text: """Define some functions to sort substructures of parameter by importance.
  """
  # Copyright (c) 2020  PaddlePaddle Authors. All Rights Reserved.
  #
  # 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.
  
  import logging
  import numpy as np
  from ..core import GraphWrapper
  from ..common import get_logger
  from ..core import Registry
  
  __all__ = ["IDX_SELECTOR"]
  
  IDX_SELECTOR = Registry('idx_selector')
  
  
  @IDX_SELECTOR.register
  def default_idx_selector(group, ratio):
      """Get the pruned indexes by given ratio.
  
      This function return a list of parameters' pruned indexes on given axis.
      Each element of list is a tuple with format (name, axis, indexes) in which 'name' is parameter's name
      and 'axis' is the axis pruning on and `indexes` is indexes to be pruned.
  
      Args:
         group(list): A group of parameters. The first parameter of the group is convolution layer's weight
                      while the others are parameters affected by pruning the first one. Each parameter in group
                      is represented as tuple '(name, axis, score)' in which `name` is the parameter's name and
                      `axis` is the axis pruning on and `score` is a np.array storing the importance of strucure
                      on `axis`. Show as below:
  
                      .. code-block: text
  
                         [("conv1_weights", 0, [0.7, 0.5, 0.6]), ("conv1_bn.scale", 0, [0.1, 0.2, 0.4])]
  
                      The shape of "conv1_weights" is `[out_channel, in_channel, filter_size, filter_size]`, so
                      `[0.7, 0.5, 0.6]` are the importance sores of each output channel in "conv1_weights"
                      while axis is 0.
       
      Returns:
  
         list: pruned indexes
  
      """
      name, axis, score, _ = group[
          0]  # sort channels by the first convolution's score
      sorted_idx = score.argsort()
  
      pruned_num = int(round(len(sorted_idx) * ratio))
      pruned_idx = sorted_idx[:pruned_num]
      idxs = []
      for name, axis, score, transforms in group:
          idxs.append((name, axis, pruned_idx, transforms))
      return idxs
  
  
  @IDX_SELECTOR.register
  def optimal_threshold(group, ratio):
      """Get the pruned indexes by given ratio.
  
      This function return a list of parameters' pruned indexes on given axis.
      Each element of list is a tuple with format (name, axis, indexes) in which 'name' is parameter's name
      and 'axis' is the axis pruning on and `indexes` is indexes to be pruned.
  
      Args:
         group(list): A group of parameters. The first parameter of the group is convolution layer's weight
                      while the others are parameters affected by pruning the first one. Each parameter in group
                      is represented as tuple '(name, axis, score)' in which `name` is the parameter's name and
                      `axis` is the axis pruning on and `score` is a np.array storing the importance of strucure
                      on `axis`. Show as below:
  
                      .. code-block: text
  
                         [("conv1_weights", 0, [0.7, 0.5, 0.6]), ("conv1_bn.scale", 0, [0.1, 0.2, 0.4])]
  
                      The shape of "conv1_weights" is `[out_channel, in_channel, filter_size, filter_size]`, so
                      `[0.7, 0.5, 0.6]` are the importance sores of each output channel in "conv1_weights"
                      while axis is 0.
       
      Returns:
  
         list: pruned indexes
  
      """
      name, axis, score, _ = group[
          0]  # sort channels by the first convolution's score
  
      score[score < 1e-18] = 1e-18
      score_sorted = np.sort(score)
      score_square = score_sorted**2
      total_sum = score_square.sum()
      acc_sum = 0
      for i in range(score_square.size):
          acc_sum += score_square[i]
          if acc_sum / total_sum > ratio:
              break
      th = (score_sorted[i - 1] + score_sorted[i]) / 2 if i > 0 else 0
  
      pruned_idx = np.squeeze(np.argwhere(score < th))
  
      idxs = []
      for name, axis, score, transforms in group:
          idxs.append((name, axis, pruned_idx, transforms))
      return idxs
  