code: def _log_ndtr(a: np.ndarray) -> np.ndarray:
      return np.frompyfunc(_log_ndtr_single, 1, 1)(a).astype(float)
  
imports: import functools
  import math
  import sys
  from typing import Callable
  from typing import Optional
  from typing import Union
  import numpy
  from optuna.samplers._tpe._erf import erf
label_desc: Use image node_id 6 for calling a global function with example usage: _log_ndtr(a) and returns: np