code: def prepare_trend_spec(trend):
      # Trend
      if trend is None or trend == "n":
          polynomial_trend = np.ones(0)
      elif trend == "c":
          polynomial_trend = np.r_[1]
      elif trend == "t":
          polynomial_trend = np.r_[0, 1]
      elif trend == "ct":
          polynomial_trend = np.r_[1, 1]
      elif trend == "ctt":
          # TODO deprecate ctt?
          polynomial_trend = np.r_[1, 1, 1]
      else:
          trend = np.array(trend)
          if trend.ndim > 0:
              polynomial_trend = (trend > 0).astype(int)
          else:
              raise ValueError(
                  "Valid trend inputs are 'c' (constant), 't' (linear trend in "
                  "time), 'ct' (both), 'ctt' (both with trend squared) or an "
                  "interable defining a polynomial, e.g., [1, 1, 0, 1] is `a + "
                  f"b*t + ct**3`. Received {trend}"
              )
  
      # Note: k_trend is not the degree of the trend polynomial, because e.g.
      # k_trend = 1 corresponds to the degree zero polynomial (with only a
      # constant term).
      k_trend = int(np.sum(polynomial_trend))
  
      return polynomial_trend, k_trend
  
imports: import numpy
  from scipy.linalg import solve_sylvester
  import pandas
  from statsmodels.compat.pandas import Appender
  from statsmodels.tools.data import _is_using_pandas
  from scipy.linalg.blas import find_best_blas_type
  from .None import _initialization, _representation, _kalman_filter, _kalman_smoother, _simulation_smoother, _cfa_simulation_smoother, _tools
label_desc: Use image node_id 29 for calling a global function with example usage: prepare_trend_spec(trend) and returns: polynomial_trend,  k_trend