code: def einsum(*operands, **kwargs):
      """einsum(subscripts, *operands, dtype=None, optimize=False)
  
      Evaluates the Einstein summation convention on the operands.
      Using the Einstein summation convention, many common multi-dimensional
      array operations can be represented in a simple fashion. This function
      provides a way to compute such summations.
  
      .. note::
  
         - Memory contiguity of the returned array is not always compatible with
           that of :func:`numpy.einsum`.
         - ``out``, ``order``, and ``casting`` options are not supported.
         - If :envvar:`CUPY_ACCELERATORS` includes ``cutensornet``, the `einsum`
           calculation will be performed by the cuTensorNet backend if possible.
  
             - The support of the ``optimize`` option is limited (currently, only
               `False`, 'cutensornet', or a custom path for pairwise contraction
               is supported, and the maximum intermediate size is ignored). If
               you need finer control for path optimization, consider replacing
               :func:`cupy.einsum` by :func:`cuquantum.contract` instead.
             - Requires `cuQuantum Python`_ (v22.03+).
  
         - If :envvar:`CUPY_ACCELERATORS` includes ``cutensor``, `einsum` will be
           accelerated by the cuTENSOR backend whenever possible.
  
      Args:
          subscripts (str): Specifies the subscripts for summation.
          operands (sequence of arrays): These are the arrays for the operation.
          dtype: If provided, forces the calculation to use the data type
              specified. Default is None.
          optimize: Valid options include {`False`, `True`, 'greedy', 'optimal'}.
              Controls if intermediate optimization should occur. No optimization
              will occur if `False`, and `True` will default to the 'greedy'
              algorithm. Also accepts an explicit contraction list from
              :func:`numpy.einsum_path`. Defaults to `False`. If a pair is
              supplied, the second argument is assumed to be the maximum
              intermediate size created.
  
      Returns:
          cupy.ndarray:
              The calculation based on the Einstein summation convention.
  
      .. seealso:: :func:`numpy.einsum`
      .. _cuQuantum Python: https://docs.nvidia.com/cuda/cuquantum/python/
      """
      out = _try_use_cutensornet(*operands, **kwargs)
      if out is not None:
          return out
  
      (
          input_subscripts,
          output_subscript,
          operands,
      ) = _parse_einsum_input(operands)
      assert isinstance(input_subscripts, list)
      assert isinstance(operands, list)
  
      dtype = kwargs.pop("dtype", None)
  
      # casting = kwargs.pop('casting', 'safe')
      casting_kwargs = {}  # casting is not supported yet in astype
  
      optimize = kwargs.pop("optimize", False)
      if optimize is True:
          optimize = "greedy"
      if kwargs:
          raise TypeError(
              "Did not understand the following kwargs: %s"
              % list(kwargs.keys())
          )
  
      result_dtype = (
          cupy.result_type(*operands) if dtype is None else dtype
      )
      operands = [cupy.asanyarray(arr) for arr in operands]
  
      input_subscripts = [
          _parse_ellipsis_subscript(sub, idx, ndim=arr.ndim)
          for idx, (sub, arr) in enumerate(
              zip(input_subscripts, operands)
          )
      ]
  
      # Get length of each unique dimension and ensure all dimensions are correct
      dimension_dict = {}
      for idx, sub in enumerate(input_subscripts):
          sh = operands[idx].shape
          for axis, label in enumerate(sub):
              dim = sh[axis]
              if label in dimension_dict.keys():
                  # For broadcasting cases we always want the largest dim size
                  if dimension_dict[label] == 1:
                      dimension_dict[label] = dim
                  elif dim not in (1, dimension_dict[label]):
                      dim_old = dimension_dict[label]
                      raise ValueError(
                          "Size of label '%s' for operand %d (%d) "
                          "does not match previous terms (%d)."
                          % (_chr(label), idx, dim, dim_old)
                      )
              else:
                  dimension_dict[label] = dim
  
      if output_subscript is None:
          # Build output subscripts
          tmp_subscripts = list(
              itertools.chain.from_iterable(input_subscripts)
          )
          output_subscript = [
              label
              for label in sorted(set(tmp_subscripts))
              if label < 0 or tmp_subscripts.count(label) == 1
          ]
      else:
          if not options["sum_ellipsis"]:
              if "@" not in output_subscript and -1 in dimension_dict:
                  raise ValueError(
                      "output has more dimensions than subscripts "
                      "given in einstein sum, but no '...' ellipsis "
                      "provided to broadcast the extra dimensions."
                  )
          output_subscript = _parse_ellipsis_subscript(
              output_subscript,
              None,
              ellipsis_len=sum(
                  label < 0 for label in dimension_dict.keys()
              ),
          )
  
          # Make sure output subscripts are in the input
          tmp_subscripts = set(
              itertools.chain.from_iterable(input_subscripts)
          )
          for label in output_subscript:
              if label not in tmp_subscripts:
                  raise ValueError(
                      "einstein sum subscripts string included output subscript "
                      "'%s' which never appeared in an input"
                      % _chr(label)
                  )
          if len(output_subscript) != len(set(output_subscript)):
              for label in output_subscript:
                  if output_subscript.count(label) >= 2:
                      raise ValueError(
                          "einstein sum subscripts string includes output "
                          "subscript '%s' multiple times" % _chr(label)
                      )
  
      _einsum_diagonals(input_subscripts, operands)
  
      # no more raises
  
      if len(operands) >= 2:
          if any(arr.size == 0 for arr in operands):
              return cupy.zeros(
                  tuple(
                      dimension_dict[label]
                      for label in output_subscript
                  ),
                  dtype=result_dtype,
              )
  
          # Don't squeeze if unary, because this affects later (in trivial sum)
          # whether the return is a writeable view.
          for idx in range(len(operands)):
              arr = operands[idx]
              if 1 in arr.shape:
                  squeeze_indices = []
                  sub = []
                  for axis, label in enumerate(input_subscripts[idx]):
                      if arr.shape[axis] == 1:
                          squeeze_indices.append(axis)
                      else:
                          sub.append(label)
                  input_subscripts[idx] = sub
                  operands[idx] = cupy.squeeze(
                      arr, axis=tuple(squeeze_indices)
                  )
                  assert operands[idx].ndim == len(
                      input_subscripts[idx]
                  )
              del arr
  
      # unary einsum without summation should return a (writeable) view
      returns_view = len(operands) == 1
  
      # unary sum
      for idx, sub in enumerate(input_subscripts):
          other_subscripts = copy.copy(input_subscripts)
          other_subscripts[idx] = output_subscript
          other_subscripts = set(
              itertools.chain.from_iterable(other_subscripts)
          )
          sum_axes = tuple(
              axis
              for axis, label in enumerate(sub)
              if label not in other_subscripts
          )
          if sum_axes:
              returns_view = False
              input_subscripts[idx] = [
                  label
                  for axis, label in enumerate(sub)
                  if axis not in sum_axes
              ]
  
              operands[idx] = operands[idx].sum(
                  axis=sum_axes, dtype=result_dtype
              )
  
      if returns_view:
          operands = [a.view() for a in operands]
      else:
          operands = [
              a.astype(result_dtype, copy=False, **casting_kwargs)
              for a in operands
          ]
  
      # no more casts
  
      optimize_algorithms = {
          "greedy": _greedy_path,
          "optimal": _optimal_path,
      }
      if optimize is False:
          path = [tuple(range(len(operands)))]
      elif len(optimize) and (optimize[0] == "einsum_path"):
          path = optimize[1:]
      else:
          try:
              if len(optimize) == 2 and isinstance(
                  optimize[1], (int, float)
              ):
                  algo = optimize_algorithms[optimize[0]]
                  memory_limit = int(optimize[1])
              else:
                  algo = optimize_algorithms[optimize]
                  memory_limit = 2**31  # TODO(kataoka): fix?
          except (TypeError, KeyError):  # unhashable type or not found
              raise TypeError(
                  "Did not understand the path (optimize): %s"
                  % str(optimize)
              )
          input_sets = [set(sub) for sub in input_subscripts]
          output_set = set(output_subscript)
          path = algo(
              input_sets, output_set, dimension_dict, memory_limit
          )
          if any(len(indices) > 2 for indices in path):
              warnings.warn(
                  "memory efficient einsum is not supported yet",
                  _util.PerformanceWarning,
              )
  
      for idx0, idx1 in _iter_path_pairs(path):
          # "reduced" binary einsum
          arr0 = operands.pop(idx0)
          sub0 = input_subscripts.pop(idx0)
          arr1 = operands.pop(idx1)
          sub1 = input_subscripts.pop(idx1)
          sub_others = list(
              itertools.chain(
                  output_subscript,
                  itertools.chain.from_iterable(input_subscripts),
              )
          )
          arr_out, sub_out = reduced_binary_einsum(
              arr0, sub0, arr1, sub1, sub_others
          )
          operands.append(arr_out)
          input_subscripts.append(sub_out)
          del arr0, arr1
  
      # unary einsum at last
      (arr0,) = operands
      (sub0,) = input_subscripts
  
      transpose_axes = []
      for label in output_subscript:
          if label in sub0:
              transpose_axes.append(sub0.index(label))
  
      arr_out = arr0.transpose(transpose_axes).reshape(
          [dimension_dict[label] for label in output_subscript]
      )
      assert returns_view or arr_out.dtype == result_dtype
      return arr_out
  
imports: import copy
  import itertools
  import operator
  import string
  import warnings
  import cupy
  from cupy._core import _accelerator
  from cupy import _util
  from cupy.linalg._einsum_opt import _greedy_path
  from cupy.linalg._einsum_opt import _optimal_path
  from cupy.linalg._einsum_cutn import _try_use_cutensornet
label_desc: Use image node_id 15 for calling a global function with example usage: einsum() and returns: arr_out, out, cupy