code: def norm_log_probabilities(log_probabilities, kernel, h, d):
      if kernel == "gaussian":
          factor = 0.5 * d * np.log(2 * np.pi)
      elif kernel == "tophat":
          factor = logVn(d)
      elif kernel == "epanechnikov":
          factor = logVn(d) + np.log(2.0 / (d + 2.0))
      elif kernel == "exponential":
          factor = logSn(d - 1) + math.lgamma(d)
      elif kernel == "linear":
          factor = logVn(d) - np.log(d + 1.0)
      elif kernel == "cosine":
          factor = 0.0
          tmp = 2.0 / np.pi
          for k in range(1, d + 1, 2):
              factor += tmp
              tmp *= -(d - k) * (d - k - 1) * (2.0 / np.pi) ** 2
          factor = np.log(factor) + logSn(d - 1)
      else:
          raise ValueError("Unsupported kernel.")
  
      return log_probabilities - (factor + d * np.log(h))
  
imports: from cuml.common.exceptions import NotFittedError
  from cuml.internals.import_utils import has_scipy
  from cuml.metrics import pairwise_distances
  from cuml.internals.base import Base
  from cuml.internals.input_utils import input_to_cuml_array
  from cuml.internals.input_utils import input_to_cupy_array
  from cuml.internals.safe_imports import gpu_only_import_from
  import math
  from cuml.internals.safe_imports import cpu_only_import
  from cuml.internals.safe_imports import gpu_only_import
label_desc: Use image node_id 9 for calling a global function with example usage: norm_log_probabilities(log_probabilities, kernel, h, d) and returns: unknown