class_docstr: Integrated Maximum Probability of Improvement acquisition function
  
  :param model: GPyOpt class of model
  :param space: GPyOpt class of domain
  :param optimizer: optimizer of the acquisition. Should be a GPyOpt optimizer
  :param cost_withGradients: function
  :param jitter: positive value to make the acquisition more explorative
  
  .. Note:: allows to compute the Improvement per unit of cost
docstr: Integrated Expected Improvement and its derivative
docstr_tok: ["Integrated","Expected","Improvement","and","its","derivative"]
code: def _compute_acq_withGradients(self, x):
      """
      Integrated Expected Improvement and its derivative
      """
      means, stds, dmdxs, dsdxs = self.model.predict_withGradients(x)
      fmins = self.model.get_fmin()
      f_acqu = None
      df_acqu = None
      for m, s, fmin, dmdx, dsdx in zip(
          means, stds, fmins, dmdxs, dsdxs
      ):
          phi, Phi, u = get_quantiles(self.jitter, fmin, m, s)
          f = Phi
          df = -(phi / s) * (dmdx + dsdx * u)
          if f_acqu is None:
              f_acqu = f
              df_acqu = df
          else:
              f_acqu += f
              df_acqu += df
      return f_acqu / (len(means)), df_acqu / (len(means))
  
imports: from .MPI import AcquisitionMPI
  from ..util.general import get_quantiles
label_desc: Use image node_id 3 for calling the AcquisitionMPI_MCMC obj's underlying member method code with example usage: obj._compute_acq_withGradients(x) and returns: unknown,  unknown