code: def levinson_durbin_pacf(pacf, nlags=None):
      """
      Levinson-Durbin algorithm that returns the acf and ar coefficients.
  
      Parameters
      ----------
      pacf : array_like
          Partial autocorrelation array for lags 0, 1, ... p.
      nlags : int, optional
          Number of lags in the AR model.  If omitted, returns coefficients from
          an AR(p) and the first p autocorrelations.
  
      Returns
      -------
      arcoefs : ndarray
          AR coefficients computed from the partial autocorrelations.
      acf : ndarray
          The acf computed from the partial autocorrelations. Array returned
          contains the autocorrelations corresponding to lags 0, 1, ..., p.
  
      References
      ----------
      .. [1] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series
          and forecasting. Springer.
      """
      pacf = array_like(pacf, "pacf")
      nlags = int_like(nlags, "nlags", optional=True)
      pacf = np.squeeze(np.asarray(pacf))
  
      if pacf[0] != 1:
          raise ValueError(
              "The first entry of the pacf corresponds to lags 0 "
              "and so must be 1."
          )
      pacf = pacf[1:]
      n = pacf.shape[0]
      if nlags is not None:
          if nlags > n:
              raise ValueError(
                  "Must provide at least as many values from the "
                  "pacf as the number of lags."
              )
          pacf = pacf[:nlags]
          n = pacf.shape[0]
  
      acf = np.zeros(n + 1)
      acf[1] = pacf[0]
      nu = np.cumprod(1 - pacf**2)
      arcoefs = pacf.copy()
      for i in range(1, n):
          prev = arcoefs[: -(n - i)].copy()
          arcoefs[: -(n - i)] = prev - arcoefs[i] * prev[::-1]
          acf[i + 1] = arcoefs[i] * nu[i - 1] + prev.dot(
              acf[1 : -(n - i)][::-1]
          )
      acf[0] = 1
      return arcoefs, acf
  
imports: from __future__ import annotations
  from statsmodels.compat.numpy import lstsq
  from statsmodels.compat.pandas import deprecate_kwarg
  from statsmodels.compat.python import Literal, lzip
  from statsmodels.compat.scipy import _next_regular
  from typing import Union
  import warnings
  import numpy
  from numpy.linalg import LinAlgError
  import pandas
  from scipy import stats
  from scipy.interpolate import interp1d
  from scipy.signal import correlate
  from statsmodels.regression.linear_model import OLS, yule_walker
  from statsmodels.tools.sm_exceptions import CollinearityWarning, InfeasibleTestError, InterpolationWarning, MissingDataError, ValueWarning
  from statsmodels.tools.tools import Bunch, add_constant
  from statsmodels.tools.validation import array_like, bool_like, dict_like, float_like, int_like, string_like
  from statsmodels.tsa._bds import bds
  from statsmodels.tsa._innovations import innovations_algo, innovations_filter
  from statsmodels.tsa.adfvalues import mackinnoncrit, mackinnonp
  from statsmodels.tsa.tsatools import add_trend, lagmat, lagmat2ds
label_desc: Use image node_id 13 for calling a global function with example usage: levinson_durbin_pacf(pacf, nlags) and returns: arcoefs,  acf