text: # Copyright 2019 The TensorNetwork Authors
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #      http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import numpy as np
  from tensornetwork.block_sparse.charge import BaseCharge, fuse_charges
  import copy
  from typing import List, Union
  
  
  class Index:
    """
    An index class to store indices of a symmetric tensor.
    """
  
    def __init__(self, charges: Union[List[BaseCharge], BaseCharge],
                 flow: Union[List[bool], bool]) -> None:
      """
      Initialize an `Index` object.
      """
      if isinstance(charges, BaseCharge):
        charges = [charges]
      self._charges = charges
      if np.isscalar(flow):
        flow = [flow]
      if not all([isinstance(f, (np.bool_, np.bool, bool)) for f in flow]):
        raise TypeError("flows have to be boolean. Found flow = {}".format(flow))
      self.flow = flow
  
    def __len__(self):
      return self.dim
  
    def __repr__(self):
      return str(self.dim)
  
    @property
    def dim(self):
      return np.prod([i.dim for i in self._charges])
  
    def __eq__(self, other):
      if len(other._charges) != len(self._charges):
        return False
      for n in range(len(self._charges)):
        if not np.array_equal(self._charges[n].unique_charges,
                              other._charges[n].unique_charges):
          return False
        if not np.array_equal(self._charges[n].charge_labels,
                              other._charges[n].charge_labels):
          return False
      if not np.all(np.asarray(self.flow) == np.asarray(other.flow)):
        return False
      return True
  
    def copy(self):
      """
      Returns:
        Index: A deep copy of `Index`. Note that all children of
          `Index` are copied as well.
      """
      index_copy = Index(
          charges=[c.copy() for c in self._charges],
          flow=copy.deepcopy(self.flow))
  
      return index_copy
  
    @property
    def flat_charges(self) -> List:
      """
      Returns:
      List: A list containing the elementary indices (the leaves) 
        of `Index`.
      """
      return self._charges
  
    @property
    def flat_flows(self) -> List:
      """
      Returns:
      List: A list containing the elementary indices (the leaves) 
        of `Index`.
      """
      return list(self.flow)
  
    def flip_flow(self):
      """
      Flip the flow if `Index` in place.
      Returns:
        Index
      """
      self.flow = np.logical_not(self.flow)
      return self
  
    def __mul__(self, index: "Index") -> "Index":
      """
      Merge `index` and self into a single larger index.
      The flow of the resulting index is set to 1.
      Flows of `self` and `index` are multiplied into 
      the charges upon fusing.n
      """
      return fuse_index_pair(self, index)
  
    @property
    def charges(self):
      """
      Return the fused charges of the index. Note that
      flows are merged into the charges.
      """
      return fuse_charges(self.flat_charges, self.flat_flows)
  
  
  def fuse_index_pair(left_index: Index, right_index: Index) -> Index:
    """
    Fuse two consecutive indices (legs) of a symmetric tensor.
    Args:
      left_index: A tensor Index.
      right_index: A tensor Index.
      flow: An optional flow of the resulting `Index` object.
    Returns:
      Index: The result of fusing `index1` and `index2`.
    """
  
    return Index(
        charges=left_index.flat_charges + right_index.flat_charges,
        flow=left_index.flat_flows + right_index.flat_flows)
  
  
  def fuse_indices(indices: List[Index]) -> Index:
    """
    Fuse a list of indices (legs) of a symmetric tensor.
    Args:
      indices: A list of tensor Index objects
      flow: An optional flow of the resulting `Index` object.
    Returns:
      Index: The result of fusing `indices`.
    """
  
    index = indices[0]
    for n in range(1, len(indices)):
      index = fuse_index_pair(index, indices[n])
    return index
  