class_docstr: Class for performing sampling in Continuous model
  using Hamiltonian Monte Carlo with dual averaging for
  adaptaion of parameter stepsize.
  
  Parameters
  ----------
  model: An instance pgmpy.models
      Model from which sampling has to be done
  
  grad_log_pdf: A subclass of pgmpy.inference.continuous.GradientLogPDF
      Class to compute the log and gradient log of distribution
  
  simulate_dynamics: A subclass of pgmpy.inference.continuous.BaseSimulateHamiltonianDynamics
      Class to propose future states of position and momentum in time by simulating
      HamiltonianDynamics
  
  delta: float (in between 0 and 1), defaults to 0.65
      The target HMC acceptance probability
  
  Example
  -------
  >>> from pgmpy.sampling import HamiltonianMCDA as HMCda, LeapFrog, GradLogPDFGaussian as GLPG
  >>> from pgmpy.factors.continuous import GaussianDistribution as JGD
  >>> import numpy as np
  >>> mean = np.array([1, 2, 3])
  >>> covariance = np.array([[2, 0.4, 0.5], [0.4, 3, 0.6], [0.5, 0.6, 4]])
  >>> model = JGD(['x', 'y', 'z'], mean, covariance)
  >>> sampler = HMCda(model=model, grad_log_pdf=GLPG)
  >>> samples = sampler.sample(np.array([0, 0, 0]), num_adapt=10000, num_samples = 10000, trajectory_length=7,
  ...                          return_type='recarray')
  >>> samples_array = np.array([samples[var_name] for var_name in model.variables])
  >>> np.cov(samples_array)
  array([[ 1.83023816,  0.40449162,  0.51200707],
         [ 0.40449162,  2.85863596,  0.76747343],
         [ 0.51200707,  0.76747343,  3.87020982]])
  >>> sampler.acceptance_rate
  0.9929
  
  References
  -----------
  Matthew D. Hoffman, Andrew Gelman, The No-U-Turn Sampler: Adaptively
  Setting Path Lengths in Hamiltonian Monte Carlo. Journal of
  Machine Learning Research 15 (2014) 1351-1381
  Algorithm 5 : Hamiltonian Monte Carlo with dual averaging
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docstr: Run tha adaptation for stepsize for better proposals of position
docstr_tok: ["Run","tha","adaptation","for","stepsize","for","better","proposals","of","position"]
code: def _adapt_params(
      self, stepsize, stepsize_bar, h_bar, mu, index_i, alpha, n_alpha=1
  ):
      """
      Run tha adaptation for stepsize for better proposals of position
      """
      gamma = 0.05  # free parameter that controls the amount of shrinkage towards mu
      t0 = 10.0  # free parameter that stabilizes the initial iterations
      kappa = 0.75
      # See equation (6) section 3.2.1 for details
  
      estimate = 1.0 / (index_i + t0)
      h_bar = (1 - estimate) * h_bar + estimate * (
          self.delta - alpha / n_alpha
      )
  
      stepsize = np.exp(mu - sqrt(index_i) / gamma * h_bar)
      i_kappa = index_i ** (-kappa)
      stepsize_bar = np.exp(
          i_kappa * np.log(stepsize)
          + (1 - i_kappa) * np.log(stepsize_bar)
      )
  
      return stepsize, stepsize_bar, h_bar
  
file_path: pgmpy/pgmpy/sampling/HMC.py
imports: from math import sqrt
  import numpy
  from tqdm.auto import tqdm
  from pgmpy.sampling import BaseGradLogPDF, BaseSimulateHamiltonianDynamics, LeapFrog, _return_samples
  from pgmpy.utils import _check_1d_array_object, _check_length_equal
label_desc: Use image node_id 2 for calling the HamiltonianMCDA obj's underlying member method code with example usage: obj._adapt_params(stepsize, stepsize_bar, h_bar, mu, index_i, alpha, n_alpha) and returns: stepsize,  stepsize_bar,  h_bar