text: import unittest
  
  import numpy
  
  import chainer
  from chainer import cuda
  from chainer import gradient_check
  from chainer import testing
  from chainer.testing import attr
  from chainer.testing import condition
  
  import einsum
  
  
  @testing.parameterize(*testing.product_dict(
      [
          # 1 array
          {'subs': 'ij->j',
           'operands_shapes': ((2, 3),),
           'y_shape': (3,)},
          {'subs': 'ij->',
           'operands_shapes': ((2, 3),),
           'y_shape': ()},
          {'subs': 'ij->ij',
           'operands_shapes': ((2, 3),),
           'y_shape': (2, 3)},
          {'subs': 'ij->ji',
           'operands_shapes': ((2, 3),),
           'y_shape': (3, 2)},
          # TODO: failed cases
          # {'subs': 'ij',
          #  'operands_shapes': ((2, 3),),
          #  'y_shape': (2, 3)},
          # {'subs': 'ii',
          #  'operands_shapes': ((3, 3),),
          #  'y_shape': ()},
  
          # 2 arrays
          {'subs': 'ijk,ijk->ijk', 'operands_shapes': ((2, 3, 4), (2, 3, 4)),
           'y_shape': (2, 3, 4)},
          {'subs': 'ijk,ijk', 'operands_shapes': ((2, 3, 4), (2, 3, 4)),
           'y_shape': ()},
          {'subs': 'ijk,ijk->ij', 'operands_shapes': ((2, 3, 4), (2, 3, 4)),
           'y_shape': (2, 3)},
          {'subs': 'ijk,jk->ik', 'operands_shapes': ((2, 3, 4), (3, 4)),
           'y_shape': (2, 4)},
          {'subs': 'bij,ij->bi', 'operands_shapes': ((5, 2, 4), (2, 4)),
           'y_shape': (5, 2)},
          {'subs': 'bij,ij->ij', 'operands_shapes': ((5, 2, 3), (2, 3)),
           'y_shape': (2, 3)},
          {'subs': 'bijk,ijk->', 'operands_shapes': ((5, 2, 3, 4), (2, 3, 4)),
           'y_shape': ()},
          {'subs': 'bijk,ijk', 'operands_shapes': ((5, 2, 3, 4), (2, 3, 4)),
           'y_shape': (5,)},
          {'subs': 'bij,ijk->bi', 'operands_shapes': ((5, 2, 3), (2, 3, 6)),
           'y_shape': (5, 2)},
          {'subs': 'bij,ijk->ij', 'operands_shapes': ((5, 2, 3), (2, 3, 6)),
           'y_shape': (2, 3)},
          {'subs': 'bij,ijk->bik', 'operands_shapes': ((5, 2, 3), (2, 3, 6)),
           'y_shape': (5, 2, 6)},
          {'subs': 'bi,ik->kb', 'operands_shapes': ((5, 2), (2, 6)),
           'y_shape': (6, 5)},
          {'subs': 'bij,ijk->jk', 'operands_shapes': ((5, 2, 3), (2, 3, 6)),
           'y_shape': (3, 6)},
          {'subs': 'ij,ij->ij', 'operands_shapes': ((2, 3), (2, 3)),
           'y_shape': (2, 3)},
          {'subs': 'ij,kl->ijkl', 'operands_shapes': ((2, 3), (4, 5)),
           'y_shape': (2, 3, 4, 5)},
          {'subs': 'ij,kl->kilj', 'operands_shapes': ((2, 3), (4, 5)),
           'y_shape': (4, 2, 5, 3)},
          # TODO: failed cases
          # cupy.einsum tries to make a huge array internally and fails
          # {'subs': 'biu,ijvu->bjiv',
          # 'operands_shapes': ((125, 1152, 8), (1152, 10, 16, 8)),
          # 'y_shape': (125, 10, 1152, 16)},
  
  
          # 3 arrays
          {'subs': 'ij,jk,kl->il',
           'operands_shapes': ((2, 3), (3, 4), (4, 5)),
           'y_shape': (2, 5)},
          {'subs': 'ij,jk,kl->i',
           'operands_shapes': ((2, 3), (3, 4), (4, 5)),
           'y_shape': (2)},
          {'subs': 'bijk,ijk,jkl->bl',
           'operands_shapes': ((5, 2, 3, 4), (2, 3, 4), (3, 4, 6)),
           'y_shape': (5, 6)},
          {'subs': 'bijk,ijk,jkl->j',
           'operands_shapes': ((5, 2, 3, 4), (2, 3, 4), (3, 4, 6)),
           'y_shape': (3,)},
          {'subs': 'bijk,ijk,jkl->b',
           'operands_shapes': ((5, 2, 3, 4), (2, 3, 4), (3, 4, 6)),
           'y_shape': (5,)},
          {'subs': 'bijk,ijk,jkl->',
           'operands_shapes': ((5, 2, 3, 4), (2, 3, 4), (3, 4, 6)),
           'y_shape': ()},
  
          # subscripts with white spaces
          {'subs': ' ij , ij -> ij ', 'operands_shapes': ((2, 3), (2, 3)),
           'y_shape': (2, 3)},
      ],
      [
  #        {'dtype': numpy.float16},  # TODO: fix np.einsum for float16
          {'dtype': numpy.float32},
          {'dtype': numpy.float64},
      ],
  ))
  class TestEinsum(unittest.TestCase):
      def setUp(self):
          self.operands = []
          for shape in self.operands_shapes:
              operand = numpy.random.uniform(-1, 1, shape).astype(self.dtype)
              self.operands.append(operand)
          self.gy = numpy.random.uniform(-1, 1, self.y_shape).astype(self.dtype)
  
          if self.dtype == numpy.float16:
              self.check_forward_options = {'atol': 2e-3}
              self.check_backward_options = {'atol': 2e-3}
          else:
              self.check_forward_options = {}
              self.check_backward_options = {}
  
      def check_forward(self, subscripts, operands_data):
          xp = cuda.get_array_module(*operands_data)
          operands = [
              chainer.Variable(operand_data) for operand_data in operands_data]
          y = einsum.einsum(subscripts, *operands)
          self.assertEqual(y.data.dtype, self.dtype)
          y_expect = xp.asarray(numpy.einsum(self.subs, *self.operands))
          testing.assert_allclose(y_expect, y.data,
                                  **self.check_forward_options)
  
      @condition.retry(3)
      def test_forward_cpu(self):
          self.check_forward(self.subs, self.operands)
  
      @attr.gpu
      @condition.retry(3)
      def test_forward_gpu(self):
          operands = [cuda.to_gpu(operand) for operand in self.operands]
          self.check_forward(self.subs, operands)
  
      def check_backward(self,  subscripts, operands_data, y_grad):
          print(subscripts)
          gradient_check.check_backward(
              lambda *operands_: einsum.einsum(subscripts, *operands_),
              operands_data, y_grad,
              dtype=numpy.float64, **self.check_backward_options)
  
      @condition.retry(3)
      def test_backward_cpu(self):
          self.check_backward(self.subs, self.operands, self.gy)
  
      @attr.gpu
      @condition.retry(3)
      def test_backward_gpu(self):
          operands = [cuda.to_gpu(operand) for operand in self.operands]
          self.check_backward(self.subs, operands, cuda.to_gpu(self.gy))
  
  
  @testing.parameterize(*testing.product_dict(
      [
          {'sub': 'ijk,ijk', 'in_subs': ['ijk', 'ijk'], 'out_sub': '',
           'broadcast_subs': ['', '']},
          {'sub': 'ijk,ijk->ij', 'in_subs': ['ijk', 'ijk'], 'out_sub': 'ij',
           'broadcast_subs': ['', '']},
          {'sub': 'bijk,ijk->bi', 'in_subs': ['bijk', 'ijk'], 'out_sub': 'bi',
           'broadcast_subs': ['', '']},
          {'sub': 'bij,ij->', 'in_subs': ['bij', 'ij'], 'out_sub': '',
           'broadcast_subs': ['b', '']},
          {'sub': 'bij,ij', 'in_subs': ['bij', 'ij'], 'out_sub': 'b',
           'broadcast_subs': ['', '']},
          {'sub': ' bijk , ijk -> bi ',
           'in_subs': ['bijk', 'ijk'], 'out_sub': 'bi',
           'broadcast_subs': ['', '']},
      ]
  ))
  class TestParseSubscripts(unittest.TestCase):
  
      def check_parse_subscripts(
              self, subscripts, expected_in_subs, expected_out_sub,
              expected_broadcast_subs):
          in_subs, out_sub, broadcast_subs = einsum._parse_subscripts(subscripts)
          self.assertEqual(out_sub, expected_out_sub)
          for in_sub, expected_in_sub in zip(in_subs, expected_in_subs):
              assert in_sub == expected_in_sub, '''
      actual  : {}
      expected: {}'''.format(in_sub, expected_in_sub)
          assert out_sub == expected_out_sub, '''
      actual  : {}
      expected: {}'''.format(out_sub, expected_out_sub)
          for broadcast_sub, expected_broadcast_sub in zip(
                  broadcast_subs, expected_broadcast_subs):
              assert broadcast_sub == expected_broadcast_sub, '''
      actual  : {}
      expected: {}'''.format(broadcast_sub, expected_broadcast_sub)
  
      def test_parse_subscripts(self):
          self.check_parse_subscripts(self.sub, self.in_subs, self.out_sub,
                                      self.broadcast_subs)
  
  
  testing.run_module(__name__, __file__)
  