code: def minimize(
      target_func,
      initial_parameters,
      reference_parameters,
      step_func,
      max_step=2,
      verbose=False,
      all_values=None,
  ):
      """Find a dict of parameters that minimizes the target function using
      the initial dict of parameters and a step function that progresses
      a specified parameter in a dict of parameters.
  
      Parameters
      ----------
      target_func (callable): a functional with the signature
        ``target_func(parameters: dict) -> float``
      initial_parameters (dict): a set of parameters used as an initial
        value to the minimization process.
      reference_parameters (dict): a set of parameters used as an
        reference value with respect to which the speed up is computed.
      step_func (callable): a functional with the signature
        ``step_func(parameter_name:str, parameter_value:int, direction:int, parameters:dict) -> int``
        that increments or decrements (when ``direction`` is positive or
        negative, respectively) the parameter with given name and value.
        When return value is equal to ``parameter_value``, it means that
        no step along the given direction can be made.
  
      Returns
      -------
      parameters (dict): a set of parameters that minimizes the target
        function.
      speedup_incr (float): a speedup change given in percentage.
      timing (float): the value of the target function at the parameters.
      sensitivity_message (str): a message containing sensitivity.
        information of parameters around the target function minimizer.
      """
  
      def to_key(parameters):
          return tuple(parameters[k] for k in sorted(parameters))
  
      def from_key(key, parameters):
          return dict(zip(sorted(parameters), key))
  
      if all_values is None:
          all_values = dict()
  
      directions = list(range(-max_step, max_step + 1))
      names = sorted(initial_parameters)
      all_directions = []
      for d_tuple in itertools.product(*((directions,) * len(names))):
          dist = sum(map(abs, d_tuple))
          if dist > 0 and dist <= max_step:
              all_directions.append((dist, d_tuple))
      all_directions.sort()
  
      try:
          reference_target = target_func(reference_parameters)
      except Exception as msg:
          if verbose and "out of resource" not in str(msg):
              print(f"{reference_parameters=} lead to failure: {msg}.")
          reference_target = None
      if reference_target is not None:
          all_values[to_key(reference_parameters)] = reference_target
  
      parameters = initial_parameters
      try:
          initial_target = target_func(parameters)
      except Exception as msg:
          if reference_target is None:
              if verbose:
                  print(
                      f"{initial_parameters=} lead to failure: {msg}. Optimization failed!"
                  )
              return {}, -1, -1, f"{msg}"
          if verbose and "out of resource" not in str(msg):
              print(
                  f"{initial_parameters=} lead to failure: {msg}. Using reference parameters instead of initial parameters."
              )
          parameters = reference_parameters
          initial_target = reference_target
  
      if reference_target is None:
          if verbose:
              print(
                  "Using initial parameters instead of reference parameters."
              )
          reference_target = initial_target
  
      initial_key = to_key(parameters)
      minimal_target = all_values[initial_key] = initial_target
      pbar = tqdm(
          total=len(all_directions),
          desc="Tuning...",
          disable=not verbose,
          ncols=75,
      )
      while True:
          for i, (_, d_tuple) in enumerate(all_directions):
              pbar.update(1)
              next_parameters = parameters.copy()
              for name, direction in zip(names, d_tuple):
                  value = next_parameters[name]
                  if direction == 0:
                      continue
                  next_value = step_func(
                      name, value, direction, parameters
                  )
                  if next_value == value:
                      break
                  next_parameters[name] = next_value
              else:
                  next_key = to_key(next_parameters)
                  if next_key in all_values:
                      continue
                  try:
                      next_target = target_func(next_parameters)
                  except Exception as msg:
                      all_values[next_key] = str(msg)
                      if verbose and "out of resource" not in str(msg):
                          print(
                              f"{next_parameters=} lead to failure: {msg}. Skipping."
                          )
                      continue
                  all_values[next_key] = next_target
  
                  if next_target < minimal_target:
                      minimal_target = next_target
                      parameters = next_parameters
                      pbar.total += i + 1
                      break
          else:
              # ensure stable minimizer:
              minimizer_keys = {
                  k
                  for k, v in all_values.items()
                  if isinstance(v, float)
                  and abs(1 - v / minimal_target) < 0.001
              }
              minimizer_key = (
                  initial_key
                  if initial_key in minimizer_keys
                  else min(minimizer_keys)
              )
              minimizer_target = all_values[minimizer_key]
              parameters = from_key(minimizer_key, parameters)
              speedup_incr = (
                  1 - minimal_target / reference_target
              ) * 100
              if speedup_incr < 0:
                  if verbose:
                      print(
                          f"{speedup_incr=} is negative. Rerunning minimize with reference parameters as initial parameters."
                      )
                  return minimize(
                      target_func,
                      reference_parameters,
                      reference_parameters,
                      step_func,
                      max_step=max_step,
                      verbose=verbose,
                      all_values=all_values,
                  )
              sensitivity = []
              for name in parameters:
                  value = parameters[name]
                  rel_diffs = []
                  for direction in range(-max_step, max_step + 1):
                      if direction == 0:
                          continue
                      next_value = step_func(
                          name, value, direction, parameters
                      )
                      if next_value == value:
                          rel_diffs.append(0)
                          continue
                      next_parameters = parameters.copy()
                      next_parameters[name] = next_value
                      next_key = to_key(next_parameters)
                      next_target = all_values.get(next_key)
                      if next_target is None or isinstance(
                          next_target, str
                      ):
                          rel_diffs.append(0)
                          continue
                      rel_diff = (
                          next_target / minimal_target - 1
                      ) * 100
                      rel_diffs.append(rel_diff)
                  sensitivity.append((max(rel_diffs), rel_diffs, name))
  
              sensitivity_message = [f"timing0={initial_target:.3f}"]
              for _, rel_diffs, name in sorted(
                  sensitivity, reverse=True
              ):
                  left_diffs = "|".join(
                      [
                          f"{rel_diff:.1f}"
                          for rel_diff in rel_diffs[:max_step]
                      ]
                  )
                  right_diffs = "|".join(
                      [
                          f"{rel_diff:.1f}"
                          for rel_diff in rel_diffs[max_step:]
                      ]
                  )
                  sensitivity_message.append(
                      f"{name}={parameters[name]} ({left_diffs}...{right_diffs} %)"
                  )
              sensitivity_message = ", ".join(sensitivity_message)
              return (
                  parameters,
                  speedup_incr,
                  minimal_target,
                  sensitivity_message,
              )
  
file_path: pytorch/torch/sparse/_triton_ops_meta.py
imports: import inspect
  import itertools
  import re
  import warnings
  from typing import Any, Dict
  import torch
  from torch.hub import tqdm
  from torch.testing import make_tensor
label_desc: Use image node_id 4 for calling a global function with example usage: minimize(target_func, initial_parameters, reference_parameters, step_func, max_step, verbose, all_values) and returns: tuple, dict, parameters,  speedup_incr,  minimal_target,  sensitivity_message, dict,  unknown,  unknown,  msg, minimize