code: def split_lhs_space_both_contract(self, mesh_dim_0, mesh_dim_1):
      # handle the case SR = SS x SR
      name = f"S{mesh_dim_0}R = S{mesh_dim_0}S{mesh_dim_1} x S{mesh_dim_1}R"
  
      # get sharding spec mapping
      dim_partition_dict_mapping = {
          "input": {0: [mesh_dim_0], -1: [mesh_dim_1]},
          "other": {0: [mesh_dim_1]},
          "bias": {},
          "output": {0: [mesh_dim_0]},
      }
  
      # linear bias only has one dimension, but addmm bias has same dimensions
      # as the output logically.
      if self.linear_projection_type == "linear":
          dim_partition_dict_mapping["bias"] = {}
      elif self.linear_projection_type == "addmm":
          dim_partition_dict_mapping["bias"] = {0: [mesh_dim_0]}
      else:
          raise ("Unsupported linear projection type")
  
      sharding_spec_mapping = self.to_sharding_spec_mapping(
          dim_partition_dict_mapping
      )
  
      # get communication action mapping
      communication_action_mapping = {}
  
      output_comm_action = self.get_communication_action(
          sharding_spec=sharding_spec_mapping["output"],
          communication_pattern=CollectiveCommPattern.ALLREDUCE_FWD_IDENTITY_BWD,
          logical_process_axis=mesh_dim_1,
          comm_type=CommType.AFTER,
      )
  
      if self.is_param("other"):
          other_comm_action = self.get_communication_action(
              sharding_spec_mapping["other"],
              communication_pattern=CollectiveCommPattern.IDENTITY_FWD_ALLREDUCE_BWD,
              logical_process_axis=mesh_dim_0,
              comm_type=CommType.HOOK,
          )
      else:
          other_comm_action = self.get_communication_action(
              sharding_spec_mapping["other"],
              communication_pattern=CollectiveCommPattern.IDENTITY_FWD_ALLREDUCE_BWD,
              logical_process_axis=mesh_dim_0,
              comm_type=CommType.BEFORE,
              arg_index=1,
          )
  
      communication_action_mapping["other"] = other_comm_action
      communication_action_mapping["output"] = output_comm_action
  
      # we only add allreduce comm action for linear bias, because
      # allreduce comm action for addmm bias will be considered in post processing
      if self.has_bias and self.linear_projection_type == "linear":
          if self.is_param("bias"):
              bias_comm_action = self.get_communication_action(
                  sharding_spec_mapping["bias"],
                  communication_pattern=CollectiveCommPattern.IDENTITY_FWD_ALLREDUCE_BWD,
                  logical_process_axis=mesh_dim_0,
                  comm_type=CommType.HOOK,
              )
          else:
              bias_comm_action = self.get_communication_action(
                  sharding_spec_mapping["bias"],
                  communication_pattern=CollectiveCommPattern.IDENTITY_FWD_ALLREDUCE_BWD,
                  logical_process_axis=mesh_dim_0,
                  comm_type=CommType.BEFORE,
                  key_for_kwarg="bias",
              )
          communication_action_mapping["bias"] = bias_comm_action
  
      return self.get_sharding_strategy(
          name=name,
          sharding_spec_mapping=sharding_spec_mapping,
          communication_action_mapping=communication_action_mapping,
      )
  
imports: import operator
  from functools import reduce
  from typing import List
  from colossalai.auto_parallel.tensor_shard.options import SolverPerference
  from colossalai.auto_parallel.tensor_shard.sharding_strategy import CommType, MemoryCost, ShardingStrategy, TrainCycleItem
  from colossalai.auto_parallel.tensor_shard.utils import ignore_sharding_exception
  from colossalai.tensor.shape_consistency import CollectiveCommPattern
  from .strategy_generator import StrategyGenerator
label_desc: Use image node_id 8 for calling the LinearProjectionStrategyGenerator obj's underlying member method code with example usage: obj.split_lhs_space_both_contract(mesh_dim_0, mesh_dim_1) and returns: self