code: def ref_periodic_kernel(
      X: AnyNDArray,
      base_name: str,
      lengthscales: AnyNDArray,
      signal_variance: AnyNDArray,
      period: AnyNDArray,
  ) -> AnyNDArray:
      """
      Calculates K(X) for the periodic kernel based on various base kernels.
      """
      sine_arg = np.pi * (X[:, None, :] - X[None, :, :]) / period
      sine_base = np.sin(sine_arg) / lengthscales
      exp_dist: AnyNDArray
      if base_name in {"RBF", "SquaredExponential"}:
          dist = 0.5 * np.sum(np.square(sine_base), axis=-1)
          exp_dist = np.exp(-dist)
      elif base_name == "Matern12":
          dist = np.sum(np.abs(sine_base), axis=-1)
          exp_dist = np.exp(-dist)
      elif base_name == "Matern32":
          dist = np.sqrt(3) * np.sum(np.abs(sine_base), axis=-1)
          exp_dist = (1 + dist) * np.exp(-dist)
      elif base_name == "Matern52":
          dist = np.sqrt(5) * np.sum(np.abs(sine_base), axis=-1)
          exp_dist = (1 + dist + dist**2 / 3) * np.exp(-dist)
      return signal_variance * exp_dist
  
imports: import numpy
  from check_shapes import check_shapes
  from gpflow.base import AnyNDArray
label_desc: Use image node_id 3 for calling a global function with example usage: ref_periodic_kernel(X, base_name, lengthscales, signal_variance, period) and returns: unknown