docstr: Synthetic function implementation.
  
  Args:
      X (numpy.ndarray): an n by d array, where n represents the number
          of observations and d is the dimensionality of the inputs.
  
  Returns:
      numpy.ndarray: an n-dimensional array.
code: def f(self, X: np.ndarray) -> Union[float, np.ndarray]:
      """Synthetic function implementation.
  
      Args:
          X (numpy.ndarray): an n by d array, where n represents the number
              of observations and d is the dimensionality of the inputs.
  
      Returns:
          numpy.ndarray: an n-dimensional array.
      """
      assert isinstance(X, np.ndarray), "X must be a numpy (nd)array."
      if self.required_dimensionality:
          if len(X.shape) == 1:
              input_dim = X.shape[0]
          elif len(X.shape) == 2:
              input_dim = X.shape[1]
          else:
              raise ValueError(
                  "Synthetic function call expects input of either 1-d array or "
                  "n by d array, where n is number of observations and d is "
                  "dimensionality of the input."
              )
          assert input_dim == self.required_dimensionality, (
              f"Input violates required dimensionality of {self.name}: "
              f"{self.required_dimensionality}. Got {input_dim}."
          )
      X = X.astype(np.float64)
      if len(X.shape) == 1:
          return self._f(X=X)
      else:
          return np.array([self._f(X=x) for x in X])
  
imports: from abc import ABC, abstractmethod
  from typing import Any, Callable, List, Optional, Tuple, Union
  import numpy
  import torch
  from ax.utils.common.docutils import copy_doc
  from ax.utils.common.typeutils import checked_cast, not_none
  from botorch.test_functions import synthetic
label_desc: Use image node_id 3 for calling the SyntheticFunction obj's underlying member method code with example usage: obj.f(X) and returns: self, np