code: import logging
  import george
  import numpy as np
  import inspect
  
  from pybnn import BaseModel
  from pybnn.dngo import DNGO
  
  from robo.priors.default_priors import DefaultPrior
  from robo.models.base_model import BaseModel as BaseModel_
  from robo.models.wrapper_bohamiann import WrapperBohamiann
  from robo.models.gaussian_process import GaussianProcess
  from robo.models.gaussian_process_mcmc import GaussianProcessMCMC
  from robo.models.random_forest import RandomForest
  from robo.maximizers.base_maximizer import BaseMaximizer
  from robo.maximizers.scipy_optimizer import SciPyOptimizer
  from robo.maximizers.random_sampling import RandomSampling
  from robo.maximizers.differential_evolution import DifferentialEvolution
  from robo.solver.bayesian_optimization import BayesianOptimization
  from robo.acquisition_functions.base_acquisition import BaseAcquisitionFunction
  from robo.acquisition_functions.ei import EI
  from robo.acquisition_functions.pi import PI
  from robo.acquisition_functions.log_ei import LogEI
  from robo.acquisition_functions.lcb import LCB
  from robo.acquisition_functions.marginalization import MarginalizationGPMCMC
  from robo.initial_design import init_latin_hypercube_sampling
  
  
  logger = logging.getLogger(__name__)
  
  
  def bayesian_optimization(objective_function, lower, upper, num_iterations=30, X_init=None, Y_init=None,
                            maximizer="random", acquisition_func="log_ei", model_type="gp_mcmc",
                            n_init=3, rng=None, output_path=None):
      """
      General interface for Bayesian optimization for global black box
      optimization problems.
  
      Parameters
      ----------
      objective_function: function
          The objective function that is minimized. This function gets a numpy
          array (D,) as input and returns the function value (scalar)
      lower: np.ndarray (D,)
          The lower bound of the search space
      upper: np.ndarray (D,)
          The upper bound of the search space
      num_iterations: int
          The number of iterations (initial design + BO)
      X_init: np.ndarray(N,D)
              Initial points to warmstart BO
      Y_init: np.ndarray(N,1)
              Function values of the already initial points
      maximizer: {"random", "scipy", "differential_evolution"}
          The optimizer for the acquisition function.
      acquisition_func: {"ei", "log_ei", "lcb", "pi"}
          The acquisition function
      model_type: {"gp", "gp_mcmc", "rf", "bohamiann", "dngo"}
          The model for the objective function.
      n_init: int
          Number of points for the initial design. Make sure that it
          is <= num_iterations.
      output_path: string
          Specifies the path where the intermediate output after each iteration will be saved.
          If None no output will be saved to disk.
      rng: numpy.random.RandomState
          Random number generator
  
      Returns
      -------
          dict with all results
      """
      assert upper.shape[0] == lower.shape[0], "Dimension miss match"
      assert np.all(lower < upper), "Lower bound >= upper bound"
      assert n_init <= num_iterations, "Number of initial design point has to be <= than the number of iterations"
  
      if rng is None:
          rng = np.random.RandomState(np.random.randint(0, 10000))
  
      cov_amp = 2
      n_dims = lower.shape[0]
  
      initial_ls = np.ones([n_dims])
      exp_kernel = george.kernels.Matern52Kernel(initial_ls,
                                                 ndim=n_dims)
      kernel = cov_amp * exp_kernel
  
      prior = DefaultPrior(len(kernel) + 1)
  
      n_hypers = 3 * len(kernel)
      if n_hypers % 2 == 1:
          n_hypers += 1
  
      if model_type == "gp":
          model = GaussianProcess(kernel, prior=prior, rng=rng,
                                  normalize_output=False, normalize_input=True,
                                  lower=lower, upper=upper)
      elif model_type == "gp_mcmc":
          model = GaussianProcessMCMC(kernel, prior=prior,
                                      n_hypers=n_hypers,
                                      chain_length=200,
                                      burnin_steps=100,
                                      normalize_input=True,
                                      normalize_output=False,
                                      rng=rng, lower=lower, upper=upper)
  
      elif model_type == "rf":
          model = RandomForest(rng=rng)
  
      elif model_type == "bohamiann":
          model = WrapperBohamiann()
  
      elif model_type == "dngo":
          model = DNGO()
  
      elif isinstance(model_type, (BaseModel, BaseModel_)):
          model = model_type
  
      elif callable(model_type):
          model = model_type()
  
      else:
          raise ValueError("'{}' is not a valid model".format(model_type))
  
      if acquisition_func == "ei":
          a = EI(model)
      elif acquisition_func == "log_ei":
          a = LogEI(model)
      elif acquisition_func == "pi":
          a = PI(model)
      elif acquisition_func == "lcb":
          a = LCB(model)
      elif isinstance(acquisition_func, BaseAcquisitionFunction):
          a = acquisition_func
      elif callable(acquisition_func):
          a = acquisition_func(model)
      else:
          raise ValueError("'{}' is not a valid acquisition function"
                           .format(acquisition_func))
  
      if model_type == "gp_mcmc":
          acquisition_func = MarginalizationGPMCMC(a)
      else:
          acquisition_func = a
  
      if maximizer == "random":
          max_func = RandomSampling(acquisition_func, lower, upper, rng=rng)
      elif maximizer == "scipy":
          max_func = SciPyOptimizer(acquisition_func, lower, upper, rng=rng)
      elif maximizer == "differential_evolution":
          max_func = DifferentialEvolution(acquisition_func, lower, upper, rng=rng)
      elif isinstance(maximizer, BaseMaximizer):
          max_func = maximizer
      elif callable(maximizer):
          max_func = maximizer(acquisition_func, lower, upper, rng=rng)
      else:
          raise ValueError("'{}' is not a valid function to maximize the "
                           "acquisition function".format(maximizer))
  
      bo = BayesianOptimization(objective_function, lower, upper,
                                acquisition_func, model, max_func,
                                initial_points=n_init, rng=rng,
                                initial_design=init_latin_hypercube_sampling,
                                output_path=output_path)
  
      x_best, f_min = bo.run(num_iterations, X=X_init, y=Y_init)
  
      results = dict()
      results["x_opt"] = x_best
      results["f_opt"] = f_min
      results["incumbents"] = [inc for inc in bo.incumbents]
      results["incumbent_values"] = [val for val in bo.incumbents_values]
      results["runtime"] = bo.runtime
      results["overhead"] = bo.time_overhead
      results["X"] = [x.tolist() for x in bo.X]
      results["y"] = [y for y in bo.y]
      return results
   import sys
  import numpy as np
  import scipy as sp
  
  from robo.maximizers.base_maximizer import BaseMaximizer
  
  
  class DifferentialEvolution(BaseMaximizer):
  
      def __init__(self, objective_function, lower, upper, n_iters=20, rng=None):
          """
  
          Parameters
          ----------
          objective_function: acquisition function
              The acquisition function which will be maximized
          lower: np.ndarray (D)
              Lower bounds of the input space
          upper: np.ndarray (D)
              Upper bounds of the input space
          n_iters: int
              Number of iterations
          """
          self.n_iters = n_iters
          super(DifferentialEvolution, self).__init__(objective_function, lower, upper, rng)
  
      def _acquisition_fkt_wrapper(self, acq_f):
          def _l(x):
              a = -acq_f(np.array([np.clip(x, self.lower, self.upper)]))
              if np.any(np.isinf(a)):
                  return sys.float_info.max
              return a
  
          return _l
  
      def maximize(self):
          """
          Maximizes the given acquisition function.
  
          Returns
          -------
          np.ndarray(N,D)
              Point with highest acquisition value.
          """
  
          bounds = list(zip(self.lower, self.upper))
  
          res = sp.optimize.differential_evolution(self._acquisition_fkt_wrapper(self.objective_func),
                                                   bounds, maxiter=self.n_iters)
  
          return np.clip(res["x"], self.lower, self.upper)
  
apis: numpy.ones numpy.all numpy.random.randint
apis: numpy.isinf numpy.clip