code: def _powerscale_sens(
      draws, *, lower_weights=None, upper_weights=None, delta=0.01
  ):
      """
      Calculate power-scaling sensitivity by finite difference
      second derivative of CJS
      """
      lower_cjs = max(
          _cjs_dist(draws=draws, weights=lower_weights),
          _cjs_dist(draws=-1 * draws, weights=lower_weights),
      )
      upper_cjs = max(
          _cjs_dist(draws=draws, weights=upper_weights),
          _cjs_dist(draws=-1 * draws, weights=upper_weights),
      )
      logdiffsquare = 2 * np.log2(1 + delta)
      grad = (lower_cjs + upper_cjs) / logdiffsquare
  
      return grad
  
imports: import itertools
  import warnings
  from copy import deepcopy
  from typing import List, Optional, Tuple, Union, Mapping, cast, Callable
  import numpy
  import pandas
  import scipy.stats
  from xarray_einstats import stats
  import xarray
  from scipy.optimize import minimize
  from typing_extensions import Literal
  from ..None import _log
  from ..data import InferenceData, convert_to_dataset, convert_to_inference_data, extract
  from ..rcparams import rcParams, ScaleKeyword, ICKeyword
  from ..utils import Numba, _numba_var, _var_names, get_coords
  from .density_utils import get_bins
  from .density_utils import histogram
  from .density_utils import kde
  from .diagnostics import _mc_error, _multichain_statistics, ess
  from .stats_utils import ELPDData, _circular_standard_deviation, smooth_data
  from .stats_utils import get_log_likelihood
  from .stats_utils import get_log_prior
  from .stats_utils import logsumexp
  from .stats_utils import make_ufunc
  from .stats_utils import stats_variance_2d
  from .stats_utils import wrap_xarray_ufunc
  from ..sel_utils import xarray_var_iter
  from ..labels import BaseLabeller
label_desc: Use image node_id 21 for calling a global function with example usage: _powerscale_sens(draws) and returns: grad