code: def _initialize_logging_old_style(config: dict[Any, Any]) -> None:
      """
      Initialize logging using the "old-style" configuration scheme, e.g.:
          {
          'logging': {
              'distributed': 'info',
              'tornado': 'critical',
              'tornado.application': 'error',
              }
          }
      """
      loggers: dict[str, str | int] = {  # default values
          "distributed": "info",
          "distributed.client": "warning",
          "bokeh": "error",
          "tornado": "critical",
          "tornado.application": "error",
      }
      base_config = _find_logging_config(config)
      loggers.update(base_config.get("logging", {}))
  
      handler = logging.StreamHandler(sys.stderr)
      handler.setFormatter(
          logging.Formatter(
              dask.config.get(
                  "distributed.admin.log-format", config=config
              )
          )
      )
      logging_names = _logging_get_level_names_mapping()
      for name, raw_level in sorted(loggers.items()):
          level = (
              logging_names[raw_level.upper()]
              if isinstance(raw_level, str)
              else raw_level
          )
          logger = logging.getLogger(name)
          logger.setLevel(level)
  
          # Ensure that we're not registering the logger twice in this hierarchy.
          anc = logging.getLogger(None)
          already_registered = False
  
          for ancestor in name.split("."):
              if anc.handlers:
                  already_registered = True
                  break
              anc.getChild(ancestor)
  
          if not already_registered:
              logger.addHandler(handler)
              logger.propagate = False
  
file_path: distributed/distributed/config.py
imports: from __future__ import annotations
  import asyncio
  import logging.config
  import os
  import sys
  from collections.abc import Callable
  from typing import Any
  import yaml
  import dask
  from dask.utils import import_required
label_desc: Use image node_id 1 for calling a global function with example usage: _initialize_logging_old_style(config) without return types