np.zeros(shape, dtype=(dtype, 0))
  
          # not constructable directly
          dtype = np.dtype([('x', dtype, 0)])
          return np.zeros(shape, dtype=dtype)['x']
  
      def test_create(self):
          zs = self._zeros(10, bytes)
          assert_equal(zs.itemsize, 0)
          zs = self._zeros(10, np.void)
          assert_equal(zs.itemsize, 0)
          zs = self._zeros(10, str)
          assert_equal(zs.itemsize, 0)
  
      def _test_sort_partition(self, name, kinds, **kwargs):
          # Previously, these would all hang
          for dt in [bytes, np.void, str]:
              zs = self._zeros(10, dt)
              sort_method = getattr(zs, name)
              sort_func = getattr(np, name)
              for kind in kinds:
                  sort_method(kind=kind, **kwargs)
                  sort_func(zs, kind=kind, **kwargs)
  
      def test_sort(self):
          self._test_sort_partition('sort', kinds='qhs')
  
      def test_argsort(self):
          self._test_sort_partition('argsort', kinds='qhs')
  
      def test_partition(self):
          self._test_sort_partition('partition', kinds=['introselect'], kth=2)
  
      def test_argpartition(self):
          self._test_sort_partition('argpartition', kinds=['introselect'], kth=2)
  
      def test_resize(self):
          # previously an error
          for dt in [bytes, np.void, str]:
              zs = self._zeros(10, dt)
              zs.resize(25)
              zs.resize((10, 10))
  
      def test_view(self):
          for dt in [bytes, np.void, str]:
              zs = self._zeros(10, dt)
  
              # viewing as itself should be allowed
              assert_equal(zs.view(dt).dtype, np.dtype(dt))
  
              # viewing as any non-empty type gives an empty result
              assert_equal(zs.view((dt, 1)).shape, (0,))
  
      def test_dumps(self):
          zs = self._zeros(10, int)
          assert_equal(zs, pickle.loads(zs.dumps()))
  
      def test_pickle(self):
          for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
              for dt in [bytes, np.void, str]:
                  zs = self._zeros(10, dt)
                  p = pickle.dumps(zs, protocol=proto)
                  zs2 = pickle.loads(p)
  
                  assert_equal(zs.dtype, zs2.dtype)
  
      @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL < 5,
                          reason="requires pickle protocol 5")
      def test_pickle_with_buffercallback(self):
          array = np.arange(10)
          buffers = []
          bytes_string = pickle.dumps(array, buffer_callback=buffers.append,
                                      protocol=5)
          array_from_buffer = pickle.loads(bytes_string, buffers=buffers)
          # when using pickle protocol 5 with buffer callbacks,
          # array_from_buffer is reconstructed from a buffer holding a view
          # to the initial array's data, so modifying an element in array
          # should modify it in array_from_buffer too.
          array[0] = -1
          assert array_from_buffer[0] == -1, array_from_buffer[0]
  
  
  class TestMethods:
  
      sort_kinds = ['quicksort', 'heapsort', 'stable']
  
      def test_compress(self):
          tgt = [[5, 6, 7, 8, 9]]
          arr = np.arange(10).reshape(2, 5)
          out = arr.compress([0, 1], axis=0)
          assert_equal(out, tgt)
  
          tgt = [[1, 3], [6, 8]]
          out = arr.compress([0, 1, 0, 1, 0], axis=1)
          assert_equal(out, tgt)
  
          tgt = [[1], [6]]
          arr = np.arange(10).reshape(2, 5)
          out = arr.compress([0, 1], axis=1)
          assert_equal(out, tgt)
  
          arr = np.arange(10).reshape(2, 5)
          out = arr.compress([0, 1])
          assert_equal(out, 1)
  
      def test_choose(self):
          x = 2*np.ones((3,), dtype=int)
          y = 3*np.ones((3,), dtype=int)
          x2 = 2*np.ones((2, 3), dtype=int)
          y2 = 3*np.ones((2, 3), dtype=int)
          ind = np.array([0, 0, 1])
  
          A = ind.choose((x, y))
          assert_equal(A, [2, 2, 3])
  
          A = ind.choose((x2, y2))
          assert_equal(A, [[2, 2, 3], [2, 2, 3]])
  
          A = ind.choose((x, y2))
          assert_equal(A, [[2, 2, 3], [2, 2, 3]])
  
          oned = np.ones(1)
          # gh-12031, caused SEGFAULT
          assert_raises(TypeError, oned.choose,np.void(0), [oned])
  
          out = np.array(0)
          ret = np.choose(np.array(1), [10, 20, 30], out=out)
          assert out is ret
          assert_equal(out[()], 20)
  
          # gh-6272 check overlap on out
          x = np.arange(5)
          y = np.choose([0,0,0], [x[:3], x[:3], x[:3]], out=x[1:4], mode='wrap')
          assert_equal(y, np.array([0, 1, 2]))
  
      def test_prod(self):
          ba = [1, 2, 10, 11, 6, 5, 4]
          ba2 = [[1, 2, 3, 4], [5, 6, 7, 9], [10, 3, 4, 5]]
  
          for ctype in [np.int16, np.uint16, np.int32, np.uint32,
                        np.float32, np.float64, np.complex64, np.complex128]:
              a = np.array(ba, ctype)
              a2 = np.array(ba2, ctype)
              if ctype in ['1', 'b']:
                  assert_raises(ArithmeticError, a.prod)
                  assert_raises(ArithmeticError, a2.prod, axis=1)
              else:
                  assert_equal(a.prod(axis=0), 26400)
                  assert_array_equal(a2.prod(axis=0),
                                     np.array([50, 36, 84, 180], ctype))
                  assert_array_equal(a2.prod(axis=-1),
                                     np.array([24, 1890, 600], ctype))
  
      def test_repeat(self):
          m = np.array([1, 2, 3, 4, 5, 6])
          m_rect = m.reshape((2, 3))
  
          A = m.repeat([1, 3, 2, 1, 1, 2])
          assert_equal(A, [1, 2, 2, 2, 3,
                           3, 4, 5, 6, 6])
  
          A = m.repeat(2)
          assert_equal(A, [1, 1, 2, 2, 3, 3,
                           4, 4, 5, 5, 6, 6])
  
          A = m_rect.repeat([2, 1], axis=0)
          assert_equal(A, [[1, 2, 3],
                           [1, 2, 3],
                           [4, 5, 6]])
  
          A = m_rect.repeat([1, 3, 2], axis=1)
          assert_equal(A, [[1, 2, 2, 2, 3, 3],
                           [4, 5, 5, 5, 6, 6]])
  
          A = m_rect.repeat(2, axis=0)
          assert_equal(A, [[1, 2, 3],
                           [1, 2, 3],
                           [4, 5, 6],
                           [4, 5, 6]])
  
          A = m_rect.repeat(2, axis=1)
          assert_equal(A, [[1, 1, 2, 2, 3, 3],
                           [4, 4, 5, 5, 6, 6]])
  
      def test_reshape(self):
          arr = np.array([[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(arr.reshape(2, 6), tgt)
  
          tgt = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
          assert_equal(arr.reshape(3, 4), tgt)
  
          tgt = [[1, 10, 8, 6], [4, 2, 11, 9], [7, 5, 3, 12]]
          assert_equal(arr.reshape((3, 4), order='F'), tgt)
  
          tgt = [[1, 4, 7, 10], [2, 5, 8, 11], [3, 6, 9, 12]]
          assert_equal(arr.T.reshape((3, 4), order='C'), tgt)
  
      def test_round(self):
          def check_round(arr, expected, *round_args):
              assert_equal(arr.round(*round_args), expected)
              # With output array
              out = np.zeros_like(arr)
              res = arr.round(*round_args, out=out)
              assert_equal(out, expected)
              assert out is res
  
          check_round(np.array([1.2, 1.5]), [1, 2])
          check_round(np.array(1.5), 2)
          check_round(np.array([12.2, 15.5]), [10, 20], -1)
          check_round(np.array([12.15, 15.51]), [12.2, 15.5], 1)
          # Complex rounding
          check_round(np.array([4.5 + 1.5j]), [4 + 2j])
          check_round(np.array([12.5 + 15.5j]), [10 + 20j], -1)
  
      def test_squeeze(self):
          a = np.array([[[1], [2], [3]]])
          assert_equal(a.squeeze(), [1, 2, 3])
          assert_equal(a.squeeze(axis=(0,)), [[1], [2], [3]])
          assert_raises(ValueError, a.squeeze, axis=(1,))
          assert_equal(a.squeeze(axis=(2,)), [[1, 2, 3]])
  
      def test_transpose(self):
          a = np.array([[1, 2], [3, 4]])
          assert_equal(a.transpose(), [[1, 3], [2, 4]])
          assert_raises(ValueError, lambda: a.transpose(0))
          assert_raises(ValueError, lambda: a.transpose(0, 0))
          assert_raises(ValueError, lambda: a.transpose(0, 1, 2))
  
      def test_sort(self):
          # test ordering for floats and complex containing nans. It is only
          # necessary to check the less-than comparison, so sorts that
          # only follow the insertion sort path are sufficient. We only
          # test doubles and complex doubles as the logic is the same.
  
          # check doubles
          msg = "Test real sort order with nans"
          a = np.array([np.nan, 1, 0])
          b = np.sort(a)
          assert_equal(b, a[::-1], msg)
          # check complex
          msg = "Test complex sort order with nans"
          a = np.zeros(9, dtype=np.complex128)
          a.real += [np.nan, np.nan, np.nan, 1, 0, 1, 1, 0, 0]
          a.imag += [np.nan, 1, 0, np.nan, np.nan, 1, 0, 1, 0]
          b = np.sort(a)
          assert_equal(b, a[::-1], msg)
  
      # all c scalar sorts use the same code with different types
      # so it suffices to run a quick check with one type. The number
      # of sorted items must be greater than ~50 to check the actual
      # algorithm because quick and merge sort fall over to insertion
      # sort for small arrays.
  
      @pytest.mark.parametrize('dtype', [np.uint8, np.uint16, np.uint32, np.uint64,
                                         np.float16, np.float32, np.float64,
                                         np.longdouble])
      def test_sort_unsigned(self, dtype):
          a = np.arange(101, dtype=dtype)
          b = a[::-1].copy()
          for kind in self.sort_kinds:
              msg = "scalar sort, kind=%s" % kind
              c = a.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
              c = b.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
  
      @pytest.mark.parametrize('dtype',
                               [np.int8, np.int16, np.int32, np.int64, np.float16,
                                np.float32, np.float64, np.longdouble])
      def test_sort_signed(self, dtype):
          a = np.arange(-50, 51, dtype=dtype)
          b = a[::-1].copy()
          for kind in self.sort_kinds:
              msg = "scalar sort, kind=%s" % (kind)
              c = a.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
              c = b.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
  
      @pytest.mark.parametrize('dtype', [np.float32, np.float64, np.longdouble])
      @pytest.mark.parametrize('part', ['real', 'imag'])
      def test_sort_complex(self, part, dtype):
          # test complex sorts. These use the same code as the scalars
          # but the compare function differs.
          cdtype = {
              np.single: np.csingle,
              np.double: np.cdouble,
              np.longdouble: np.clongdouble,
          }[dtype]
          a = np.arange(-50, 51, dtype=dtype)
          b = a[::-1].copy()
          ai = (a * (1+1j)).astype(cdtype)
          bi = (b * (1+1j)).astype(cdtype)
          setattr(ai, part, 1)
          setattr(bi, part, 1)
          for kind in self.sort_kinds:
              msg = "complex sort, %s part == 1, kind=%s" % (part, kind)
              c = ai.copy()
              c.sort(kind=kind)
              assert_equal(c, ai, msg)
              c = bi.copy()
              c.sort(kind=kind)
              assert_equal(c, ai, msg)
  
      def test_sort_complex_byte_swapping(self):
          # test sorting of complex arrays requiring byte-swapping, gh-5441
          for endianness in '<>':
              for dt in np.typecodes['Complex']:
                  arr = np.array([1+3.j, 2+2.j, 3+1.j], dtype=endianness + dt)
                  c = arr.copy()
                  c.sort()
                  msg = 'byte-swapped complex sort, dtype={0}'.format(dt)
                  assert_equal(c, arr, msg)
  
      @pytest.mark.parametrize('dtype', [np.bytes_, np.unicode_])
      def test_sort_string(self, dtype):
          # np.array will perform the encoding to bytes for us in the bytes test
          a = np.array(['aaaaaaaa' + chr(i) for i in range(101)], dtype=dtype)
          b = a[::-1].copy()
          for kind in self.sort_kinds:
              msg = "kind=%s" % kind
              c = a.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
              c = b.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
  
      def test_sort_object(self):
          # test object array sorts.
          a = np.empty((101,), dtype=object)
          a[:] = list(range(101))
          b = a[::-1]
          for kind in ['q', 'h', 'm']:
              msg = "kind=%s" % kind
              c = a.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
              c = b.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
  
      def test_sort_structured(self):
          # test record array sorts.
          dt = np.dtype([('f', float), ('i', int)])
          a = np.array([(i, i) for i in range(101)], dtype=dt)
          b = a[::-1]
          for kind in ['q', 'h', 'm']:
              msg = "kind=%s" % kind
              c = a.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
              c = b.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
  
      @pytest.mark.parametrize('dtype', ['datetime64[D]', 'timedelta64[D]'])
      def test_sort_time(self, dtype):
          # test datetime64 and timedelta64 sorts.
          a = np.arange(0, 101, dtype=dtype)
          b = a[::-1]
          for kind in ['q', 'h', 'm']:
              msg = "kind=%s" % kind
              c = a.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
              c = b.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
  
      def test_sort_axis(self):
          # check axis handling. This should be the same for all type
          # specific sorts, so we only check it for one type and one kind
          a = np.array([[3, 2], [1, 0]])
          b = np.array([[1, 0], [3, 2]])
          c = np.array([[2, 3], [0, 1]])
          d = a.copy()
          d.sort(axis=0)
          assert_equal(d, b, "test sort with axis=0")
          d = a.copy()
          d.sort(axis=1)
          assert_equal(d, c, "test sort with axis=1")
          d = a.copy()
          d.sort()
          assert_equal(d, c, "test sort with default axis")
  
      def test_sort_size_0(self):
          # check axis handling for multidimensional empty arrays
          a = np.array([])
          a.shape = (3, 2, 1, 0)
          for axis in range(-a.ndim, a.ndim):
              msg = 'test empty array sort with axis={0}'.format(axis)
              assert_equal(np.sort(a, axis=axis), a, msg)
          msg = 'test empty array sort with axis=None'
          assert_equal(np.sort(a, axis=None), a.ravel(), msg)
  
      def test_sort_bad_ordering(self):
          # test generic class with bogus ordering,
          # should not segfault.
          class Boom:
              def __lt__(self, other):
                  return True
  
          a = np.array([Boom()] * 100, dtype=object)
          for kind in self.sort_kinds:
              msg = "kind=%s" % kind
              c = a.copy()
              c.sort(kind=kind)
              assert_equal(c, a, msg)
  
      def test_void_sort(self):
          # gh-8210 - previously segfaulted
          for i in range(4):
              rand = np.random.randint(256, size=4000, dtype=np.uint8)
              arr = rand.view('V4')
              arr[::-1].sort()
  
          dt = np.dtype([('val', 'i4', (1,))])
          for i in range(4):
              rand = np.random.randint(256, size=4000, dtype=np.uint8)
              arr = rand.view(dt)
              arr[::-1].sort()
  
      def test_sort_raises(self):
          #gh-9404
          arr = np.array([0, datetime.now(), 1], dtype=object)
          for kind in self.sort_kinds:
              assert_raises(TypeError, arr.sort, kind=kind)
          #gh-3879
          class Raiser:
              def raises_anything(*args, **kwargs):
                  raise TypeError("SOMETHING ERRORED")
              __eq__ = __ne__ = __lt__ = __gt__ = __ge__ = __le__ = raises_anything
          arr = np.array([[Raiser(), n] for n in range(10)]).reshape(-1)
          np.random.shuffle(arr)
          for kind in self.sort_kinds:
              assert_raises(TypeError, arr.sort, kind=kind)
  
      def test_sort_degraded(self):
          # test degraded dataset would take minutes to run with normal qsort
          d = np.arange(1000000)
          do = d.copy()
          x = d
          # create a median of 3 killer where each median is the sorted second
          # last element of the quicksort partition
          while x.size > 3:
              mid = x.size // 2
              x[mid], x[-2] = x[-2], x[mid]
              x = x[:-2]
  
          assert_equal(np.sort(d), do)
          assert_equal(d[np.argsort(d)], do)
  
      def test_copy(self):
          def assert_fortran(arr):
              assert_(arr.flags.fortran)
              assert_(arr.flags.f_contiguous)
              assert_(not arr.flags.c_contiguous)
  
          def assert_c(arr):
              assert_(not arr.flags.fortran)
              assert_(not arr.flags.f_contiguous)
              assert_(arr.flags.c_contiguous)
  
          a = np.empty((2, 2), order='F')
          # Test copying a Fortran array
          assert_c(a.copy())
          assert_c(a.copy('C'))
          assert_fortran(a.copy('F'))
          assert_fortran(a.copy('A'))
  
          # Now test starting with a C array.
          a = np.empty((2, 2), order='C')
          assert_c(a.copy())
          assert_c(a.copy('C'))
          assert_fortran(a.copy('F'))
          assert_c(a.copy('A'))
  
      def test_sort_order(self):
          # Test sorting an array with fields
          x1 = np.array([21, 32, 14])
          x2 = np.array(['my', 'first', 'name'])
          x3 = np.array([3.1, 4.5, 6.2])
          r = np.rec.fromarrays([x1, x2, x3], names='id,word,number')
  
          r.sort(order=['id'])
          assert_equal(r.id, np.array([14, 21, 32]))
          assert_equal(r.word, np.array(['name', 'my', 'first']))
          assert_equal(r.number, np.array([6.2, 3.1, 4.5]))
  
          r.sort(order=['word'])
          assert_equal(r.id, np.array([32, 21, 14]))
          assert_equal(r.word, np.array(['first', 'my', 'name']))
          assert_equal(r.number, np.array([4.5, 3.1, 6.2]))
  
          r.sort(order=['number'])
          assert_equal(r.id, np.array([21, 32, 14]))
          assert_equal(r.word, np.array(['my', 'first', 'name']))
          assert_equal(r.number, np.array([3.1, 4.5, 6.2]))
  
          assert_raises_regex(ValueError, 'duplicate',
              lambda: r.sort(order=['id', 'id']))
  
          if sys.byteorder == 'little':
              strtype = '>i2'
          else:
              strtype = '<i2'
          mydtype = [('name', strchar + '5'), ('col2', strtype)]
          r = np.array([('a', 1), ('b', 255), ('c', 3), ('d', 258)],
                       dtype=mydtype)
          r.sort(order='col2')
          assert_equal(r['col2'], [1, 3, 255, 258])
          assert_equal(r, np.array([('a', 1), ('c', 3), ('b', 255), ('d', 258)],
                                   dtype=mydtype))
  
      def test_argsort(self):
          # all c scalar argsorts use the same code with different types
          # so it suffices to run a quick check with one type. The number
          # of sorted items must be greater than ~50 to check the actual
          # algorithm because quick and merge sort fall over to insertion
          # sort for small arrays.
  
          for dtype in [np.int32, np.uint32, np.float32]:
              a = np.arange(101, dtype=dtype)
              b = a[::-1].copy()
              for kind in self.sort_kinds:
                  msg = "scalar argsort, kind=%s, dtype=%s" % (kind, dtype)
                  assert_equal(a.copy().argsort(kind=kind), a, msg)
                  assert_equal(b.copy().argsort(kind=kind), b, msg)
  
          # test complex argsorts. These use the same code as the scalars
          # but the compare function differs.
          ai = a*1j + 1
          bi = b*1j + 1
          for kind in self.sort_kinds:
              msg = "complex argsort, kind=%s" % kind
              assert_equal(ai.copy().argsort(kind=kind), a, msg)
              assert_equal(bi.copy().argsort(kind=kind), b, msg)
          ai = a + 1j
          bi = b + 1j
          for kind in self.sort_kinds:
              msg = "complex argsort, kind=%s" % kind
              assert_equal(ai.copy().argsort(kind=kind), a, msg)
              assert_equal(bi.copy().argsort(kind=kind), b, msg)
  
          # test argsort of complex arrays requiring byte-swapping, gh-5441
          for endianness in '<>':
              for dt in np.typecodes['Complex']:
                  arr = np.array([1+3.j, 2+2.j, 3+1.j], dtype=endianness + dt)
                  msg = 'byte-swapped complex argsort, dtype={0}'.format(dt)
                  assert_equal(arr.argsort(),
                               np.arange(len(arr), dtype=np.intp), msg)
  
          # test string argsorts.
          s = 'aaaaaaaa'
          a = np.array([s + chr(i) for i in range(101)])
          b = a[::-1].copy()
          r = np.arange(101)
          rr = r[::-1]
          for kind in self.sort_kinds:
              msg = "string argsort, kind=%s" % kind
              assert_equal(a.copy().argsort(kind=kind), r, msg)
              assert_equal(b.copy().argsort(kind=kind), rr, msg)
  
          # test unicode argsorts.
          s = 'aaaaaaaa'
          a = np.array([s + chr(i) for i in range(101)], dtype=np.unicode_)
          b = a[::-1]
          r = np.arange(101)
          rr = r[::-1]
          for kind in self.sort_kinds:
              msg = "unicode argsort, kind=%s" % kind
              assert_equal(a.copy().argsort(kind=kind), r, msg)
              assert_equal(b.copy().argsort(kind=kind), rr, msg)
  
          # test object array argsorts.
          a = np.empty((101,), dtype=object)
          a[:] = list(range(101))
          b = a[::-1]
          r = np.arange(101)
          rr = r[::-1]
          for kind in self.sort_kinds:
              msg = "object argsort, kind=%s" % kind
              assert_equal(a.copy().argsort(kind=kind), r, msg)
              assert_equal(b.copy().argsort(kind=kind), rr, msg)
  
          # test structured array argsorts.
          dt = np.dtype([('f', float), ('i', int)])
          a = np.array([(i, i) for i in range(101)], dtype=dt)
          b = a[::-1]
          r = np.arange(101)
          rr = r[::-1]
          for kind in self.sort_kinds:
              msg = "structured array argsort, kind=%s" % kind
              assert_equal(a.copy().argsort(kind=kind), r, msg)
              assert_equal(b.copy().argsort(kind=kind), rr, msg)
  
          # test datetime64 argsorts.
          a = np.arange(0, 101, dtype='datetime64[D]')
          b = a[::-1]
          r = np.arange(101)
          rr = r[::-1]
          for kind in ['q', 'h', 'm']:
              msg = "datetime64 argsort, kind=%s" % kind
              assert_equal(a.copy().argsort(kind=kind), r, msg)
              assert_equal(b.copy().argsort(kind=kind), rr, msg)
  
          # test timedelta64 argsorts.
          a = np.arange(0, 101, dtype='timedelta64[D]')
          b = a[::-1]
          r = np.arange(101)
          rr = r[::-1]
          for kind in ['q', 'h', 'm']:
              msg = "timedelta64 argsort, kind=%s" % kind
              assert_equal(a.copy().argsort(kind=kind), r, msg)
              assert_equal(b.copy().argsort(kind=kind), rr, msg)
  
          # check axis handling. This should be the same for all type
          # specific argsorts, so we only check it for one type and one kind
          a = np.array([[3, 2], [1, 0]])
          b = np.array([[1, 1], [0, 0]])
          c = np.array([[1, 0], [1, 0]])
          assert_equal(a.copy().argsort(axis=0), b)
          assert_equal(a.copy().argsort(axis=1), c)
          assert_equal(a.copy().argsort(), c)
  
          # check axis handling for multidimensional empty arrays
          a = np.array([])
          a.shape = (3, 2, 1, 0)
          for axis in range(-a.ndim, a.ndim):
              msg = 'test empty array argsort with axis={0}'.format(axis)
              assert_equal(np.argsort(a, axis=axis),
                           np.zeros_like(a, dtype=np.intp), msg)
          msg = 'test empty array argsort with axis=None'
          assert_equal(np.argsort(a, axis=None),
                       np.zeros_like(a.ravel(), dtype=np.intp), msg)
  
          # check that stable argsorts are stable
          r = np.arange(100)
          # scalars
          a = np.zeros(100)
          assert_equal(a.argsort(kind='m'), r)
          # complex
          a = np.zeros(100, dtype=complex)
          assert_equal(a.argsort(kind='m'), r)
          # string
          a = np.array(['aaaaaaaaa' for i in range(100)])
          assert_equal(a.argsort(kind='m'), r)
          # unicode
          a = np.array(['aaaaaaaaa' for i in range(100)], dtype=np.unicode_)
          assert_equal(a.argsort(kind='m'), r)
  
      def test_sort_unicode_kind(self):
          d = np.arange(10)
          k = b'\xc3\xa4'.decode("UTF8")
          assert_raises(ValueError, d.sort, kind=k)
          assert_raises(ValueError, d.argsort, kind=k)
  
      def test_searchsorted(self):
          # test for floats and complex containing nans. The logic is the
          # same for all float types so only test double types for now.
          # The search sorted routines use the compare functions for the
          # array type, so this checks if that is consistent with the sort
          # order.
  
          # check double
          a = np.array([0, 1, np.nan])
          msg = "Test real searchsorted with nans, side='l'"
          b = a.searchsorted(a, side='l')
          assert_equal(b, np.arange(3), msg)
          msg = "Test real searchsorted with nans, side='r'"
          b = a.searchsorted(a, side='r')
          assert_equal(b, np.arange(1, 4), msg)
          # check keyword arguments
          a.searchsorted(v=1)
          # check double complex
          a = np.zeros(9, dtype=np.complex128)
          a.real += [0, 0, 1, 1, 0, 1, np.nan, np.nan, np.nan]
          a.imag += [0, 1, 0, 1, np.nan, np.nan, 0, 1, np.nan]
          msg = "Test complex searchsorted with nans, side='l'"
          b = a.searchsorted(a, side='l')
          assert_equal(b, np.arange(9), msg)
          msg = "Test complex searchsorted with nans, side='r'"
          b = a.searchsorted(a, side='r')
          assert_equal(b, np.arange(1, 10), msg)
          msg = "Test searchsorted with little endian, side='l'"
          a = np.array([0, 128], dtype='<i4')
          b = a.searchsorted(np.array(128, dtype='<i4'))
          assert_equal(b, 1, msg)
          msg = "Test searchsorted with big endian, side='l'"
          a = np.array([0, 128], dtype='>i4')
          b = a.searchsorted(np.array(128, dtype='>i4'))
          assert_equal(b, 1, msg)
  
          # Check 0 elements
          a = np.ones(0)
          b = a.searchsorted([0, 1, 2], 'l')
          assert_equal(b, [0, 0, 0])
          b = a.searchsorted([0, 1, 2], 'r')
          assert_equal(b, [0, 0, 0])
          a = np.ones(1)
          # Check 1 element
          b = a.searchsorted([0, 1, 2], 'l')
          assert_equal(b, [0, 0, 1])
          b = a.searchsorted([0, 1, 2], 'r')
          assert_equal(b, [0, 1, 1])
          # Check all elements equal
          a = np.ones(2)
          b = a.searchsorted([0, 1, 2], 'l')
          assert_equal(b, [0, 0, 2])
          b = a.searchsorted([0, 1, 2], 'r')
          assert_equal(b, [0, 2, 2])
  
          # Test searching unaligned array
          a = np.arange(10)
          aligned = np.empty(a.itemsize * a.size + 1, 'uint8')
          unaligned = aligned[1:].view(a.dtype)
          unaligned[:] = a
          # Test searching unaligned array
          b = unaligned.searchsorted(a, 'l')
          assert_equal(b, a)
          b = unaligned.searchsorted(a, 'r')
          assert_equal(b, a + 1)
          # Test searching for unaligned keys
          b = a.searchsorted(unaligned, 'l')
          assert_equal(b, a)
          b = a.searchsorted(unaligned, 'r')
          assert_equal(b, a + 1)
  
          # Test smart resetting of binsearch indices
          a = np.arange(5)
          b = a.searchsorted([6, 5, 4], 'l')
          assert_equal(b, [5, 5, 4])
          b = a.searchsorted([6, 5, 4], 'r')
          assert_equal(b, [5, 5, 5])
  
          # Test all type specific binary search functions
          types = ''.join((np.typecodes['AllInteger'], np.typecodes['AllFloat'],
                           np.typecodes['Datetime'], '?O'))
          for dt in types:
              if dt == 'M':
                  dt = 'M8[D]'
              if dt == '?':
                  a = np.arange(2, dtype=dt)
                  out = np.arange(2)
              else:
                  a = np.arange(0, 5, dtype=dt)
                  out = np.arange(5)
              b = a.searchsorted(a, 'l')
              assert_equal(b, out)
              b = a.searchsorted(a, 'r')
              assert_equal(b, out + 1)
              # Test empty array, use a fresh array to get warnings in
              # valgrind if access happens.
              e = np.ndarray(shape=0, buffer=b'', dtype=dt)
              b = e.searchsorted(a, 'l')
              assert_array_equal(b, np.zeros(len(a), dtype=np.intp))
              b = a.searchsorted(e, 'l')
              assert_array_equal(b, np.zeros(0, dtype=np.intp))
  
      def test_searchsorted_unicode(self):
          # Test searchsorted on unicode strings.
  
          # 1.6.1 contained a string length miscalculation in
          # arraytypes.c.src:UNICODE_compare() which manifested as
          # incorrect/inconsistent results from searchsorted.
          a = np.array(['P:\\20x_dapi_cy3\\20x_dapi_cy3_20100185_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100186_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100187_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100189_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100190_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100191_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100192_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100193_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100194_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100195_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100196_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100197_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100198_1',
                        'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100199_1'],
                       dtype=np.unicode_)
          ind = np.arange(len(a))
          assert_equal([a.searchsorted(v, 'left') for v in a], ind)
          assert_equal([a.searchsorted(v, 'right') for v in a], ind + 1)
          assert_equal([a.searchsorted(a[i], 'left') for i in ind], ind)
          assert_equal([a.searchsorted(a[i], 'right') for i in ind], ind + 1)
  
      def test_searchsorted_with_invalid_sorter(self):
          a = np.array([5, 2, 1, 3, 4])
          s = np.argsort(a)
          assert_raises(TypeError, np.searchsorted, a, 0,
                        sorter=np.array((1, (2, 3)), dtype=object))
          assert_raises(TypeError, np.searchsorted, a, 0, sorter=[1.1])
          assert_raises(ValueError, np.searchsorted, a, 0, sorter=[1, 2, 3, 4])
          assert_raises(ValueError, np.searchsorted, a, 0, sorter=[1, 2, 3, 4, 5, 6])
  
          # bounds check
          assert_raises(ValueError, np.searchsorted, a, 4, sorter=[0, 1, 2, 3, 5])
          assert_raises(ValueError, np.searchsorted, a, 0, sorter=[-1, 0, 1, 2, 3])
          assert_raises(ValueError, np.searchsorted, a, 0, sorter=[4, 0, -1, 2, 3])
  
      def test_searchsorted_with_sorter(self):
          a = np.random.rand(300)
          s = a.argsort()
          b = np.sort(a)
          k = np.linspace(0, 1, 20)
          assert_equal(b.searchsorted(k), a.searchsorted(k, sorter=s))
  
          a = np.array([0, 1, 2, 3, 5]*20)
          s = a.argsort()
          k = [0, 1, 2, 3, 5]
          expected = [0, 20, 40, 60, 80]
          assert_equal(a.searchsorted(k, side='l', sorter=s), expected)
          expected = [20, 40, 60, 80, 100]
          assert_equal(a.searchsorted(k, side='r', sorter=s), expected)
  
          # Test searching unaligned array
          keys = np.arange(10)
          a = keys.copy()
          np.random.shuffle(s)
          s = a.argsort()
          aligned = np.empty(a.itemsize * a.size + 1, 'uint8')
          unaligned = aligned[1:].view(a.dtype)
          # Test searching unaligned array
          unaligned[:] = a
          b = unaligned.searchsorted(keys, 'l', s)
          assert_equal(b, keys)
          b = unaligned.searchsorted(keys, 'r', s)
          assert_equal(b, keys + 1)
          # Test searching for unaligned keys
          unaligned[:] = keys
          b = a.searchsorted(unaligned, 'l', s)
          assert_equal(b, keys)
          b = a.searchsorted(unaligned, 'r', s)
          assert_equal(b, keys + 1)
  
          # Test all type specific indirect binary search functions
          types = ''.join((np.typecodes['AllInteger'], np.typecodes['AllFloat'],
                           np.typecodes['Datetime'], '?O'))
          for dt in types:
              if dt == 'M':
                  dt = 'M8[D]'
              if dt == '?':
                  a = np.array([1, 0], dtype=dt)
                  # We want the sorter array to be of a type that is different
                  # from np.intp in all platforms, to check for #4698
                  s = np.array([1, 0], dtype=np.int16)
                  out = np.array([1, 0])
              else:
                  a = np.array([3, 4, 1, 2, 0], dtype=dt)
                  # We want the sorter array to be of a type that is different
                  # from np.intp in all platforms, to check for #4698
                  s = np.array([4, 2, 3, 0, 1], dtype=np.int16)
                  out = np.array([3, 4, 1, 2, 0], dtype=np.intp)
              b = a.searchsorted(a, 'l', s)
              assert_equal(b, out)
              b = a.searchsorted(a, 'r', s)
              assert_equal(b, out + 1)
              # Test empty array, use a fresh array to get warnings in
              # valgrind if access happens.
              e = np.ndarray(shape=0, buffer=b'', dtype=dt)
              b = e.searchsorted(a, 'l', s[:0])
              assert_array_equal(b, np.zeros(len(a), dtype=np.intp))
              b = a.searchsorted(e, 'l', s)
              assert_array_equal(b, np.zeros(0, dtype=np.intp))
  
          # Test non-contiguous sorter array
          a = np.array([3, 4, 1, 2, 0])
          srt = np.empty((10,), dtype=np.intp)
          srt[1::2] = -1
          srt[::2] = [4, 2, 3, 0, 1]
          s = srt[::2]
          out = np.array([3, 4, 1, 2, 0], dtype=np.intp)
          b = a.searchsorted(a, 'l', s)
          assert_equal(b, out)
          b = a.searchsorted(a, 'r', s)
          assert_equal(b, out + 1)
  
      def test_searchsorted_return_type(self):
          # Functions returning indices should always return base ndarrays
          class A(np.ndarray):
              pass
          a = np.arange(5).view(A)
          b = np.arange(1, 3).view(A)
          s = np.arange(5).view(A)
          assert_(not isinstance(a.searchsorted(b, 'l'), A))
          assert_(not isinstance(a.searchsorted(b, 'r'), A))
          assert_(not isinstance(a.searchsorted(b, 'l', s), A))
          assert_(not isinstance(a.searchsorted(b, 'r', s), A))
  
      def test_argpartition_out_of_range(self):
          # Test out of range values in kth raise an error, gh-5469
          d = np.arange(10)
          assert_raises(ValueError, d.argpartition, 10)
          assert_raises(ValueError, d.argpartition, -11)
          # Test also for generic type argpartition, which uses sorting
          # and used to not bound check kth
          d_obj = np.arange(10, dtype=object)
          assert_raises(ValueError, d_obj.argpartition, 10)
          assert_raises(ValueError, d_obj.argpartition, -11)
  
      def test_partition_out_of_range(self):
          # Test out of range values in kth raise an error, gh-5469
          d = np.arange(10)
          assert_raises(ValueError, d.partition, 10)
          assert_raises(ValueError, d.partition, -11)
          # Test also for generic type partition, which uses sorting
          # and used to not bound check kth
          d_obj = np.arange(10, dtype=object)
          assert_raises(ValueError, d_obj.partition, 10)
          assert_raises(ValueError, d_obj.partition, -11)
  
      def test_argpartition_integer(self):
          # Test non-integer values in kth raise an error/
          d = np.arange(10)
          assert_raises(TypeError, d.argpartition, 9.)
          # Test also for generic type argpartition, which uses sorting
          # and used to not bound check kth
          d_obj = np.arange(10, dtype=object)
          assert_raises(TypeError, d_obj.argpartition, 9.)
  
      def test_partition_integer(self):
          # Test out of range values in kth raise an error, gh-5469
          d = np.arange(10)
          assert_raises(TypeError, d.partition, 9.)
          # Test also for generic type partition, which uses sorting
          # and used to not bound check kth
          d_obj = np.arange(10, dtype=object)
          assert_raises(TypeError, d_obj.partition, 9.)
  
      def test_partition_empty_array(self):
          # check axis handling for multidimensional empty arrays
          a = np.array([])
          a.shape = (3, 2, 1, 0)
          for axis in range(-a.ndim, a.ndim):
              msg = 'test empty array partition with axis={0}'.format(axis)
              assert_equal(np.partition(a, 0, axis=axis), a, msg)
          msg = 'test empty array partition with axis=None'
          assert_equal(np.partition(a, 0, axis=None), a.ravel(), msg)
  
      def test_argpartition_empty_array(self):
          # check axis handling for multidimensional empty arrays
          a = np.array([])
          a.shape = (3, 2, 1, 0)
          for axis in range(-a.ndim, a.ndim):
              msg = 'test empty array argpartition with axis={0}'.format(axis)
              assert_equal(np.partition(a, 0, axis=axis),
                           np.zeros_like(a, dtype=np.intp), msg)
          msg = 'test empty array argpartition with axis=None'
          assert_equal(np.partition(a, 0, axis=None),
                       np.zeros_like(a.ravel(), dtype=np.intp), msg)
  
      def test_partition(self):
          d = np.arange(10)
          assert_raises(TypeError, np.partition, d, 2, kind=1)
          assert_raises(ValueError, np.partition, d, 2, kind="nonsense")
          assert_raises(ValueError, np.argpartition, d, 2, kind="nonsense")
          assert_raises(ValueError, d.partition, 2, axis=0, kind="nonsense")
          assert_raises(ValueError, d.argpartition, 2, axis=0, kind="nonsense")
          for k in ("introselect",):
              d = np.array([])
              assert_array_equal(np.partition(d, 0, kind=k), d)
              assert_array_equal(np.argpartition(d, 0, kind=k), d)
              d = np.ones(1)
              assert_array_equal(np.partition(d, 0, kind=k)[0], d)
              assert_array_equal(d[np.argpartition(d, 0, kind=k)],
                                 np.partition(d, 0, kind=k))
  
              # kth not modified
              kth = np.array([30, 15, 5])
              okth = kth.copy()
              np.partition(np.arange(40), kth)
              assert_array_equal(kth, okth)
  
              for r in ([2, 1], [1, 2], [1, 1]):
                  d = np.array(r)
                  tgt = np.sort(d)
                  assert_array_equal(np.partition(d, 0, kind=k)[0], tgt[0])
                  assert_array_equal(np.partition(d, 1, kind=k)[1], tgt[1])
                  assert_array_equal(d[np.argpartition(d, 0, kind=k)],
                                     np.partition(d, 0, kind=k))
                  assert_array_equal(d[np.argpartition(d, 1, kind=k)],
                                     np.partition(d, 1, kind=k))
                  for i in range(d.size):
                      d[i:].partition(0, kind=k)
                  assert_array_equal(d, tgt)
  
              for r in ([3, 2, 1], [1, 2, 3], [2, 1, 3], [2, 3, 1],
                        [1, 1, 1], [1, 2, 2], [2, 2, 1], [1, 2, 1]):
                  d = np.array(r)
                  tgt = np.sort(d)
                  assert_array_equal(np.partition(d, 0, kind=k)[0], tgt[0])
                  assert_array_equal(np.partition(d, 1, kind=k)[1], tgt[1])
                  assert_array_equal(np.partition(d, 2, kind=k)[2], tgt[2])
                  assert_array_equal(d[np.argpartition(d, 0, kind=k)],
                                     np.partition(d, 0, kind=k))
                  assert_array_equal(d[np.argpartition(d, 1, kind=k)],
                                     np.partition(d, 1, kind=k))
                  assert_array_equal(d[np.argpartition(d, 2, kind=k)],
                                     np.partition(d, 2, kind=k))
                  for i in range(d.size):
                      d[i:].partition(0, kind=k)
                  assert_array_equal(d, tgt)
  
              d = np.ones(50)
              assert_array_equal(np.partition(d, 0, kind=k), d)
              assert_array_equal(d[np.argpartition(d, 0, kind=k)],
                                 np.partition(d, 0, kind=k))
  
              # sorted
              d = np.arange(49)
              assert_equal(np.partition(d, 5, kind=k)[5], 5)
              assert_equal(np.partition(d, 15, kind=k)[15], 15)
              assert_array_equal(d[np.argpartition(d, 5, kind=k)],
                                 np.partition(d, 5, kind=k))
              assert_array_equal(d[np.argpartition(d, 15, kind=k)],
                                 np.partition(d, 15, kind=k))
  
              # rsorted
              d = np.arange(47)[::-1]
              assert_equal(np.partition(d, 6, kind=k)[6], 6)
              assert_equal(np.partition(d, 16, kind=k)[16], 16)
              assert_array_equal(d[np.argpartition(d, 6, kind=k)],
                                 np.partition(d, 6, kind=k))
              assert_array_equal(d[np.argpartition(d, 16, kind=k)],
                                 np.partition(d, 16, kind=k))
  
              assert_array_equal(np.partition(d, -6, kind=k),
                                 np.partition(d, 41, kind=k))
              assert_array_equal(np.partition(d, -16, kind=k),
                                 np.partition(d, 31, kind=k))
              assert_array_equal(d[np.argpartition(d, -6, kind=k)],
                                 np.partition(d, 41, kind=k))
  
              # median of 3 killer, O(n^2) on pure median 3 pivot quickselect
              # exercises the median of median of 5 code used to keep O(n)
              d = np.arange(1000000)
              x = np.roll(d, d.size // 2)
              mid = x.size // 2 + 1
              assert_equal(np.partition(x, mid)[mid], mid)
              d = np.arange(1000001)
              x = np.roll(d, d.size // 2 + 1)
              mid = x.size // 2 + 1
              assert_equal(np.partition(x, mid)[mid], mid)
  
              # max
              d = np.ones(10)
              d[1] = 4
              assert_equal(np.partition(d, (2, -1))[-1], 4)
              assert_equal(np.partition(d, (2, -1))[2], 1)
              assert_equal(d[np.argpartition(d, (2, -1))][-1], 4)
              assert_equal(d[np.argpartition(d, (2, -1))][2], 1)
              d[1] = np.nan
              assert_(np.isnan(d[np.argpartition(d, (2, -1))][-1]))
              assert_(np.isnan(np.partition(d, (2, -1))[-1]))
  
              # equal elements
              d = np.arange(47) % 7
              tgt = np.sort(np.arange(47) % 7)
              np.random.shuffle(d)
              for i in range(d.size):
                  assert_equal(np.partition(d, i, kind=k)[i], tgt[i])
              assert_array_equal(d[np.argpartition(d, 6, kind=k)],
                                 np.partition(d, 6, kind=k))
              assert_array_equal(d[np.argpartition(d, 16, kind=k)],
                                 np.partition(d, 16, kind=k))
              for i in range(d.size):
                  d[i:].partition(0, kind=k)
              assert_array_equal(d, tgt)
  
              d = np.array([0, 1, 2, 3, 4, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
                            7, 7, 7, 7, 7, 9])
              kth = [0, 3, 19, 20]
              assert_equal(np.partition(d, kth, kind=k)[kth], (0, 3, 7, 7))
              assert_equal(d[np.argpartition(d, kth, kind=k)][kth], (0, 3, 7, 7))
  
              d = np.array([2, 1])
              d.partition(0, kind=k)
              assert_raises(ValueError, d.partition, 2)
              assert_raises(np.AxisError, d.partition, 3, axis=1)
              assert_raises(ValueError, np.partition, d, 2)
              assert_raises(np.AxisError, np.partition, d, 2, axis=1)
              assert_raises(ValueError, d.argpartition, 2)
              assert_raises(np.AxisError, d.argpartition, 3, axis=1)
              assert_raises(ValueError, np.argpartition, d, 2)
              assert_raises(np.AxisError, np.argpartition, d, 2, axis=1)
              d = np.arange(10).reshape((2, 5))
              d.partition(1, axis=0, kind=k)
              d.partition(4, axis=1, kind=k)
              np.partition(d, 1, axis=0, kind=k)
              np.partition(d, 4, axis=1, kind=k)
              np.partition(d, 1, axis=None, kind=k)
              np.partition(d, 9, axis=None, kind=k)
              d.argpartition(1, axis=0, kind=k)
              d.argpartition(4, axis=1, kind=k)
              np.argpartition(d, 1, axis=0, kind=k)
              np.argpartition(d, 4, axis=1, kind=k)
              np.argpartition(d, 1, axis=None, kind=k)
              np.argpartition(d, 9, axis=None, kind=k)
              assert_raises(ValueError, d.partition, 2, axis=0)
              assert_raises(ValueError, d.partition, 11, axis=1)
              assert_raises(TypeError, d.partition, 2, axis=None)
              assert_raises(ValueError, np.partition, d, 9, axis=1)
              assert_raises(ValueError, np.partition, d, 11, axis=None)
              assert_raises(ValueError, d.argpartition, 2, axis=0)
              assert_raises(ValueError, d.argpartition, 11, axis=1)
              assert_raises(ValueError, np.argpartition, d, 9, axis=1)
              assert_raises(ValueError, np.argpartition, d, 11, axis=None)
  
              td = [(dt, s) for dt in [np.int32, np.float32, np.complex64]
                    for s in (9, 16)]
              for dt, s in td:
                  aae = assert_array_equal
                  at = assert_
  
                  d = np.arange(s, dtype=dt)
                  np.random.shuffle(d)
                  d1 = np.tile(np.arange(s, dtype=dt), (4, 1))
                  map(np.random.shuffle, d1)
                  d0 = np.transpose(d1)
                  for i in range(d.size):
                      p = np.partition(d, i, kind=k)
                      assert_equal(p[i], i)
                      # all before are smaller
                      assert_array_less(p[:i], p[i])
                      # all after are larger
                      assert_array_less(p[i], p[i + 1:])
                      aae(p, d[np.argpartition(d, i, kind=k)])
  
                      p = np.partition(d1, i, axis=1, kind=k)
                      aae(p[:, i], np.array([i] * d1.shape[0], dtype=dt))
                      # array_less does not seem to work right
                      at((p[:, :i].T <= p[:, i]).all(),
                         msg="%d: %r <= %r" % (i, p[:, i], p[:, :i].T))
                      at((p[:, i + 1:].T > p[:, i]).all(),
                         msg="%d: %r < %r" % (i, p[:, i], p[:, i + 1:].T))
                      aae(p, d1[np.arange(d1.shape[0])[:, None],
                          np.argpartition(d1, i, axis=1, kind=k)])
  
                      p = np.partition(d0, i, axis=0, kind=k)
                      aae(p[i, :], np.array([i] * d1.shape[0], dtype=dt))
                      # array_less does not seem to work right
                      at((p[:i, :] <= p[i, :]).all(),
                         msg="%d: %r <= %r" % (i, p[i, :], p[:i, :]))
                      at((p[i + 1:, :] > p[i, :]).all(),
                         msg="%d: %r < %r" % (i, p[i, :], p[:, i + 1:]))
                      aae(p, d0[np.argpartition(d0, i, axis=0, kind=k),
                          np.arange(d0.shape[1])[None, :]])
  
                      # check inplace
                      dc = d.copy()
                      dc.partition(i, kind=k)
                      assert_equal(dc, np.partition(d, i, kind=k))
                      dc = d0.copy()
                      dc.partition(i, axis=0, kind=k)
                      assert_equal(dc, np.partition(d0, i, axis=0, kind=k))
                      dc = d1.copy()
                      dc.partition(i, axis=1, kind=k)
                      assert_equal(dc, np.partition(d1, i, axis=1, kind=k))
  
      def assert_partitioned(self, d, kth):
          prev = 0
          for k in np.sort(kth):
              assert_array_less(d[prev:k], d[k], err_msg='kth %d' % k)
              assert_((d[k:] >= d[k]).all(),
                      msg="kth %d, %r not greater equal %d" % (k, d[k:], d[k]))
              prev = k + 1
  
      def test_partition_iterative(self):
              d = np.arange(17)
              kth = (0, 1, 2, 429, 231)
              assert_raises(ValueError, d.partition, kth)
              assert_raises(ValueError, d.argpartition, kth)
              d = np.arange(10).reshape((2, 5))
              assert_raises(ValueError, d.partition, kth, axis=0)
              assert_raises(ValueError, d.partition, kth, axis=1)
              assert_raises(ValueError, np.partition, d, kth, axis=1)
              assert_raises(ValueError, np.partition, d, kth, axis=None)
  
              d = np.array([3, 4, 2, 1])
              p = np.partition(d, (0, 3))
              self.assert_partitioned(p, (0, 3))
              self.assert_partitioned(d[np.argpartition(d, (0, 3))], (0, 3))
  
              assert_array_equal(p, np.partition(d, (-3, -1)))
              assert_array_equal(p, d[np.argpartition(d, (-3, -1))])
  
              d = np.arange(17)
              np.random.shuffle(d)
              d.partition(range(d.size))
              assert_array_equal(np.arange(17), d)
              np.random.shuffle(d)
              assert_array_equal(np.arange(17), d[d.argpartition(range(d.size))])
  
              # test unsorted kth
              d = np.arange(17)
              np.random.shuffle(d)
              keys = np.array([1, 3, 8, -2])
              np.random.shuffle(d)
              p = np.partition(d, keys)
              self.assert_partitioned(p, keys)
              p = d[np.argpartition(d, keys)]
              self.assert_partitioned(p, keys)
              np.random.shuffle(keys)
              assert_array_equal(np.partition(d, keys), p)
              assert_array_equal(d[np.argpartition(d, keys)], p)
  
              # equal kth
              d = np.arange(20)[::-1]
              self.assert_partitioned(np.partition(d, [5]*4), [5])
              self.assert_partitioned(np.partition(d, [5]*4 + [6, 13]),
                                      [5]*4 + [6, 13])
              self.assert_partitioned(d[np.argpartition(d, [5]*4)], [5])
              self.assert_partitioned(d[np.argpartition(d, [5]*4 + [6, 13])],
                                      [5]*4 + [6, 13])
  
              d = np.arange(12)
              np.random.shuffle(d)
              d1 = np.tile(np.arange(12), (4, 1))
              map(np.random.shuffle, d1)
              d0 = np.transpose(d1)
  
              kth = (1, 6, 7, -1)
              p = np.partition(d1, kth, axis=1)
              pa = d1[np.arange(d1.shape[0])[:, None],
                      d1.argpartition(kth, axis=1)]
              assert_array_equal(p, pa)
              for i in range(d1.shape[0]):
                  self.assert_partitioned(p[i,:], kth)
              p = np.partition(d0, kth, axis=0)
              pa = d0[np.argpartition(d0, kth, axis=0),
                      np.arange(d0.shape[1])[None,:]]
              assert_array_equal(p, pa)
              for i in range(d0.shape[1]):
                  self.assert_partitioned(p[:, i], kth)
  
      def test_partition_cdtype(self):
          d = np.array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
                     ('Lancelot', 1.9, 38)],
                    dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
  
          tgt = np.sort(d, order=['age', 'height'])
          assert_array_equal(np.partition(d, range(d.size),
                                          order=['age', 'height']),
                             tgt)
          assert_array_equal(d[np.argpartition(d, range(d.size),
                                               order=['age', 'height'])],
                             tgt)
          for k in range(d.size):
              assert_equal(np.partition(d, k, order=['age', 'height'])[k],
                          tgt[k])
              assert_equal(d[np.argpartition(d, k, order=['age', 'height'])][k],
                           tgt[k])
  
          d = np.array(['Galahad', 'Arthur', 'zebra', 'Lancelot'])
          tgt = np.sort(d)
          assert_array_equal(np.partition(d, range(d.size)), tgt)
          for k in range(d.size):
              assert_equal(np.partition(d, k)[k], tgt[k])
              assert_equal(d[np.argpartition(d, k)][k], tgt[k])
  
      def test_partition_unicode_kind(self):
          d = np.arange(10)
          k = b'\xc3\xa4'.decode("UTF8")
          assert_raises(ValueError, d.partition, 2, kind=k)
          assert_raises(ValueError, d.argpartition, 2, kind=k)
  
      def test_partition_fuzz(self):
          # a few rounds of random data testing
          for j in range(10, 30):
              for i in range(1, j - 2):
                  d = np.arange(j)
                  np.random.shuffle(d)
                  d = d % np.random.randint(2, 30)
                  idx = np.random.randint(d.size)
                  kth = [0, idx, i, i + 1]
                  tgt = np.sort(d)[kth]
                  assert_array_equal(np.partition(d, kth)[kth], tgt,
                                     err_msg="data: %r\n kth: %r" % (d, kth))
  
      def test_argpartition_gh5524(self):
          #  A test for functionality of argpartition on lists.
          d = [6,7,3,2,9,0]
          p = np.argpartition(d,1)
          self.assert_partitioned(np.array(d)[p],[1])
  
      def test_flatten(self):
          x0 = np.array([[1, 2, 3], [4, 5, 6]], np.int32)
          x1 = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]], np.int32)
          y0 = np.array([1, 2, 3, 4, 5, 6], np.int32)
          y0f = np.array([1, 4, 2, 5, 3, 6], np.int32)
          y1 = np.array([1, 2, 3, 4, 5, 6, 7, 8], np.int32)
          y1f = np.array([1, 5, 3, 7, 2, 6, 4, 8], np.int32)
          assert_equal(x0.flatten(), y0)
          assert_equal(x0.flatten('F'), y0f)
          assert_equal(x0.flatten('F'), x0.T.flatten())
          assert_equal(x1.flatten(), y1)
          assert_equal(x1.flatten('F'), y1f)
          assert_equal(x1.flatten('F'), x1.T.flatten())
  
  
      @pytest.mark.parametrize('func', (np.dot, np.matmul))
      def test_arr_mult(self, func):
          a = np.array([[1, 0], [0, 1]])
          b = np.array([[0, 1], [1, 0]])
          c = np.array([[9, 1], [1, -9]])
          d = np.arange(24).reshape(4, 6)
          ddt = np.array(
              [[  55,  145,  235,  325],
               [ 145,  451,  757, 1063],
               [ 235,  757, 1279, 1801],
               [ 325, 1063, 1801, 2539]]
          )
          dtd = np.array(
              [[504, 540, 576, 612, 648, 684],
               [540, 580, 620, 660, 700, 740],
               [576, 620, 664, 708, 752, 796],
               [612, 660, 708, 756, 804, 852],
               [648, 700, 752, 804, 856, 908],
               [684, 740, 796, 852, 908, 964]]
          )
  
  
          # gemm vs syrk optimizations
          for et in [np.float32, np.float64, np.complex64, np.complex128]:
              eaf = a.astype(et)
              assert_equal(func(eaf, eaf), eaf)
              assert_equal(func(eaf.T, eaf), eaf)
              assert_equal(func(eaf, eaf.T), eaf)
              assert_equal(func(eaf.T, eaf.T), eaf)
              assert_equal(func(eaf.T.copy(), eaf), eaf)
              assert_equal(func(eaf, eaf.T.copy()), eaf)
              assert_equal(func(eaf.T.copy(), eaf.T.copy()), eaf)
  
          # syrk validations
          for et in [np.float32, np.float64, np.complex64, np.complex128]:
              eaf = a.astype(et)
              ebf = b.astype(et)
              assert_equal(func(ebf, ebf), eaf)
              assert_equal(func(ebf.T, ebf), eaf)
              assert_equal(func(ebf, ebf.T), eaf)
              assert_equal(func(ebf.T, ebf.T), eaf)
  
          # syrk - different shape, stride, and view validations
          for et in [np.float32, np.float64, np.complex64, np.complex128]:
              edf = d.astype(et)
              assert_equal(
                  func(edf[::-1, :], edf.T),
                  func(edf[::-1, :].copy(), edf.T.copy())
              )
              assert_equal(
                  func(edf[:, ::-1], edf.T),
                  func(edf[:, ::-1].copy(), edf.T.copy())
              )
              assert_equal(
                  func(edf, edf[::-1, :].T),
                  func(edf, edf[::-1, :].T.copy())
              )
              assert_equal(
                  func(edf, edf[:, ::-1].T),
                  func(edf, edf[:, ::-1].T.copy())
              )
              assert_equal(
                  func(edf[:edf.shape[0] // 2, :], edf[::2, :].T),
                  func(edf[:edf.shape[0] // 2, :].copy(), edf[::2, :].T.copy())
              )
              assert_equal(
                  func(edf[::2, :], edf[:edf.shape[0] // 2, :].T),
                  func(edf[::2, :].copy(), edf[:edf.shape[0] // 2, :].T.copy())
              )
  
          # syrk - different shape
          for et in [np.float32, np.float64, np.complex64, np.complex128]:
              edf = d.astype(et)
              eddtf = ddt.astype(et)
              edtdf = dtd.astype(et)
              assert_equal(func(edf, edf.T), eddtf)
              assert_equal(func(edf.T, edf), edtdf)
  
      @pytest.mark.parametrize('func', (np.dot, np.matmul))
      @pytest.mark.parametrize('dtype', 'ifdFD')
      def test_no_dgemv(self, func, dtype):
          # check vector arg for contiguous before gemv
          # gh-12156
          a = np.arange(8.0, dtype=dtype).reshape(2, 4)
          b = np.broadcast_to(1., (4, 1))
          ret1 = func(a, b)
          ret2 = func(a, b.copy())
          assert_equal(ret1, ret2)
  
          ret1 = func(b.T, a.T)
          ret2 = func(b.T.copy(), a.T)
          assert_equal(ret1, ret2)
  
          # check for unaligned data
          dt = np.dtype(dtype)
          a = np.zeros(8 * dt.itemsize // 2 + 1, dtype='int16')[1:].view(dtype)
          a = a.reshape(2, 4)
          b = a[0]
          # make sure it is not aligned
          assert_(a.__array_interface__['data'][0] % dt.itemsize != 0)
          ret1 = func(a, b)
          ret2 = func(a.copy(), b.copy())
          assert_equal(ret1, ret2)
  
          ret1 = func(b.T, a.T)
          ret2 = func(b.T.copy(), a.T.copy())
          assert_equal(ret1, ret2)
  
      def test_dot(self):
          a = np.array([[1, 0], [0, 1]])
          b = np.array([[0, 1], [1, 0]])
          c = np.array([[9, 1], [1, -9]])
          # function versus methods
          assert_equal(np.dot(a, b), a.dot(b))
          assert_equal(np.dot(np.dot(a, b), c), a.dot(b).dot(c))
  
          # test passing in an output array
          c = np.zeros_like(a)
          a.dot(b, c)
          assert_equal(c, np.dot(a, b))
  
          # test keyword args
          c = np.zeros_like(a)
          a.dot(b=b, out=c)
          assert_equal(c, np.dot(a, b))
  
      def test_dot_type_mismatch(self):
          c = 1.
          A = np.array((1,1), dtype='i,i')
  
          assert_raises(TypeError, np.dot, c, A)
          assert_raises(TypeError, np.dot, A, c)
  
      def test_dot_out_mem_overlap(self):
          np.random.seed(1)
  
          # Test BLAS and non-BLAS code paths, including all dtypes
          # that dot() supports
          dtypes = [np.dtype(code) for code in np.typecodes['All']
                    if code not in 'USVM']
          for dtype in dtypes:
              a = np.random.rand(3, 3).astype(dtype)
  
              # Valid dot() output arrays must be aligned
              b = _aligned_zeros((3, 3), dtype=dtype)
              b[...] = np.random.rand(3, 3)
  
              y = np.dot(a, b)
              x = np.dot(a, b, out=b)
              assert_equal(x, y, err_msg=repr(dtype))
  
              # Check invalid output array
              assert_raises(ValueError, np.dot, a, b, out=b[::2])
              assert_raises(ValueError, np.dot, a, b, out=b.T)
  
      def test_dot_matmul_out(self):
          # gh-9641
          class Sub(np.ndarray):
              pass
          a = np.ones((2, 2)).view(Sub)
          b = np.ones((2, 2)).view(Sub)
          out = np.ones((2, 2))
  
          # make sure out can be any ndarray (not only subclass of inputs)
          np.dot(a, b, out=out)
          np.matmul(a, b, out=out)
  
      def test_dot_matmul_inner_array_casting_fails(self):
  
          class A:
              def __array__(self, *args, **kwargs):
                  raise NotImplementedError
  
          # Don't override the error from calling __array__()
          assert_raises(NotImplementedError, np.dot, A(), A())
          assert_raises(NotImplementedError, np.matmul, A(), A())
          assert_raises(NotImplementedError, np.inner, A(), A())
  
      def test_matmul_out(self):
          # overlapping memory
          a = np.arange(18).reshape(2, 3, 3)
          b = np.matmul(a, a)
          c = np.matmul(a, a, out=a)
          assert_(c is a)
          assert_equal(c, b)
          a = np.arange(18).reshape(2, 3, 3)
          c = np.matmul(a, a, out=a[::-1, ...])
          assert_(c.base is a.base)
          assert_equal(c, b)
  
      def test_diagonal(self):
          a = np.arange(12).reshape((3, 4))
          assert_equal(a.diagonal(), [0, 5, 10])
          assert_equal(a.diagonal(0), [0, 5, 10])
          assert_equal(a.diagonal(1), [1, 6, 11])
          assert_equal(a.diagonal(-1), [4, 9])
          assert_raises(np.AxisError, a.diagonal, axis1=0, axis2=5)
          assert_raises(np.AxisError, a.diagonal, axis1=5, axis2=0)
          assert_raises(np.AxisError, a.diagonal, axis1=5, axis2=5)
          assert_raises(ValueError, a.diagonal, axis1=1, axis2=1)
  
          b = np.arange(8).reshape((2, 2, 2))
          assert_equal(b.diagonal(), [[0, 6], [1, 7]])
          assert_equal(b.diagonal(0), [[0, 6], [1, 7]])
          assert_equal(b.diagonal(1), [[2], [3]])
          assert_equal(b.diagonal(-1), [[4], [5]])
          assert_raises(ValueError, b.diagonal, axis1=0, axis2=0)
          assert_equal(b.diagonal(0, 1, 2), [[0, 3], [4, 7]])
          assert_equal(b.diagonal(0, 0, 1), [[0, 6], [1, 7]])
          assert_equal(b.diagonal(offset=1, axis1=0, axis2=2), [[1], [3]])
          # Order of axis argument doesn't matter:
          assert_equal(b.diagonal(0, 2, 1), [[0, 3], [4, 7]])
  
      def test_diagonal_view_notwriteable(self):
          a = np.eye(3).diagonal()
          assert_(not a.flags.writeable)
          assert_(not a.flags.owndata)
  
          a = np.diagonal(np.eye(3))
          assert_(not a.flags.writeable)
          assert_(not a.flags.owndata)
  
          a = np.diag(np.eye(3))
          assert_(not a.flags.writeable)
          assert_(not a.flags.owndata)
  
      def test_diagonal_memleak(self):
          # Regression test for a bug that crept in at one point
          a = np.zeros((100, 100))
          if HAS_REFCOUNT:
              assert_(sys.getrefcount(a) < 50)
          for i in range(100):
              a.diagonal()
          if HAS_REFCOUNT:
              assert_(sys.getrefcount(a) < 50)
  
      def test_size_zero_memleak(self):
          # Regression test for issue 9615
          # Exercises a special-case code path for dot products of length
          # zero in cblasfuncs (making it is specific to floating dtypes).
          a = np.array([], dtype=np.float64)
          x = np.array(2.0)
          for _ in range(100):
              np.dot(a, a, out=x)
          if HAS_REFCOUNT:
              assert_(sys.getrefcount(x) < 50)
  
      def test_trace(self):
          a = np.arange(12).reshape((3, 4))
          assert_equal(a.trace(), 15)
          assert_equal(a.trace(0), 15)
          assert_equal(a.trace(1), 18)
          assert_equal(a.trace(-1), 13)
  
          b = np.arange(8).reshape((2, 2, 2))
          assert_equal(b.trace(), [6, 8])
          assert_equal(b.trace(0), [6, 8])
          assert_equal(b.trace(1), [2, 3])
          assert_equal(b.trace(-1), [4, 5])
          assert_equal(b.trace(0, 0, 1), [6, 8])
          assert_equal(b.trace(0, 0, 2), [5, 9])
          assert_equal(b.trace(0, 1, 2), [3, 11])
          assert_equal(b.trace(offset=1, axis1=0, axis2=2), [1, 3])
  
          out = np.array(1)
          ret = a.trace(out=out)
          assert ret is out
  
      def test_trace_subclass(self):
          # The class would need to overwrite trace to ensure single-element
          # output also has the right subclass.
          class MyArray(np.ndarray):
              pass
  
          b = np.arange(8).reshape((2, 2, 2)).view(MyArray)
          t = b.trace()
          assert_(isinstance(t, MyArray))
  
      def test_put(self):
          icodes = np.typecodes['AllInteger']
          fcodes = np.typecodes['AllFloat']
          for dt in icodes + fcodes + 'O':
              tgt = np.array([0, 1, 0, 3, 0, 5], dtype=dt)
  
              # test 1-d
              a = np.zeros(6, dtype=dt)
              a.put([1, 3, 5], [1, 3, 5])
              assert_equal(a, tgt)
  
              # test 2-d
              a = np.zeros((2, 3), dtype=dt)
              a.put([1, 3, 5], [1, 3, 5])
              assert_equal(a, tgt.reshape(2, 3))
  
          for dt in '?':
              tgt = np.array([False, True, False, True, False, True], dtype=dt)
  
              # test 1-d
              a = np.zeros(6, dtype=dt)
              a.put([1, 3, 5], [True]*3)
              assert_equal(a, tgt)
  
              # test 2-d
              a = np.zeros((2, 3), dtype=dt)
              a.put([1, 3, 5], [True]*3)
              assert_equal(a, tgt.reshape(2, 3))
  
          # check must be writeable
          a = np.zeros(6)
          a.flags.writeable = False
          assert_raises(ValueError, a.put, [1, 3, 5], [1, 3, 5])
  
          # when calling np.put, make sure a
          # TypeError is raised if the object
          # isn't an ndarray
          bad_array = [1, 2, 3]
          assert_raises(TypeError, np.put, bad_array, [0, 2], 5)
  
      def test_ravel(self):
          a = np.array([[0, 1], [2, 3]])
          assert_equal(a.ravel(), [0, 1, 2, 3])
          assert_(not a.ravel().flags.owndata)
          assert_equal(a.ravel('F'), [0, 2, 1, 3])
          assert_equal(a.ravel(order='C'), [0, 1, 2, 3])
          assert_equal(a.ravel(order='F'), [0, 2, 1, 3])
          assert_equal(a.ravel(order='A'), [0, 1, 2, 3])
          assert_(not a.ravel(order='A').flags.owndata)
          assert_equal(a.ravel(order='K'), [0, 1, 2, 3])
          assert_(not a.ravel(order='K').flags.owndata)
          assert_equal(a.ravel(), a.reshape(-1))
  
          a = np.array([[0, 1], [2, 3]], order='F')
          assert_equal(a.ravel(), [0, 1, 2, 3])
          assert_equal(a.ravel(order='A'), [0, 2, 1, 3])
          assert_equal(a.ravel(order='K'), [0, 2, 1, 3])
          assert_(not a.ravel(order='A').flags.owndata)
          assert_(not a.ravel(order='K').flags.owndata)
          assert_equal(a.ravel(), a.reshape(-1))
          assert_equal(a.ravel(order='A'), a.reshape(-1, order='A'))
  
          a = np.array([[0, 1], [2, 3]])[::-1, :]
          assert_equal(a.ravel(), [2, 3, 0, 1])
          assert_equal(a.ravel(order='C'), [2, 3, 0, 1])
          assert_equal(a.ravel(order='F'), [2, 0, 3, 1])
          assert_equal(a.ravel(order='A'), [2, 3, 0, 1])
          # 'K' doesn't reverse the axes of negative strides
          assert_equal(a.ravel(order='K'), [2, 3, 0, 1])
          assert_(a.ravel(order='K').flags.owndata)
  
          # Test simple 1-d copy behaviour:
          a = np.arange(10)[::2]
          assert_(a.ravel('K').flags.owndata)
          assert_(a.ravel('C').flags.owndata)
          assert_(a.ravel('F').flags.owndata)
  
          # Not contiguous and 1-sized axis with non matching stride
          a = np.arange(2**3 * 2)[::2]
          a = a.reshape(2, 1, 2, 2).swapaxes(-1, -2)
          strides = list(a.strides)
          strides[1] = 123
          a.strides = strides
          assert_(a.ravel(order='K').flags.owndata)
          assert_equal(a.ravel('K'), np.arange(0, 15, 2))
  
          # contiguous and 1-sized axis with non matching stride works:
          a = np.arange(2**3)
          a = a.reshape(2, 1, 2, 2).swapaxes(-1, -2)
          strides = list(a.strides)
          strides[1] = 123
          a.strides = strides
          assert_(np.may_share_memory(a.ravel(order='K'), a))
          assert_equal(a.ravel(order='K'), np.arange(2**3))
  
          # Test negative strides (not very interesting since non-contiguous):
          a = np.arange(4)[::-1].reshape(2, 2)
          assert_(a.ravel(order='C').flags.owndata)
          assert_(a.ravel(order='K').flags.owndata)
          assert_equal(a.ravel('C'), [3, 2, 1, 0])
          assert_equal(a.ravel('K'), [3, 2, 1, 0])
  
          # 1-element tidy strides test (NPY_RELAXED_STRIDES_CHECKING):
          a = np.array([[1]])
          a.strides = (123, 432)
          # If the stride is not 8, NPY_RELAXED_STRIDES_CHECKING is messing
          # them up on purpose:
          if np.ones(1).strides == (8,):
              assert_(np.may_share_memory(a.ravel('K'), a))
              assert_equal(a.ravel('K').strides, (a.dtype.itemsize,))
  
          for order in ('C', 'F', 'A', 'K'):
              # 0-d corner case:
              a = np.array(0)
              assert_equal(a.ravel(order), [0])
              assert_(np.may_share_memory(a.ravel(order), a))
  
          # Test that certain non-inplace ravels work right (mostly) for 'K':
          b = np.arange(2**4 * 2)[::2].reshape(2, 2, 2, 2)
          a = b[..., ::2]
          assert_equal(a.ravel('K'), [0, 4, 8, 12, 16, 20, 24, 28])
          assert_equal(a.ravel('C'), [0, 4, 8, 12, 16, 20, 24, 28])
          assert_equal(a.ravel('A'), [0, 4, 8, 12, 16, 20, 24, 28])
          assert_equal(a.ravel('F'), [0, 16, 8, 24, 4, 20, 12, 28])
  
          a = b[::2, ...]
          assert_equal(a.ravel('K'), [0, 2, 4, 6, 8, 10, 12, 14])
          assert_equal(a.ravel('C'), [0, 2, 4, 6, 8, 10, 12, 14])
          assert_equal(a.ravel('A'), [0, 2, 4, 6, 8, 10, 12, 14])
          assert_equal(a.ravel('F'), [0, 8, 4, 12, 2, 10, 6, 14])
  
      def test_ravel_subclass(self):
          class ArraySubclass(np.ndarray):
              pass
  
          a = np.arange(10).view(ArraySubclass)
          assert_(isinstance(a.ravel('C'), ArraySubclass))
          assert_(isinstance(a.ravel('F'), ArraySubclass))
          assert_(isinstance(a.ravel('A'), ArraySubclass))
          assert_(isinstance(a.ravel('K'), ArraySubclass))
  
          a = np.arange(10)[::2].view(ArraySubclass)
          assert_(isinstance(a.ravel('C'), ArraySubclass))
          assert_(isinstance(a.ravel('F'), ArraySubclass))
          assert_(isinstance(a.ravel('A'), ArraySubclass))
          assert_(isinstance(a.ravel('K'), ArraySubclass))
  
      def test_swapaxes(self):
          a = np.arange(1*2*3*4).reshape(1, 2, 3, 4).copy()
          idx = np.indices(a.shape)
          assert_(a.flags['OWNDATA'])
          b = a.copy()
          # check exceptions
          assert_raises(np.AxisError, a.swapaxes, -5, 0)
          assert_raises(np.AxisError, a.swapaxes, 4, 0)
          assert_raises(np.AxisError, a.swapaxes, 0, -5)
          assert_raises(np.AxisError, a.swapaxes, 0, 4)
  
          for i in range(-4, 4):
              for j in range(-4, 4):
                  for k, src in enumerate((a, b)):
                      c = src.swapaxes(i, j)
                      # check shape
                      shape = list(src.shape)
                      shape[i] = src.shape[j]
                      shape[j] = src.shape[i]
                      assert_equal(c.shape, shape, str((i, j, k)))
                      # check array contents
                      i0, i1, i2, i3 = [dim-1 for dim in c.shape]
                      j0, j1, j2, j3 = [dim-1 for dim in src.shape]
                      assert_equal(src[idx[j0], idx[j1], idx[j2], idx[j3]],
                                   c[idx[i0], idx[i1], idx[i2], idx[i3]],
                                   str((i, j, k)))
                      # check a view is always returned, gh-5260
                      assert_(not c.flags['OWNDATA'], str((i, j, k)))
                      # check on non-contiguous input array
                      if k == 1:
                          b = c
  
      def test_conjugate(self):
          a = np.array([1-1j, 1+1j, 23+23.0j])
          ac = a.conj()
          assert_equal(a.real, ac.real)
          assert_equal(a.imag, -ac.imag)
          assert_equal(ac, a.conjugate())
          assert_equal(ac, np.conjugate(a))
  
          a = np.array([1-1j, 1+1j, 23+23.0j], 'F')
          ac = a.conj()
          assert_equal(a.real, ac.real)
          assert_equal(a.imag, -ac.imag)
          assert_equal(ac, a.conjugate())
          assert_equal(ac, np.conjugate(a))
  
          a = np.array([1, 2, 3])
          ac = a.conj()
          assert_equal(a, ac)
          assert_equal(ac, a.conjugate())
          assert_equal(ac, np.conjugate(a))
  
          a = np.array([1.0, 2.0, 3.0])
          ac = a.conj()
          assert_equal(a, ac)
          assert_equal(ac, a.conjugate())
          assert_equal(ac, np.conjugate(a))
  
          a = np.array([1-1j, 1+1j, 1, 2.0], object)
          ac = a.conj()
          assert_equal(ac, [k.conjugate() for k in a])
          assert_equal(ac, a.conjugate())
          assert_equal(ac, np.conjugate(a))
  
          a = np.array([1-1j, 1, 2.0, 'f'], object)
          assert_raises(TypeError, lambda: a.conj())
          assert_raises(TypeError, lambda: a.conjugate())
  
      def test__complex__(self):
          dtypes = ['i1', 'i2', 'i4', 'i8',
                    'u1', 'u2', 'u4', 'u8',
                    'f', 'd', 'g', 'F', 'D', 'G',
                    '?', 'O']
          for dt in dtypes:
              a = np.array(7, dtype=dt)
              b = np.array([7], dtype=dt)
              c = np.array([[[[[7]]]]], dtype=dt)
  
              msg = 'dtype: {0}'.format(dt)
              ap = complex(a)
              assert_equal(ap, a, msg)
              bp = complex(b)
              assert_equal(bp, b, msg)
              cp = complex(c)
              assert_equal(cp, c, msg)
  
      def test__complex__should_not_work(self):
          dtypes = ['i1', 'i2', 'i4', 'i8',
                    'u1', 'u2', 'u4', 'u8',
                    'f', 'd', 'g', 'F', 'D', 'G',
                    '?', 'O']
          for dt in dtypes:
              a = np.array([1, 2, 3], dtype=dt)
              assert_raises(TypeError, complex, a)
  
          dt = np.dtype([('a', 'f8'), ('b', 'i1')])
          b = np.array((1.0, 3), dtype=dt)
          assert_raises(TypeError, complex, b)
  
          c = np.array([(1.0, 3), (2e-3, 7)], dtype=dt)
          assert_raises(TypeError, complex, c)
  
          d = np.array('1+1j')
          assert_raises(TypeError, complex, d)
  
          e = np.array(['1+1j'], 'U')
          assert_raises(TypeError, complex, e)
  
  class TestCequenceMethods:
      def test_array_contains(self):
          assert_(4.0 in np.arange(16.).reshape(4,4))
          assert_(20.0 not in np.arange(16.).reshape(4,4))
  
  class TestBinop:
      def test_inplace(self):
          # test refcount 1 inplace conversion
          assert_array_almost_equal(np.array([0.5]) * np.array([1.0, 2.0]),
                                    [0.5, 1.0])
  
          d = np.array([0.5, 0.5])[::2]
          assert_array_almost_equal(d * (d * np.array([1.0, 2.0])),
                                    [0.25, 0.5])
  
          a = np.array([0.5])
          b = np.array([0.5])
          c = a + b
          c = a - b
          c = a * b
          c = a / b
          assert_equal(a, b)
          assert_almost_equal(c, 1.)
  
          c = a + b * 2. / b * a - a / b
          assert_equal(a, b)
          assert_equal(c, 0.5)
  
          # true divide
          a = np.array([5])
          b = np.array([3])
          c = (a * a) / b
  
          assert_almost_equal(c, 25 / 3)
          assert_equal(a, 5)
          assert_equal(b, 3)
  
      # ndarray.__rop__ always calls ufunc
      # ndarray.__iop__ always calls ufunc
      # ndarray.__op__, __rop__:
      #   - defer if other has __array_ufunc__ and it is None
      #           or other is not a subclass and has higher array priority
      #   - else, call ufunc
      def test_ufunc_binop_interaction(self):
          # Python method name (without underscores)
          #   -> (numpy ufunc, has_in_place_version, preferred_dtype)
          ops = {
              'add':      (np.add, True, float),
              'sub':      (np.subtract, True, float),
              'mul':      (np.multiply, True, float),
              'truediv':  (np.true_divide, True, float),
              'floordiv': (np.floor_divide, True, float),
              'mod':      (np.remainder, True, float),
              'divmod':   (np.divmod, False, float),
              'pow':      (np.power, True, int),
              'lshift':   (np.left_shift, True, int),
              'rshift':   (np.right_shift, True, int),
              'and':      (np.bitwise_and, True, int),
              'xor':      (np.bitwise_xor, True, int),
              'or':       (np.bitwise_or, True, int),
              'matmul':   (np.matmul, False, float),
              # 'ge':       (np.less_equal, False),
              # 'gt':       (np.less, False),
              # 'le':       (np.greater_equal, False),
              # 'lt':       (np.greater, False),
              # 'eq':       (np.equal, False),
              # 'ne':       (np.not_equal, False),
          }
  
          class Coerced(Exception):
              pass
  
          def array_impl(self):
              raise Coerced
  
          def op_impl(self, other):
              return "forward"
  
          def rop_impl(self, other):
              return "reverse"
  
          def iop_impl(self, other):
              return "in-place"
  
          def array_ufunc_impl(self, ufunc, method, *args, **kwargs):
              return ("__array_ufunc__", ufunc, method, args, kwargs)
  
          # Create an object with the given base, in the given module, with a
          # bunch of placeholder __op__ methods, and optionally a
          # __array_ufunc__ and __array_priority__.
          def make_obj(base, array_priority=False, array_ufunc=False,
                       alleged_module="__main__"):
              class_namespace = {"__array__": array_impl}
              if array_priority is not False:
                  class_namespace["__array_priority__"] = array_priority
              for op in ops:
                  class_namespace["__{0}__".format(op)] = op_impl
                  class_namespace["__r{0}__".format(op)] = rop_impl
                  class_namespace["__i{0}__".format(op)] = iop_impl
              if array_ufunc is not False:
                  class_namespace["__array_ufunc__"] = array_ufunc
              eval_namespace = {"base": base,
                                "class_namespace": class_namespace,
                                "__name__": alleged_module,
                                }
              MyType = eval("type('MyType', (base,), class_namespace)",
                            eval_namespace)
              if issubclass(MyType, np.ndarray):
                  # Use this range to avoid special case weirdnesses around
                  # divide-by-0, pow(x, 2), overflow due to pow(big, big), etc.
                  return np.arange(3, 7).reshape(2, 2).view(MyType)
              else:
                  return MyType()
  
          def check(obj, binop_override_expected, ufunc_override_expected,
                    inplace_override_expected, check_scalar=True):
              for op, (ufunc, has_inplace, dtype) in ops.items():
                  err_msg = ('op: %s, ufunc: %s, has_inplace: %s, dtype: %s'
                             % (op, ufunc, has_inplace, dtype))
                  check_objs = [np.arange(3, 7, dtype=dtype).reshape(2, 2)]
                  if check_scalar:
                      check_objs.append(check_objs[0][0])
                  for arr in check_objs:
                      arr_method = getattr(arr, "__{0}__".format(op))
  
                      def first_out_arg(result):
                          if op == "divmod":
                              assert_(isinstance(result, tuple))
                              return result[0]
                          else:
                              return result
  
                      # arr __op__ obj
                      if binop_override_expected:
                          assert_equal(arr_method(obj), NotImplemented, err_msg)
                      elif ufunc_override_expected:
                          assert_equal(arr_method(obj)[0], "__array_ufunc__",
                                       err_msg)
                      else:
                          if (isinstance(obj, np.ndarray) and
                              (type(obj).__array_ufunc__ is
                               np.ndarray.__array_ufunc__)):
                              # __array__ gets ignored
                              res = first_out_arg(arr_method(obj))
                              assert_(res.__class__ is obj.__class__, err_msg)
                          else:
                              assert_raises((TypeError, Coerced),
                                            arr_method, obj, err_msg=err_msg)
                      # obj __op__ arr
                      arr_rmethod = getattr(arr, "__r{0}__".format(op))
                      if ufunc_override_expected:
                          res = arr_rmethod(obj)
                          assert_equal(res[0], "__array_ufunc__",
                                       err_msg=err_msg)
                          assert_equal(res[1], ufunc, err_msg=err_msg)
                      else:
                          if (isinstance(obj, np.ndarray) and
                                  (type(obj).__array_ufunc__ is
                                   np.ndarray.__array_ufunc__)):
                              # __array__ gets ignored
                              res = first_out_arg(arr_rmethod(obj))
                              assert_(res.__class__ is obj.__class__, err_msg)
                          else:
                              # __array_ufunc__ = "asdf" creates a TypeError
                              assert_raises((TypeError, Coerced),
                                            arr_rmethod, obj, err_msg=err_msg)
  
                      # arr __iop__ obj
                      # array scalars don't have in-place operators
                      if has_inplace and isinstance(arr, np.ndarray):
                          arr_imethod = getattr(arr, "__i{0}__".format(op))
                          if inplace_override_expected:
                              assert_equal(arr_method(obj), NotImplemented,
                                           err_msg=err_msg)
                          elif ufunc_override_expected:
                              res = arr_imethod(obj)
                              assert_equal(res[0], "__array_ufunc__", err_msg)
                              assert_equal(res[1], ufunc, err_msg)
                              assert_(type(res[-1]["out"]) is tuple, err_msg)
                              assert_(res[-1]["out"][0] is arr, err_msg)
                          else:
                              if (isinstance(obj, np.ndarray) and
                                      (type(obj).__array_ufunc__ is
                                      np.ndarray.__array_ufunc__)):
                                  # __array__ gets ignored
                                  assert_(arr_imethod(obj) is arr, err_msg)
                              else:
                                  assert_raises((TypeError, Coerced),
                                                arr_imethod, obj,
                                                err_msg=err_msg)
  
                      op_fn = getattr(operator, op, None)
                      if op_fn is None:
                          op_fn = getattr(operator, op + "_", None)
                      if op_fn is None:
                          op_fn = getattr(builtins, op)
                      assert_equal(op_fn(obj, arr), "forward", err_msg)
                      if not isinstance(obj, np.ndarray):
                          if binop_override_expected:
                              assert_equal(op_fn(arr, obj), "reverse", err_msg)
                          elif ufunc_override_expected:
                              assert_equal(op_fn(arr, obj)[0], "__array_ufunc__",
                                           err_msg)
                      if ufunc_override_expected:
                          assert_equal(ufunc(obj, arr)[0], "__array_ufunc__",
                                       err_msg)
  
          # No array priority, no array_ufunc -> nothing called
          check(make_obj(object), False, False, False)
          # Negative array priority, no array_ufunc -> nothing called
          # (has to be very negative, because scalar priority is -1000000.0)
          check(make_obj(object, array_priority=-2**30), False, False, False)
          # Positive array priority, no array_ufunc -> binops and iops only
          check(make_obj(object, array_priority=1), True, False, True)
          # ndarray ignores array_priority for ndarray subclasses
          check(make_obj(np.ndarray, array_priority=1), False, False, False,
                check_scalar=False)
          # Positive array_priority and array_ufunc -> array_ufunc only
          check(make_obj(object, array_priority=1,
                         array_ufunc=array_ufunc_impl), False, True, False)
          check(make_obj(np.ndarray, array_priority=1,
                         array_ufunc=array_ufunc_impl), False, True, False)
          # array_ufunc set to None -> defer binops only
          check(make_obj(object, array_ufunc=None), True, False, False)
          check(make_obj(np.ndarray, array_ufunc=None), True, False, False,
                check_scalar=False)
  
      def test_ufunc_override_normalize_signature(self):
          # gh-5674
          class SomeClass:
              def __array_ufunc__(self, ufunc, method, *inputs, **kw):
                  return kw
  
          a = SomeClass()
          kw = np.add(a, [1])
          assert_('sig' not in kw and 'signature' not in kw)
          kw = np.add(a, [1], sig='ii->i')
          assert_('sig' not in kw and 'signature' in kw)
          assert_equal(kw['signature'], 'ii->i')
          kw = np.add(a, [1], signature='ii->i')
          assert_('sig' not in kw and 'signature' in kw)
          assert_equal(kw['signature'], 'ii->i')
  
      def test_array_ufunc_index(self):
          # Check that index is set appropriately, also if only an output
          # is passed on (latter is another regression tests for github bug 4753)
          # This also checks implicitly that 'out' is always a tuple.
          class CheckIndex:
              def __array_ufunc__(self, ufunc, method, *inputs, **kw):
                  for i, a in enumerate(inputs):
                      if a is self:
                          return i
                  # calls below mean we must be in an output.
                  for j, a in enumerate(kw['out']):
                      if a is self:
                          return (j,)
  
          a = CheckIndex()
          dummy = np.arange(2.)
          # 1 input, 1 output
          assert_equal(np.sin(a), 0)
          assert_equal(np.sin(dummy, a), (0,))
          assert_equal(np.sin(dummy, out=a), (0,))
          assert_equal(np.sin(dummy, out=(a,)), (0,))
          assert_equal(np.sin(a, a), 0)
          assert_equal(np.sin(a, out=a), 0)
          assert_equal(np.sin(a, out=(a,)), 0)
          # 1 input, 2 outputs
          assert_equal(np.modf(dummy, a), (0,))
          assert_equal(np.modf(dummy, None, a), (1,))
          assert_equal(np.modf(dummy, dummy, a), (1,))
          assert_equal(np.modf(dummy, out=(a, None)), (0,))
          assert_equal(np.modf(dummy, out=(a, dummy)), (0,))
          assert_equal(np.modf(dummy, out=(None, a)), (1,))
          assert_equal(np.modf(dummy, out=(dummy, a)), (1,))
          assert_equal(np.modf(a, out=(dummy, a)), 0)
          with assert_raises(TypeError):
              # Out argument must be tuple, since there are multiple outputs
              np.modf(dummy, out=a)
  
          assert_raises(ValueError, np.modf, dummy, out=(a,))
  
          # 2 inputs, 1 output
          assert_equal(np.add(a, dummy), 0)
          assert_equal(np.add(dummy, a), 1)
          assert_equal(np.add(dummy, dummy, a), (0,))
          assert_equal(np.add(dummy, a, a), 1)
          assert_equal(np.add(dummy, dummy, out=a), (0,))
          assert_equal(np.add(dummy, dummy, out=(a,)), (0,))
          assert_equal(np.add(a, dummy, out=a), 0)
  
      def test_out_override(self):
          # regression test for github bug 4753
          class OutClass(np.ndarray):
              def __array_ufunc__(self, ufunc, method, *inputs, **kw):
                  if 'out' in kw:
                      tmp_kw = kw.copy()
                      tmp_kw.pop('out')
                      func = getattr(ufunc, method)
                      kw['out'][0][...] = func(*inputs, **tmp_kw)
  
          A = np.array([0]).view(OutClass)
          B = np.array([5])
          C = np.array([6])
          np.multiply(C, B, A)
          assert_equal(A[0], 30)
          assert_(isinstance(A, OutClass))
          A[0] = 0
          np.multiply(C, B, out=A)
          assert_equal(A[0], 30)
          assert_(isinstance(A, OutClass))
  
      def test_pow_override_with_errors(self):
          # regression test for gh-9112
          class PowerOnly(np.ndarray):
              def __array_ufunc__(self, ufunc, method, *inputs, **kw):
                  if ufunc is not np.power:
                      raise NotImplementedError
                  return "POWER!"
          # explicit cast to float, to ensure the fast power path is taken.
          a = np.array(5., dtype=np.float64).view(PowerOnly)
          assert_equal(a ** 2.5, "POWER!")
          with assert_raises(NotImplementedError):
              a ** 0.5
          with assert_raises(NotImplementedError):
              a ** 0
          with assert_raises(NotImplementedError):
              a ** 1
          with assert_raises(NotImplementedError):
              a ** -1
          with assert_raises(NotImplementedError):
              a ** 2
  
      def test_pow_array_object_dtype(self):
          # test pow on arrays of object dtype
          class SomeClass:
              def __init__(self, num=None):
                  self.num = num
  
              # want to ensure a fast pow path is not taken
              def __mul__(self, other):
                  raise AssertionError('__mul__ should not be called')
  
              def __div__(self, other):
                  raise AssertionError('__div__ should not be called')
  
              def __pow__(self, exp):
                  return SomeClass(num=self.num ** exp)
  
              def __eq__(self, other):
                  if isinstance(other, SomeClass):
                      return self.num == other.num
  
              __rpow__ = __pow__
  
          def pow_for(exp, arr):
              return np.array([x ** exp for x in arr])
  
          obj_arr = np.array([SomeClass(1), SomeClass(2), SomeClass(3)])
  
          assert_equal(obj_arr ** 0.5, pow_for(0.5, obj_arr))
          assert_equal(obj_arr ** 0, pow_for(0, obj_arr))
          assert_equal(obj_arr ** 1, pow_for(1, obj_arr))
          assert_equal(obj_arr ** -1, pow_for(-1, obj_arr))
          assert_equal(obj_arr ** 2, pow_for(2, obj_arr))
  
      def test_pos_array_ufunc_override(self):
          class A(np.ndarray):
              def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
                  return getattr(ufunc, method)(*[i.view(np.ndarray) for
                                                  i in inputs], **kwargs)
          tst = np.array('foo').view(A)
          with assert_raises(TypeError):
              +tst
  
  
  class TestTemporaryElide:
      # elision is only triggered on relatively large arrays
  
      def test_extension_incref_elide(self):
          # test extension (e.g. cython) calling PyNumber_* slots without
          # increasing the reference counts
          #
          # def incref_elide(a):
          #    d = input.copy() # refcount 1
          #    return d, d + d # PyNumber_Add without increasing refcount
          from numpy.core._multiarray_tests import incref_elide
          d = np.ones(100000)
          orig, res = incref_elide(d)
          d + d
          # the return original should not be changed to an inplace operation
          assert_array_equal(orig, d)
          assert_array_equal(res, d + d)
  
      def test_extension_incref_elide_stack(self):
          # scanning if the refcount == 1 object is on the python stack to check
          # that we are called directly from python is flawed as object may still
          # be above the stack pointer and we have no access to the top of it
          #
          # def incref_elide_l(d):
          #    return l[4] + l[4] # PyNumber_Add without increasing refcount
          from numpy.core._multiarray_tests import incref_elide_l
          # padding with 1 makes sure the object on the stack is not overwritten
          l = [1, 1, 1, 1, np.ones(100000)]
          res = incref_elide_l(l)
          # the return original should not be changed to an inplace operation
          assert_array_equal(l[4], np.ones(100000))
          assert_array_equal(res, l[4] + l[4])
  
      def test_temporary_with_cast(self):
          # check that we don't elide into a temporary which would need casting
          d = np.ones(200000, dtype=np.int64)
          assert_equal(((d + d) + 2**222).dtype, np.dtype('O'))
  
          r = ((d + d) / 2)
          assert_equal(r.dtype, np.dtype('f8'))
  
          r = np.true_divide((d + d), 2)
          assert_equal(r.dtype, np.dtype('f8'))
  
          r = ((d + d) / 2.)
          assert_equal(r.dtype, np.dtype('f8'))
  
          r = ((d + d) // 2)
          assert_equal(r.dtype, np.dtype(np.int64))
  
          # commutative elision into the astype result
          f = np.ones(100000, dtype=np.float32)
          assert_equal(((f + f) + f.astype(np.float64)).dtype, np.dtype('f8'))
  
          # no elision into lower type
          d = f.astype(np.float64)
          assert_equal(((f + f) + d).dtype, d.dtype)
          l = np.ones(100000, dtype=np.longdouble)
          assert_equal(((d + d) + l).dtype, l.dtype)
  
          # test unary abs with different output dtype
          for dt in (np.complex64, np.complex128, np.clongdouble):
              c = np.ones(100000, dtype=dt)
              r = abs(c * 2.0)
              assert_equal(r.dtype, np.dtype('f%d' % (c.itemsize // 2)))
  
      def test_elide_broadcast(self):
          # test no elision on broadcast to higher dimension
          # only triggers elision code path in debug mode as triggering it in
          # normal mode needs 256kb large matching dimension, so a lot of memory
          d = np.ones((2000, 1), dtype=int)
          b = np.ones((2000), dtype=bool)
          r = (1 - d) + b
          assert_equal(r, 1)
          assert_equal(r.shape, (2000, 2000))
  
      def test_elide_scalar(self):
          # check inplace op does not create ndarray from scalars
          a = np.bool_()
          assert_(type(~(a & a)) is np.bool_)
  
      def test_elide_scalar_readonly(self):
          # The imaginary part of a real array is readonly. This needs to go
          # through fast_scalar_power which is only called for powers of
          # +1, -1, 0, 0.5, and 2, so use 2. Also need valid refcount for
          # elision which can be gotten for the imaginary part of a real
          # array. Should not error.
          a = np.empty(100000, dtype=np.float64)
          a.imag ** 2
  
      def test_elide_readonly(self):
          # don't try to elide readonly temporaries
          r = np.asarray(np.broadcast_to(np.zeros(1), 100000).flat) * 0.0
          assert_equal(r, 0)
  
      def test_elide_updateifcopy(self):
          a = np.ones(2**20)[::2]
          b = a.flat.__array__() + 1
          del b
          assert_equal(a, 1)
  
  
  class TestCAPI:
      def test_IsPythonScalar(self):
          from numpy.core._multiarray_tests import IsPythonScalar
          assert_(IsPythonScalar(b'foobar'))
          assert_(IsPythonScalar(1))
          assert_(IsPythonScalar(2**80))
          assert_(IsPythonScalar(2.))
          assert_(IsPythonScalar("a"))
  
  
  class TestSubscripting:
      def test_test_zero_rank(self):
          x = np.array([1, 2, 3])
          assert_(isinstance(x[0], np.int_))
          assert_(type(x[0, ...]) is np.ndarray)
  
  
  class TestPickling:
      @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL >= 5,
                          reason=('this tests the error messages when trying to'
                                  'protocol 5 although it is not available'))
      def test_correct_protocol5_error_message(self):
          array = np.arange(10)
  
          if sys.version_info[:2] in ((3, 6), (3, 7)):
              # For the specific case of python3.6 and 3.7, raise a clear import
              # error about the pickle5 backport when trying to use protocol=5
              # without the pickle5 package
              with pytest.raises(ImportError):
                  array.__reduce_ex__(5)
  
          elif sys.version_info[:2] < (3, 6):
              # when calling __reduce_ex__ explicitly with protocol=5 on python
              # raise a ValueError saying that protocol 5 is not available for
              # this python version
              with pytest.raises(ValueError):
                  array.__reduce_ex__(5)
  
      def test_record_array_with_object_dtype(self):
          my_object = object()
  
          arr_with_object = np.array(
                  [(my_object, 1, 2.0)],
                  dtype=[('a', object), ('b', int), ('c', float)])
          arr_without_object = np.array(
                  [('xxx', 1, 2.0)],
                  dtype=[('a', str), ('b', int), ('c', float)])
  
          for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
              depickled_arr_with_object = pickle.loads(
                      pickle.dumps(arr_with_object, protocol=proto))
              depickled_arr_without_object = pickle.loads(
                      pickle.dumps(arr_without_object, protocol=proto))
  
              assert_equal(arr_with_object.dtype,
                           depickled_arr_with_object.dtype)
              assert_equal(arr_without_object.dtype,
                           depickled_arr_without_object.dtype)
  
      @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL < 5,
                          reason="requires pickle protocol 5")
      def test_f_contiguous_array(self):
          f_contiguous_array = np.array([[1, 2, 3], [4, 5, 6]], order='F')
          buffers = []
  
          # When using pickle protocol 5, Fortran-contiguous arrays can be
          # serialized using out-of-band buffers
          bytes_string = pickle.dumps(f_contiguous_array, protocol=5,
                                      buffer_callback=buffers.append)
  
          assert len(buffers) > 0
  
          depickled_f_contiguous_array = pickle.loads(bytes_string,
                                                      buffers=buffers)
  
          assert_equal(f_contiguous_array, depickled_f_contiguous_array)
  
      def test_non_contiguous_array(self):
          non_contiguous_array = np.arange(12).reshape(3, 4)[:, :2]
          assert not non_contiguous_array.flags.c_contiguous
          assert not non_contiguous_array.flags.f_contiguous
  
          # make sure non-contiguous arrays can be pickled-depickled
          # using any protocol
          for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
              depickled_non_contiguous_array = pickle.loads(
                      pickle.dumps(non_contiguous_array, protocol=proto))
  
              assert_equal(non_contiguous_array, depickled_non_contiguous_array)
  
      def test_roundtrip(self):
          for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
              carray = np.array([[2, 9], [7, 0], [3, 8]])
              DATA = [
                  carray,
                  np.transpose(carray),
                  np.array([('xxx', 1, 2.0)], dtype=[('a', (str, 3)), ('b', int),
                                                     ('c', float)])
              ]
  
              refs = [weakref.ref(a) for a in DATA]
              for a in DATA:
                  assert_equal(
                          a, pickle.loads(pickle.dumps(a, protocol=proto)),
                          err_msg="%r" % a)
              del a, DATA, carray
              break_cycles()
              # check for reference leaks (gh-12793)
              for ref in refs:
                  assert ref() is None
  
      def _loads(self, obj):
          return pickle.loads(obj, encoding='latin1')
  
      # version 0 pickles, using protocol=2 to pickle
      # version 0 doesn't have a version field
      def test_version0_int8(self):
          s = b'\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x04\x85cnumpy\ndtype\nq\x04U\x02i1K\x00K\x01\x87Rq\x05(U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x04\x01\x02\x03\x04tb.'
          a = np.array([1, 2, 3, 4], dtype=np.int8)
          p = self._loads(s)
          assert_equal(a, p)
  
      def test_version0_float32(self):
          s = b'\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x04\x85cnumpy\ndtype\nq\x04U\x02f4K\x00K\x01\x87Rq\x05(U\x01<NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x10\x00\x00\x80?\x00\x00\x00@\x00\x00@@\x00\x00\x80@tb.'
          a = np.array([1.0, 2.0, 3.0, 4.0], dtype=np.float32)
          p = self._loads(s)
          assert_equal(a, p)
  
      def test_version0_object(self):
          s = b'\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x02\x85cnumpy\ndtype\nq\x04U\x02O8K\x00K\x01\x87Rq\x05(U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89]q\x06(}q\x07U\x01aK\x01s}q\x08U\x01bK\x02setb.'
          a = np.array([{'a': 1}, {'b': 2}])
          p = self._loads(s)
          assert_equal(a, p)
  
      # version 1 pickles, using protocol=2 to pickle
      def test_version1_int8(self):
          s = b'\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x01K\x04\x85cnumpy\ndtype\nq\x04U\x02i1K\x00K\x01\x87Rq\x05(K\x01U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x04\x01\x02\x03\x04tb.'
          a = np.array([1, 2, 3, 4], dtype=np.int8)
          p = self._loads(s)
          assert_equal(a, p)
  
      def test_version1_float32(self):
          s = b'\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x01K\x04\x85cnumpy\ndtype\nq\x04U\x02f4K\x00K\x01\x87Rq\x05(K\x01U\x01<NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x10\x00\x00\x80?\x00\x00\x00@\x00\x00@@\x00\x00\x80@tb.'
          a = np.array([1.0, 2.0, 3.0, 4.0], dtype=np.float32)
          p = self._loads(s)
          assert_equal(a, p)
  
      def test_version1_object(self):
          s = b'\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x01K\x02\x85cnumpy\ndtype\nq\x04U\x02O8K\x00K\x01\x87Rq\x05(K\x01U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89]q\x06(}q\x07U\x01aK\x01s}q\x08U\x01bK\x02setb.'
          a = np.array([{'a': 1}, {'b': 2}])
          p = self._loads(s)
          assert_equal(a, p)
  
      def test_subarray_int_shape(self):
          s = b"cnumpy.core.multiarray\n_reconstruct\np0\n(cnumpy\nndarray\np1\n(I0\ntp2\nS'b'\np3\ntp4\nRp5\n(I1\n(I1\ntp6\ncnumpy\ndtype\np7\n(S'V6'\np8\nI0\nI1\ntp9\nRp10\n(I3\nS'|'\np11\nN(S'a'\np12\ng3\ntp13\n(dp14\ng12\n(g7\n(S'V4'\np15\nI0\nI1\ntp16\nRp17\n(I3\nS'|'\np18\n(g7\n(S'i1'\np19\nI0\nI1\ntp20\nRp21\n(I3\nS'|'\np22\nNNNI-1\nI-1\nI0\ntp23\nb(I2\nI2\ntp24\ntp25\nNNI4\nI1\nI0\ntp26\nbI0\ntp27\nsg3\n(g7\n(S'V2'\np28\nI0\nI1\ntp29\nRp30\n(I3\nS'|'\np31\n(g21\nI2\ntp32\nNNI2\nI1\nI0\ntp33\nbI4\ntp34\nsI6\nI1\nI0\ntp35\nbI00\nS'\\x01\\x01\\x01\\x01\\x01\\x02'\np36\ntp37\nb."
          a = np.array([(1, (1, 2))], dtype=[('a', 'i1', (2, 2)), ('b', 'i1', 2)])
          p = self._loads(s)
          assert_equal(a, p)
  
      def test_datetime64_byteorder(self):
          original = np.array([['2015-02-24T00:00:00.000000000']], dtype='datetime64[ns]')
  
          original_byte_reversed = original.copy(order='K')
          original_byte_reversed.dtype = original_byte_reversed.dtype.newbyteorder('S')
          original_byte_reversed.byteswap(inplace=True)
  
          new = pickle.loads(pickle.dumps(original_byte_reversed))
  
          assert_equal(original.dtype, new.dtype)
  
  
  class TestFancyIndexing:
      def test_list(self):
          x = np.ones((1, 1))
          x[:, [0]] = 2.0
          assert_array_equal(x, np.array([[2.0]]))
  
          x = np.ones((1, 1, 1))
          x[:, :, [0]] = 2.0
          assert_array_equal(x, np.array([[[2.0]]]))
  
      def test_tuple(self):
          x = np.ones((1, 1))
          x[:, (0,)] = 2.0
          assert_array_equal(x, np.array([[2.0]]))
          x = np.ones((1, 1, 1))
          x[:, :, (0,)] = 2.0
          assert_array_equal(x, np.array([[[2.0]]]))
  
      def test_mask(self):
          x = np.array([1, 2, 3, 4])
          m = np.array([0, 1, 0, 0], bool)
          assert_array_equal(x[m], np.array([2]))
  
      def test_mask2(self):
          x = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])
          m = np.array([0, 1], bool)
          m2 = np.array([[0, 1, 0, 0], [1, 0, 0, 0]], bool)
          m3 = np.array([[0, 1, 0, 0], [0, 0, 0, 0]], bool)
          assert_array_equal(x[m], np.array([[5, 6, 7, 8]]))
          assert_array_equal(x[m2], np.array([2, 5]))
          assert_array_equal(x[m3], np.array([2]))
  
      def test_assign_mask(self):
          x = np.array([1, 2, 3, 4])
          m = np.array([0, 1, 0, 0], bool)
          x[m] = 5
          assert_array_equal(x, np.array([1, 5, 3, 4]))
  
      def test_assign_mask2(self):
          xorig = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])
          m = np.array([0, 1], bool)
          m2 = np.array([[0, 1, 0, 0], [1, 0, 0, 0]], bool)
          m3 = np.array([[0, 1, 0, 0], [0, 0, 0, 0]], bool)
          x = xorig.copy()
          x[m] = 10
          assert_array_equal(x, np.array([[1, 2, 3, 4], [10, 10, 10, 10]]))
          x = xorig.copy()
          x[m2] = 10
          assert_array_equal(x, np.array([[1, 10, 3, 4], [10, 6, 7, 8]]))
          x = xorig.copy()
          x[m3] = 10
          assert_array_equal(x, np.array([[1, 10, 3, 4], [5, 6, 7, 8]]))
  
  
  class TestStringCompare:
      def test_string(self):
          g1 = np.array(["This", "is", "example"])
          g2 = np.array(["This", "was", "example"])
          assert_array_equal(g1 == g2, [g1[i] == g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 != g2, [g1[i] != g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 <= g2, [g1[i] <= g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 >= g2, [g1[i] >= g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 < g2, [g1[i] < g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 > g2, [g1[i] > g2[i] for i in [0, 1, 2]])
  
      def test_mixed(self):
          g1 = np.array(["spam", "spa", "spammer", "and eggs"])
          g2 = "spam"
          assert_array_equal(g1 == g2, [x == g2 for x in g1])
          assert_array_equal(g1 != g2, [x != g2 for x in g1])
          assert_array_equal(g1 < g2, [x < g2 for x in g1])
          assert_array_equal(g1 > g2, [x > g2 for x in g1])
          assert_array_equal(g1 <= g2, [x <= g2 for x in g1])
          assert_array_equal(g1 >= g2, [x >= g2 for x in g1])
  
      def test_unicode(self):
          g1 = np.array([u"This", u"is", u"example"])
          g2 = np.array([u"This", u"was", u"example"])
          assert_array_equal(g1 == g2, [g1[i] == g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 != g2, [g1[i] != g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 <= g2, [g1[i] <= g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 >= g2, [g1[i] >= g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 < g2,  [g1[i] < g2[i] for i in [0, 1, 2]])
          assert_array_equal(g1 > g2,  [g1[i] > g2[i] for i in [0, 1, 2]])
  
  
  class TestArgmax:
  
      nan_arr = [
          ([0, 1, 2, 3, np.nan], 4),
          ([0, 1, 2, np.nan, 3], 3),
          ([np.nan, 0, 1, 2, 3], 0),
          ([np.nan, 0, np.nan, 2, 3], 0),
          ([0, 1, 2, 3, complex(0, np.nan)], 4),
          ([0, 1, 2, 3, complex(np.nan, 0)], 4),
          ([0, 1, 2, complex(np.nan, 0), 3], 3),
          ([0, 1, 2, complex(0, np.nan), 3], 3),
          ([complex(0, np.nan), 0, 1, 2, 3], 0),
          ([complex(np.nan, np.nan), 0, 1, 2, 3], 0),
          ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, 1)], 0),
          ([complex(np.nan, np.nan), complex(np.nan, 2), complex(np.nan, 1)], 0),
          ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, np.nan)], 0),
  
          ([complex(0, 0), complex(0, 2), complex(0, 1)], 1),
          ([complex(1, 0), complex(0, 2), complex(0, 1)], 0),
          ([complex(1, 0), complex(0, 2), complex(1, 1)], 2),
  
          ([np.datetime64('1923-04-14T12:43:12'),
            np.datetime64('1994-06-21T14:43:15'),
            np.datetime64('2001-10-15T04:10:32'),
            np.datetime64('1995-11-25T16:02:16'),
            np.datetime64('2005-01-04T03:14:12'),
            np.datetime64('2041-12-03T14:05:03')], 5),
          ([np.datetime64('1935-09-14T04:40:11'),
            np.datetime64('1949-10-12T12:32:11'),
            np.datetime64('2010-01-03T05:14:12'),
            np.datetime64('2015-11-20T12:20:59'),
            np.datetime64('1932-09-23T10:10:13'),
            np.datetime64('2014-10-10T03:50:30')], 3),
          # Assorted tests with NaTs
          ([np.datetime64('NaT'),
            np.datetime64('NaT'),
            np.datetime64('2010-01-03T05:14:12'),
            np.datetime64('NaT'),
            np.datetime64('2015-09-23T10:10:13'),
            np.datetime64('1932-10-10T03:50:30')], 0),
          ([np.datetime64('2059-03-14T12:43:12'),
            np.datetime64('1996-09-21T14:43:15'),
            np.datetime64('NaT'),
            np.datetime64('2022-12-25T16:02:16'),
            np.datetime64('1963-10-04T03:14:12'),
            np.datetime64('2013-05-08T18:15:23')], 2),
          ([np.timedelta64(2, 's'),
            np.timedelta64(1, 's'),
            np.timedelta64('NaT', 's'),
            np.timedelta64(3, 's')], 2),
          ([np.timedelta64('NaT', 's')] * 3, 0),
  
          ([timedelta(days=5, seconds=14), timedelta(days=2, seconds=35),
            timedelta(days=-1, seconds=23)], 0),
          ([timedelta(days=1, seconds=43), timedelta(days=10, seconds=5),
            timedelta(days=5, seconds=14)], 1),
          ([timedelta(days=10, seconds=24), timedelta(days=10, seconds=5),
            timedelta(days=10, seconds=43)], 2),
  
          ([False, False, False, False, True], 4),
          ([False, False, False, True, False], 3),
          ([True, False, False, False, False], 0),
          ([True, False, True, False, False], 0),
      ]
  
      def test_all(self):
          a = np.random.normal(0, 1, (4, 5, 6, 7, 8))
          for i in range(a.ndim):
              amax = a.max(i)
              aargmax = a.argmax(i)
              axes = list(range(a.ndim))
              axes.remove(i)
              assert_(np.all(amax == aargmax.choose(*a.transpose(i,*axes))))
  
      def test_combinations(self):
          for arr, pos in self.nan_arr:
              with suppress_warnings() as sup:
                  sup.filter(RuntimeWarning,
                             "invalid value encountered in reduce")
                  max_val = np.max(arr)
  
              assert_equal(np.argmax(arr), pos, err_msg="%r" % arr)
              assert_equal(arr[np.argmax(arr)], max_val, err_msg="%r" % arr)
  
      def test_output_shape(self):
          # see also gh-616
          a = np.ones((10, 5))
          # Check some simple shape mismatches
          out = np.ones(11, dtype=np.int_)
          assert_raises(ValueError, a.argmax, -1, out)
  
          out = np.ones((2, 5), dtype=np.int_)
          assert_raises(ValueError, a.argmax, -1, out)
  
          # these could be relaxed possibly (used to allow even the previous)
          out = np.ones((1, 10), dtype=np.int_)
          assert_raises(ValueError, a.argmax, -1, out)
  
          out = np.ones(10, dtype=np.int_)
          a.argmax(-1, out=out)
          assert_equal(out, a.argmax(-1))
  
      @pytest.mark.parametrize('ndim', [0, 1])
      def test_ret_is_out(self, ndim):
          a = np.ones((4,) + (3,)*ndim)
          out = np.empty((3,)*ndim, dtype=np.intp)
          ret = a.argmax(axis=0, out=out)
          assert ret is out
  
      def test_argmax_unicode(self):
          d = np.zeros(6031, dtype='<U9')
          d[5942] = "as"
          assert_equal(d.argmax(), 5942)
  
      def test_np_vs_ndarray(self):
          # make sure both ndarray.argmax and numpy.argmax support out/axis args
          a = np.random.normal(size=(2,3))
  
          # check positional args
          out1 = np.zeros(2, dtype=int)
          out2 = np.zeros(2, dtype=int)
          assert_equal(a.argmax(1, out1), np.argmax(a, 1, out2))
          assert_equal(out1, out2)
  
          # check keyword args
          out1 = np.zeros(3, dtype=int)
          out2 = np.zeros(3, dtype=int)
          assert_equal(a.argmax(out=out1, axis=0), np.argmax(a, out=out2, axis=0))
          assert_equal(out1, out2)
  
      @pytest.mark.leaks_references(reason="replaces None with NULL.")
      def test_object_argmax_with_NULLs(self):
          # See gh-6032
          a = np.empty(4, dtype='O')
          ctypes.memset(a.ctypes.data, 0, a.nbytes)
          assert_equal(a.argmax(), 0)
          a[3] = 10
          assert_equal(a.argmax(), 3)
          a[1] = 30
          assert_equal(a.argmax(), 1)
  
  
  class TestArgmin:
  
      nan_arr = [
          ([0, 1, 2, 3, np.nan], 4),
          ([0, 1, 2, np.nan, 3], 3),
          ([np.nan, 0, 1, 2, 3], 0),
          ([np.nan, 0, np.nan, 2, 3], 0),
          ([0, 1, 2, 3, complex(0, np.nan)], 4),
          ([0, 1, 2, 3, complex(np.nan, 0)], 4),
          ([0, 1, 2, complex(np.nan, 0), 3], 3),
          ([0, 1, 2, complex(0, np.nan), 3], 3),
          ([complex(0, np.nan), 0, 1, 2, 3], 0),
          ([complex(np.nan, np.nan), 0, 1, 2, 3], 0),
          ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, 1)], 0),
          ([complex(np.nan, np.nan), complex(np.nan, 2), complex(np.nan, 1)], 0),
          ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, np.nan)], 0),
  
          ([complex(0, 0), complex(0, 2), complex(0, 1)], 0),
          ([complex(1, 0), complex(0, 2), complex(0, 1)], 2),
          ([complex(1, 0), complex(0, 2), complex(1, 1)], 1),
  
          ([np.datetime64('1923-04-14T12:43:12'),
            np.datetime64('1994-06-21T14:43:15'),
            np.datetime64('2001-10-15T04:10:32'),
            np.datetime64('1995-11-25T16:02:16'),
            np.datetime64('2005-01-04T03:14:12'),
            np.datetime64('2041-12-03T14:05:03')], 0),
          ([np.datetime64('1935-09-14T04:40:11'),
            np.datetime64('1949-10-12T12:32:11'),
            np.datetime64('2010-01-03T05:14:12'),
            np.datetime64('2014-11-20T12:20:59'),
            np.datetime64('2015-09-23T10:10:13'),
            np.datetime64('1932-10-10T03:50:30')], 5),
          # Assorted tests with NaTs
          ([np.datetime64('NaT'),
            np.datetime64('NaT'),
            np.datetime64('2010-01-03T05:14:12'),
            np.datetime64('NaT'),
            np.datetime64('2015-09-23T10:10:13'),
            np.datetime64('1932-10-10T03:50:30')], 0),
          ([np.datetime64('2059-03-14T12:43:12'),
            np.datetime64('1996-09-21T14:43:15'),
            np.datetime64('NaT'),
            np.datetime64('2022-12-25T16:02:16'),
            np.datetime64('1963-10-04T03:14:12'),
            np.datetime64('2013-05-08T18:15:23')], 2),
          ([np.timedelta64(2, 's'),
            np.timedelta64(1, 's'),
            np.timedelta64('NaT', 's'),
            np.timedelta64(3, 's')], 2),
          ([np.timedelta64('NaT', 's')] * 3, 0),
  
          ([timedelta(days=5, seconds=14), timedelta(days=2, seconds=35),
            timedelta(days=-1, seconds=23)], 2),
          ([timedelta(days=1, seconds=43), timedelta(days=10, seconds=5),
            timedelta(days=5, seconds=14)], 0),
          ([timedelta(days=10, seconds=24), timedelta(days=10, seconds=5),
            timedelta(days=10, seconds=43)], 1),
  
          ([True, True, True, True, False], 4),
          ([True, True, True, False, True], 3),
          ([False, True, True, True, True], 0),
          ([False, True, False, True, True], 0),
      ]
  
      def test_all(self):
          a = np.random.normal(0, 1, (4, 5, 6, 7, 8))
          for i in range(a.ndim):
              amin = a.min(i)
              aargmin = a.argmin(i)
              axes = list(range(a.ndim))
              axes.remove(i)
              assert_(np.all(amin == aargmin.choose(*a.transpose(i,*axes))))
  
      def test_combinations(self):
          for arr, pos in self.nan_arr:
              with suppress_warnings() as sup:
                  sup.filter(RuntimeWarning,
                             "invalid value encountered in reduce")
                  min_val = np.min(arr)
  
              assert_equal(np.argmin(arr), pos, err_msg="%r" % arr)
              assert_equal(arr[np.argmin(arr)], min_val, err_msg="%r" % arr)
  
      def test_minimum_signed_integers(self):
  
          a = np.array([1, -2**7, -2**7 + 1], dtype=np.int8)
          assert_equal(np.argmin(a), 1)
  
          a = np.array([1, -2**15, -2**15 + 1], dtype=np.int16)
          assert_equal(np.argmin(a), 1)
  
          a = np.array([1, -2**31, -2**31 + 1], dtype=np.int32)
          assert_equal(np.argmin(a), 1)
  
          a = np.array([1, -2**63, -2**63 + 1], dtype=np.int64)
          assert_equal(np.argmin(a), 1)
  
      def test_output_shape(self):
          # see also gh-616
          a = np.ones((10, 5))
          # Check some simple shape mismatches
          out = np.ones(11, dtype=np.int_)
          assert_raises(ValueError, a.argmin, -1, out)
  
          out = np.ones((2, 5), dtype=np.int_)
          assert_raises(ValueError, a.argmin, -1, out)
  
          # these could be relaxed possibly (used to allow even the previous)
          out = np.ones((1, 10), dtype=np.int_)
          assert_raises(ValueError, a.argmin, -1, out)
  
          out = np.ones(10, dtype=np.int_)
          a.argmin(-1, out=out)
          assert_equal(out, a.argmin(-1))
  
      @pytest.mark.parametrize('ndim', [0, 1])
      def test_ret_is_out(self, ndim):
          a = np.ones((4,) + (3,)*ndim)
          out = np.empty((3,)*ndim, dtype=np.intp)
          ret = a.argmin(axis=0, out=out)
          assert ret is out
  
      def test_argmin_unicode(self):
          d = np.ones(6031, dtype='<U9')
          d[6001] = "0"
          assert_equal(d.argmin(), 6001)
  
      def test_np_vs_ndarray(self):
          # make sure both ndarray.argmin and numpy.argmin support out/axis args
          a = np.random.normal(size=(2, 3))
  
          # check positional args
          out1 = np.zeros(2, dtype=int)
          out2 = np.ones(2, dtype=int)
          assert_equal(a.argmin(1, out1), np.argmin(a, 1, out2))
          assert_equal(out1, out2)
  
          # check keyword args
          out1 = np.zeros(3, dtype=int)
          out2 = np.ones(3, dtype=int)
          assert_equal(a.argmin(out=out1, axis=0), np.argmin(a, out=out2, axis=0))
          assert_equal(out1, out2)
  
      @pytest.mark.leaks_references(reason="replaces None with NULL.")
      def test_object_argmin_with_NULLs(self):
          # See gh-6032
          a = np.empty(4, dtype='O')
          ctypes.memset(a.ctypes.data, 0, a.nbytes)
          assert_equal(a.argmin(), 0)
          a[3] = 30
          assert_equal(a.argmin(), 3)
          a[1] = 10
          assert_equal(a.argmin(), 1)
  
  
  class TestMinMax:
  
      def test_scalar(self):
          assert_raises(np.AxisError, np.amax, 1, 1)
          assert_raises(np.AxisError, np.amin, 1, 1)
  
          assert_equal(np.amax(1, axis=0), 1)
          assert_equal(np.amin(1, axis=0), 1)
          assert_equal(np.amax(1, axis=None), 1)
          assert_equal(np.amin(1, axis=None), 1)
  
      def test_axis(self):
          assert_raises(np.AxisError, np.amax, [1, 2, 3], 1000)
          assert_equal(np.amax([[1, 2, 3]], axis=1), 3)
  
      def test_datetime(self):
          # Do not ignore NaT
          for dtype in ('m8[s]', 'm8[Y]'):
              a = np.arange(10).astype(dtype)
              assert_equal(np.amin(a), a[0])
              assert_equal(np.amax(a), a[9])
              a[3] = 'NaT'
              assert_equal(np.amin(a), a[3])
              assert_equal(np.amax(a), a[3])
  
  
  class TestNewaxis:
      def test_basic(self):
          sk = np.array([0, -0.1, 0.1])
          res = 250*sk[:, np.newaxis]
          assert_almost_equal(res.ravel(), 250*sk)
  
  
  class TestClip:
      def _check_range(self, x, cmin, cmax):
          assert_(np.all(x >= cmin))
          assert_(np.all(x <= cmax))
  
      def _clip_type(self, type_group, array_max,
                     clip_min, clip_max, inplace=False,
                     expected_min=None, expected_max=None):
          if expected_min is None:
              expected_min = clip_min
          if expected_max is None:
              expected_max = clip_max
  
          for T in np.sctypes[type_group]:
              if sys.byteorder == 'little':
                  byte_orders = ['=', '>']
              else:
                  byte_orders = ['<', '=']
  
              for byteorder in byte_orders:
                  dtype = np.dtype(T).newbyteorder(byteorder)
  
                  x = (np.random.random(1000) * array_max).astype(dtype)
                  if inplace:
                      # The tests that call us pass clip_min and clip_max that
                      # might not fit in the destination dtype. They were written
                      # assuming the previous unsafe casting, which now must be
                      # passed explicitly to avoid a warning.
                      x.clip(clip_min, clip_max, x, casting='unsafe')
                  else:
                      x = x.clip(clip_min, clip_max)
                      byteorder = '='
  
                  if x.dtype.byteorder == '|':
                      byteorder = '|'
                  assert_equal(x.dtype.byteorder, byteorder)
                  self._check_range(x, expected_min, expected_max)
          return x
  
      def test_basic(self):
          for inplace in [False, True]:
              self._clip_type(
                  'float', 1024, -12.8, 100.2, inplace=inplace)
              self._clip_type(
                  'float', 1024, 0, 0, inplace=inplace)
  
              self._clip_type(
                  'int', 1024, -120, 100, inplace=inplace)
              self._clip_type(
                  'int', 1024, 0, 0, inplace=inplace)
  
              self._clip_type(
                  'uint', 1024, 0, 0, inplace=inplace)
              self._clip_type(
                  'uint', 1024, -120, 100, inplace=inplace, expected_min=0)
  
      def test_record_array(self):
          rec = np.array([(-5, 2.0, 3.0), (5.0, 4.0, 3.0)],
                         dtype=[('x', '<f8'), ('y', '<f8'), ('z', '<f8')])
          y = rec['x'].clip(-0.3, 0.5)
          self._check_range(y, -0.3, 0.5)
  
      def test_max_or_min(self):
          val = np.array([0, 1, 2, 3, 4, 5, 6, 7])
          x = val.clip(3)
          assert_(np.all(x >= 3))
          x = val.clip(min=3)
          assert_(np.all(x >= 3))
          x = val.clip(max=4)
          assert_(np.all(x <= 4))
  
      def test_nan(self):
          input_arr = np.array([-2., np.nan, 0.5, 3., 0.25, np.nan])
          result = input_arr.clip(-1, 1)
          expected = np.array([-1., np.nan, 0.5, 1., 0.25, np.nan])
          assert_array_equal(result, expected)
  
  
  class TestCompress:
      def test_axis(self):
          tgt = [[5, 6, 7, 8, 9]]
          arr = np.arange(10).reshape(2, 5)
          out = np.compress([0, 1], arr, axis=0)
          assert_equal(out, tgt)
  
          tgt = [[1, 3], [6, 8]]
          out = np.compress([0, 1, 0, 1, 0], arr, axis=1)
          assert_equal(out, tgt)
  
      def test_truncate(self):
          tgt = [[1], [6]]
          arr = np.arange(10).reshape(2, 5)
          out = np.compress([0, 1], arr, axis=1)
          assert_equal(out, tgt)
  
      def test_flatten(self):
          arr = np.arange(10).reshape(2, 5)
          out = np.compress([0, 1], arr)
          assert_equal(out, 1)
  
  
  class TestPutmask:
      def tst_basic(self, x, T, mask, val):
          np.putmask(x, mask, val)
          assert_equal(x[mask], np.array(val, T))
  
      def test_ip_types(self):
          unchecked_types = [bytes, str, np.void]
  
          x = np.random.random(1000)*100
          mask = x < 40
  
          for val in [-100, 0, 15]:
              for types in np.sctypes.values():
                  for T in types:
                      if T not in unchecked_types:
                          self.tst_basic(x.copy().astype(T), T, mask, val)
  
              # Also test string of a length which uses an untypical length
              dt = np.dtype("S3")
              self.tst_basic(x.astype(dt), dt.type, mask, dt.type(val)[:3])
  
      def test_mask_size(self):
          assert_raises(ValueError, np.putmask, np.array([1, 2, 3]), [True], 5)
  
      @pytest.mark.parametrize('dtype', ('>i4', '<i4'))
      def test_byteorder(self, dtype):
          x = np.array([1, 2, 3], dtype)
          np.putmask(x, [True, False, True], -1)
          assert_array_equal(x, [-1, 2, -1])
  
      def test_record_array(self):
          # Note mixed byteorder.
          rec = np.array([(-5, 2.0, 3.0), (5.0, 4.0, 3.0)],
                        dtype=[('x', '<f8'), ('y', '>f8'), ('z', '<f8')])
          np.putmask(rec['x'], [True, False], 10)
          assert_array_equal(rec['x'], [10, 5])
          assert_array_equal(rec['y'], [2, 4])
          assert_array_equal(rec['z'], [3, 3])
          np.putmask(rec['y'], [True, False], 11)
          assert_array_equal(rec['x'], [10, 5])
          assert_array_equal(rec['y'], [11, 4])
          assert_array_equal(rec['z'], [3, 3])
  
      def test_overlaps(self):
          # gh-6272 check overlap
          x = np.array([True, False, True, False])
          np.putmask(x[1:4], [True, True, True], x[:3])
          assert_equal(x, np.array([True, True, False, True]))
  
          x = np.array([True, False, True, False])
          np.putmask(x[1:4], x[:3], [True, False, True])
          assert_equal(x, np.array([True, True, True, True]))
  
  
  class TestTake:
      def tst_basic(self, x):
          ind = list(range(x.shape[0]))
          assert_array_equal(x.take(ind, axis=0), x)
  
      def test_ip_types(self):
          unchecked_types = [bytes, str, np.void]
  
          x = np.random.random(24)*100
          x.shape = 2, 3, 4
          for types in np.sctypes.values():
              for T in types:
                  if T not in unchecked_types:
                      self.tst_basic(x.copy().astype(T))
  
              # Also test string of a length which uses an untypical length
              self.tst_basic(x.astype("S3"))
  
      def test_raise(self):
          x = np.random.random(24)*100
          x.shape = 2, 3, 4
          assert_raises(IndexError, x.take, [0, 1, 2], axis=0)
          assert_raises(IndexError, x.take, [-3], axis=0)
          assert_array_equal(x.take([-1], axis=0)[0], x[1])
  
      def test_clip(self):
          x = np.random.random(24)*100
          x.shape = 2, 3, 4
          assert_array_equal(x.take([-1], axis=0, mode='clip')[0], x[0])
          assert_array_equal(x.take([2], axis=0, mode='clip')[0], x[1])
  
      def test_wrap(self):
          x = np.random.random(24)*100
          x.shape = 2, 3, 4
          assert_array_equal(x.take([-1], axis=0, mode='wrap')[0], x[1])
          assert_array_equal(x.take([2], axis=0, mode='wrap')[0], x[0])
          assert_array_equal(x.take([3], axis=0, mode='wrap')[0], x[1])
  
      @pytest.mark.parametrize('dtype', ('>i4', '<i4'))
      def test_byteorder(self, dtype):
          x = np.array([1, 2, 3], dtype)
          assert_array_equal(x.take([0, 2, 1]), [1, 3, 2])
  
      def test_record_array(self):
          # Note mixed byteorder.
          rec = np.array([(-5, 2.0, 3.0), (5.0, 4.0, 3.0)],
                        dtype=[('x', '<f8'), ('y', '>f8'), ('z', '<f8')])
          rec1 = rec.take([1])
          assert_(rec1['x'] == 5.0 and rec1['y'] == 4.0)
  
      def test_out_overlap(self):
          # gh-6272 check overlap on out
          x = np.arange(5)
          y = np.take(x, [1, 2, 3], out=x[2:5], mode='wrap')
          assert_equal(y, np.array([1, 2, 3]))
  
      @pytest.mark.parametrize('shape', [(1, 2), (1,), ()])
      def test_ret_is_out(self, shape):
          # 0d arrays should not be an exception to this rule
          x = np.arange(5)
          inds = np.zeros(shape, dtype=np.intp)
          out = np.zeros(shape, dtype=x.dtype)
          ret = np.take(x, inds, out=out)
          assert ret is out
  
  
  class TestLexsort:
      @pytest.mark.parametrize('dtype',[
          np.uint8, np.uint16, np.uint32, np.uint64,
          np.int8, np.int16, np.int32, np.int64,
          np.float16, np.float32, np.float64
      ])
      def test_basic(self, dtype):
          a = np.array([1, 2, 1, 3, 1, 5], dtype=dtype)
          b = np.array([0, 4, 5, 6, 2, 3], dtype=dtype)
          idx = np.lexsort((b, a))
          expected_idx = np.array([0, 4, 2, 1, 3, 5])
          assert_array_equal(idx, expected_idx)
          assert_array_equal(a[idx], np.sort(a))
  
      def test_mixed(self):
          a = np.array([1, 2, 1, 3, 1, 5])
          b = np.array([0, 4, 5, 6, 2, 3], dtype='datetime64[D]')
  
          idx = np.lexsort((b, a))
          expected_idx = np.array([0, 4, 2, 1, 3, 5])
          assert_array_equal(idx, expected_idx)
  
      def test_datetime(self):
          a = np.array([0,0,0], dtype='datetime64[D]')
          b = np.array([2,1,0], dtype='datetime64[D]')
          idx = np.lexsort((b, a))
          expected_idx = np.array([2, 1, 0])
          assert_array_equal(idx, expected_idx)
  
          a = np.array([0,0,0], dtype='timedelta64[D]')
          b = np.array([2,1,0], dtype='timedelta64[D]')
          idx = np.lexsort((b, a))
          expected_idx = np.array([2, 1, 0])
          assert_array_equal(idx, expected_idx)
  
      def test_object(self):  # gh-6312
          a = np.random.choice(10, 1000)
          b = np.random.choice(['abc', 'xy', 'wz', 'efghi', 'qwst', 'x'], 1000)
  
          for u in a, b:
              left = np.lexsort((u.astype('O'),))
              right = np.argsort(u, kind='mergesort')
              assert_array_equal(left, right)
  
          for u, v in (a, b), (b, a):
              idx = np.lexsort((u, v))
              assert_array_equal(idx, np.lexsort((u.astype('O'), v)))
              assert_array_equal(idx, np.lexsort((u, v.astype('O'))))
              u, v = np.array(u, dtype='object'), np.array(v, dtype='object')
              assert_array_equal(idx, np.lexsort((u, v)))
  
      def test_invalid_axis(self): # gh-7528
          x = np.linspace(0., 1., 42*3).reshape(42, 3)
          assert_raises(np.AxisError, np.lexsort, x, axis=2)
  
  class TestIO:
      """Test tofile, fromfile, tobytes, and fromstring"""
  
      def setup(self):
          shape = (2, 4, 3)
          rand = np.random.random
          self.x = rand(shape) + rand(shape).astype(complex)*1j
          self.x[0,:, 1] = [np.nan, np.inf, -np.inf, np.nan]
          self.dtype = self.x.dtype
          self.tempdir = tempfile.mkdtemp()
          self.filename = tempfile.mktemp(dir=self.tempdir)
  
      def teardown(self):
          shutil.rmtree(self.tempdir)
  
      def test_nofile(self):
          # this should probably be supported as a file
          # but for now test for proper errors
          b = io.BytesIO()
          assert_raises(IOError, np.fromfile, b, np.uint8, 80)
          d = np.ones(7)
          assert_raises(IOError, lambda x: x.tofile(b), d)
  
      def test_bool_fromstring(self):
          v = np.array([True, False, True, False], dtype=np.bool_)
          y = np.fromstring('1 0 -2.3 0.0', sep=' ', dtype=np.bool_)
          assert_array_equal(v, y)
  
      def test_uint64_fromstring(self):
          d = np.fromstring("9923372036854775807 104783749223640",
                            dtype=np.uint64, sep=' ')
          e = np.array([9923372036854775807, 104783749223640], dtype=np.uint64)
          assert_array_equal(d, e)
  
      def test_int64_fromstring(self):
          d = np.fromstring("-25041670086757 104783749223640",
                            dtype=np.int64, sep=' ')
          e = np.array([-25041670086757, 104783749223640], dtype=np.int64)
          assert_array_equal(d, e)
  
      def test_empty_files_binary(self):
          with open(self.filename, 'w') as f:
              pass
          y = np.fromfile(self.filename)
          assert_(y.size == 0, "Array not empty")
  
      def test_empty_files_text(self):
          with open(self.filename, 'wb') as f:
              pass
          y = np.fromfile(self.filename, sep=" ")
          assert_(y.size == 0, "Array not empty")
  
      def test_roundtrip_file(self):
          with open(self.filename, 'wb') as f:
              self.x.tofile(f)
          # NB. doesn't work with flush+seek, due to use of C stdio
          with open(self.filename, 'rb') as f:
              y = np.fromfile(f, dtype=self.dtype)
          assert_array_equal(y, self.x.flat)
  
      def test_roundtrip_filename(self):
          self.x.tofile(self.filename)
          y = np.fromfile(self.filename, dtype=self.dtype)
          assert_array_equal(y, self.x.flat)
  
      def test_roundtrip_pathlib(self):
          p = pathlib.Path(self.filename)
          self.x.tofile(p)
          y = np.fromfile(p, dtype=self.dtype)
          assert_array_equal(y, self.x.flat)
  
      def test_roundtrip_dump_pathlib(self):
          p = pathlib.Path(self.filename)
          self.x.dump(p)
          y = np.load(p, allow_pickle=True)
          assert_array_equal(y, self.x)
  
      def test_roundtrip_binary_str(self):
          s = self.x.tobytes()
          y = np.frombuffer(s, dtype=self.dtype)
          assert_array_equal(y, self.x.flat)
  
          s = self.x.tobytes('F')
          y = np.frombuffer(s, dtype=self.dtype)
          assert_array_equal(y, self.x.flatten('F'))
  
      def test_roundtrip_str(self):
          x = self.x.real.ravel()
          s = "@".join(map(str, x))
          y = np.fromstring(s, sep="@")
          # NB. str imbues less precision
          nan_mask = ~np.isfinite(x)
          assert_array_equal(x[nan_mask], y[nan_mask])
          assert_array_almost_equal(x[~nan_mask], y[~nan_mask], decimal=5)
  
      def test_roundtrip_repr(self):
          x = self.x.real.ravel()
          s = "@".join(map(repr, x))
          y = np.fromstring(s, sep="@")
          assert_array_equal(x, y)
  
      def test_unseekable_fromfile(self):
          # gh-6246
          self.x.tofile(self.filename)
  
          def fail(*args, **kwargs):
              raise IOError('Can not tell or seek')
  
          with io.open(self.filename, 'rb', buffering=0) as f:
              f.seek = fail
              f.tell = fail
              assert_raises(IOError, np.fromfile, f, dtype=self.dtype)
  
      def test_io_open_unbuffered_fromfile(self):
          # gh-6632
          self.x.tofile(self.filename)
          with io.open(self.filename, 'rb', buffering=0) as f:
              y = np.fromfile(f, dtype=self.dtype)
              assert_array_equal(y, self.x.flat)
  
      def test_largish_file(self):
          # check the fallocate path on files > 16MB
          d = np.zeros(4 * 1024 ** 2)
          d.tofile(self.filename)
          assert_equal(os.path.getsize(self.filename), d.nbytes)
          assert_array_equal(d, np.fromfile(self.filename))
          # check offset
          with open(self.filename, "r+b") as f:
              f.seek(d.nbytes)
              d.tofile(f)
              assert_equal(os.path.getsize(self.filename), d.nbytes * 2)
          # check append mode (gh-8329)
          open(self.filename, "w").close() # delete file contents
          with open(self.filename, "ab") as f:
              d.tofile(f)
          assert_array_equal(d, np.fromfile(self.filename))
          with open(self.filename, "ab") as f:
              d.tofile(f)
          assert_equal(os.path.getsize(self.filename), d.nbytes * 2)
  
      def test_io_open_buffered_fromfile(self):
          # gh-6632
          self.x.tofile(self.filename)
          with io.open(self.filename, 'rb', buffering=-1) as f:
              y = np.fromfile(f, dtype=self.dtype)
          assert_array_equal(y, self.x.flat)
  
      def test_file_position_after_fromfile(self):
          # gh-4118
          sizes = [io.DEFAULT_BUFFER_SIZE//8,
                   io.DEFAULT_BUFFER_SIZE,
                   io.DEFAULT_BUFFER_SIZE*8]
  
          for size in sizes:
              with open(self.filename, 'wb') as f:
                  f.seek(size-1)
                  f.write(b'\0')
  
              for mode in ['rb', 'r+b']:
                  err_msg = "%d %s" % (size, mode)
  
                  with open(self.filename, mode) as f:
                      f.read(2)
                      np.fromfile(f, dtype=np.float64, count=1)
                      pos = f.tell()
                  assert_equal(pos, 10, err_msg=err_msg)
  
      def test_file_position_after_tofile(self):
          # gh-4118
          sizes = [io.DEFAULT_BUFFER_SIZE//8,
                   io.DEFAULT_BUFFER_SIZE,
                   io.DEFAULT_BUFFER_SIZE*8]
  
          for size in sizes:
              err_msg = "%d" % (size,)
  
              with open(self.filename, 'wb') as f:
                  f.seek(size-1)
                  f.write(b'\0')
                  f.seek(10)
                  f.write(b'12')
                  np.array([0], dtype=np.float64).tofile(f)
                  pos = f.tell()
              assert_equal(pos, 10 + 2 + 8, err_msg=err_msg)
  
              with open(self.filename, 'r+b') as f:
                  f.read(2)
                  f.seek(0, 1)  # seek between read&write required by ANSI C
                  np.array([0], dtype=np.float64).tofile(f)
                  pos = f.tell()
              assert_equal(pos, 10, err_msg=err_msg)
  
      def test_load_object_array_fromfile(self):
          # gh-12300
          with open(self.filename, 'w') as f:
              # Ensure we have a file with consistent contents
              pass
  
          with open(self.filename, 'rb') as f:
              assert_raises_regex(ValueError, "Cannot read into object array",
                                  np.fromfile, f, dtype=object)
  
          assert_raises_regex(ValueError, "Cannot read into object array",
                              np.fromfile, self.filename, dtype=object)
  
      def test_fromfile_offset(self):
          with open(self.filename, 'wb') as f:
              self.x.tofile(f)
  
          with open(self.filename, 'rb') as f:
              y = np.fromfile(f, dtype=self.dtype, offset=0)
              assert_array_equal(y, self.x.flat)
  
          with open(self.filename, 'rb') as f:
              count_items = len(self.x.flat) // 8
              offset_items = len(self.x.flat) // 4
              offset_bytes = self.dtype.itemsize * offset_items
              y = np.fromfile(f, dtype=self.dtype, count=count_items, offset=offset_bytes)
              assert_array_equal(y, self.x.flat[offset_items:offset_items+count_items])
  
              # subsequent seeks should stack
              offset_bytes = self.dtype.itemsize
              z = np.fromfile(f, dtype=self.dtype, offset=offset_bytes)
              assert_array_equal(z, self.x.flat[offset_items+count_items+1:])
  
          with open(self.filename, 'wb') as f:
              self.x.tofile(f, sep=",")
  
          with open(self.filename, 'rb') as f:
              assert_raises_regex(
                      TypeError,
                      "'offset' argument only permitted for binary files",
                      np.fromfile, self.filename, dtype=self.dtype,
                      sep=",", offset=1)
  
      def _check_from(self, s, value, **kw):
          if 'sep' not in kw:
              y = np.frombuffer(s, **kw)
          else:
              y = np.fromstring(s, **kw)
          assert_array_equal(y, value)
  
          with open(self.filename, 'wb') as f:
              f.write(s)
          y = np.fromfile(self.filename, **kw)
          assert_array_equal(y, value)
  
      def test_nan(self):
          self._check_from(
              b"nan +nan -nan NaN nan(foo) +NaN(BAR) -NAN(q_u_u_x_)",
              [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan],
              sep=' ')
  
      def test_inf(self):
          self._check_from(
              b"inf +inf -inf infinity -Infinity iNfInItY -inF",
              [np.inf, np.inf, -np.inf, np.inf, -np.inf, np.inf, -np.inf],
              sep=' ')
  
      def test_numbers(self):
          self._check_from(b"1.234 -1.234 .3 .3e55 -123133.1231e+133",
                           [1.234, -1.234, .3, .3e55, -123133.1231e+133], sep=' ')
  
      def test_binary(self):
          self._check_from(b'\x00\x00\x80?\x00\x00\x00@\x00\x00@@\x00\x00\x80@',
                           np.array([1, 2, 3, 4]),
                           dtype='<f4')
  
      @pytest.mark.slow  # takes > 1 minute on mechanical hard drive
      def test_big_binary(self):
          """Test workarounds for 32-bit limited fwrite, fseek, and ftell
          calls in windows. These normally would hang doing something like this.
          See http://projects.scipy.org/numpy/ticket/1660"""
          if sys.platform != 'win32':
              return
          try:
              # before workarounds, only up to 2**32-1 worked
              fourgbplus = 2**32 + 2**16
              testbytes = np.arange(8, dtype=np.int8)
              n = len(testbytes)
              flike = tempfile.NamedTemporaryFile()
              f = flike.file
              np.tile(testbytes, fourgbplus // testbytes.nbytes).tofile(f)
              flike.seek(0)
              a = np.fromfile(f, dtype=np.int8)
              flike.close()
              assert_(len(a) == fourgbplus)
              # check only start and end for speed:
              assert_((a[:n] == testbytes).all())
              assert_((a[-n:] == testbytes).all())
          except (MemoryError, ValueError):
              pass
  
      def test_string(self):
          self._check_from(b'1,2,3,4', [1., 2., 3., 4.], sep=',')
  
      def test_counted_string(self):
          self._check_from(b'1,2,3,4', [1., 2., 3., 4.], count=4, sep=',')
          self._check_from(b'1,2,3,4', [1., 2., 3.], count=3, sep=',')
          self._check_from(b'1,2,3,4', [1., 2., 3., 4.], count=-1, sep=',')
  
      def test_string_with_ws(self):
          self._check_from(b'1 2  3     4   ', [1, 2, 3, 4], dtype=int, sep=' ')
  
      def test_counted_string_with_ws(self):
          self._check_from(b'1 2  3     4   ', [1, 2, 3], count=3, dtype=int,
                           sep=' ')
  
      def test_ascii(self):
          self._check_from(b'1 , 2 , 3 , 4', [1., 2., 3., 4.], sep=',')
          self._check_from(b'1,2,3,4', [1., 2., 3., 4.], dtype=float, sep=',')
  
      def test_malformed(self):
          with assert_warns(DeprecationWarning):
              self._check_from(b'1.234 1,234', [1.234, 1.], sep=' ')
  
      def test_long_sep(self):
          self._check_from(b'1_x_3_x_4_x_5', [1, 3, 4, 5], sep='_x_')
  
      def test_dtype(self):
          v = np.array([1, 2, 3, 4], dtype=np.int_)
          self._check_from(b'1,2,3,4', v, sep=',', dtype=np.int_)
  
      def test_dtype_bool(self):
          # can't use _check_from because fromstring can't handle True/False
          v = np.array([True, False, True, False], dtype=np.bool_)
          s = b'1,0,-2.3,0'
          with open(self.filename, 'wb') as f:
              f.write(s)
          y = np.fromfile(self.filename, sep=',', dtype=np.bool_)
          assert_(y.dtype == '?')
          assert_array_equal(y, v)
  
      def test_tofile_sep(self):
          x = np.array([1.51, 2, 3.51, 4], dtype=float)
          with open(self.filename, 'w') as f:
              x.tofile(f, sep=',')
          with open(self.filename, 'r') as f:
              s = f.read()
          #assert_equal(s, '1.51,2.0,3.51,4.0')
          y = np.array([float(p) for p in s.split(',')])
          assert_array_equal(x,y)
  
      def test_tofile_format(self):
          x = np.array([1.51, 2, 3.51, 4], dtype=float)
          with open(self.filename, 'w') as f:
              x.tofile(f, sep=',', format='%.2f')
          with open(self.filename, 'r') as f:
              s = f.read()
          assert_equal(s, '1.51,2.00,3.51,4.00')
  
      def test_locale(self):
          with CommaDecimalPointLocale():
              self.test_numbers()
              self.test_nan()
              self.test_inf()
              self.test_counted_string()
              self.test_ascii()
              self.test_malformed()
              self.test_tofile_sep()
              self.test_tofile_format()
  
      def test_fromfile_subarray_binary(self):
          # Test subarray dtypes which are absorbed into the shape
          x = np.arange(24, dtype="i4").reshape(2, 3, 4)
          x.tofile(self.filename)
          res = np.fromfile(self.filename, dtype="(3,4)i4")
          assert_array_equal(x, res)
  
          x_str = x.tobytes()
          with assert_warns(DeprecationWarning):
              # binary fromstring is deprecated
              res = np.fromstring(x_str, dtype="(3,4)i4")
              assert_array_equal(x, res)
  
  
  class TestFromBuffer:
      @pytest.mark.parametrize('byteorder', ['<', '>'])
      @pytest.mark.parametrize('dtype', [float, int, complex])
      def test_basic(self, byteorder, dtype):
          dt = np.dtype(dtype).newbyteorder(byteorder)
          x = (np.random.random((4, 7)) * 5).astype(dt)
          buf = x.tobytes()
          assert_array_equal(np.frombuffer(buf, dtype=dt), x.flat)
  
      def test_empty(self):
          assert_array_equal(np.frombuffer(b''), np.array([]))
  
  
  class TestFlat:
      def setup(self):
          a0 = np.arange(20.0)
          a = a0.reshape(4, 5)
          a0.shape = (4, 5)
          a.flags.writeable = False
          self.a = a
          self.b = a[::2, ::2]
          self.a0 = a0
          self.b0 = a0[::2, ::2]
  
      def test_contiguous(self):
          testpassed = False
          try:
              self.a.flat[12] = 100.0
          except ValueError:
              testpassed = True
          assert_(testpassed)
          assert_(self.a.flat[12] == 12.0)
  
      def test_discontiguous(self):
          testpassed = False
          try:
              self.b.flat[4] = 100.0
          except ValueError:
              testpassed = True
          assert_(testpassed)
          assert_(self.b.flat[4] == 12.0)
  
      def test___array__(self):
          c = self.a.flat.__array__()
          d = self.b.flat.__array__()
          e = self.a0.flat.__array__()
          f = self.b0.flat.__array__()
  
          assert_(c.flags.writeable is False)
          assert_(d.flags.writeable is False)
          # for 1.14 all are set to non-writeable on the way to replacing the
          # UPDATEIFCOPY array returned for non-contiguous arrays.
          assert_(e.flags.writeable is True)
          assert_(f.flags.writeable is False)
          with assert_warns(DeprecationWarning):
              assert_(c.flags.updateifcopy is False)
          with assert_warns(DeprecationWarning):
              assert_(d.flags.updateifcopy is False)
          with assert_warns(DeprecationWarning):
              assert_(e.flags.updateifcopy is False)
          with assert_warns(DeprecationWarning):
              # UPDATEIFCOPY is removed.
              assert_(f.flags.updateifcopy is False)
          assert_(c.flags.writebackifcopy is False)
          assert_(d.flags.writebackifcopy is False)
          assert_(e.flags.writebackifcopy is False)
          assert_(f.flags.writebackifcopy is False)
  
      @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
      def test_refcount(self):
          # includes regression test for reference count error gh-13165
          inds = [np.intp(0), np.array([True]*self.a.size), np.array([0]), None]
          indtype = np.dtype(np.intp)
          rc_indtype = sys.getrefcount(indtype)
          for ind in inds:
              rc_ind = sys.getrefcount(ind)
              for _ in range(100):
                  try:
                      self.a.flat[ind]
                  except IndexError:
                      pass
              assert_(abs(sys.getrefcount(ind) - rc_ind) < 50)
              assert_(abs(sys.getrefcount(indtype) - rc_indtype) < 50)
  
  
  class TestResize:
  
      @_no_tracing
      def test_basic(self):
          x = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
          if IS_PYPY:
              x.resize((5, 5), refcheck=False)
          else:
              x.resize((5, 5))
          assert_array_equal(x.flat[:9],
                  np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]).flat)
          assert_array_equal(x[9:].flat, 0)
  
      def test_check_reference(self):
          x = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
          y = x
          assert_raises(ValueError, x.resize, (5, 1))
          del y  # avoid pyflakes unused variable warning.
  
      @_no_tracing
      def test_int_shape(self):
          x = np.eye(3)
          if IS_PYPY:
              x.resize(3, refcheck=False)
          else:
              x.resize(3)
          assert_array_equal(x, np.eye(3)[0,:])
  
      def test_none_shape(self):
          x = np.eye(3)
          x.resize(None)
          assert_array_equal(x, np.eye(3))
          x.resize()
          assert_array_equal(x, np.eye(3))
  
      def test_0d_shape(self):
          # to it multiple times to test it does not break alloc cache gh-9216
          for i in range(10):
              x = np.empty((1,))
              x.resize(())
              assert_equal(x.shape, ())
              assert_equal(x.size, 1)
              x = np.empty(())
              x.resize((1,))
              assert_equal(x.shape, (1,))
              assert_equal(x.size, 1)
  
      def test_invalid_arguments(self):
          assert_raises(TypeError, np.eye(3).resize, 'hi')
          assert_raises(ValueError, np.eye(3).resize, -1)
          assert_raises(TypeError, np.eye(3).resize, order=1)
          assert_raises(TypeError, np.eye(3).resize, refcheck='hi')
  
      @_no_tracing
      def test_freeform_shape(self):
          x = np.eye(3)
          if IS_PYPY:
              x.resize(3, 2, 1, refcheck=False)
          else:
              x.resize(3, 2, 1)
          assert_(x.shape == (3, 2, 1))
  
      @_no_tracing
      def test_zeros_appended(self):
          x = np.eye(3)
          if IS_PYPY:
              x.resize(2, 3, 3, refcheck=False)
          else:
              x.resize(2, 3, 3)
          assert_array_equal(x[0], np.eye(3))
          assert_array_equal(x[1], np.zeros((3, 3)))
  
      @_no_tracing
      def test_obj_obj(self):
          # check memory is initialized on resize, gh-4857
          a = np.ones(10, dtype=[('k', object, 2)])
          if IS_PYPY:
              a.resize(15, refcheck=False)
          else:
              a.resize(15,)
          assert_equal(a.shape, (15,))
          assert_array_equal(a['k'][-5:], 0)
          assert_array_equal(a['k'][:-5], 1)
  
      def test_empty_view(self):
          # check that sizes containing a zero don't trigger a reallocate for
          # already empty arrays
          x = np.zeros((10, 0), int)
          x_view = x[...]
          x_view.resize((0, 10))
          x_view.resize((0, 100))
  
      def test_check_weakref(self):
          x = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
          xref = weakref.ref(x)
          assert_raises(ValueError, x.resize, (5, 1))
          del xref  # avoid pyflakes unused variable warning.
  
  
  class TestRecord:
      def test_field_rename(self):
          dt = np.dtype([('f', float), ('i', int)])
          dt.names = ['p', 'q']
          assert_equal(dt.names, ['p', 'q'])
  
      def test_multiple_field_name_occurrence(self):
          def test_dtype_init():
              np.dtype([("A", "f8"), ("B", "f8"), ("A", "f8")])
  
          # Error raised when multiple fields have the same name
          assert_raises(ValueError, test_dtype_init)
  
      def test_bytes_fields(self):
          # Bytes are not allowed in field names and not recognized in titles
          # on Py3
          assert_raises(TypeError, np.dtype, [(b'a', int)])
          assert_raises(TypeError, np.dtype, [(('b', b'a'), int)])
  
          dt = np.dtype([((b'a', 'b'), int)])
          assert_raises(TypeError, dt.__getitem__, b'a')
  
          x = np.array([(1,), (2,), (3,)], dtype=dt)
          assert_raises(IndexError, x.__getitem__, b'a')
  
          y = x[0]
          assert_raises(IndexError, y.__getitem__, b'a')
  
      def test_multiple_field_name_unicode(self):
          def test_dtype_unicode():
              np.dtype([("\u20B9", "f8"), ("B", "f8"), ("\u20B9", "f8")])
  
          # Error raised when multiple fields have the same name(unicode included)
          assert_raises(ValueError, test_dtype_unicode)
  
      def test_fromarrays_unicode(self):
          # A single name string provided to fromarrays() is allowed to be unicode
          # on both Python 2 and 3:
          x = np.core.records.fromarrays([[0], [1]], names=u'a,b', formats=u'i4,i4')
          assert_equal(x['a'][0], 0)
          assert_equal(x['b'][0], 1)
  
      def test_unicode_order(self):
          # Test that we can sort with order as a unicode field name in both Python 2 and
          # 3:
          name = u'b'
          x = np.array([1, 3, 2], dtype=[(name, int)])
          x.sort(order=name)
          assert_equal(x[u'b'], np.array([1, 2, 3]))
  
      def test_field_names(self):
          # Test unicode and 8-bit / byte strings can be used
          a = np.zeros((1,), dtype=[('f1', 'i4'),
                                    ('f2', 'i4'),
                                    ('f3', [('sf1', 'i4')])])
          # byte string indexing fails gracefully
          assert_raises(IndexError, a.__setitem__, b'f1', 1)
          assert_raises(IndexError, a.__getitem__, b'f1')
          assert_raises(IndexError, a['f1'].__setitem__, b'sf1', 1)
          assert_raises(IndexError, a['f1'].__getitem__, b'sf1')
          b = a.copy()
          fn1 = str('f1')
          b[fn1] = 1
          assert_equal(b[fn1], 1)
          fnn = str('not at all')
          assert_raises(ValueError, b.__setitem__, fnn, 1)
          assert_raises(ValueError, b.__getitem__, fnn)
          b[0][fn1] = 2
          assert_equal(b[fn1], 2)
          # Subfield
          assert_raises(ValueError, b[0].__setitem__, fnn, 1)
          assert_raises(ValueError, b[0].__getitem__, fnn)
          # Subfield
          fn3 = str('f3')
          sfn1 = str('sf1')
          b[fn3][sfn1] = 1
          assert_equal(b[fn3][sfn1], 1)
          assert_raises(ValueError, b[fn3].__setitem__, fnn, 1)
          assert_raises(ValueError, b[fn3].__getitem__, fnn)
          # multiple subfields
          fn2 = str('f2')
          b[fn2] = 3
  
          assert_equal(b[['f1', 'f2']][0].tolist(), (2, 3))
          assert_equal(b[['f2', 'f1']][0].tolist(), (3, 2))
          assert_equal(b[['f1', 'f3']][0].tolist(), (2, (1,)))
  
          # non-ascii unicode field indexing is well behaved
          assert_raises(ValueError, a.__setitem__, u'\u03e0', 1)
          assert_raises(ValueError, a.__getitem__, u'\u03e0')
  
      def test_record_hash(self):
          a = np.array([(1, 2), (1, 2)], dtype='i1,i2')
          a.flags.writeable = False
          b = np.array([(1, 2), (3, 4)], dtype=[('num1', 'i1'), ('num2', 'i2')])
          b.flags.writeable = False
          c = np.array([(1, 2), (3, 4)], dtype='i1,i2')
          c.flags.writeable = False
          assert_(hash(a[0]) == hash(a[1]))
          assert_(hash(a[0]) == hash(b[0]))
          assert_(hash(a[0]) != hash(b[1]))
          assert_(hash(c[0]) == hash(a[0]) and c[0] == a[0])
  
      def test_record_no_hash(self):
          a = np.array([(1, 2), (1, 2)], dtype='i1,i2')
          assert_raises(TypeError, hash, a[0])
  
      def test_empty_structure_creation(self):
          # make sure these do not raise errors (gh-5631)
          np.array([()], dtype={'names': [], 'formats': [],
                             'offsets': [], 'itemsize': 12})
          np.array([(), (), (), (), ()], dtype={'names': [], 'formats': [],
                                             'offsets': [], 'itemsize': 12})
  
      def test_multifield_indexing_view(self):
          a = np.ones(3, dtype=[('a', 'i4'), ('b', 'f4'), ('c', 'u4')])
          v = a[['a', 'c']]
          assert_(v.base is a)
          assert_(v.dtype == np.dtype({'names': ['a', 'c'],
                                       'formats': ['i4', 'u4'],
                                       'offsets': [0, 8]}))
          v[:] = (4,5)
          assert_equal(a[0].item(), (4, 1, 5))
  
  class TestView:
      def test_basic(self):
          x = np.array([(1, 2, 3, 4), (5, 6, 7, 8)],
                       dtype=[('r', np.int8), ('g', np.int8),
                              ('b', np.int8), ('a', np.int8)])
          # We must be specific about the endianness here:
          y = x.view(dtype='<i4')
          # ... and again without the keyword.
          z = x.view('<i4')
          assert_array_equal(y, z)
          assert_array_equal(y, [67305985, 134678021])
  
  
  def _mean(a, **args):
      return a.mean(**args)
  
  
  def _var(a, **args):
      return a.var(**args)
  
  
  def _std(a, **args):
      return a.std(**args)
  
  
  class TestStats:
  
      funcs = [_mean, _var, _std]
  
      def setup(self):
          np.random.seed(range(3))
          self.rmat = np.random.random((4, 5))
          self.cmat = self.rmat + 1j * self.rmat
          self.omat = np.array([Decimal(repr(r)) for r in self.rmat.flat])
          self.omat = self.omat.reshape(4, 5)
  
      def test_python_type(self):
          for x in (np.float16(1.), 1, 1., 1+0j):
              assert_equal(np.mean([x]), 1.)
              assert_equal(np.std([x]), 0.)
              assert_equal(np.var([x]), 0.)
  
      def test_keepdims(self):
          mat = np.eye(3)
          for f in self.funcs:
              for axis in [0, 1]:
                  res = f(mat, axis=axis, keepdims=True)
                  assert_(res.ndim == mat.ndim)
                  assert_(res.shape[axis] == 1)
              for axis in [None]:
                  res = f(mat, axis=axis, keepdims=True)
                  assert_(res.shape == (1, 1))
  
      def test_out(self):
          mat = np.eye(3)
          for f in self.funcs:
              out = np.zeros(3)
              tgt = f(mat, axis=1)
              res = f(mat, axis=1, out=out)
              assert_almost_equal(res, out)
              assert_almost_equal(res, tgt)
          out = np.empty(2)
          assert_raises(ValueError, f, mat, axis=1, out=out)
          out = np.empty((2, 2))
          assert_raises(ValueError, f, mat, axis=1, out=out)
  
      def test_dtype_from_input(self):
  
          icodes = np.typecodes['AllInteger']
          fcodes = np.typecodes['AllFloat']
  
          # object type
          for f in self.funcs:
              mat = np.array([[Decimal(1)]*3]*3)
              tgt = mat.dtype.type
              res = f(mat, axis=1).dtype.type
              assert_(res is tgt)
              # scalar case
              res = type(f(mat, axis=None))
              assert_(res is Decimal)
  
          # integer types
          for f in self.funcs:
              for c in icodes:
                  mat = np.eye(3, dtype=c)
                  tgt = np.float64
                  res = f(mat, axis=1).dtype.type
                  assert_(res is tgt)
                  # scalar case
                  res = f(mat, axis=None).dtype.type
                  assert_(res is tgt)
  
          # mean for float types
          for f in [_mean]:
              for c in fcodes:
                  mat = np.eye(3, dtype=c)
                  tgt = mat.dtype.type
                  res = f(mat, axis=1).dtype.type
                  assert_(res is tgt)
                  # scalar case
                  res = f(mat, axis=None).dtype.type
                  assert_(res is tgt)
  
          # var, std for float types
          for f in [_var, _std]:
              for c in fcodes:
                  mat = np.eye(3, dtype=c)
                  # deal with complex types
                  tgt = mat.real.dtype.type
                  res = f(mat, axis=1).dtype.type
                  assert_(res is tgt)
                  # scalar case
                  res = f(mat, axis=None).dtype.type
                  assert_(res is tgt)
  
      def test_dtype_from_dtype(self):
          mat = np.eye(3)
  
          # stats for integer types
          # FIXME:
          # this needs definition as there are lots places along the line
          # where type casting may take place.
  
          # for f in self.funcs:
          #    for c in np.typecodes['AllInteger']:
          #        tgt = np.dtype(c).type
          #        res = f(mat, axis=1, dtype=c).dtype.type
          #        assert_(res is tgt)
          #        # scalar case
          #        res = f(mat, axis=None, dtype=c).dtype.type
          #        assert_(res is tgt)
  
          # stats for float types
          for f in self.funcs:
              for c in np.typecodes['AllFloat']:
                  tgt = np.dtype(c).type
                  res = f(mat, axis=1, dtype=c).dtype.type
                  assert_(res is tgt)
                  # scalar case
                  res = f(mat, axis=None, dtype=c).dtype.type
                  assert_(res is tgt)
  
      def test_ddof(self):
          for f in [_var]:
              for ddof in range(3):
                  dim = self.rmat.shape[1]
                  tgt = f(self.rmat, axis=1) * dim
                  res = f(self.rmat, axis=1, ddof=ddof) * (dim - ddof)
          for f in [_std]:
              for ddof in range(3):
                  dim = self.rmat.shape[1]
                  tgt = f(self.rmat, axis=1) * np.sqrt(dim)
                  res = f(self.rmat, axis=1, ddof=ddof) * np.sqrt(dim - ddof)
                  assert_almost_equal(res, tgt)
                  assert_almost_equal(res, tgt)
  
      def test_ddof_too_big(self):
          dim = self.rmat.shape[1]
          for f in [_var, _std]:
              for ddof in range(dim, dim + 2):
                  with warnings.catch_warnings(record=True) as w:
                      warnings.simplefilter('always')
                      res = f(self.rmat, axis=1, ddof=ddof)
                      assert_(not (res < 0).any())
                      assert_(len(w) > 0)
                      assert_(issubclass(w[0].category, RuntimeWarning))
  
      def test_empty(self):
          A = np.zeros((0, 3))
          for f in self.funcs:
              for axis in [0, None]:
                  with warnings.catch_warnings(record=True) as w:
                      warnings.simplefilter('always')
                      assert_(np.isnan(f(A, axis=axis)).all())
                      assert_(len(w) > 0)
                      assert_(issubclass(w[0].category, RuntimeWarning))
              for axis in [1]:
                  with warnings.catch_warnings(record=True) as w:
                      warnings.simplefilter('always')
                      assert_equal(f(A, axis=axis), np.zeros([]))
  
      def test_mean_values(self):
          for mat in [self.rmat, self.cmat, self.omat]:
              for axis in [0, 1]:
                  tgt = mat.sum(axis=axis)
                  res = _mean(mat, axis=axis) * mat.shape[axis]
                  assert_almost_equal(res, tgt)
              for axis in [None]:
                  tgt = mat.sum(axis=axis)
                  res = _mean(mat, axis=axis) * np.prod(mat.shape)
                  assert_almost_equal(res, tgt)
  
      def test_mean_float16(self):
          # This fail if the sum inside mean is done in float16 instead
          # of float32.
          assert_(_mean(np.ones(100000, dtype='float16')) == 1)
  
      def test_mean_axis_error(self):
          # Ensure that AxisError is raised instead of IndexError when axis is
          # out of bounds, see gh-15817.
          with assert_raises(np.core._exceptions.AxisError):
              np.arange(10).mean(axis=2)
  
      def test_var_values(self):
          for mat in [self.rmat, self.cmat, self.omat]:
              for axis in [0, 1, None]:
                  msqr = _mean(mat * mat.conj(), axis=axis)
                  mean = _mean(mat, axis=axis)
                  tgt = msqr - mean * mean.conjugate()
                  res = _var(mat, axis=axis)
                  assert_almost_equal(res, tgt)
  
      @pytest.mark.parametrize(('complex_dtype', 'ndec'), (
          ('complex64', 6),
          ('complex128', 7),
          ('clongdouble', 7),
      ))
      def test_var_complex_values(self, complex_dtype, ndec):
          # Test fast-paths for every builtin complex type
          for axis in [0, 1, None]:
              mat = self.cmat.copy().astype(complex_dtype)
              msqr = _mean(mat * mat.conj(), axis=axis)
              mean = _mean(mat, axis=axis)
              tgt = msqr - mean * mean.conjugate()
              res = _var(mat, axis=axis)
              assert_almost_equal(res, tgt, decimal=ndec)
  
      def test_var_dimensions(self):
          # _var paths for complex number introduce additions on views that
          # increase dimensions. Ensure this generalizes to higher dims
          mat = np.stack([self.cmat]*3)
          for axis in [0, 1, 2, -1, None]:
              msqr = _mean(mat * mat.conj(), axis=axis)
              mean = _mean(mat, axis=axis)
              tgt = msqr - mean * mean.conjugate()
              res = _var(mat, axis=axis)
              assert_almost_equal(res, tgt)
  
      def test_var_complex_byteorder(self):
          # Test that var fast-path does not cause failures for complex arrays
          # with non-native byteorder
          cmat = self.cmat.copy().astype('complex128')
          cmat_swapped = cmat.astype(cmat.dtype.newbyteorder())
          assert_almost_equal(cmat.var(), cmat_swapped.var())
  
      def test_var_axis_error(self):
          # Ensure that AxisError is raised instead of IndexError when axis is
          # out of bounds, see gh-15817.
          with assert_raises(np.core._exceptions.AxisError):
              np.arange(10).var(axis=2)
  
      def test_std_values(self):
          for mat in [self.rmat, self.cmat, self.omat]:
              for axis in [0, 1, None]:
                  tgt = np.sqrt(_var(mat, axis=axis))
                  res = _std(mat, axis=axis)
                  assert_almost_equal(res, tgt)
  
      def test_subclass(self):
          class TestArray(np.ndarray):
              def __new__(cls, data, info):
                  result = np.array(data)
                  result = result.view(cls)
                  result.info = info
                  return result
  
              def __array_finalize__(self, obj):
                  self.info = getattr(obj, "info", '')
  
          dat = TestArray([[1, 2, 3, 4], [5, 6, 7, 8]], 'jubba')
          res = dat.mean(1)
          assert_(res.info == dat.info)
          res = dat.std(1)
          assert_(res.info == dat.info)
          res = dat.var(1)
          assert_(res.info == dat.info)
  
  class TestVdot:
      def test_basic(self):
          dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
          dt_complex = np.typecodes['Complex']
  
          # test real
          a = np.eye(3)
          for dt in dt_numeric + 'O':
              b = a.astype(dt)
              res = np.vdot(b, b)
              assert_(np.isscalar(res))
              assert_equal(np.vdot(b, b), 3)
  
          # test complex
          a = np.eye(3) * 1j
          for dt in dt_complex + 'O':
              b = a.astype(dt)
              res = np.vdot(b, b)
              assert_(np.isscalar(res))
              assert_equal(np.vdot(b, b), 3)
  
          # test boolean
          b = np.eye(3, dtype=bool)
          res = np.vdot(b, b)
          assert_(np.isscalar(res))
          assert_equal(np.vdot(b, b), True)
  
      def test_vdot_array_order(self):
          a = np.array([[1, 2], [3, 4]], order='C')
          b = np.array([[1, 2], [3, 4]], order='F')
          res = np.vdot(a, a)
  
          # integer arrays are exact
          assert_equal(np.vdot(a, b), res)
          assert_equal(np.vdot(b, a), res)
          assert_equal(np.vdot(b, b), res)
  
      def test_vdot_uncontiguous(self):
          for size in [2, 1000]:
              # Different sizes match different branches in vdot.
              a = np.zeros((size, 2, 2))
              b = np.zeros((size, 2, 2))
              a[:, 0, 0] = np.arange(size)
              b[:, 0, 0] = np.arange(size) + 1
              # Make a and b uncontiguous:
              a = a[..., 0]
              b = b[..., 0]
  
              assert_equal(np.vdot(a, b),
                           np.vdot(a.flatten(), b.flatten()))
              assert_equal(np.vdot(a, b.copy()),
                           np.vdot(a.flatten(), b.flatten()))
              assert_equal(np.vdot(a.copy(), b),
                           np.vdot(a.flatten(), b.flatten()))
              assert_equal(np.vdot(a.copy('F'), b),
                           np.vdot(a.flatten(), b.flatten()))
              assert_equal(np.vdot(a, b.copy('F')),
                           np.vdot(a.flatten(), b.flatten()))
  
  
  class TestDot:
      def setup(self):
          np.random.seed(128)
          self.A = np.random.rand(4, 2)
          self.b1 = np.random.rand(2, 1)
          self.b2 = np.random.rand(2)
          self.b3 = np.random.rand(1, 2)
          self.b4 = np.random.rand(4)
          self.N = 7
  
      def test_dotmatmat(self):
          A = self.A
          res = np.dot(A.transpose(), A)
          tgt = np.array([[1.45046013, 0.86323640],
                          [0.86323640, 0.84934569]])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotmatvec(self):
          A, b1 = self.A, self.b1
          res = np.dot(A, b1)
          tgt = np.array([[0.32114320], [0.04889721],
                          [0.15696029], [0.33612621]])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotmatvec2(self):
          A, b2 = self.A, self.b2
          res = np.dot(A, b2)
          tgt = np.array([0.29677940, 0.04518649, 0.14468333, 0.31039293])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotvecmat(self):
          A, b4 = self.A, self.b4
          res = np.dot(b4, A)
          tgt = np.array([1.23495091, 1.12222648])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotvecmat2(self):
          b3, A = self.b3, self.A
          res = np.dot(b3, A.transpose())
          tgt = np.array([[0.58793804, 0.08957460, 0.30605758, 0.62716383]])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotvecmat3(self):
          A, b4 = self.A, self.b4
          res = np.dot(A.transpose(), b4)
          tgt = np.array([1.23495091, 1.12222648])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotvecvecouter(self):
          b1, b3 = self.b1, self.b3
          res = np.dot(b1, b3)
          tgt = np.array([[0.20128610, 0.08400440], [0.07190947, 0.03001058]])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotvecvecinner(self):
          b1, b3 = self.b1, self.b3
          res = np.dot(b3, b1)
          tgt = np.array([[ 0.23129668]])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotcolumnvect1(self):
          b1 = np.ones((3, 1))
          b2 = [5.3]
          res = np.dot(b1, b2)
          tgt = np.array([5.3, 5.3, 5.3])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotcolumnvect2(self):
          b1 = np.ones((3, 1)).transpose()
          b2 = [6.2]
          res = np.dot(b2, b1)
          tgt = np.array([6.2, 6.2, 6.2])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotvecscalar(self):
          np.random.seed(100)
          b1 = np.random.rand(1, 1)
          b2 = np.random.rand(1, 4)
          res = np.dot(b1, b2)
          tgt = np.array([[0.15126730, 0.23068496, 0.45905553, 0.00256425]])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_dotvecscalar2(self):
          np.random.seed(100)
          b1 = np.random.rand(4, 1)
          b2 = np.random.rand(1, 1)
          res = np.dot(b1, b2)
          tgt = np.array([[0.00256425],[0.00131359],[0.00200324],[ 0.00398638]])
          assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_all(self):
          dims = [(), (1,), (1, 1)]
          dout = [(), (1,), (1, 1), (1,), (), (1,), (1, 1), (1,), (1, 1)]
          for dim, (dim1, dim2) in zip(dout, itertools.product(dims, dims)):
              b1 = np.zeros(dim1)
              b2 = np.zeros(dim2)
              res = np.dot(b1, b2)
              tgt = np.zeros(dim)
              assert_(res.shape == tgt.shape)
              assert_almost_equal(res, tgt, decimal=self.N)
  
      def test_vecobject(self):
          class Vec:
              def __init__(self, sequence=None):
                  if sequence is None:
                      sequence = []
                  self.array = np.array(sequence)
  
              def __add__(self, other):
                  out = Vec()
                  out.array = self.array + other.array
                  return out
  
              def __sub__(self, other):
                  out = Vec()
                  out.array = self.array - other.array
                  return out
  
              def __mul__(self, other):  # with scalar
                  out = Vec(self.array.copy())
                  out.array *= other
                  return out
  
              def __rmul__(self, other):
                  return self*other
  
          U_non_cont = np.transpose([[1., 1.], [1., 2.]])
          U_cont = np.ascontiguousarray(U_non_cont)
          x = np.array([Vec([1., 0.]), Vec([0., 1.])])
          zeros = np.array([Vec([0., 0.]), Vec([0., 0.])])
          zeros_test = np.dot(U_cont, x) - np.dot(U_non_cont, x)
          assert_equal(zeros[0].array, zeros_test[0].array)
          assert_equal(zeros[1].array, zeros_test[1].array)
  
      def test_dot_2args(self):
          from numpy.core.multiarray import dot
  
          a = np.array([[1, 2], [3, 4]], dtype=float)
          b = np.array([[1, 0], [1, 1]], dtype=float)
          c = np.array([[3, 2], [7, 4]], dtype=float)
  
          d = dot(a, b)
          assert_allclose(c, d)
  
      def test_dot_3args(self):
          from numpy.core.multiarray import dot
  
          np.random.seed(22)
          f = np.random.random_sample((1024, 16))
          v = np.random.random_sample((16, 32))
  
          r = np.empty((1024, 32))
          for i in range(12):
              dot(f, v, r)
          if HAS_REFCOUNT:
              assert_equal(sys.getrefcount(r), 2)
          r2 = dot(f, v, out=None)
          assert_array_equal(r2, r)
          assert_(r is dot(f, v, out=r))
  
          v = v[:, 0].copy()  # v.shape == (16,)
          r = r[:, 0].copy()  # r.shape == (1024,)
          r2 = dot(f, v)
          assert_(r is dot(f, v, r))
          assert_array_equal(r2, r)
  
      def test_dot_3args_errors(self):
          from numpy.core.multiarray import dot
  
          np.random.seed(22)
          f = np.random.random_sample((1024, 16))
          v = np.random.random_sample((16, 32))
  
          r = np.empty((1024, 31))
          assert_raises(ValueError, dot, f, v, r)
  
          r = np.empty((1024,))
          assert_raises(ValueError, dot, f, v, r)
  
          r = np.empty((32,))
          assert_raises(ValueError, dot, f, v, r)
  
          r = np.empty((32, 1024))
          assert_raises(ValueError, dot, f, v, r)
          assert_raises(ValueError, dot, f, v, r.T)
  
          r = np.empty((1024, 64))
          assert_raises(ValueError, dot, f, v, r[:, ::2])
          assert_raises(ValueError, dot, f, v, r[:, :32])
  
          r = np.empty((1024, 32), dtype=np.float32)
          assert_raises(ValueError, dot, f, v, r)
  
          r = np.empty((1024, 32), dtype=int)
          assert_raises(ValueError, dot, f, v, r)
  
      def test_dot_array_order(self):
          a = np.array([[1, 2], [3, 4]], order='C')
          b = np.array([[1, 2], [3, 4]], order='F')
          res = np.dot(a, a)
  
          # integer arrays are exact
          assert_equal(np.dot(a, b), res)
          assert_equal(np.dot(b, a), res)
          assert_equal(np.dot(b, b), res)
  
      def test_accelerate_framework_sgemv_fix(self):
  
          def aligned_array(shape, align, dtype, order='C'):
              d = dtype(0)
              N = np.prod(shape)
              tmp = np.zeros(N * d.nbytes + align, dtype=np.uint8)
              address = tmp.__array_interface__["data"][0]
              for offset in range(align):
                  if (address + offset) % align == 0:
                      break
              tmp = tmp[offset:offset+N*d.nbytes].view(dtype=dtype)
              return tmp.reshape(shape, order=order)
  
          def as_aligned(arr, align, dtype, order='C'):
              aligned = aligned_array(arr.shape, align, dtype, order)
              aligned[:] = arr[:]
              return aligned
  
          def assert_dot_close(A, X, desired):
              assert_allclose(np.dot(A, X), desired, rtol=1e-5, atol=1e-7)
  
          m = aligned_array(100, 15, np.float32)
          s = aligned_array((100, 100), 15, np.float32)
          np.dot(s, m)  # this will always segfault if the bug is present
  
          testdata = itertools.product((15,32), (10000,), (200,89), ('C','F'))
          for align, m, n, a_order in testdata:
              # Calculation in double precision
              A_d = np.random.rand(m, n)
              X_d = np.random.rand(n)
              desired = np.dot(A_d, X_d)
              # Calculation with aligned single precision
              A_f = as_aligned(A_d, align, np.float32, order=a_order)
              X_f = as_aligned(X_d, align, np.float32)
              assert_dot_close(A_f, X_f, desired)
              # Strided A rows
              A_d_2 = A_d[::2]
              desired = np.dot(A_d_2, X_d)
              A_f_2 = A_f[::2]
              assert_dot_close(A_f_2, X_f, desired)
              # Strided A columns, strided X vector
              A_d_22 = A_d_2[:, ::2]
              X_d_2 = X_d[::2]
              desired = np.dot(A_d_22, X_d_2)
              A_f_22 = A_f_2[:, ::2]
              X_f_2 = X_f[::2]
              assert_dot_close(A_f_22, X_f_2, desired)
              # Check the strides are as expected
              if a_order == 'F':
                  assert_equal(A_f_22.strides, (8, 8 * m))
              else:
                  assert_equal(A_f_22.strides, (8 * n, 8))
              assert_equal(X_f_2.strides, (8,))
              # Strides in A rows + cols only
              X_f_2c = as_aligned(X_f_2, align, np.float32)
              assert_dot_close(A_f_22, X_f_2c, desired)
              # Strides just in A cols
              A_d_12 = A_d[:, ::2]
              desired = np.dot(A_d_12, X_d_2)
              A_f_12 = A_f[:, ::2]
              assert_dot_close(A_f_12, X_f_2c, desired)
              # Strides in A cols and X
              assert_dot_close(A_f_12, X_f_2, desired)
  
  
  class MatmulCommon:
      """Common tests for '@' operator and numpy.matmul.
  
      """
      # Should work with these types. Will want to add
      # "O" at some point
      types = "?bhilqBHILQefdgFDGO"
  
      def test_exceptions(self):
          dims = [
              ((1,), (2,)),            # mismatched vector vector
              ((2, 1,), (2,)),         # mismatched matrix vector
              ((2,), (1, 2)),          # mismatched vector matrix
              ((1, 2), (3, 1)),        # mismatched matrix matrix
              ((1,), ()),              # vector scalar
              ((), (1)),               # scalar vector
              ((1, 1), ()),            # matrix scalar
              ((), (1, 1)),            # scalar matrix
              ((2, 2, 1), (3, 1, 2)),  # cannot broadcast
              ]
  
          for dt, (dm1, dm2) in itertools.product(self.types, dims):
              a = np.ones(dm1, dtype=dt)
              b = np.ones(dm2, dtype=dt)
              assert_raises(ValueError, self.matmul, a, b)
  
      def test_shapes(self):
          dims = [
              ((1, 1), (2, 1, 1)),     # broadcast first argument
              ((2, 1, 1), (1, 1)),     # broadcast second argument
              ((2, 1, 1), (2, 1, 1)),  # matrix stack sizes match
              ]
  
          for dt, (dm1, dm2) in itertools.product(self.types, dims):
              a = np.ones(dm1, dtype=dt)
              b = np.ones(dm2, dtype=dt)
              res = self.matmul(a, b)
              assert_(res.shape == (2, 1, 1))
  
          # vector vector returns scalars.
          for dt in self.types:
              a = np.ones((2,), dtype=dt)
              b = np.ones((2,), dtype=dt)
              c = self.matmul(a, b)
              assert_(np.array(c).shape == ())
  
      def test_result_types(self):
          mat = np.ones((1,1))
          vec = np.ones((1,))
          for dt in self.types:
              m = mat.astype(dt)
              v = vec.astype(dt)
              for arg in [(m, v), (v, m), (m, m)]:
                  res = self.matmul(*arg)
                  assert_(res.dtype == dt)
  
              # vector vector returns scalars
              if dt != "O":
                  res = self.matmul(v, v)
                  assert_(type(res) is np.dtype(dt).type)
  
      def test_scalar_output(self):
          vec1 = np.array([2])
          vec2 = np.array([3, 4]).reshape(1, -1)
          tgt = np.array([6, 8])
          for dt in self.types[1:]:
              v1 = vec1.astype(dt)
              v2 = vec2.astype(dt)
              res = self.matmul(v1, v2)
              assert_equal(res, tgt)
              res = self.matmul(v2.T, v1)
              assert_equal(res, tgt)
  
          # boolean type
          vec = np.array([True, True], dtype='?').reshape(1, -1)
          res = self.matmul(vec[:, 0], vec)
          assert_equal(res, True)
  
      def test_vector_vector_values(self):
          vec1 = np.array([1, 2])
          vec2 = np.array([3, 4]).reshape(-1, 1)
          tgt1 = np.array([11])
          tgt2 = np.array([[3, 6], [4, 8]])
          for dt in self.types[1:]:
              v1 = vec1.astype(dt)
              v2 = vec2.astype(dt)
              res = self.matmul(v1, v2)
              assert_equal(res, tgt1)
              # no broadcast, we must make v1 into a 2d ndarray
              res = self.matmul(v2, v1.reshape(1, -1))
              assert_equal(res, tgt2)
  
          # boolean type
          vec = np.array([True, True], dtype='?')
          res = self.matmul(vec, vec)
          assert_equal(res, True)
  
      def test_vector_matrix_values(self):
          vec = np.array([1, 2])
          mat1 = np.array([[1, 2], [3, 4]])
          mat2 = np.stack([mat1]*2, axis=0)
          tgt1 = np.array([7, 10])
          tgt2 = np.stack([tgt1]*2, axis=0)
          for dt in self.types[1:]:
              v = vec.astype(dt)
              m1 = mat1.astype(dt)
              m2 = mat2.astype(dt)
              res = self.matmul(v, m1)
              assert_equal(res, tgt1)
              res = self.matmul(v, m2)
              assert_equal(res, tgt2)
  
          # boolean type
          vec = np.array([True, False])
          mat1 = np.array([[True, False], [False, True]])
          mat2 = np.stack([mat1]*2, axis=0)
          tgt1 = np.array([True, False])
          tgt2 = np.stack([tgt1]*2, axis=0)
  
          res = self.matmul(vec, mat1)
          assert_equal(res, tgt1)
          res = self.matmul(vec, mat2)
          assert_equal(res, tgt2)
  
      def test_matrix_vector_values(self):
          vec = np.array([1, 2])
          mat1 = np.array([[1, 2], [3, 4]])
          mat2 = np.stack([mat1]*2, axis=0)
          tgt1 = np.array([5, 11])
          tgt2 = np.stack([tgt1]*2, axis=0)
          for dt in self.types[1:]:
              v = vec.astype(dt)
              m1 = mat1.astype(dt)
              m2 = mat2.astype(dt)
              res = self.matmul(m1, v)
              assert_equal(res, tgt1)
              res = self.matmul(m2, v)
              assert_equal(res, tgt2)
  
          # boolean type
          vec = np.array([True, False])
          mat1 = np.array([[True, False], [False, True]])
          mat2 = np.stack([mat1]*2, axis=0)
          tgt1 = np.array([True, False])
          tgt2 = np.stack([tgt1]*2, axis=0)
  
          res = self.matmul(vec, mat1)
          assert_equal(res, tgt1)
          res = self.matmul(vec, mat2)
          assert_equal(res, tgt2)
  
      def test_matrix_matrix_values(self):
          mat1 = np.array([[1, 2], [3, 4]])
          mat2 = np.array([[1, 0], [1, 1]])
          mat12 = np.stack([mat1, mat2], axis=0)
          mat21 = np.stack([mat2, mat1], axis=0)
          tgt11 = np.array([[7, 10], [15, 22]])
          tgt12 = np.array([[3, 2], [7, 4]])
          tgt21 = np.array([[1, 2], [4, 6]])
          tgt12_21 = np.stack([tgt12, tgt21], axis=0)
          tgt11_12 = np.stack((tgt11, tgt12), axis=0)
          tgt11_21 = np.stack((tgt11, tgt21), axis=0)
          for dt in self.types[1:]:
              m1 = mat1.astype(dt)
              m2 = mat2.astype(dt)
              m12 = mat12.astype(dt)
              m21 = mat21.astype(dt)
  
              # matrix @ matrix
              res = self.matmul(m1, m2)
              assert_equal(res, tgt12)
              res = self.matmul(m2, m1)
              assert_equal(res, tgt21)
  
              # stacked @ matrix
              res = self.matmul(m12, m1)
              assert_equal(res, tgt11_21)
  
              # matrix @ stacked
              res = self.matmul(m1, m12)
              assert_equal(res, tgt11_12)
  
              # stacked @ stacked
              res = self.matmul(m12, m21)
              assert_equal(res, tgt12_21)
  
          # boolean type
          m1 = np.array([[1, 1], [0, 0]], dtype=np.bool_)
          m2 = np.array([[1, 0], [1, 1]], dtype=np.bool_)
          m12 = np.stack([m1, m2], axis=0)
          m21 = np.stack([m2, m1], axis=0)
          tgt11 = m1
          tgt12 = m1
          tgt21 = np.array([[1, 1], [1, 1]], dtype=np.bool_)
          tgt12_21 = np.stack([tgt12, tgt21], axis=0)
          tgt11_12 = np.stack((tgt11, tgt12), axis=0)
          tgt11_21 = np.stack((tgt11, tgt21), axis=0)
  
          # matrix @ matrix
          res = self.matmul(m1, m2)
          assert_equal(res, tgt12)
          res = self.matmul(m2, m1)
          assert_equal(res, tgt21)
  
          # stacked @ matrix
          res = self.matmul(m12, m1)
          assert_equal(res, tgt11_21)
  
          # matrix @ stacked
          res = self.matmul(m1, m12)
          assert_equal(res, tgt11_12)
  
          # stacked @ stacked
          res = self.matmul(m12, m21)
          assert_equal(res, tgt12_21)
  
  
  class TestMatmul(MatmulCommon):
      matmul = np.matmul
  
      def test_out_arg(self):
          a = np.ones((5, 2), dtype=float)
          b = np.array([[1, 3], [5, 7]], dtype=float)
          tgt = np.dot(a, b)
  
          # test as positional argument
          msg = "out positional argument"
          out = np.zeros((5, 2), dtype=float)
          self.matmul(a, b, out)
          assert_array_equal(out, tgt, err_msg=msg)
  
          # test as keyword argument
          msg = "out keyword argument"
          out = np.zeros((5, 2), dtype=float)
          self.matmul(a, b, out=out)
          assert_array_equal(out, tgt, err_msg=msg)
  
          # test out with not allowed type cast (safe casting)
          msg = "Cannot cast ufunc .* output"
          out = np.zeros((5, 2), dtype=np.int32)
          assert_raises_regex(TypeError, msg, self.matmul, a, b, out=out)
  
          # test out with type upcast to complex
          out = np.zeros((5, 2), dtype=np.complex128)
          c = self.matmul(a, b, out=out)
          assert_(c is out)
          with suppress_warnings() as sup:
              sup.filter(np.ComplexWarning, '')
              c = c.astype(tgt.dtype)
          assert_array_equal(c, tgt)
  
      def test_out_contiguous(self):
          a = np.ones((5, 2), dtype=float)
          b = np.array([[1, 3], [5, 7]], dtype=float)
          v = np.array([1, 3], dtype=float)
          tgt = np.dot(a, b)
          tgt_mv = np.dot(a, v)
  
          # test out non-contiguous
          out = np.ones((5, 2, 2), dtype=float)
          c = self.matmul(a, b, out=out[..., 0])
          assert c.base is out
          assert_array_equal(c, tgt)
          c = self.matmul(a, v, out=out[:, 0, 0])
          assert_array_equal(c, tgt_mv)
          c = self.matmul(v, a.T, out=out[:, 0, 0])
          assert_array_equal(c, tgt_mv)
  
          # test out contiguous in only last dim
          out = np.ones((10, 2), dtype=float)
          c = self.matmul(a, b, out=out[::2, :])
          assert_array_equal(c, tgt)
  
          # test transposes of out, args
          out = np.ones((5, 2), dtype=float)
          c = self.matmul(b.T, a.T, out=out.T)
          assert_array_equal(out, tgt)
  
      m1 = np.arange(15.).reshape(5, 3)
      m2 = np.arange(21.).reshape(3, 7)
      m3 = np.arange(30.).reshape(5, 6)[:, ::2]  # non-contiguous
      vc = np.arange(10.)
      vr = np.arange(6.)
      m0 = np.zeros((3, 0))
      @pytest.mark.parametrize('args', (
              # matrix-matrix
              (m1, m2), (m2.T, m1.T), (m2.T.copy(), m1.T), (m2.T, m1.T.copy()),
              # matrix-matrix-transpose, contiguous and non
              (m1, m1.T), (m1.T, m1), (m1, m3.T), (m3, m1.T),
              (m3, m3.T), (m3.T, m3),
              # matrix-matrix non-contiguous
              (m3, m2), (m2.T, m3.T), (m2.T.copy(), m3.T),
              # vector-matrix, matrix-vector, contiguous
              (m1, vr[:3]), (vc[:5], m1), (m1.T, vc[:5]), (vr[:3], m1.T),
              # vector-matrix, matrix-vector, vector non-contiguous
              (m1, vr[::2]), (vc[::2], m1), (m1.T, vc[::2]), (vr[::2], m1.T),
              # vector-matrix, matrix-vector, matrix non-contiguous
              (m3, vr[:3]), (vc[:5], m3), (m3.T, vc[:5]), (vr[:3], m3.T),
              # vector-matrix, matrix-vector, both non-contiguous
              (m3, vr[::2]), (vc[::2], m3), (m3.T, vc[::2]), (vr[::2], m3.T),
              # size == 0
              (m0, m0.T), (m0.T, m0), (m1, m0), (m0.T, m1.T),
          ))
      def test_dot_equivalent(self, args):
          r1 = np.matmul(*args)
          r2 = np.dot(*args)
          assert_equal(r1, r2)
  
          r3 = np.matmul(args[0].copy(), args[1].copy())
          assert_equal(r1, r3)
  
      def test_matmul_object(self):
          import fractions
  
          f = np.vectorize(fractions.Fraction)
          def random_ints():
              return np.random.randint(1, 1000, size=(10, 3, 3))
          M1 = f(random_ints(), random_ints())
          M2 = f(random_ints(), random_ints())
  
          M3 = self.matmul(M1, M2)
  
          [N1, N2, N3] = [a.astype(float) for a in [M1, M2, M3]]
  
          assert_allclose(N3, self.matmul(N1, N2))
  
      def test_matmul_object_type_scalar(self):
          from fractions import Fraction as F
          v = np.array([F(2,3), F(5,7)])
          res = self.matmul(v, v)
          assert_(type(res) is F)
  
      def test_matmul_empty(self):
          a = np.empty((3, 0), dtype=object)
          b = np.empty((0, 3), dtype=object)
          c = np.zeros((3, 3))
          assert_array_equal(np.matmul(a, b), c)
  
      def test_matmul_exception_multiply(self):
          # test that matmul fails if `__mul__` is missing
          class add_not_multiply():
              def __add__(self, other):
                  return self
          a = np.full((3,3), add_not_multiply())
          with assert_raises(TypeError):
              b = np.matmul(a, a)
  
      def test_matmul_exception_add(self):
          # test that matmul fails if `__add__` is missing
          class multiply_not_add():
              def __mul__(self, other):
                  return self
          a = np.full((3,3), multiply_not_add())
          with assert_raises(TypeError):
              b = np.matmul(a, a)
  
      def test_matmul_bool(self):
          # gh-14439
          a = np.array([[1, 0],[1, 1]], dtype=bool)
          assert np.max(a.view(np.uint8)) == 1
          b = np.matmul(a, a)
          # matmul with boolean output should always be 0, 1
          assert np.max(b.view(np.uint8)) == 1
  
          rg = np.random.default_rng(np.random.PCG64(43))
          d = rg.integers(2, size=4*5, dtype=np.int8)
          d = d.reshape(4, 5) > 0
          out1 = np.matmul(d, d.reshape(5, 4))
          out2 = np.dot(d, d.reshape(5, 4))
          assert_equal(out1, out2)
  
          c = np.matmul(np.zeros((2, 0), dtype=bool), np.zeros(0, dtype=bool))
          assert not np.any(c)
  
  
  class TestMatmulOperator(MatmulCommon):
      import operator
      matmul = operator.matmul
  
      def test_array_priority_override(self):
  
          class A:
              __array_priority__ = 1000
  
              def __matmul__(self, other):
                  return "A"
  
              def __rmatmul__(self, other):
                  return "A"
  
          a = A()
          b = np.ones(2)
          assert_equal(self.matmul(a, b), "A")
          assert_equal(self.matmul(b, a), "A")
  
      def test_matmul_raises(self):
          assert_raises(TypeError, self.matmul, np.int8(5), np.int8(5))
          assert_raises(TypeError, self.matmul, np.void(b'abc'), np.void(b'abc'))
          assert_raises(ValueError, self.matmul, np.arange(10), np.void(b'abc'))
  
  def test_matmul_inplace():
      # It would be nice to support in-place matmul eventually, but for now
      # we don't have a working implementation, so better just to error out
      # and nudge people to writing "a = a @ b".
      a = np.eye(3)
      b = np.eye(3)
      assert_raises(TypeError, a.__imatmul__, b)
      import operator
      assert_raises(TypeError, operator.imatmul, a, b)
      assert_raises(TypeError, exec, "a @= b", globals(), locals())
  
  def test_matmul_axes():
      a = np.arange(3*4*5).reshape(3, 4, 5)
      c = np.matmul(a, a, axes=[(-2, -1), (-1, -2), (1, 2)])
      assert c.shape == (3, 4, 4)
      d = np.matmul(a, a, axes=[(-2, -1), (-1, -2), (0, 1)])
      assert d.shape == (4, 4, 3)
      e = np.swapaxes(d, 0, 2)
      assert_array_equal(e, c)
      f = np.matmul(a, np.arange(3), axes=[(1, 0), (0), (0)])
      assert f.shape == (4, 5)
  
  
  class TestInner:
  
      def test_inner_type_mismatch(self):
          c = 1.
          A = np.array((1,1), dtype='i,i')
  
          assert_raises(TypeError, np.inner, c, A)
          assert_raises(TypeError, np.inner, A, c)
  
      def test_inner_scalar_and_vector(self):
          for dt in np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?':
              sca = np.array(3, dtype=dt)[()]
              vec = np.array([1, 2], dtype=dt)
              desired = np.array([3, 6], dtype=dt)
              assert_equal(np.inner(vec, sca), desired)
              assert_equal(np.inner(sca, vec), desired)
  
      def test_vecself(self):
          # Ticket 844.
          # Inner product of a vector with itself segfaults or give
          # meaningless result
          a = np.zeros(shape=(1, 80), dtype=np.float64)
          p = np.inner(a, a)
          assert_almost_equal(p, 0, decimal=14)
  
      def test_inner_product_with_various_contiguities(self):
          # github issue 6532
          for dt in np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?':
              # check an inner product involving a matrix transpose
              A = np.array([[1, 2], [3, 4]], dtype=dt)
              B = np.array([[1, 3], [2, 4]], dtype=dt)
              C = np.array([1, 1], dtype=dt)
              desired = np.array([4, 6], dtype=dt)
              assert_equal(np.inner(A.T, C), desired)
              assert_equal(np.inner(C, A.T), desired)
              assert_equal(np.inner(B, C), desired)
              assert_equal(np.inner(C, B), desired)
              # check a matrix product
              desired = np.array([[7, 10], [15, 22]], dtype=dt)
              assert_equal(np.inner(A, B), desired)
              # check the syrk vs. gemm paths
              desired = np.array([[5, 11], [11, 25]], dtype=dt)
              assert_equal(np.inner(A, A), desired)
              assert_equal(np.inner(A, A.copy()), desired)
              # check an inner product involving an aliased and reversed view
              a = np.arange(5).astype(dt)
              b = a[::-1]
              desired = np.array(10, dtype=dt).item()
              assert_equal(np.inner(b, a), desired)
  
      def test_3d_tensor(self):
          for dt in np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?':
              a = np.arange(24).reshape(2,3,4).astype(dt)
              b = np.arange(24, 48).reshape(2,3,4).astype(dt)
              desired = np.array(
                  [[[[ 158,  182,  206],
                     [ 230,  254,  278]],
  
                    [[ 566,  654,  742],
                     [ 830,  918, 1006]],
  
                    [[ 974, 1126, 1278],
                     [1430, 1582, 1734]]],
  
                   [[[1382, 1598, 1814],
                     [2030, 2246, 2462]],
  
                    [[1790, 2070, 2350],
                     [2630, 2910, 3190]],
  
                    [[2198, 2542, 2886],
                     [3230, 3574, 3918]]]],
                  dtype=dt
              )
              assert_equal(np.inner(a, b), desired)
              assert_equal(np.inner(b, a).transpose(2,3,0,1), desired)
  
  
  class TestAlen:
      def test_basic(self):
          with pytest.warns(DeprecationWarning):
              m = np.array([1, 2, 3])
              assert_equal(np.alen(m), 3)
  
              m = np.array([[1, 2, 3], [4, 5, 7]])
              assert_equal(np.alen(m), 2)
  
              m = [1, 2, 3]
              assert_equal(np.alen(m), 3)
  
              m = [[1, 2, 3], [4, 5, 7]]
              assert_equal(np.alen(m), 2)
  
      def test_singleton(self):
          with pytest.warns(DeprecationWarning):
              assert_equal(np.alen(5), 1)
  
  
  class TestChoose:
      def setup(self):
          self.x = 2*np.ones((3,), dtype=int)
          self.y = 3*np.ones((3,), dtype=int)
          self.x2 = 2*np.ones((2, 3), dtype=int)
          self.y2 = 3*np.ones((2, 3), dtype=int)
          self.ind = [0, 0, 1]
  
      def test_basic(self):
          A = np.choose(self.ind, (self.x, self.y))
          assert_equal(A, [2, 2, 3])
  
      def test_broadcast1(self):
          A = np.choose(self.ind, (self.x2, self.y2))
          assert_equal(A, [[2, 2, 3], [2, 2, 3]])
  
      def test_broadcast2(self):
          A = np.choose(self.ind, (self.x, self.y2))
          assert_equal(A, [[2, 2, 3], [2, 2, 3]])
  
      @pytest.mark.parametrize("ops",
          [(1000, np.array([1], dtype=np.uint8)),
           (-1, np.array([1], dtype=np.uint8)),
           (1., np.float32(3)),
           (1., np.array([3], dtype=np.float32))],)
      def test_output_dtype(self, ops):
          expected_dt = np.result_type(*ops)
          assert(np.choose([0], ops).dtype == expected_dt)
  
  
  class TestRepeat:
      def setup(self):
          self.m = np.array([1, 2, 3, 4, 5, 6])
          self.m_rect = self.m.reshape((2, 3))
  
      def test_basic(self):
          A = np.repeat(self.m, [1, 3, 2, 1, 1, 2])
          assert_equal(A, [1, 2, 2, 2, 3,
                           3, 4, 5, 6, 6])
  
      def test_broadcast1(self):
          A = np.repeat(self.m, 2)
          assert_equal(A, [1, 1, 2, 2, 3, 3,
                           4, 4, 5, 5, 6, 6])
  
      def test_axis_spec(self):
          A = np.repeat(self.m_rect, [2, 1], axis=0)
          assert_equal(A, [[1, 2, 3],
                           [1, 2, 3],
                           [4, 5, 6]])
  
          A = np.repeat(self.m_rect, [1, 3, 2], axis=1)
          assert_equal(A, [[1, 2, 2, 2, 3, 3],
                           [4, 5, 5, 5, 6, 6]])
  
      def test_broadcast2(self):
          A = np.repeat(self.m_rect, 2, axis=0)
          assert_equal(A, [[1, 2, 3],
                           [1, 2, 3],
                           [4, 5, 6],
                           [4, 5, 6]])
  
          A = np.repeat(self.m_rect, 2, axis=1)
          assert_equal(A, [[1, 1, 2, 2, 3, 3],
                           [4, 4, 5, 5, 6, 6]])
  
  
  # TODO: test for multidimensional
  NEIGH_MODE = {'zero': 0, 'one': 1, 'constant': 2, 'circular': 3, 'mirror': 4}
  
  
  @pytest.mark.parametrize('dt', [float, Decimal], ids=['float', 'object'])
  class TestNeighborhoodIter:
      # Simple, 2d tests
      def test_simple2d(self, dt):
          # Test zero and one padding for simple data type
          x = np.array([[0, 1], [2, 3]], dtype=dt)
          r = [np.array([[0, 0, 0], [0, 0, 1]], dtype=dt),
               np.array([[0, 0, 0], [0, 1, 0]], dtype=dt),
               np.array([[0, 0, 1], [0, 2, 3]], dtype=dt),
               np.array([[0, 1, 0], [2, 3, 0]], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-1, 0, -1, 1], x[0], NEIGH_MODE['zero'])
          assert_array_equal(l, r)
  
          r = [np.array([[1, 1, 1], [1, 0, 1]], dtype=dt),
               np.array([[1, 1, 1], [0, 1, 1]], dtype=dt),
               np.array([[1, 0, 1], [1, 2, 3]], dtype=dt),
               np.array([[0, 1, 1], [2, 3, 1]], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-1, 0, -1, 1], x[0], NEIGH_MODE['one'])
          assert_array_equal(l, r)
  
          r = [np.array([[4, 4, 4], [4, 0, 1]], dtype=dt),
               np.array([[4, 4, 4], [0, 1, 4]], dtype=dt),
               np.array([[4, 0, 1], [4, 2, 3]], dtype=dt),
               np.array([[0, 1, 4], [2, 3, 4]], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-1, 0, -1, 1], 4, NEIGH_MODE['constant'])
          assert_array_equal(l, r)
  
      def test_mirror2d(self, dt):
          x = np.array([[0, 1], [2, 3]], dtype=dt)
          r = [np.array([[0, 0, 1], [0, 0, 1]], dtype=dt),
               np.array([[0, 1, 1], [0, 1, 1]], dtype=dt),
               np.array([[0, 0, 1], [2, 2, 3]], dtype=dt),
               np.array([[0, 1, 1], [2, 3, 3]], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-1, 0, -1, 1], x[0], NEIGH_MODE['mirror'])
          assert_array_equal(l, r)
  
      # Simple, 1d tests
      def test_simple(self, dt):
          # Test padding with constant values
          x = np.linspace(1, 5, 5).astype(dt)
          r = [[0, 1, 2], [1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 0]]
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-1, 1], x[0], NEIGH_MODE['zero'])
          assert_array_equal(l, r)
  
          r = [[1, 1, 2], [1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 1]]
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-1, 1], x[0], NEIGH_MODE['one'])
          assert_array_equal(l, r)
  
          r = [[x[4], 1, 2], [1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, x[4]]]
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-1, 1], x[4], NEIGH_MODE['constant'])
          assert_array_equal(l, r)
  
      # Test mirror modes
      def test_mirror(self, dt):
          x = np.linspace(1, 5, 5).astype(dt)
          r = np.array([[2, 1, 1, 2, 3], [1, 1, 2, 3, 4], [1, 2, 3, 4, 5],
                  [2, 3, 4, 5, 5], [3, 4, 5, 5, 4]], dtype=dt)
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-2, 2], x[1], NEIGH_MODE['mirror'])
          assert_([i.dtype == dt for i in l])
          assert_array_equal(l, r)
  
      # Circular mode
      def test_circular(self, dt):
          x = np.linspace(1, 5, 5).astype(dt)
          r = np.array([[4, 5, 1, 2, 3], [5, 1, 2, 3, 4], [1, 2, 3, 4, 5],
                  [2, 3, 4, 5, 1], [3, 4, 5, 1, 2]], dtype=dt)
          l = _multiarray_tests.test_neighborhood_iterator(
                  x, [-2, 2], x[0], NEIGH_MODE['circular'])
          assert_array_equal(l, r)
  
  
  # Test stacking neighborhood iterators
  class TestStackedNeighborhoodIter:
      # Simple, 1d test: stacking 2 constant-padded neigh iterators
      def test_simple_const(self):
          dt = np.float64
          # Test zero and one padding for simple data type
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([0], dtype=dt),
               np.array([0], dtype=dt),
               np.array([1], dtype=dt),
               np.array([2], dtype=dt),
               np.array([3], dtype=dt),
               np.array([0], dtype=dt),
               np.array([0], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-2, 4], NEIGH_MODE['zero'], [0, 0], NEIGH_MODE['zero'])
          assert_array_equal(l, r)
  
          r = [np.array([1, 0, 1], dtype=dt),
               np.array([0, 1, 2], dtype=dt),
               np.array([1, 2, 3], dtype=dt),
               np.array([2, 3, 0], dtype=dt),
               np.array([3, 0, 1], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['zero'], [-1, 1], NEIGH_MODE['one'])
          assert_array_equal(l, r)
  
      # 2nd simple, 1d test: stacking 2 neigh iterators, mixing const padding and
      # mirror padding
      def test_simple_mirror(self):
          dt = np.float64
          # Stacking zero on top of mirror
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([0, 1, 1], dtype=dt),
               np.array([1, 1, 2], dtype=dt),
               np.array([1, 2, 3], dtype=dt),
               np.array([2, 3, 3], dtype=dt),
               np.array([3, 3, 0], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['mirror'], [-1, 1], NEIGH_MODE['zero'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([1, 0, 0], dtype=dt),
               np.array([0, 0, 1], dtype=dt),
               np.array([0, 1, 2], dtype=dt),
               np.array([1, 2, 3], dtype=dt),
               np.array([2, 3, 0], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['zero'], [-2, 0], NEIGH_MODE['mirror'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero: 2nd
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([0, 1, 2], dtype=dt),
               np.array([1, 2, 3], dtype=dt),
               np.array([2, 3, 0], dtype=dt),
               np.array([3, 0, 0], dtype=dt),
               np.array([0, 0, 3], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['zero'], [0, 2], NEIGH_MODE['mirror'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero: 3rd
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([1, 0, 0, 1, 2], dtype=dt),
               np.array([0, 0, 1, 2, 3], dtype=dt),
               np.array([0, 1, 2, 3, 0], dtype=dt),
               np.array([1, 2, 3, 0, 0], dtype=dt),
               np.array([2, 3, 0, 0, 3], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['zero'], [-2, 2], NEIGH_MODE['mirror'])
          assert_array_equal(l, r)
  
      # 3rd simple, 1d test: stacking 2 neigh iterators, mixing const padding and
      # circular padding
      def test_simple_circular(self):
          dt = np.float64
          # Stacking zero on top of mirror
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([0, 3, 1], dtype=dt),
               np.array([3, 1, 2], dtype=dt),
               np.array([1, 2, 3], dtype=dt),
               np.array([2, 3, 1], dtype=dt),
               np.array([3, 1, 0], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['circular'], [-1, 1], NEIGH_MODE['zero'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([3, 0, 0], dtype=dt),
               np.array([0, 0, 1], dtype=dt),
               np.array([0, 1, 2], dtype=dt),
               np.array([1, 2, 3], dtype=dt),
               np.array([2, 3, 0], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['zero'], [-2, 0], NEIGH_MODE['circular'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero: 2nd
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([0, 1, 2], dtype=dt),
               np.array([1, 2, 3], dtype=dt),
               np.array([2, 3, 0], dtype=dt),
               np.array([3, 0, 0], dtype=dt),
               np.array([0, 0, 1], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['zero'], [0, 2], NEIGH_MODE['circular'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero: 3rd
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([3, 0, 0, 1, 2], dtype=dt),
               np.array([0, 0, 1, 2, 3], dtype=dt),
               np.array([0, 1, 2, 3, 0], dtype=dt),
               np.array([1, 2, 3, 0, 0], dtype=dt),
               np.array([2, 3, 0, 0, 1], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [-1, 3], NEIGH_MODE['zero'], [-2, 2], NEIGH_MODE['circular'])
          assert_array_equal(l, r)
  
      # 4th simple, 1d test: stacking 2 neigh iterators, but with lower iterator
      # being strictly within the array
      def test_simple_strict_within(self):
          dt = np.float64
          # Stacking zero on top of zero, first neighborhood strictly inside the
          # array
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([1, 2, 3, 0], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [1, 1], NEIGH_MODE['zero'], [-1, 2], NEIGH_MODE['zero'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero, first neighborhood strictly inside the
          # array
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([1, 2, 3, 3], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [1, 1], NEIGH_MODE['zero'], [-1, 2], NEIGH_MODE['mirror'])
          assert_array_equal(l, r)
  
          # Stacking mirror on top of zero, first neighborhood strictly inside the
          # array
          x = np.array([1, 2, 3], dtype=dt)
          r = [np.array([1, 2, 3, 1], dtype=dt)]
          l = _multiarray_tests.test_neighborhood_iterator_oob(
                  x, [1, 1], NEIGH_MODE['zero'], [-1, 2], NEIGH_MODE['circular'])
          assert_array_equal(l, r)
  
  class TestWarnings:
  
      def test_complex_warning(self):
          x = np.array([1, 2])
          y = np.array([1-2j, 1+2j])
  
          with warnings.catch_warnings():
              warnings.simplefilter("error", np.ComplexWarning)
              assert_raises(np.ComplexWarning, x.__setitem__, slice(None), y)
              assert_equal(x, [1, 2])
  
  
  class TestMinScalarType:
  
      def test_usigned_shortshort(self):
          dt = np.min_scalar_type(2**8-1)
          wanted = np.dtype('uint8')
          assert_equal(wanted, dt)
  
      def test_usigned_short(self):
          dt = np.min_scalar_type(2**16-1)
          wanted = np.dtype('uint16')
          assert_equal(wanted, dt)
  
      def test_usigned_int(self):
          dt = np.min_scalar_type(2**32-1)
          wanted = np.dtype('uint32')
          assert_equal(wanted, dt)
  
      def test_usigned_longlong(self):
          dt = np.min_scalar_type(2**63-1)
          wanted = np.dtype('uint64')
          assert_equal(wanted, dt)
  
      def test_object(self):
          dt = np.min_scalar_type(2**64)
          wanted = np.dtype('O')
          assert_equal(wanted, dt)
  
  
  from numpy.core._internal import _dtype_from_pep3118
  
  
  class TestPEP3118Dtype:
      def _check(self, spec, wanted):
          dt = np.dtype(wanted)
          actual = _dtype_from_pep3118(spec)
          assert_equal(actual, dt,
                       err_msg="spec %r != dtype %r" % (spec, wanted))
  
      def test_native_padding(self):
          align = np.dtype('i').alignment
          for j in range(8):
              if j == 0:
                  s = 'bi'
              else:
                  s = 'b%dxi' % j
              self._check('@'+s, {'f0': ('i1', 0),
                                  'f1': ('i', align*(1 + j//align))})
              self._check('='+s, {'f0': ('i1', 0),
                                  'f1': ('i', 1+j)})
  
      def test_native_padding_2(self):
          # Native padding should work also for structs and sub-arrays
          self._check('x3T{xi}', {'f0': (({'f0': ('i', 4)}, (3,)), 4)})
          self._check('^x3T{xi}', {'f0': (({'f0': ('i', 1)}, (3,)), 1)})
  
      def test_trailing_padding(self):
          # Trailing padding should be included, *and*, the item size
          # should match the alignment if in aligned mode
          align = np.dtype('i').alignment
          size = np.dtype('i').itemsize
  
          def aligned(n):
              return align*(1 + (n-1)//align)
  
          base = dict(formats=['i'], names=['f0'])
  
          self._check('ix',    dict(itemsize=aligned(size + 1), **base))
          self._check('ixx',   dict(itemsize=aligned(size + 2), **base))
          self._check('ixxx',  dict(itemsize=aligned(size + 3), **base))
          self._check('ixxxx', dict(itemsize=aligned(size + 4), **base))
          self._check('i7x',   dict(itemsize=aligned(size + 7), **base))
  
          self._check('^ix',    dict(itemsize=size + 1, **base))
          self._check('^ixx',   dict(itemsize=size + 2, **base))
          self._check('^ixxx',  dict(itemsize=size + 3, **base))
          self._check('^ixxxx', dict(itemsize=size + 4, **base))
          self._check('^i7x',   dict(itemsize=size + 7, **base))
  
      def test_native_padding_3(self):
          dt = np.dtype(
                  [('a', 'b'), ('b', 'i'),
                      ('sub', np.dtype('b,i')), ('c', 'i')],
                  align=True)
          self._check("T{b:a:xxxi:b:T{b:f0:=i:f1:}:sub:xxxi:c:}", dt)
  
          dt = np.dtype(
                  [('a', 'b'), ('b', 'i'), ('c', 'b'), ('d', 'b'),
                      ('e', 'b'), ('sub', np.dtype('b,i', align=True))])
          self._check("T{b:a:=i:b:b:c:b:d:b:e:T{b:f0:xxxi:f1:}:sub:}", dt)
  
      def test_padding_with_array_inside_struct(self):
          dt = np.dtype(
                  [('a', 'b'), ('b', 'i'), ('c', 'b', (3,)),
                      ('d', 'i')],
                  align=True)
          self._check("T{b:a:xxxi:b:3b:c:xi:d:}", dt)
  
      def test_byteorder_inside_struct(self):
          # The byte order after @T{=i} should be '=', not '@'.
          # Check this by noting the absence of native alignment.
          self._check('@T{^i}xi', {'f0': ({'f0': ('i', 0)}, 0),
                                   'f1': ('i', 5)})
  
      def test_intra_padding(self):
          # Natively aligned sub-arrays may require some internal padding
          align = np.dtype('i').alignment
          size = np.dtype('i').itemsize
  
          def aligned(n):
              return (align*(1 + (n-1)//align))
  
          self._check('(3)T{ix}', (dict(
              names=['f0'],
              formats=['i'],
              offsets=[0],
              itemsize=aligned(size + 1)
          ), (3,)))
  
      def test_char_vs_string(self):
          dt = np.dtype('c')
          self._check('c', dt)
  
          dt = np.dtype([('f0', 'S1', (4,)), ('f1', 'S4')])
          self._check('4c4s', dt)
  
      def test_field_order(self):
          # gh-9053 - previously, we relied on dictionary key order
          self._check("(0)I:a:f:b:", [('a', 'I', (0,)), ('b', 'f')])
          self._check("(0)I:b:f:a:", [('b', 'I', (0,)), ('a', 'f')])
  
      def test_unnamed_fields(self):
          self._check('ii',     [('f0', 'i'), ('f1', 'i')])
          self._check('ii:f0:', [('f1', 'i'), ('f0', 'i')])
  
          self._check('i', 'i')
          self._check('i:f0:', [('f0', 'i')])
  
  
  class TestNewBufferProtocol:
      """ Test PEP3118 buffers """
  
      def _check_roundtrip(self, obj):
          obj = np.asarray(obj)
          x = memoryview(obj)
          y = np.asarray(x)
          y2 = np.array(x)
          assert_(not y.flags.owndata)
          assert_(y2.flags.owndata)
  
          assert_equal(y.dtype, obj.dtype)
          assert_equal(y.shape, obj.shape)
          assert_array_equal(obj, y)
  
          assert_equal(y2.dtype, obj.dtype)
          assert_equal(y2.shape, obj.shape)
          assert_array_equal(obj, y2)
  
      def test_roundtrip(self):
          x = np.array([1, 2, 3, 4, 5], dtype='i4')
          self._check_roundtrip(x)
  
          x = np.array([[1, 2], [3, 4]], dtype=np.float64)
          self._check_roundtrip(x)
  
          x = np.zeros((3, 3, 3), dtype=np.float32)[:, 0,:]
          self._check_roundtrip(x)
  
          dt = [('a', 'b'),
                ('b', 'h'),
                ('c', 'i'),
                ('d', 'l'),
                ('dx', 'q'),
                ('e', 'B'),
                ('f', 'H'),
                ('g', 'I'),
                ('h', 'L'),
                ('hx', 'Q'),
                ('i', np.single),
                ('j', np.double),
                ('k', np.longdouble),
                ('ix', np.csingle),
                ('jx', np.cdouble),
                ('kx', np.clongdouble),
                ('l', 'S4'),
                ('m', 'U4'),
                ('n', 'V3'),
                ('o', '?'),
                ('p', np.half),
                ]
          x = np.array(
                  [(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                      b'aaaa', 'bbbb', b'xxx', True, 1.0)],
                  dtype=dt)
          self._check_roundtrip(x)
  
          x = np.array(([[1, 2], [3, 4]],), dtype=[('a', (int, (2, 2)))])
          self._check_roundtrip(x)
  
          x = np.array([1, 2, 3], dtype='>i2')
          self._check_roundtrip(x)
  
          x = np.array([1, 2, 3], dtype='<i2')
          self._check_roundtrip(x)
  
          x = np.array([1, 2, 3], dtype='>i4')
          self._check_roundtrip(x)
  
          x = np.array([1, 2, 3], dtype='<i4')
          self._check_roundtrip(x)
  
          # check long long can be represented as non-native
          x = np.array([1, 2, 3], dtype='>q')
          self._check_roundtrip(x)
  
          # Native-only data types can be passed through the buffer interface
          # only in native byte order
          if sys.byteorder == 'little':
              x = np.array([1, 2, 3], dtype='>g')
              assert_raises(ValueError, self._check_roundtrip, x)
              x = np.array([1, 2, 3], dtype='<g')
              self._check_roundtrip(x)
          else:
              x = np.array([1, 2, 3], dtype='>g')
              self._check_roundtrip(x)
              x = np.array([1, 2, 3], dtype='<g')
              assert_raises(ValueError, self._check_roundtrip, x)
  
      def test_roundtrip_half(self):
          half_list = [
              1.0,
              -2.0,
              6.5504 * 10**4,  # (max half precision)
              2**-14,  # ~= 6.10352 * 10**-5 (minimum positive normal)
              2**-24,  # ~= 5.96046 * 10**-8 (minimum strictly positive subnormal)
              0.0,
              -0.0,
              float('+inf'),
              float('-inf'),
              0.333251953125,  # ~= 1/3
          ]
  
          x = np.array(half_list, dtype='>e')
          self._check_roundtrip(x)
          x = np.array(half_list, dtype='<e')
          self._check_roundtrip(x)
  
      def test_roundtrip_single_types(self):
          for typ in np.typeDict.values():
              dtype = np.dtype(typ)
  
              if dtype.char in 'Mm':
                  # datetimes cannot be used in buffers
                  continue
              if dtype.char == 'V':
                  # skip void
                  continue
  
              x = np.zeros(4, dtype=dtype)
              self._check_roundtrip(x)
  
              if dtype.char not in 'qQgG':
                  dt = dtype.newbyteorder('<')
                  x = np.zeros(4, dtype=dt)
                  self._check_roundtrip(x)
  
                  dt = dtype.newbyteorder('>')
                  x = np.zeros(4, dtype=dt)
                  self._check_roundtrip(x)
  
      def test_roundtrip_scalar(self):
          # Issue #4015.
          self._check_roundtrip(0)
  
      def test_invalid_buffer_format(self):
          # datetime64 cannot be used fully in a buffer yet
          # Should be fixed in the next Numpy major release
          dt = np.dtype([('a', 'uint16'), ('b', 'M8[s]')])
          a = np.empty(3, dt)
          assert_raises((ValueError, BufferError), memoryview, a)
          assert_raises((ValueError, BufferError), memoryview, np.array((3), 'M8[D]'))
  
      def test_export_simple_1d(self):
          x = np.array([1, 2, 3, 4, 5], dtype='i')
          y = memoryview(x)
          assert_equal(y.format, 'i')
          assert_equal(y.shape, (5,))
          assert_equal(y.ndim, 1)
          assert_equal(y.strides, (4,))
          assert_equal(y.suboffsets, ())
          assert_equal(y.itemsize, 4)
  
      def test_export_simple_nd(self):
          x = np.array([[1, 2], [3, 4]], dtype=np.float64)
          y = memoryview(x)
          assert_equal(y.format, 'd')
          assert_equal(y.shape, (2, 2))
          assert_equal(y.ndim, 2)
          assert_equal(y.strides, (16, 8))
          assert_equal(y.suboffsets, ())
          assert_equal(y.itemsize, 8)
  
      def test_export_discontiguous(self):
          x = np.zeros((3, 3, 3), dtype=np.float32)[:, 0,:]
          y = memoryview(x)
          assert_equal(y.format, 'f')
          assert_equal(y.shape, (3, 3))
          assert_equal(y.ndim, 2)
          assert_equal(y.strides, (36, 4))
          assert_equal(y.suboffsets, ())
          assert_equal(y.itemsize, 4)
  
      def test_export_record(self):
          dt = [('a', 'b'),
                ('b', 'h'),
                ('c', 'i'),
                ('d', 'l'),
                ('dx', 'q'),
                ('e', 'B'),
                ('f', 'H'),
                ('g', 'I'),
                ('h', 'L'),
                ('hx', 'Q'),
                ('i', np.single),
                ('j', np.double),
                ('k', np.longdouble),
                ('ix', np.csingle),
                ('jx', np.cdouble),
                ('kx', np.clongdouble),
                ('l', 'S4'),
                ('m', 'U4'),
                ('n', 'V3'),
                ('o', '?'),
                ('p', np.half),
                ]
          x = np.array(
                  [(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                      b'aaaa', 'bbbb', b'   ', True, 1.0)],
                  dtype=dt)
          y = memoryview(x)
          assert_equal(y.shape, (1,))
          assert_equal(y.ndim, 1)
          assert_equal(y.suboffsets, ())
  
          sz = sum([np.dtype(b).itemsize for a, b in dt])
          if np.dtype('l').itemsize == 4:
              assert_equal(y.format, 'T{b:a:=h:b:i:c:l:d:q:dx:B:e:@H:f:=I:g:L:h:Q:hx:f:i:d:j:^g:k:=Zf:ix:Zd:jx:^Zg:kx:4s:l:=4w:m:3x:n:?:o:@e:p:}')
          else:
              assert_equal(y.format, 'T{b:a:=h:b:i:c:q:d:q:dx:B:e:@H:f:=I:g:Q:h:Q:hx:f:i:d:j:^g:k:=Zf:ix:Zd:jx:^Zg:kx:4s:l:=4w:m:3x:n:?:o:@e:p:}')
          # Cannot test if NPY_RELAXED_STRIDES_CHECKING changes the strides
          if not (np.ones(1).strides[0] == np.iinfo(np.intp).max):
              assert_equal(y.strides, (sz,))
          assert_equal(y.itemsize, sz)
  
      def test_export_subarray(self):
          x = np.array(([[1, 2], [3, 4]],), dtype=[('a', ('i', (2, 2)))])
          y = memoryview(x)
          assert_equal(y.format, 'T{(2,2)i:a:}')
          assert_equal(y.shape, ())
          assert_equal(y.ndim, 0)
          assert_equal(y.strides, ())
          assert_equal(y.suboffsets, ())
          assert_equal(y.itemsize, 16)
  
      def test_export_endian(self):
          x = np.array([1, 2, 3], dtype='>i')
          y = memoryview(x)
          if sys.byteorder == 'little':
              assert_equal(y.format, '>i')
          else:
              assert_equal(y.format, 'i')
  
          x = np.array([1, 2, 3], dtype='<i')
          y = memoryview(x)
          if sys.byteorder == 'little':
              assert_equal(y.format, 'i')
          else:
              assert_equal(y.format, '<i')
  
      def test_export_flags(self):
          # Check SIMPLE flag, see also gh-3613 (exception should be BufferError)
          assert_raises(ValueError,
                        _multiarray_tests.get_buffer_info,
                         np.arange(5)[::2], ('SIMPLE',))
  
      def test_padding(self):
          for j in range(8):
              x = np.array([(1,), (2,)], dtype={'f0': (int, j)})
              self._check_roundtrip(x)
  
      def test_reference_leak(self):
          if HAS_REFCOUNT:
              count_1 = sys.getrefcount(np.core._internal)
          a = np.zeros(4)
          b = memoryview(a)
          c = np.asarray(b)
          if HAS_REFCOUNT:
              count_2 = sys.getrefcount(np.core._internal)
              assert_equal(count_1, count_2)
          del c  # avoid pyflakes unused variable warning.
  
      def test_padded_struct_array(self):
          dt1 = np.dtype(
                  [('a', 'b'), ('b', 'i'), ('sub', np.dtype('b,i')), ('c', 'i')],
                  align=True)
          x1 = np.arange(dt1.itemsize, dtype=np.int8).view(dt1)
          self._check_roundtrip(x1)
  
          dt2 = np.dtype(
                  [('a', 'b'), ('b', 'i'), ('c', 'b', (3,)), ('d', 'i')],
                  align=True)
          x2 = np.arange(dt2.itemsize, dtype=np.int8).view(dt2)
          self._check_roundtrip(x2)
  
          dt3 = np.dtype(
                  [('a', 'b'), ('b', 'i'), ('c', 'b'), ('d', 'b'),
                      ('e', 'b'), ('sub', np.dtype('b,i', align=True))])
          x3 = np.arange(dt3.itemsize, dtype=np.int8).view(dt3)
          self._check_roundtrip(x3)
  
      def test_relaxed_strides(self):
          # Test that relaxed strides are converted to non-relaxed
          c = np.ones((1, 10, 10), dtype='i8')
  
          # Check for NPY_RELAXED_STRIDES_CHECKING:
          if np.ones((10, 1), order="C").flags.f_contiguous:
              c.strides = (-1, 80, 8)
  
          assert_(memoryview(c).strides == (800, 80, 8))
  
          # Writing C-contiguous data to a BytesIO buffer should work
          fd = io.BytesIO()
          fd.write(c.data)
  
          fortran = c.T
          assert_(memoryview(fortran).strides == (8, 80, 800))
  
          arr = np.ones((1, 10))
          if arr.flags.f_contiguous:
              shape, strides = _multiarray_tests.get_buffer_info(
                      arr, ['F_CONTIGUOUS'])
              assert_(strides[0] == 8)
              arr = np.ones((10, 1), order='F')
              shape, strides = _multiarray_tests.get_buffer_info(
                      arr, ['C_CONTIGUOUS'])
              assert_(strides[-1] == 8)
  
      def test_out_of_order_fields(self):
          dt = np.dtype(dict(
              formats=['<i4', '<i4'],
              names=['one', 'two'],
              offsets=[4, 0],
              itemsize=8
          ))
  
          # overlapping fields cannot be represented by PEP3118
          arr = np.empty(1, dt)
          with assert_raises(ValueError):
              memoryview(arr)
  
      def test_max_dims(self):
          a = np.empty((1,) * 32)
          self._check_roundtrip(a)
  
      @pytest.mark.slow
      def test_error_too_many_dims(self):
          def make_ctype(shape, scalar_type):
              t = scalar_type
              for dim in shape[::-1]:
                  t = dim * t
              return t
  
          # construct a memoryview with 33 dimensions
          c_u8_33d = make_ctype((1,)*33, ctypes.c_uint8)
          m = memoryview(c_u8_33d())
          assert_equal(m.ndim, 33)
  
          assert_raises_regex(
              RuntimeError, "ndim",
              np.array, m)
  
          # The above seems to create some deep cycles, clean them up for
          # easier reference count debugging:
          del c_u8_33d, m
          for i in range(33):
              if gc.collect() == 0:
                  break
  
      def test_error_pointer_type(self):
          # gh-6741
          m = memoryview(ctypes.pointer(ctypes.c_uint8()))
          assert_('&' in m.format)
  
          assert_raises_regex(
              ValueError, "format string",
              np.array, m)
  
      def test_error_message_unsupported(self):
          # wchar has no corresponding numpy type - if this changes in future, we
          # need a better way to construct an invalid memoryview format.
          t = ctypes.c_wchar * 4
          with assert_raises(ValueError) as cm:
              np.array(t())
  
          exc = cm.exception
          with assert_raises_regex(
              NotImplementedError,
              r"Unrepresentable .* 'u' \(UCS-2 strings\)"
          ):
              raise exc.__cause__
  
      def test_ctypes_integer_via_memoryview(self):
          # gh-11150, due to bpo-10746
          for c_integer in {ctypes.c_int, ctypes.c_long, ctypes.c_longlong}:
              value = c_integer(42)
              with warnings.catch_warnings(record=True):
                  warnings.filterwarnings('always', r'.*\bctypes\b', RuntimeWarning)
                  np.asarray(value)
  
      def test_ctypes_struct_via_memoryview(self):
          # gh-10528
          class foo(ctypes.Structure):
              _fields_ = [('a', ctypes.c_uint8), ('b', ctypes.c_uint32)]
          f = foo(a=1, b=2)
  
          with warnings.catch_warnings(record=True):
              warnings.filterwarnings('always', r'.*\bctypes\b', RuntimeWarning)
              arr = np.asarray(f)
  
          assert_equal(arr['a'], 1)
          assert_equal(arr['b'], 2)
          f.a = 3
          assert_equal(arr['a'], 3)
  
  
  class TestArrayAttributeDeletion:
  
      def test_multiarray_writable_attributes_deletion(self):
          # ticket #2046, should not seqfault, raise AttributeError
          a = np.ones(2)
          attr = ['shape', 'strides', 'data', 'dtype', 'real', 'imag', 'flat']
          with suppress_warnings() as sup:
              sup.filter(DeprecationWarning, "Assigning the 'data' attribute")
              for s in attr:
                  assert_raises(AttributeError, delattr, a, s)
  
      def test_multiarray_not_writable_attributes_deletion(self):
          a = np.ones(2)
          attr = ["ndim", "flags", "itemsize", "size", "nbytes", "base",
                  "ctypes", "T", "__array_interface__", "__array_struct__",
                  "__array_priority__", "__array_finalize__"]
          for s in attr:
              assert_raises(AttributeError, delattr, a, s)
  
      def test_multiarray_flags_writable_attribute_deletion(self):
          a = np.ones(2).flags
          attr = ['writebackifcopy', 'updateifcopy', 'aligned', 'writeable']
          for s in attr:
              assert_raises(AttributeError, delattr, a, s)
  
      def test_multiarray_flags_not_writable_attribute_deletion(self):
          a = np.ones(2).flags
          attr = ["contiguous", "c_contiguous", "f_contiguous", "fortran",
                  "owndata", "fnc", "forc", "behaved", "carray", "farray",
                  "num"]
          for s in attr:
              assert_raises(AttributeError, delattr, a, s)
  
  
  class TestArrayInterface():
      class Foo:
          def __init__(self, value):
              self.value = value
              self.iface = {'typestr': 'f8'}
  
          def __float__(self):
              return float(self.value)
  
          @property
          def __array_interface__(self):
              return self.iface
  
  
      f = Foo(0.5)
  
      @pytest.mark.parametrize('val, iface, expected', [
          (f, {}, 0.5),
          ([f], {}, [0.5]),
          ([f, f], {}, [0.5, 0.5]),
          (f, {'shape': ()}, 0.5),
          (f, {'shape': None}, TypeError),
          (f, {'shape': (1, 1)}, [[0.5]]),
          (f, {'shape': (2,)}, ValueError),
          (f, {'strides': ()}, 0.5),
          (f, {'strides': (2,)}, ValueError),
          (f, {'strides': 16}, TypeError),
          ])
      def test_scalar_interface(self, val, iface, expected):
          # Test scalar coercion within the array interface
          self.f.iface = {'typestr': 'f8'}
          self.f.iface.update(iface)
          if HAS_REFCOUNT:
              pre_cnt = sys.getrefcount(np.dtype('f8'))
          if isinstance(expected, type):
              assert_raises(expected, np.array, val)
          else:
              result = np.array(val)
              assert_equal(np.array(val), expected)
              assert result.dtype == 'f8'
              del result
          if HAS_REFCOUNT:
              post_cnt = sys.getrefcount(np.dtype('f8'))
              assert_equal(pre_cnt, post_cnt)
  
  def test_interface_no_shape():
      class ArrayLike:
          array = np.array(1)
          __array_interface__ = array.__array_interface__
      assert_equal(np.array(ArrayLike()), 1)
  
  
  def test_array_interface_itemsize():
      # See gh-6361
      my_dtype = np.dtype({'names': ['A', 'B'], 'formats': ['f4', 'f4'],
                           'offsets': [0, 8], 'itemsize': 16})
      a = np.ones(10, dtype=my_dtype)
      descr_t = np.dtype(a.__array_interface__['descr'])
      typestr_t = np.dtype(a.__array_interface__['typestr'])
      assert_equal(descr_t.itemsize, typestr_t.itemsize)
  
  
  def test_array_interface_empty_shape():
      # See gh-7994
      arr = np.array([1, 2, 3])
      interface1 = dict(arr.__array_interface__)
      interface1['shape'] = ()
  
      class DummyArray1:
          __array_interface__ = interface1
  
      # NOTE: Because Py2 str/Py3 bytes supports the buffer interface, setting
      # the interface data to bytes would invoke the bug this tests for, that
      # __array_interface__ with shape=() is not allowed if the data is an object
      # exposing the buffer interface
      interface2 = dict(interface1)
      interface2['data'] = arr[0].tobytes()
  
      class DummyArray2:
          __array_interface__ = interface2
  
      arr1 = np.asarray(DummyArray1())
      arr2 = np.asarray(DummyArray2())
      arr3 = arr[:1].reshape(())
      assert_equal(arr1, arr2)
      assert_equal(arr1, arr3)
  
  def test_array_interface_offset():
      arr = np.array([1, 2, 3], dtype='int32')
      interface = dict(arr.__array_interface__)
      interface['data'] = memoryview(arr)
      interface['shape'] = (2,)
      interface['offset'] = 4
  
  
      class DummyArray:
          __array_interface__ = interface
  
      arr1 = np.asarray(DummyArray())
      assert_equal(arr1, arr[1:])
  
  def test_flat_element_deletion():
      it = np.ones(3).flat
      try:
          del it[1]
          del it[1:2]
      except TypeError:
          pass
      except Exception:
          raise AssertionError
  
  
  def test_scalar_element_deletion():
      a = np.zeros(2, dtype=[('x', 'int'), ('y', 'int')])
      assert_raises(ValueError, a[0].__delitem__, 'x')
  
  
  class TestMemEventHook:
      def test_mem_seteventhook(self):
          # The actual tests are within the C code in
          # multiarray/_multiarray_tests.c.src
          _multiarray_tests.test_pydatamem_seteventhook_start()
          # force an allocation and free of a numpy array
          # needs to be larger then limit of small memory cacher in ctors.c
          a = np.zeros(1000)
          del a
          break_cycles()
          _multiarray_tests.test_pydatamem_seteventhook_end()
  
  class TestMapIter:
      def test_mapiter(self):
          # The actual tests are within the C code in
          # multiarray/_multiarray_tests.c.src
  
          a = np.arange(12).reshape((3, 4)).astype(float)
          index = ([1, 1, 2, 0],
                   [0, 0, 2, 3])
          vals = [50, 50, 30, 16]
  
          _multiarray_tests.test_inplace_increment(a, index, vals)
          assert_equal(a, [[0.00, 1., 2.0, 19.],
                           [104., 5., 6.0, 7.0],
                           [8.00, 9., 40., 11.]])
  
          b = np.arange(6).astype(float)
          index = (np.array([1, 2, 0]),)
          vals = [50, 4, 100.1]
          _multiarray_tests.test_inplace_increment(b, index, vals)
          assert_equal(b, [100.1,  51.,   6.,   3.,   4.,   5.])
  
  
  class TestAsCArray:
      def test_1darray(self):
          array = np.arange(24, dtype=np.double)
          from_c = _multiarray_tests.test_as_c_array(array, 3)
          assert_equal(array[3], from_c)
  
      def test_2darray(self):
          array = np.arange(24, dtype=np.double).reshape(3, 8)
          from_c = _multiarray_tests.test_as_c_array(array, 2, 4)
          assert_equal(array[2, 4], from_c)
  
      def test_3darray(self):
          array = np.arange(24, dtype=np.double).reshape(2, 3, 4)
          from_c = _multiarray_tests.test_as_c_array(array, 1, 2, 3)
          assert_equal(array[1, 2, 3], from_c)
  
  
  class TestConversion:
      def test_array_scalar_relational_operation(self):
          # All integer
          for dt1 in np.typecodes['AllInteger']:
              assert_(1 > np.array(0, dtype=dt1), "type %s failed" % (dt1,))
              assert_(not 1 < np.array(0, dtype=dt1), "type %s failed" % (dt1,))
  
              for dt2 in np.typecodes['AllInteger']:
                  assert_(np.array(1, dtype=dt1) > np.array(0, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
                  assert_(not np.array(1, dtype=dt1) < np.array(0, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
  
          # Unsigned integers
          for dt1 in 'BHILQP':
              assert_(-1 < np.array(1, dtype=dt1), "type %s failed" % (dt1,))
              assert_(not -1 > np.array(1, dtype=dt1), "type %s failed" % (dt1,))
              assert_(-1 != np.array(1, dtype=dt1), "type %s failed" % (dt1,))
  
              # Unsigned vs signed
              for dt2 in 'bhilqp':
                  assert_(np.array(1, dtype=dt1) > np.array(-1, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
                  assert_(not np.array(1, dtype=dt1) < np.array(-1, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
                  assert_(np.array(1, dtype=dt1) != np.array(-1, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
  
          # Signed integers and floats
          for dt1 in 'bhlqp' + np.typecodes['Float']:
              assert_(1 > np.array(-1, dtype=dt1), "type %s failed" % (dt1,))
              assert_(not 1 < np.array(-1, dtype=dt1), "type %s failed" % (dt1,))
              assert_(-1 == np.array(-1, dtype=dt1), "type %s failed" % (dt1,))
  
              for dt2 in 'bhlqp' + np.typecodes['Float']:
                  assert_(np.array(1, dtype=dt1) > np.array(-1, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
                  assert_(not np.array(1, dtype=dt1) < np.array(-1, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
                  assert_(np.array(-1, dtype=dt1) == np.array(-1, dtype=dt2),
                          "type %s and %s failed" % (dt1, dt2))
  
      def test_to_bool_scalar(self):
          assert_equal(bool(np.array([False])), False)
          assert_equal(bool(np.array([True])), True)
          assert_equal(bool(np.array([[42]])), True)
          assert_raises(ValueError, bool, np.array([1, 2]))
  
          class NotConvertible:
              def __bool__(self):
                  raise NotImplementedError
  
          assert_raises(NotImplementedError, bool, np.array(NotConvertible()))
          assert_raises(NotImplementedError, bool, np.array([NotConvertible()]))
  
          self_containing = np.array([None])
          self_containing[0] = self_containing
          try:
              Error = RecursionError
          except NameError:
              Error = RuntimeError  # python < 3.5
          assert_raises(Error, bool, self_containing)  # previously stack overflow
          self_containing[0] = None  # resolve circular reference
  
      def test_to_int_scalar(self):
          # gh-9972 means that these aren't always the same
          int_funcs = (int, lambda x: x.__int__())
          for int_func in int_funcs:
              assert_equal(int_func(np.array(0)), 0)
              assert_equal(int_func(np.array([1])), 1)
              assert_equal(int_func(np.array([[42]])), 42)
              assert_raises(TypeError, int_func, np.array([1, 2]))
  
              # gh-9972
              assert_equal(4, int_func(np.array('4')))
              assert_equal(5, int_func(np.bytes_(b'5')))
              assert_equal(6, int_func(np.unicode_(u'6')))
  
              class HasTrunc:
                  def __trunc__(self):
                      return 3
              assert_equal(3, int_func(np.array(HasTrunc())))
              assert_equal(3, int_func(np.array([HasTrunc()])))
  
              class NotConvertible:
                  def __int__(self):
                      raise NotImplementedError
              assert_raises(NotImplementedError,
                  int_func, np.array(NotConvertible()))
              assert_raises(NotImplementedError,
                  int_func, np.array([NotConvertible()]))
  
  
  class TestWhere:
      def test_basic(self):
          dts = [bool, np.int16, np.int32, np.int64, np.double, np.complex128,
                 np.longdouble, np.clongdouble]
          for dt in dts:
              c = np.ones(53, dtype=bool)
              assert_equal(np.where( c, dt(0), dt(1)), dt(0))
              assert_equal(np.where(~c, dt(0), dt(1)), dt(1))
              assert_equal(np.where(True, dt(0), dt(1)), dt(0))
              assert_equal(np.where(False, dt(0), dt(1)), dt(1))
              d = np.ones_like(c).astype(dt)
              e = np.zeros_like(d)
              r = d.astype(dt)
              c[7] = False
              r[7] = e[7]
              assert_equal(np.where(c, e, e), e)
              assert_equal(np.where(c, d, e), r)
              assert_equal(np.where(c, d, e[0]), r)
              assert_equal(np.where(c, d[0], e), r)
              assert_equal(np.where(c[::2], d[::2], e[::2]), r[::2])
              assert_equal(np.where(c[1::2], d[1::2], e[1::2]), r[1::2])
              assert_equal(np.where(c[::3], d[::3], e[::3]), r[::3])
              assert_equal(np.where(c[1::3], d[1::3], e[1::3]), r[1::3])
              assert_equal(np.where(c[::-2], d[::-2], e[::-2]), r[::-2])
              assert_equal(np.where(c[::-3], d[::-3], e[::-3]), r[::-3])
              assert_equal(np.where(c[1::-3], d[1::-3], e[1::-3]), r[1::-3])
  
      def test_exotic(self):
          # object
          assert_array_equal(np.where(True, None, None), np.array(None))
          # zero sized
          m = np.array([], dtype=bool).reshape(0, 3)
          b = np.array([], dtype=np.float64).reshape(0, 3)
          assert_array_equal(np.where(m, 0, b), np.array([]).reshape(0, 3))
  
          # object cast
          d = np.array([-1.34, -0.16, -0.54, -0.31, -0.08, -0.95, 0.000, 0.313,
                        0.547, -0.18, 0.876, 0.236, 1.969, 0.310, 0.699, 1.013,
                        1.267, 0.229, -1.39, 0.487])
          nan = float('NaN')
          e = np.array(['5z', '0l', nan, 'Wz', nan, nan, 'Xq', 'cs', nan, nan,
                       'QN', nan, nan, 'Fd', nan, nan, 'kp', nan, '36', 'i1'],
                       dtype=object)
          m = np.array([0, 0, 1, 0, 1, 1, 0, 0, 1, 1,
                        0, 1, 1, 0, 1, 1, 0, 1, 0, 0], dtype=bool)
  
          r = e[:]
          r[np.where(m)] = d[np.where(m)]
          assert_array_equal(np.where(m, d, e), r)
  
          r = e[:]
          r[np.where(~m)] = d[np.where(~m)]
          assert_array_equal(np.where(m, e, d), r)
  
          assert_array_equal(np.where(m, e, e), e)
  
          # minimal dtype result with NaN scalar (e.g required by pandas)
          d = np.array([1., 2.], dtype=np.float32)
          e = float('NaN')
          assert_equal(np.where(True, d, e).dtype, np.float32)
          e = float('Infinity')
          assert_equal(np.where(True, d, e).dtype, np.float32)
          e = float('-Infinity')
          assert_equal(np.where(True, d, e).dtype, np.float32)
          # also check upcast
          e = float(1e150)
          assert_equal(np.where(True, d, e).dtype, np.float64)
  
      def test_ndim(self):
          c = [True, False]
          a = np.zeros((2, 25))
          b = np.ones((2, 25))
          r = np.where(np.array(c)[:,np.newaxis], a, b)
          assert_array_equal(r[0], a[0])
          assert_array_equal(r[1], b[0])
  
          a = a.T
          b = b.T
          r = np.where(c, a, b)
          assert_array_equal(r[:,0], a[:,0])
          assert_array_equal(r[:,1], b[:,0])
  
      def test_dtype_mix(self):
          c = np.array([False, True, False, False, False, False, True, False,
                       False, False, True, False])
          a = np.uint32(1)
          b = np.array([5., 0., 3., 2., -1., -4., 0., -10., 10., 1., 0., 3.],
                        dtype=np.float64)
          r = np.array([5., 1., 3., 2., -1., -4., 1., -10., 10., 1., 1., 3.],
                       dtype=np.float64)
          assert_equal(np.where(c, a, b), r)
  
          a = a.astype(np.float32)
          b = b.astype(np.int64)
          assert_equal(np.where(c, a, b), r)
  
          # non bool mask
          c = c.astype(int)
          c[c != 0] = 34242324
          assert_equal(np.where(c, a, b), r)
          # invert
          tmpmask = c != 0
          c[c == 0] = 41247212
          c[tmpmask] = 0
          assert_equal(np.where(c, b, a), r)
  
      def test_foreign(self):
          c = np.array([False, True, False, False, False, False, True, False,
                       False, False, True, False])
          r = np.array([5., 1., 3., 2., -1., -4., 1., -10., 10., 1., 1., 3.],
                       dtype=np.float64)
          a = np.ones(1, dtype='>i4')
          b = np.array([5., 0., 3., 2., -1., -4., 0., -10., 10., 1., 0., 3.],
                       dtype=np.float64)
          assert_equal(np.where(c, a, b), r)
  
          b = b.astype('>f8')
          assert_equal(np.where(c, a, b), r)
  
          a = a.astype('<i4')
          assert_equal(np.where(c, a, b), r)
  
          c = c.astype('>i4')
          assert_equal(np.where(c, a, b), r)
  
      def test_error(self):
          c = [True, True]
          a = np.ones((4, 5))
          b = np.ones((5, 5))
          assert_raises(ValueError, np.where, c, a, a)
          assert_raises(ValueError, np.where, c[0], a, b)
  
      def test_string(self):
          # gh-4778 check strings are properly filled with nulls
          a = np.array("abc")
          b = np.array("x" * 753)
          assert_equal(np.where(True, a, b), "abc")
          assert_equal(np.where(False, b, a), "abc")
  
          # check native datatype sized strings
          a = np.array("abcd")
          b = np.array("x" * 8)
          assert_equal(np.where(True, a, b), "abcd")
          assert_equal(np.where(False, b, a), "abcd")
  
      def test_empty_result(self):
          # pass empty where result through an assignment which reads the data of
          # empty arrays, error detectable with valgrind, see gh-8922
          x = np.zeros((1, 1))
          ibad = np.vstack(np.where(x == 99.))
          assert_array_equal(ibad,
                             np.atleast_2d(np.array([[],[]], dtype=np.intp)))
  
      def test_largedim(self):
          # invalid read regression gh-9304
          shape = [10, 2, 3, 4, 5, 6]
          np.random.seed(2)
          array = np.random.rand(*shape)
  
          for i in range(10):
              benchmark = array.nonzero()
              result = array.nonzero()
              assert_array_equal(benchmark, result)
  
  
  if not IS_PYPY:
      # sys.getsizeof() is not valid on PyPy
      class TestSizeOf:
  
          def test_empty_array(self):
              x = np.array([])
              assert_(sys.getsizeof(x) > 0)
  
          def check_array(self, dtype):
              elem_size = dtype(0).itemsize
  
              for length in [10, 50, 100, 500]:
                  x = np.arange(length, dtype=dtype)
                  assert_(sys.getsizeof(x) > length * elem_size)
  
          def test_array_int32(self):
              self.check_array(np.int32)
  
          def test_array_int64(self):
              self.check_array(np.int64)
  
          def test_array_float32(self):
              self.check_array(np.float32)
  
          def test_array_float64(self):
              self.check_array(np.float64)
  
          def test_view(self):
              d = np.ones(100)
              assert_(sys.getsizeof(d[...]) < sys.getsizeof(d))
  
          def test_reshape(self):
              d = np.ones(100)
              assert_(sys.getsizeof(d) < sys.getsizeof(d.reshape(100, 1, 1).copy()))
  
          @_no_tracing
          def test_resize(self):
              d = np.ones(100)
              old = sys.getsizeof(d)
              d.resize(50)
              assert_(old > sys.getsizeof(d))
              d.resize(150)
              assert_(old < sys.getsizeof(d))
  
          def test_error(self):
              d = np.ones(100)
              assert_raises(TypeError, d.__sizeof__, "a")
  
  
  class TestHashing:
  
      def test_arrays_not_hashable(self):
          x = np.ones(3)
          assert_raises(TypeError, hash, x)
  
      def test_collections_hashable(self):
          x = np.array([])
          assert_(not isinstance(x, collections.abc.Hashable))
  
  
  class TestArrayPriority:
      # This will go away when __array_priority__ is settled, meanwhile
      # it serves to check unintended changes.
      op = operator
      binary_ops = [
          op.pow, op.add, op.sub, op.mul, op.floordiv, op.truediv, op.mod,
          op.and_, op.or_, op.xor, op.lshift, op.rshift, op.mod, op.gt,
          op.ge, op.lt, op.le, op.ne, op.eq
          ]
  
      class Foo(np.ndarray):
          __array_priority__ = 100.
  
          def __new__(cls, *args, **kwargs):
              return np.array(*args, **kwargs).view(cls)
  
      class Bar(np.ndarray):
          __array_priority__ = 101.
  
          def __new__(cls, *args, **kwargs):
              return np.array(*args, **kwargs).view(cls)
  
      class Other:
          __array_priority__ = 1000.
  
          def _all(self, other):
              return self.__class__()
  
          __add__ = __radd__ = _all
          __sub__ = __rsub__ = _all
          __mul__ = __rmul__ = _all
          __pow__ = __rpow__ = _all
          __div__ = __rdiv__ = _all
          __mod__ = __rmod__ = _all
          __truediv__ = __rtruediv__ = _all
          __floordiv__ = __rfloordiv__ = _all
          __and__ = __rand__ = _all
          __xor__ = __rxor__ = _all
          __or__ = __ror__ = _all
          __lshift__ = __rlshift__ = _all
          __rshift__ = __rrshift__ = _all
          __eq__ = _all
          __ne__ = _all
          __gt__ = _all
          __ge__ = _all
          __lt__ = _all
          __le__ = _all
  
      def test_ndarray_subclass(self):
          a = np.array([1, 2])
          b = self.Bar([1, 2])
          for f in self.binary_ops:
              msg = repr(f)
              assert_(isinstance(f(a, b), self.Bar), msg)
              assert_(isinstance(f(b, a), self.Bar), msg)
  
      def test_ndarray_other(self):
          a = np.array([1, 2])
          b = self.Other()
          for f in self.binary_ops:
              msg = repr(f)
              assert_(isinstance(f(a, b), self.Other), msg)
              assert_(isinstance(f(b, a), self.Other), msg)
  
      def test_subclass_subclass(self):
          a = self.Foo([1, 2])
          b = self.Bar([1, 2])
          for f in self.binary_ops:
              msg = repr(f)
              assert_(isinstance(f(a, b), self.Bar), msg)
              assert_(isinstance(f(b, a), self.Bar), msg)
  
      def test_subclass_other(self):
          a = self.Foo([1, 2])
          b = self.Other()
          for f in self.binary_ops:
              msg = repr(f)
              assert_(isinstance(f(a, b), self.Other), msg)
              assert_(isinstance(f(b, a), self.Other), msg)
  
  
  class TestBytestringArrayNonzero:
  
      def test_empty_bstring_array_is_falsey(self):
          assert_(not np.array([''], dtype=str))
  
      def test_whitespace_bstring_array_is_falsey(self):
          a = np.array(['spam'], dtype=str)
          a[0] = '  \0\0'
          assert_(not a)
  
      def test_all_null_bstring_array_is_falsey(self):
          a = np.array(['spam'], dtype=str)
          a[0] = '\0\0\0\0'
          assert_(not a)
  
      def test_null_inside_bstring_array_is_truthy(self):
          a = np.array(['spam'], dtype=str)
          a[0] = ' \0 \0'
          assert_(a)
  
  
  class TestUnicodeEncoding:
      """
      Tests for encoding related bugs, such as UCS2 vs UCS4, round-tripping
      issues, etc
      """
      def test_round_trip(self):
          """ Tests that GETITEM, SETITEM, and PyArray_Scalar roundtrip """
          # gh-15363
          arr = np.zeros(shape=(), dtype="U1")
          for i in range(1, sys.maxunicode + 1):
              expected = chr(i)
              arr[()] = expected
              assert arr[()] == expected
              assert arr.item() == expected
  
      def test_assign_scalar(self):
          # gh-3258
          l = np.array(['aa', 'bb'])
          l[:] = np.unicode_('cc')
          assert_equal(l, ['cc', 'cc'])
  
      def test_fill_scalar(self):
          # gh-7227
          l = np.array(['aa', 'bb'])
          l.fill(np.unicode_('cc'))
          assert_equal(l, ['cc', 'cc'])
  
  
  class TestUnicodeArrayNonzero:
  
      def test_empty_ustring_array_is_falsey(self):
          assert_(not np.array([''], dtype=np.unicode_))
  
      def test_whitespace_ustring_array_is_falsey(self):
          a = np.array(['eggs'], dtype=np.unicode_)
          a[0] = '  \0\0'
          assert_(not a)
  
      def test_all_null_ustring_array_is_falsey(self):
          a = np.array(['eggs'], dtype=np.unicode_)
          a[0] = '\0\0\0\0'
          assert_(not a)
  
      def test_null_inside_ustring_array_is_truthy(self):
          a = np.array(['eggs'], dtype=np.unicode_)
          a[0] = ' \0 \0'
          assert_(a)
  
  
  class TestFormat:
  
      def test_0d(self):
          a = np.array(np.pi)
          assert_equal('{:0.3g}'.format(a), '3.14')
          assert_equal('{:0.3g}'.format(a[()]), '3.14')
  
      def test_1d_no_format(self):
          a = np.array([np.pi])
          assert_equal('{}'.format(a), str(a))
  
      def test_1d_format(self):
          # until gh-5543, ensure that the behaviour matches what it used to be
          a = np.array([np.pi])
          assert_raises(TypeError, '{:30}'.format, a)
  
  from numpy.testing import IS_PYPY
  
  class TestCTypes:
  
      def test_ctypes_is_available(self):
          test_arr = np.array([[1, 2, 3], [4, 5, 6]])
  
          assert_equal(ctypes, test_arr.ctypes._ctypes)
          assert_equal(tuple(test_arr.ctypes.shape), (2, 3))
  
      def test_ctypes_is_not_available(self):
          from numpy.core import _internal
          _internal.ctypes = None
          try:
              test_arr = np.array([[1, 2, 3], [4, 5, 6]])
  
              assert_(isinstance(test_arr.ctypes._ctypes,
                                 _internal._missing_ctypes))
              assert_equal(tuple(test_arr.ctypes.shape), (2, 3))
          finally:
              _internal.ctypes = ctypes
  
      def _make_readonly(x):
          x.flags.writeable = False
          return x
  
      @pytest.mark.parametrize('arr', [
          np.array([1, 2, 3]),
          np.array([['one', 'two'], ['three', 'four']]),
          np.array((1, 2), dtype='i4,i4'),
          np.zeros((2,), dtype=
              np.dtype(dict(
                  formats=['<i4', '<i4'],
                  names=['a', 'b'],
                  offsets=[0, 2],
                  itemsize=6
              ))
          ),
          np.array([None], dtype=object),
          np.array([]),
          np.empty((0, 0)),
          _make_readonly(np.array([1, 2, 3])),
      ], ids=[
          '1d',
          '2d',
          'structured',
          'overlapping',
          'object',
          'empty',
          'empty-2d',
          'readonly'
      ])
      def test_ctypes_data_as_holds_reference(self, arr):
          # gh-9647
          # create a copy to ensure that pytest does not mess with the refcounts
          arr = arr.copy()
  
          arr_ref = weakref.ref(arr)
  
          ctypes_ptr = arr.ctypes.data_as(ctypes.c_void_p)
  
          # `ctypes_ptr` should hold onto `arr`
          del arr
          break_cycles()
          assert_(arr_ref() is not None, "ctypes pointer did not hold onto a reference")
  
          # but when the `ctypes_ptr` object dies, so should `arr`
          del ctypes_ptr
          if IS_PYPY:
              # Pypy does not recycle arr objects immediately. Trigger gc to
              # release arr. Cpython uses refcounts. An explicit call to gc
              # should not be needed here.
              break_cycles()
          assert_(arr_ref() is None, "unknowable whether ctypes pointer holds a reference")
  
      def test_ctypes_as_parameter_holds_reference(self):
          arr = np.array([None]).copy()
  
          arr_ref = weakref.ref(arr)
  
          ctypes_ptr = arr.ctypes._as_parameter_
  
          # `ctypes_ptr` should hold onto `arr`
          del arr
          break_cycles()
          assert_(arr_ref() is not None, "ctypes pointer did not hold onto a reference")
  
          # but when the `ctypes_ptr` object dies, so should `arr`
          del ctypes_ptr
          if IS_PYPY:
              break_cycles()
          assert_(arr_ref() is None, "unknowable whether ctypes pointer holds a reference")
  
  
  class TestWritebackIfCopy:
      # all these tests use the WRITEBACKIFCOPY mechanism
      def test_argmax_with_out(self):
          mat = np.eye(5)
          out = np.empty(5, dtype='i2')
          res = np.argmax(mat, 0, out=out)
          assert_equal(res, range(5))
  
      def test_argmin_with_out(self):
          mat = -np.eye(5)
          out = np.empty(5, dtype='i2')
          res = np.argmin(mat, 0, out=out)
          assert_equal(res, range(5))
  
      def test_insert_noncontiguous(self):
          a = np.arange(6).reshape(2,3).T # force non-c-contiguous
          # uses arr_insert
          np.place(a, a>2, [44, 55])
          assert_equal(a, np.array([[0, 44], [1, 55], [2, 44]]))
          # hit one of the failing paths
          assert_raises(ValueError, np.place, a, a>20, [])
  
      def test_put_noncontiguous(self):
          a = np.arange(6).reshape(2,3).T # force non-c-contiguous
          np.put(a, [0, 2], [44, 55])
          assert_equal(a, np.array([[44, 3], [55, 4], [2, 5]]))
  
      def test_putmask_noncontiguous(self):
          a = np.arange(6).reshape(2,3).T # force non-c-contiguous
          # uses arr_putmask
          np.putmask(a, a>2, a**2)
          assert_equal(a, np.array([[0, 9], [1, 16], [2, 25]]))
  
      def test_take_mode_raise(self):
          a = np.arange(6, dtype='int')
          out = np.empty(2, dtype='int')
          np.take(a, [0, 2], out=out, mode='raise')
          assert_equal(out, np.array([0, 2]))
  
      def test_choose_mod_raise(self):
          a = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 1]])
          out = np.empty((3,3), dtype='int')
          choices = [-10, 10]
          np.choose(a, choices, out=out, mode='raise')
          assert_equal(out, np.array([[ 10, -10,  10],
                                      [-10,  10, -10],
                                      [ 10, -10,  10]]))
  
      def test_flatiter__array__(self):
          a = np.arange(9).reshape(3,3)
          b = a.T.flat
          c = b.__array__()
          # triggers the WRITEBACKIFCOPY resolution, assuming refcount semantics
          del c
  
      def test_dot_out(self):
          # if HAVE_CBLAS, will use WRITEBACKIFCOPY
          a = np.arange(9, dtype=float).reshape(3,3)
          b = np.dot(a, a, out=a)
          assert_equal(b, np.array([[15, 18, 21], [42, 54, 66], [69, 90, 111]]))
  
      def test_view_assign(self):
          from numpy.core._multiarray_tests import npy_create_writebackifcopy, npy_resolve
  
          arr = np.arange(9).reshape(3, 3).T
          arr_wb = npy_create_writebackifcopy(arr)
          assert_(arr_wb.flags.writebackifcopy)
          assert_(arr_wb.base is arr)
          arr_wb[...] = -100
          npy_resolve(arr_wb)
          # arr changes after resolve, even though we assigned to arr_wb
          assert_equal(arr, -100)
          # after resolve, the two arrays no longer reference each other
          assert_(arr_wb.ctypes.data != 0)
          assert_equal(arr_wb.base, None)
          # assigning to arr_wb does not get transferred to arr
          arr_wb[...] = 100
          assert_equal(arr, -100)
  
      @pytest.mark.leaks_references(
              reason="increments self in dealloc; ignore since deprecated path.")
      def test_dealloc_warning(self):
          with suppress_warnings() as sup:
              sup.record(RuntimeWarning)
              arr = np.arange(9).reshape(3, 3)
              v = arr.T
              _multiarray_tests.npy_abuse_writebackifcopy(v)
              assert len(sup.log) == 1
  
      def test_view_discard_refcount(self):
          from numpy.core._multiarray_tests import npy_create_writebackifcopy, npy_discard
  
          arr = np.arange(9).reshape(3, 3).T
          orig = arr.copy()
          if HAS_REFCOUNT:
              arr_cnt = sys.getrefcount(arr)
          arr_wb = npy_create_writebackifcopy(arr)
          assert_(arr_wb.flags.writebackifcopy)
          assert_(arr_wb.base is arr)
          arr_wb[...] = -100
          npy_discard(arr_wb)
          # arr remains unchanged after discard
          assert_equal(arr, orig)
          # after discard, the two arrays no longer reference each other
          assert_(arr_wb.ctypes.data != 0)
          assert_equal(arr_wb.base, None)
          if HAS_REFCOUNT:
              assert_equal(arr_cnt, sys.getrefcount(arr))
          # assigning to arr_wb does not get transferred to arr
          arr_wb[...] = 100
          assert_equal(arr, orig)
  
  
  class TestArange:
      def test_infinite(self):
          assert_raises_regex(
              ValueError, "size exceeded",
              np.arange, 0, np.inf
          )
  
      def test_nan_step(self):
          assert_raises_regex(
              ValueError, "cannot compute length",
              np.arange, 0, 1, np.nan
          )
  
      def test_zero_step(self):
          assert_raises(ZeroDivisionError, np.arange, 0, 10, 0)
          assert_raises(ZeroDivisionError, np.arange, 0.0, 10.0, 0.0)
  
          # empty range
          assert_raises(ZeroDivisionError, np.arange, 0, 0, 0)
          assert_raises(ZeroDivisionError, np.arange, 0.0, 0.0, 0.0)
  
  
  class TestArrayFinalize:
      """ Tests __array_finalize__ """
  
      def test_receives_base(self):
          # gh-11237
          class SavesBase(np.ndarray):
              def __array_finalize__(self, obj):
                  self.saved_base = self.base
  
          a = np.array(1).view(SavesBase)
          assert_(a.saved_base is a.base)
  
      def test_lifetime_on_error(self):
          # gh-11237
          class RaisesInFinalize(np.ndarray):
              def __array_finalize__(self, obj):
                  # crash, but keep this object alive
                  raise Exception(self)
  
          # a plain object can't be weakref'd
          class Dummy: pass
  
          # get a weak reference to an object within an array
          obj_arr = np.array(Dummy())
          obj_ref = weakref.ref(obj_arr[()])
  
          # get an array that crashed in __array_finalize__
          with assert_raises(Exception) as e:
              obj_arr.view(RaisesInFinalize)
  
          obj_subarray = e.exception.args[0]
          del e
          assert_(isinstance(obj_subarray, RaisesInFinalize))
  
          # reference should still be held by obj_arr
          break_cycles()
          assert_(obj_ref() is not None, "object should not already be dead")
  
          del obj_arr
          break_cycles()
          assert_(obj_ref() is not None, "obj_arr should not hold the last reference")
  
          del obj_subarray
          break_cycles()
          assert_(obj_ref() is None, "no references should remain")
  
  
  def test_orderconverter_with_nonASCII_unicode_ordering():
      # gh-7475
      a = np.arange(5)
      assert_raises(ValueError, a.flatten, order=u'\xe2')
  
  
  def test_equal_override():
      # gh-9153: ndarray.__eq__ uses special logic for structured arrays, which
      # did not respect overrides with __array_priority__ or __array_ufunc__.
      # The PR fixed this for __array_priority__ and __array_ufunc__ = None.
      class MyAlwaysEqual:
          def __eq__(self, other):
              return "eq"
  
          def __ne__(self, other):
              return "ne"
  
      class MyAlwaysEqualOld(MyAlwaysEqual):
          __array_priority__ = 10000
  
      class MyAlwaysEqualNew(MyAlwaysEqual):
          __array_ufunc__ = None
  
      array = np.array([(0, 1), (2, 3)], dtype='i4,i4')
      for my_always_equal_cls in MyAlwaysEqualOld, MyAlwaysEqualNew:
          my_always_equal = my_always_equal_cls()
          assert_equal(my_always_equal == array, 'eq')
          assert_equal(array == my_always_equal, 'eq')
          assert_equal(my_always_equal != array, 'ne')
          assert_equal(array != my_always_equal, 'ne')
  
  
  def test_npymath_complex():
      # Smoketest npymath functions
      from numpy.core._multiarray_tests import (
          npy_cabs, npy_carg)
  
      funcs = {npy_cabs: np.absolute,
               npy_carg: np.angle}
      vals = (1, np.inf, -np.inf, np.nan)
      types = (np.complex64, np.complex128, np.clongdouble)
  
      for fun, npfun in funcs.items():
          for x, y in itertools.product(vals, vals):
              for t in types:
                  z = t(complex(x, y))
                  got = fun(z)
                  expected = npfun(z)
                  assert_allclose(got, expected)
  
  
  def test_npymath_real():
      # Smoketest npymath functions
      from numpy.core._multiarray_tests import (
          npy_log10, npy_cosh, npy_sinh, npy_tan, npy_tanh)
  
      funcs = {npy_log10: np.log10,
               npy_cosh: np.cosh,
               npy_sinh: np.sinh,
               npy_tan: np.tan,
               npy_tanh: np.tanh}
      vals = (1, np.inf, -np.inf, np.nan)
      types = (np.float32, np.float64, np.longdouble)
  
      with np.errstate(all='ignore'):
          for fun, npfun in funcs.items():
              for x, t in itertools.product(vals, types):
                  z = t(x)
                  got = fun(z)
                  expected = npfun(z)
                  assert_allclose(got, expected)
  
  def test_uintalignment_and_alignment():
      # alignment code needs to satisfy these requirements:
      #  1. numpy structs match C struct layout
      #  2. ufuncs/casting is safe wrt to aligned access
      #  3. copy code is safe wrt to "uint alidned" access
      #
      # Complex types are the main problem, whose alignment may not be the same
      # as their "uint alignment".
      #
      # This test might only fail on certain platforms, where uint64 alignment is
      # not equal to complex64 alignment. The second 2 tests will only fail
      # for DEBUG=1.
  
      d1 = np.dtype('u1,c8', align=True)
      d2 = np.dtype('u4,c8', align=True)
      d3 = np.dtype({'names': ['a', 'b'], 'formats': ['u1', d1]}, align=True)
  
      assert_equal(np.zeros(1, dtype=d1)['f1'].flags['ALIGNED'], True)
      assert_equal(np.zeros(1, dtype=d2)['f1'].flags['ALIGNED'], True)
      assert_equal(np.zeros(1, dtype='u1,c8')['f1'].flags['ALIGNED'], False)
  
      # check that C struct matches numpy struct size
      s = _multiarray_tests.get_struct_alignments()
      for d, (alignment, size) in zip([d1,d2,d3], s):
          assert_equal(d.alignment, alignment)
          assert_equal(d.itemsize, size)
  
      # check that ufuncs don't complain in debug mode
      # (this is probably OK if the aligned flag is true above)
      src = np.zeros((2,2), dtype=d1)['f1']  # 4-byte aligned, often
      np.exp(src)  # assert fails?
  
      # check that copy code doesn't complain in debug mode
      dst = np.zeros((2,2), dtype='c8')
      dst[:,1] = src[:,1]  # assert in lowlevel_strided_loops fails?
  
  class TestAlignment:
      # adapted from scipy._lib.tests.test__util.test__aligned_zeros
      # Checks that unusual memory alignments don't trip up numpy.
      # In particular, check RELAXED_STRIDES don't trip alignment assertions in
      # NDEBUG mode for size-0 arrays (gh-12503)
  
      def check(self, shape, dtype, order, align):
          err_msg = repr((shape, dtype, order, align))
          x = _aligned_zeros(shape, dtype, order, align=align)
          if align is None:
              align = np.dtype(dtype).alignment
          assert_equal(x.__array_interface__['data'][0] % align, 0)
          if hasattr(shape, '__len__'):
              assert_equal(x.shape, shape, err_msg)
          else:
              assert_equal(x.shape, (shape,), err_msg)
          assert_equal(x.dtype, dtype)
          if order == "C":
              assert_(x.flags.c_contiguous, err_msg)
          elif order == "F":
              if x.size > 0:
                  assert_(x.flags.f_contiguous, err_msg)
          elif order is None:
              assert_(x.flags.c_contiguous, err_msg)
          else:
              raise ValueError()
  
      def test_various_alignments(self):
          for align in [1, 2, 3, 4, 8, 12, 16, 32, 64, None]:
              for n in [0, 1, 3, 11]:
                  for order in ["C", "F", None]:
                      for dtype in list(np.typecodes["All"]) + ['i4,i4,i4']:
                          if dtype == 'O':
                              # object dtype can't be misaligned
                              continue
                          for shape in [n, (1, 2, 3, n)]:
                              self.check(shape, np.dtype(dtype), order, align)
  
      def test_strided_loop_alignments(self):
          # particularly test that complex64 and float128 use right alignment
          # code-paths, since these are particularly problematic. It is useful to
          # turn on USE_DEBUG for this test, so lowlevel-loop asserts are run.
          for align in [1, 2, 4, 8, 12, 16, None]:
              xf64 = _aligned_zeros(3, np.float64)
  
              xc64 = _aligned_zeros(3, np.complex64, align=align)
              xf128 = _aligned_zeros(3, np.longdouble, align=align)
  
              # test casting, both to and from misaligned
              with suppress_warnings() as sup:
                  sup.filter(np.ComplexWarning, "Casting complex values")
                  xc64.astype('f8')
              xf64.astype(np.complex64)
              test = xc64 + xf64
  
              xf128.astype('f8')
              xf64.astype(np.longdouble)
              test = xf128 + xf64
  
              test = xf128 + xc64
  
              # test copy, both to and from misaligned
              # contig copy
              xf64[:] = xf64.copy()
              xc64[:] = xc64.copy()
              xf128[:] = xf128.copy()
              # strided copy
              xf64[::2] = xf64[::2].copy()
              xc64[::2] = xc64[::2].copy()
              xf128[::2] = xf128[::2].copy()
  
  def test_getfield():
      a = np.arange(32, dtype='uint16')
      if sys.byteorder == 'little':
          i = 0
          j = 1
      else:
          i = 1
          j = 0
      b = a.getfield('int8', i)
      assert_equal(b, a)
      b = a.getfield('int8', j)
      assert_equal(b, 0)
      pytest.raises(ValueError, a.getfield, 'uint8', -1)
      pytest.raises(ValueError, a.getfield, 'uint8', 16)
      pytest.raises(ValueError, a.getfield, 'uint64', 0)
  