class_docstr: Augmented Hartmann6 function (7-dimensional with 1 global minimum).
code: def _f(self, X: np.ndarray) -> float:
      y = 0.0
      alpha_0 = self._alpha[0] - 0.1 * (1 - X[-1])
      for j, alpha_j in enumerate(self._alpha):
          t = 0
          for k in range(6):
              t += self._A[j, k] * ((X[k] - self._P[j, k]) ** 2)
          if j == 0:
              y -= alpha_0 * np.exp(-t)
          else:
              y -= alpha_j * np.exp(-t)
      return float(y)
  
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 1 for calling the Aug_Hartmann6 obj's underlying member method code with example usage: obj._f(X) and returns: float