code: def test_einsum_broadcast(self):
      # Issue #2455 change in handling ellipsis
      # remove the 'middle broadcast' error
      # only use the 'RIGHT' iteration in prepare_op_axes
      # adds auto broadcast on left where it belongs
      # broadcast on right has to be explicit
      # We need to test the optimized parsing as well
  
      A = np.arange(2 * 3 * 4).reshape(2, 3, 4)
      B = np.arange(3)
      ref = np.einsum("ijk,j->ijk", A, B, optimize=False)
      for opt in [True, False]:
          assert_equal(
              np.einsum("ij...,j...->ij...", A, B, optimize=opt), ref
          )
          assert_equal(
              np.einsum("ij...,...j->ij...", A, B, optimize=opt), ref
          )
          assert_equal(
              np.einsum("ij...,j->ij...", A, B, optimize=opt), ref
          )  # used to raise error
  
      A = np.arange(12).reshape((4, 3))
      B = np.arange(6).reshape((3, 2))
      ref = np.einsum("ik,kj->ij", A, B, optimize=False)
      for opt in [True, False]:
          assert_equal(
              np.einsum("ik...,k...->i...", A, B, optimize=opt), ref
          )
          assert_equal(
              np.einsum("ik...,...kj->i...j", A, B, optimize=opt), ref
          )
          assert_equal(
              np.einsum("...k,kj", A, B, optimize=opt), ref
          )  # used to raise error
          assert_equal(
              np.einsum("ik,k...->i...", A, B, optimize=opt), ref
          )  # used to raise error
  
      dims = [2, 3, 4, 5]
      a = np.arange(np.prod(dims)).reshape(dims)
      v = np.arange(dims[2])
      ref = np.einsum("ijkl,k->ijl", a, v, optimize=False)
      for opt in [True, False]:
          assert_equal(np.einsum("ijkl,k", a, v, optimize=opt), ref)
          assert_equal(
              np.einsum("...kl,k", a, v, optimize=opt), ref
          )  # used to raise error
          assert_equal(np.einsum("...kl,k...", a, v, optimize=opt), ref)
  
      J, K, M = 160, 160, 120
      A = np.arange(J * K * M).reshape(1, 1, 1, J, K, M)
      B = np.arange(J * K * M * 3).reshape(J, K, M, 3)
      ref = np.einsum("...lmn,...lmno->...o", A, B, optimize=False)
      for opt in [True, False]:
          assert_equal(
              np.einsum("...lmn,lmno->...o", A, B, optimize=opt), ref
          )
  
imports: import functools
  import itertools
  from unittest import expectedFailure, skipIf, SkipTest
  import torch._numpy
  from pytest import raises
  from torch._numpy.testing import assert_, assert_allclose, assert_almost_equal, assert_array_equal, assert_equal, suppress_warnings
  from torch.testing._internal.common_utils import instantiate_parametrized_tests, parametrize, run_tests, TestCase
label_desc: Use image node_id 16 for calling the TestEinsum obj's underlying member method code with example usage: obj.test_einsum_broadcast() without return types