code: def gmm1_lpdf(_args, samples, weights, mus, sigmas, clip=None):
      """
      Gaussian Mixture Model 1D's log probability distribution function.
      """
      eps = 1e-12
  
      if clip:
          normal_cdf_low = (
              erf(
                  (clip[0] - mus) / np.maximum(np.sqrt(2) * sigmas, eps)
              )
              * 0.5
              + 0.5
          )
          normal_cdf_high = (
              erf(
                  (clip[1] - mus) / np.maximum(np.sqrt(2) * sigmas, eps)
              )
              * 0.5
              + 0.5
          )
          p_accept = np.sum(
              weights * (normal_cdf_high - normal_cdf_low)
          )
      else:
          p_accept = 1
  
      # normal lpdf
      dist = samples.reshape(-1, 1) - mus
      mahal = (dist / np.maximum(sigmas, eps)) ** 2
      z = np.sqrt(2 * np.pi) * sigmas
      coef = weights / z / p_accept
      normal_lpdf = -0.5 * mahal + np.log(coef)
  
      # log sum rows
      m = normal_lpdf.max(axis=1)
      e = np.exp(normal_lpdf - m.reshape(-1, 1))
      return np.log(e.sum(axis=1)) + m
  
imports: from __future__ import annotations
  from collections import defaultdict
  import logging
  import math
  from typing import Any, NamedTuple
  import numpy
  from scipy.special import erf
  from typing_extensions import Literal
  import nni
  from nni.common.hpo_utils import Deduplicator, OptimizeMode, format_search_space, deformat_parameters, format_parameters
  from nni.tuner import Tuner
  from nni.utils import extract_scalar_reward
  from .None import random_tuner
label_desc: Use image node_id 10 for calling a global function with example usage: gmm1_lpdf(_args, samples, weights, mus, sigmas, clip) and returns: unknown