text: import numpy as np
  import functools
  import sys
  import pytest
  
  from numpy.lib.shape_base import (
      apply_along_axis, apply_over_axes, array_split, split, hsplit, dsplit,
      vsplit, dstack, column_stack, kron, tile, expand_dims, take_along_axis,
      put_along_axis
      )
  from numpy.testing import (
      assert_, assert_equal, assert_array_equal, assert_raises, assert_warns
      )
  
  
  IS_64BIT = sys.maxsize > 2**32
  
  
  def _add_keepdims(func):
      """ hack in keepdims behavior into a function taking an axis """
      @functools.wraps(func)
      def wrapped(a, axis, **kwargs):
          res = func(a, axis=axis, **kwargs)
          if axis is None:
              axis = 0  # res is now a scalar, so we can insert this anywhere
          return np.expand_dims(res, axis=axis)
      return wrapped
  
  
  class TestTakeAlongAxis:
      def test_argequivalent(self):
          """ Test it translates from arg<func> to <func> """
          from numpy.random import rand
          a = rand(3, 4, 5)
  
          funcs = [
              (np.sort, np.argsort, dict()),
              (_add_keepdims(np.min), _add_keepdims(np.argmin), dict()),
              (_add_keepdims(np.max), _add_keepdims(np.argmax), dict()),
              (np.partition, np.argpartition, dict(kth=2)),
          ]
  
          for func, argfunc, kwargs in funcs:
              for axis in list(range(a.ndim)) + [None]:
                  a_func = func(a, axis=axis, **kwargs)
                  ai_func = argfunc(a, axis=axis, **kwargs)
                  assert_equal(a_func, take_along_axis(a, ai_func, axis=axis))
  
      def test_invalid(self):
          """ Test it errors when indices has too few dimensions """
          a = np.ones((10, 10))
          ai = np.ones((10, 2), dtype=np.intp)
  
          # sanity check
          take_along_axis(a, ai, axis=1)
  
          # not enough indices
          assert_raises(ValueError, take_along_axis, a, np.array(1), axis=1)
          # bool arrays not allowed
          assert_raises(IndexError, take_along_axis, a, ai.astype(bool), axis=1)
          # float arrays not allowed
          assert_raises(IndexError, take_along_axis, a, ai.astype(float), axis=1)
          # invalid axis
          assert_raises(np.AxisError, take_along_axis, a, ai, axis=10)
  
      def test_empty(self):
          """ Test everything is ok with empty results, even with inserted dims """
          a  = np.ones((3, 4, 5))
          ai = np.ones((3, 0, 5), dtype=np.intp)
  
          actual = take_along_axis(a, ai, axis=1)
          assert_equal(actual.shape, ai.shape)
  
      def test_broadcast(self):
          """ Test that non-indexing dimensions are broadcast in both directions """
          a  = np.ones((3, 4, 1))
          ai = np.ones((1, 2, 5), dtype=np.intp)
          actual = take_along_axis(a, ai, axis=1)
          assert_equal(actual.shape, (3, 2, 5))
  
  
  class TestPutAlongAxis:
      def test_replace_max(self):
          a_base = np.array([[10, 30, 20], [60, 40, 50]])
  
          for axis in list(range(a_base.ndim)) + [None]:
              # we mutate this in the loop
              a = a_base.copy()
  
              # replace the max with a small value
              i_max = _add_keepdims(np.argmax)(a, axis=axis)
              put_along_axis(a, i_max, -99, axis=axis)
  
              # find the new minimum, which should max
              i_min = _add_keepdims(np.argmin)(a, axis=axis)
  
              assert_equal(i_min, i_max)
  
      def test_broadcast(self):
          """ Test that non-indexing dimensions are broadcast in both directions """
          a  = np.ones((3, 4, 1))
          ai = np.arange(10, dtype=np.intp).reshape((1, 2, 5)) % 4
          put_along_axis(a, ai, 20, axis=1)
          assert_equal(take_along_axis(a, ai, axis=1), 20)
  
  
  class TestApplyAlongAxis:
      def test_simple(self):
          a = np.ones((20, 10), 'd')
          assert_array_equal(
              apply_along_axis(len, 0, a), len(a)*np.ones(a.shape[1]))
  
      def test_simple101(self):
          a = np.ones((10, 101), 'd')
          assert_array_equal(
              apply_along_axis(len, 0, a), len(a)*np.ones(a.shape[1]))
  
      def test_3d(self):
          a = np.arange(27).reshape((3, 3, 3))
          assert_array_equal(apply_along_axis(np.sum, 0, a),
                             [[27, 30, 33], [36, 39, 42], [45, 48, 51]])
  
      def test_preserve_subclass(self):
          def double(row):
              return row * 2
  
          class MyNDArray(np.ndarray):
              pass
  
          m = np.array([[0, 1], [2, 3]]).view(MyNDArray)
          expected = np.array([[0, 2], [4, 6]]).view(MyNDArray)
  
          result = apply_along_axis(double, 0, m)
          assert_(isinstance(result, MyNDArray))
          assert_array_equal(result, expected)
  
          result = apply_along_axis(double, 1, m)
          assert_(isinstance(result, MyNDArray))
          assert_array_equal(result, expected)
  
      def test_subclass(self):
          class MinimalSubclass(np.ndarray):
              data = 1
  
          def minimal_function(array):
              return array.data
  
          a = np.zeros((6, 3)).view(MinimalSubclass)
  
          assert_array_equal(
              apply_along_axis(minimal_function, 0, a), np.array([1, 1, 1])
          )
  
      def test_scalar_array(self, cls=np.ndarray):
          a = np.ones((6, 3)).view(cls)
          res = apply_along_axis(np.sum, 0, a)
          assert_(isinstance(res, cls))
          assert_array_equal(res, np.array([6, 6, 6]).view(cls))
  
      def test_0d_array(self, cls=np.ndarray):
          def sum_to_0d(x):
              """ Sum x, returning a 0d array of the same class """
              assert_equal(x.ndim, 1)
              return np.squeeze(np.sum(x, keepdims=True))
          a = np.ones((6, 3)).view(cls)
          res = apply_along_axis(sum_to_0d, 0, a)
          assert_(isinstance(res, cls))
          assert_array_equal(res, np.array([6, 6, 6]).view(cls))
  
          res = apply_along_axis(sum_to_0d, 1, a)
          assert_(isinstance(res, cls))
          assert_array_equal(res, np.array([3, 3, 3, 3, 3, 3]).view(cls))
  
      def test_axis_insertion(self, cls=np.ndarray):
          def f1to2(x):
              """produces an asymmetric non-square matrix from x"""
              assert_equal(x.ndim, 1)
              return (x[::-1] * x[1:,None]).view(cls)
  
          a2d = np.arange(6*3).reshape((6, 3))
  
          # 2d insertion along first axis
          actual = apply_along_axis(f1to2, 0, a2d)
          expected = np.stack([
              f1to2(a2d[:,i]) for i in range(a2d.shape[1])
          ], axis=-1).view(cls)
          assert_equal(type(actual), type(expected))
          assert_equal(actual, expected)
  
          # 2d insertion along last axis
          actual = apply_along_axis(f1to2, 1, a2d)
          expected = np.stack([
              f1to2(a2d[i,:]) for i in range(a2d.shape[0])
          ], axis=0).view(cls)
          assert_equal(type(actual), type(expected))
          assert_equal(actual, expected)
  
          # 3d insertion along middle axis
          a3d = np.arange(6*5*3).reshape((6, 5, 3))
  
          actual = apply_along_axis(f1to2, 1, a3d)
          expected = np.stack([
              np.stack([
                  f1to2(a3d[i,:,j]) for i in range(a3d.shape[0])
              ], axis=0)
              for j in range(a3d.shape[2])
          ], axis=-1).view(cls)
          assert_equal(type(actual), type(expected))
          assert_equal(actual, expected)
  
      def test_subclass_preservation(self):
          class MinimalSubclass(np.ndarray):
              pass
          self.test_scalar_array(MinimalSubclass)
          self.test_0d_array(MinimalSubclass)
          self.test_axis_insertion(MinimalSubclass)
  
      def test_axis_insertion_ma(self):
          def f1to2(x):
              """produces an asymmetric non-square matrix from x"""
              assert_equal(x.ndim, 1)
              res = x[::-1] * x[1:,None]
              return np.ma.masked_where(res%5==0, res)
          a = np.arange(6*3).reshape((6, 3))
          res = apply_along_axis(f1to2, 0, a)
          assert_(isinstance(res, np.ma.masked_array))
          assert_equal(res.ndim, 3)
          assert_array_equal(res[:,:,0].mask, f1to2(a[:,0]).mask)
          assert_array_equal(res[:,:,1].mask, f1to2(a[:,1]).mask)
          assert_array_equal(res[:,:,2].mask, f1to2(a[:,2]).mask)
  
      def test_tuple_func1d(self):
          def sample_1d(x):
              return x[1], x[0]
          res = np.apply_along_axis(sample_1d, 1, np.array([[1, 2], [3, 4]]))
          assert_array_equal(res, np.array([[2, 1], [4, 3]]))
  
      def test_empty(self):
          # can't apply_along_axis when there's no chance to call the function
          def never_call(x):
              assert_(False) # should never be reached
  
          a = np.empty((0, 0))
          assert_raises(ValueError, np.apply_along_axis, never_call, 0, a)
          assert_raises(ValueError, np.apply_along_axis, never_call, 1, a)
  
          # but it's sometimes ok with some non-zero dimensions
          def empty_to_1(x):
              assert_(len(x) == 0)
              return 1
  
          a = np.empty((10, 0))
          actual = np.apply_along_axis(empty_to_1, 1, a)
          assert_equal(actual, np.ones(10))
          assert_raises(ValueError, np.apply_along_axis, empty_to_1, 0, a)
  
      def test_with_iterable_object(self):
          # from issue 5248
          d = np.array([
              [{1, 11}, {2, 22}, {3, 33}],
              [{4, 44}, {5, 55}, {6, 66}]
          ])
          actual = np.apply_along_axis(lambda a: set.union(*a), 0, d)
          expected = np.array([{1, 11, 4, 44}, {2, 22, 5, 55}, {3, 33, 6, 66}])
  
          assert_equal(actual, expected)
  
          # issue 8642 - assert_equal doesn't detect this!
          for i in np.ndindex(actual.shape):
              assert_equal(type(actual[i]), type(expected[i]))
  
  
  class TestApplyOverAxes:
      def test_simple(self):
          a = np.arange(24).reshape(2, 3, 4)
          aoa_a = apply_over_axes(np.sum, a, [0, 2])
          assert_array_equal(aoa_a, np.array([[[60], [92], [124]]]))
  
  
  class TestExpandDims:
      def test_functionality(self):
          s = (2, 3, 4, 5)
          a = np.empty(s)
          for axis in range(-5, 4):
              b = expand_dims(a, axis)
              assert_(b.shape[axis] == 1)
              assert_(np.squeeze(b).shape == s)
  
      def test_axis_tuple(self):
          a = np.empty((3, 3, 3))
          assert np.expand_dims(a, axis=(0, 1, 2)).shape == (1, 1, 1, 3, 3, 3)
          assert np.expand_dims(a, axis=(0, -1, -2)).shape == (1, 3, 3, 3, 1, 1)
          assert np.expand_dims(a, axis=(0, 3, 5)).shape == (1, 3, 3, 1, 3, 1)
          assert np.expand_dims(a, axis=(0, -3, -5)).shape == (1, 1, 3, 1, 3, 3)
  
      def test_axis_out_of_range(self):
          s = (2, 3, 4, 5)
          a = np.empty(s)
          assert_raises(np.AxisError, expand_dims, a, -6)
          assert_raises(np.AxisError, expand_dims, a, 5)
  
          a = np.empty((3, 3, 3))
          assert_raises(np.AxisError, expand_dims, a, (0, -6))
          assert_raises(np.AxisError, expand_dims, a, (0, 5))
  
      def test_repeated_axis(self):
          a = np.empty((3, 3, 3))
          assert_raises(ValueError, expand_dims, a, axis=(1, 1))
  
      def test_subclasses(self):
          a = np.arange(10).reshape((2, 5))
          a = np.ma.array(a, mask=a%3 == 0)
  
          expanded = np.expand_dims(a, axis=1)
          assert_(isinstance(expanded, np.ma.MaskedArray))
          assert_equal(expanded.shape, (2, 1, 5))
          assert_equal(expanded.mask.shape, (2, 1, 5))
  
  
  class TestArraySplit:
      def test_integer_0_split(self):
          a = np.arange(10)
          assert_raises(ValueError, array_split, a, 0)
  
      def test_integer_split(self):
          a = np.arange(10)
          res = array_split(a, 1)
          desired = [np.arange(10)]
          compare_results(res, desired)
  
          res = array_split(a, 2)
          desired = [np.arange(5), np.arange(5, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 3)
          desired = [np.arange(4), np.arange(4, 7), np.arange(7, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 4)
          desired = [np.arange(3), np.arange(3, 6), np.arange(6, 8),
                     np.arange(8, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 5)
          desired = [np.arange(2), np.arange(2, 4), np.arange(4, 6),
                     np.arange(6, 8), np.arange(8, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 6)
          desired = [np.arange(2), np.arange(2, 4), np.arange(4, 6),
                     np.arange(6, 8), np.arange(8, 9), np.arange(9, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 7)
          desired = [np.arange(2), np.arange(2, 4), np.arange(4, 6),
                     np.arange(6, 7), np.arange(7, 8), np.arange(8, 9),
                     np.arange(9, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 8)
          desired = [np.arange(2), np.arange(2, 4), np.arange(4, 5),
                     np.arange(5, 6), np.arange(6, 7), np.arange(7, 8),
                     np.arange(8, 9), np.arange(9, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 9)
          desired = [np.arange(2), np.arange(2, 3), np.arange(3, 4),
                     np.arange(4, 5), np.arange(5, 6), np.arange(6, 7),
                     np.arange(7, 8), np.arange(8, 9), np.arange(9, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 10)
          desired = [np.arange(1), np.arange(1, 2), np.arange(2, 3),
                     np.arange(3, 4), np.arange(4, 5), np.arange(5, 6),
                     np.arange(6, 7), np.arange(7, 8), np.arange(8, 9),
                     np.arange(9, 10)]
          compare_results(res, desired)
  
          res = array_split(a, 11)
          desired = [np.arange(1), np.arange(1, 2), np.arange(2, 3),
                     np.arange(3, 4), np.arange(4, 5), np.arange(5, 6),
                     np.arange(6, 7), np.arange(7, 8), np.arange(8, 9),
                     np.arange(9, 10), np.array([])]
          compare_results(res, desired)
  
      def test_integer_split_2D_rows(self):
          a = np.array([np.arange(10), np.arange(10)])
          res = array_split(a, 3, axis=0)
          tgt = [np.array([np.arange(10)]), np.array([np.arange(10)]),
                     np.zeros((0, 10))]
          compare_results(res, tgt)
          assert_(a.dtype.type is res[-1].dtype.type)
  
          # Same thing for manual splits:
          res = array_split(a, [0, 1], axis=0)
          tgt = [np.zeros((0, 10)), np.array([np.arange(10)]),
                 np.array([np.arange(10)])]
          compare_results(res, tgt)
          assert_(a.dtype.type is res[-1].dtype.type)
  
      def test_integer_split_2D_cols(self):
          a = np.array([np.arange(10), np.arange(10)])
          res = array_split(a, 3, axis=-1)
          desired = [np.array([np.arange(4), np.arange(4)]),
                     np.array([np.arange(4, 7), np.arange(4, 7)]),
                     np.array([np.arange(7, 10), np.arange(7, 10)])]
          compare_results(res, desired)
  
      def test_integer_split_2D_default(self):
          """ This will fail if we change default axis
          """
          a = np.array([np.arange(10), np.arange(10)])
          res = array_split(a, 3)
          tgt = [np.array([np.arange(10)]), np.array([np.arange(10)]),
                     np.zeros((0, 10))]
          compare_results(res, tgt)
          assert_(a.dtype.type is res[-1].dtype.type)
          # perhaps should check higher dimensions
  
      @pytest.mark.skipif(not IS_64BIT, reason="Needs 64bit platform")
      def test_integer_split_2D_rows_greater_max_int32(self):
          a = np.broadcast_to([0], (1 << 32, 2))
          res = array_split(a, 4)
          chunk = np.broadcast_to([0], (1 << 30, 2))
          tgt = [chunk] * 4
          for i in range(len(tgt)):
              assert_equal(res[i].shape, tgt[i].shape)
  
      def test_index_split_simple(self):
          a = np.arange(10)
          indices = [1, 5, 7]
          res = array_split(a, indices, axis=-1)
          desired = [np.arange(0, 1), np.arange(1, 5), np.arange(5, 7),
                     np.arange(7, 10)]
          compare_results(res, desired)
  
      def test_index_split_low_bound(self):
          a = np.arange(10)
          indices = [0, 5, 7]
          res = array_split(a, indices, axis=-1)
          desired = [np.array([]), np.arange(0, 5), np.arange(5, 7),
                     np.arange(7, 10)]
          compare_results(res, desired)
  
      def test_index_split_high_bound(self):
          a = np.arange(10)
          indices = [0, 5, 7, 10, 12]
          res = array_split(a, indices, axis=-1)
          desired = [np.array([]), np.arange(0, 5), np.arange(5, 7),
                     np.arange(7, 10), np.array([]), np.array([])]
          compare_results(res, desired)
  
  
  class TestSplit:
      # The split function is essentially the same as array_split,
      # except that it test if splitting will result in an
      # equal split.  Only test for this case.
  
      def test_equal_split(self):
          a = np.arange(10)
          res = split(a, 2)
          desired = [np.arange(5), np.arange(5, 10)]
          compare_results(res, desired)
  
      def test_unequal_split(self):
          a = np.arange(10)
          assert_raises(ValueError, split, a, 3)
  
  
  class TestColumnStack:
      def test_non_iterable(self):
          assert_raises(TypeError, column_stack, 1)
  
      def test_1D_arrays(self):
          # example from docstring
          a = np.array((1, 2, 3))
          b = np.array((2, 3, 4))
          expected = np.array([[1, 2],
                               [2, 3],
                               [3, 4]])
          actual = np.column_stack((a, b))
          assert_equal(actual, expected)
  
      def test_2D_arrays(self):
          # same as hstack 2D docstring example
          a = np.array([[1], [2], [3]])
          b = np.array([[2], [3], [4]])
          expected = np.array([[1, 2],
                               [2, 3],
                               [3, 4]])
          actual = np.column_stack((a, b))
          assert_equal(actual, expected)
  
      def test_generator(self):
          with assert_warns(FutureWarning):
              column_stack((np.arange(3) for _ in range(2)))
  
  
  class TestDstack:
      def test_non_iterable(self):
          assert_raises(TypeError, dstack, 1)
  
      def test_0D_array(self):
          a = np.array(1)
          b = np.array(2)
          res = dstack([a, b])
          desired = np.array([[[1, 2]]])
          assert_array_equal(res, desired)
  
      def test_1D_array(self):
          a = np.array([1])
          b = np.array([2])
          res = dstack([a, b])
          desired = np.array([[[1, 2]]])
          assert_array_equal(res, desired)
  
      def test_2D_array(self):
          a = np.array([[1], [2]])
          b = np.array([[1], [2]])
          res = dstack([a, b])
          desired = np.array([[[1, 1]], [[2, 2, ]]])
          assert_array_equal(res, desired)
  
      def test_2D_array2(self):
          a = np.array([1, 2])
          b = np.array([1, 2])
          res = dstack([a, b])
          desired = np.array([[[1, 1], [2, 2]]])
          assert_array_equal(res, desired)
  
      def test_generator(self):
          with assert_warns(FutureWarning):
              dstack((np.arange(3) for _ in range(2)))
  
  
  # array_split has more comprehensive test of splitting.
  # only do simple test on hsplit, vsplit, and dsplit
  class TestHsplit:
      """Only testing for integer splits.
  
      """
      def test_non_iterable(self):
          assert_raises(ValueError, hsplit, 1, 1)
  
      def test_0D_array(self):
          a = np.array(1)
          try:
              hsplit(a, 2)
              assert_(0)
          except ValueError:
              pass
  
      def test_1D_array(self):
          a = np.array([1, 2, 3, 4])
          res = hsplit(a, 2)
          desired = [np.array([1, 2]), np.array([3, 4])]
          compare_results(res, desired)
  
      def test_2D_array(self):
          a = np.array([[1, 2, 3, 4],
                    [1, 2, 3, 4]])
          res = hsplit(a, 2)
          desired = [np.array([[1, 2], [1, 2]]), np.array([[3, 4], [3, 4]])]
          compare_results(res, desired)
  
  
  class TestVsplit:
      """Only testing for integer splits.
  
      """
      def test_non_iterable(self):
          assert_raises(ValueError, vsplit, 1, 1)
  
      def test_0D_array(self):
          a = np.array(1)
          assert_raises(ValueError, vsplit, a, 2)
  
      def test_1D_array(self):
          a = np.array([1, 2, 3, 4])
          try:
              vsplit(a, 2)
              assert_(0)
          except ValueError:
              pass
  
      def test_2D_array(self):
          a = np.array([[1, 2, 3, 4],
                    [1, 2, 3, 4]])
          res = vsplit(a, 2)
          desired = [np.array([[1, 2, 3, 4]]), np.array([[1, 2, 3, 4]])]
          compare_results(res, desired)
  
  
  class TestDsplit:
      # Only testing for integer splits.
      def test_non_iterable(self):
          assert_raises(ValueError, dsplit, 1, 1)
  
      def test_0D_array(self):
          a = np.array(1)
          assert_raises(ValueError, dsplit, a, 2)
  
      def test_1D_array(self):
          a = np.array([1, 2, 3, 4])
          assert_raises(ValueError, dsplit, a, 2)
  
      def test_2D_array(self):
          a = np.array([[1, 2, 3, 4],
                    [1, 2, 3, 4]])
          try:
              dsplit(a, 2)
              assert_(0)
          except ValueError:
              pass
  
      def test_3D_array(self):
          a = np.array([[[1, 2, 3, 4],
                     [1, 2, 3, 4]],
                    [[1, 2, 3, 4],
                     [1, 2, 3, 4]]])
          res = dsplit(a, 2)
          desired = [np.array([[[1, 2], [1, 2]], [[1, 2], [1, 2]]]),
                     np.array([[[3, 4], [3, 4]], [[3, 4], [3, 4]]])]
          compare_results(res, desired)
  
  
  class TestSqueeze:
      def test_basic(self):
          from numpy.random import rand
  
          a = rand(20, 10, 10, 1, 1)
          b = rand(20, 1, 10, 1, 20)
          c = rand(1, 1, 20, 10)
          assert_array_equal(np.squeeze(a), np.reshape(a, (20, 10, 10)))
          assert_array_equal(np.squeeze(b), np.reshape(b, (20, 10, 20)))
          assert_array_equal(np.squeeze(c), np.reshape(c, (20, 10)))
  
          # Squeezing to 0-dim should still give an ndarray
          a = [[[1.5]]]
          res = np.squeeze(a)
          assert_equal(res, 1.5)
          assert_equal(res.ndim, 0)
          assert_equal(type(res), np.ndarray)
  
  
  class TestKron:
      def test_return_type(self):
          class myarray(np.ndarray):
              __array_priority__ = 0.0
  
          a = np.ones([2, 2])
          ma = myarray(a.shape, a.dtype, a.data)
          assert_equal(type(kron(a, a)), np.ndarray)
          assert_equal(type(kron(ma, ma)), myarray)
          assert_equal(type(kron(a, ma)), np.ndarray)
          assert_equal(type(kron(ma, a)), myarray)
  
      def test_kron_smoke(self):
          a = np.ones([3, 3])
          b = np.ones([3, 3])
          k = np.ones([9, 9])
  
          assert np.array_equal(np.kron(a, b), k), "Smoke test for kron failed"
  
      @pytest.mark.parametrize(
          "shape_a,shape_b", [
              ((1, 1), (1, 1)),
              ((1, 2, 3), (4, 5, 6)),
              ((2, 2), (2, 2, 2)),
              ((1, 0), (1, 1)),
              ((2, 0, 2), (2, 2)),
              ((2, 0, 0, 2), (2, 0, 2)),
          ])
      def test_kron_shape(self, shape_a, shape_b):
          a = np.ones(shape_a)
          b = np.ones(shape_b)
          normalised_shape_a = (1,) * max(0, len(shape_b)-len(shape_a)) + shape_a
          normalised_shape_b = (1,) * max(0, len(shape_a)-len(shape_b)) + shape_b
          expected_shape = np.multiply(normalised_shape_a, normalised_shape_b)
  
          k = np.kron(a, b)
          assert np.array_equal(
                  k.shape, expected_shape), "Unexpected shape from kron"
  
  
  class TestTile:
      def test_basic(self):
          a = np.array([0, 1, 2])
          b = [[1, 2], [3, 4]]
          assert_equal(tile(a, 2), [0, 1, 2, 0, 1, 2])
          assert_equal(tile(a, (2, 2)), [[0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 1, 2]])
          assert_equal(tile(a, (1, 2)), [[0, 1, 2, 0, 1, 2]])
          assert_equal(tile(b, 2), [[1, 2, 1, 2], [3, 4, 3, 4]])
          assert_equal(tile(b, (2, 1)), [[1, 2], [3, 4], [1, 2], [3, 4]])
          assert_equal(tile(b, (2, 2)), [[1, 2, 1, 2], [3, 4, 3, 4],
                                         [1, 2, 1, 2], [3, 4, 3, 4]])
  
      def test_tile_one_repetition_on_array_gh4679(self):
          a = np.arange(5)
          b = tile(a, 1)
          b += 2
          assert_equal(a, np.arange(5))
  
      def test_empty(self):
          a = np.array([[[]]])
          b = np.array([[], []])
          c = tile(b, 2).shape
          d = tile(a, (3, 2, 5)).shape
          assert_equal(c, (2, 0))
          assert_equal(d, (3, 2, 0))
  
      def test_kroncompare(self):
          from numpy.random import randint
  
          reps = [(2,), (1, 2), (2, 1), (2, 2), (2, 3, 2), (3, 2)]
          shape = [(3,), (2, 3), (3, 4, 3), (3, 2, 3), (4, 3, 2, 4), (2, 2)]
          for s in shape:
              b = randint(0, 10, size=s)
              for r in reps:
                  a = np.ones(r, b.dtype)
                  large = tile(b, r)
                  klarge = kron(a, b)
                  assert_equal(large, klarge)
  
  
  class TestMayShareMemory:
      def test_basic(self):
          d = np.ones((50, 60))
          d2 = np.ones((30, 60, 6))
          assert_(np.may_share_memory(d, d))
          assert_(np.may_share_memory(d, d[::-1]))
          assert_(np.may_share_memory(d, d[::2]))
          assert_(np.may_share_memory(d, d[1:, ::-1]))
  
          assert_(not np.may_share_memory(d[::-1], d2))
          assert_(not np.may_share_memory(d[::2], d2))
          assert_(not np.may_share_memory(d[1:, ::-1], d2))
          assert_(np.may_share_memory(d2[1:, ::-1], d2))
  
  
  # Utility
  def compare_results(res, desired):
      """Compare lists of arrays."""
      if len(res) != len(desired):
          raise ValueError("Iterables have different lengths")
      # See also PEP 618 for Python 3.10
      for x, y in zip(res, desired):
          assert_array_equal(x, y)
  