code: def cascade(
      sch: te.Schedule,
      te_graph: TESubgraph,
      const_dict: Dict[int, np.ndarray],
      options: CascaderOptions,
      io_region: MemoryRegion,
      constant_region: MemoryRegion,
      working_regions: List[MemoryRegion],
      device_config: EthosuDeviceConfig,
  ) -> None:
      """Schedule a Tensor Expression graph using the technique of 'cascading'.
  
      'Cascading' is a technique whereby operations are split into smaller
      dependent tiles ('stripes') which can then execute in an interleaved
      fashion. This allows for operations to execute together rather than
      sequentially which can reduce intermediate memory requirements and in
      certain cases improve performance.
  
      For more detail on 'cascading' as well as how it is implemented, refer to
      the RFC here: https://github.com/apache/tvm-rfcs/pull/37.
  
      Parameters
      ----------
      sch : te.Schedule
          The Schedule to apply the cascading to.
      te_graph : TESubgraph
          The Tensor Expression graph from which the Schedule was created.
      const_dict : Dict[int, np.ndarray]
          A dictionary mapping input index to constant data if that input is
          to be a constant.
      options : CascaderOptions
          Configuration options for the cascading scheduler.
      io_region : MemoryRegion
          The MemoryRegion in which input/output tensors should reside.
      constant_region : MemoryRegion
          The MemoryRegion in which constants should reside.
      working_regions : List[MemoryRegion]
          The MemoryRegions in which intermediate working tensors can reside. The
          cascading scheduler will select which MemoryRegion to per tensor.
      device_config : EthosuDeviceConfig
          Target device configuration.
  
      """
      tvmc_options = tvm.transform.PassContext.current().config.get(
          "relay.ext.ethos-u.options", None
      )
      log = (
          Logging()
          if tvmc_options and tvmc_options.dev_cascader_logging
          else None
      )
      select_proposal_idx = (
          int(tvmc_options.dev_select_proposal_idx)
          if tvmc_options and tvmc_options.dev_select_proposal_idx
          else -1
      )
  
      if log:
          start = time.time()
  
      assert options.cascade_region in working_regions
      # First convert the Tensor Expression graph into a CascaderGraph
      casc_graph = create_cascader_graph(
          te_graph, const_dict, device_config
      )
      # Then create a mapping between Tensors and their possible memory homes
      home_map = create_home_map(
          casc_graph, io_region, constant_region, working_regions
      )
      # Generate Proposals for Pareto-optimal ways to cascade the CascaderGraph
      proposals = generate_proposals(casc_graph, home_map, options)
      # Select the best Proposal subject to the memory constraints
      proposal_choice = choose_proposal(
          proposals, options.cascade_region, select_proposal_idx
      )
  
      if log:
          for idx, proposal in enumerate(proposals):
              log.add_proposal(
                  idx, proposal.memory_usage, proposal.cycles
              )
              if proposal == proposal_choice:
                  log.selected_proposal_idx = idx
  
          log.cascader_runtime = time.time() - start
          log.dump_json()
  
      # Apply the selected Proposal to the Tensor Expression Schedule
      apply_proposal(proposal_choice, sch)
  
imports: from typing import Tuple, List, Dict, DefaultDict
  from collections import defaultdict
  import time
  import numpy
  import tvm
  from tvm import te
  from tvm import tir
  from tvm import PoolInfo
  from .cascader_options import CascaderOptions
  from .graph import CascaderGraph, Part, Tensor, TESubgraph
  from .parts import EthosuPart
  from .tensor_config import MemoryRegion
  from .proposal import Proposal
  from .proposal_generator import generate_proposals
  from .plan_generator import get_copy_cycles_hint
  from .graph import create_cascader_graph
  from .device_config import EthosuDeviceConfig
  from .logging import Logging
label_desc: Use image node_id 9 for calling a global function with example usage: cascade(sch, te_graph, const_dict, options, io_region, constant_region, working_regions, device_config) without return types