docstr: test historical_forecasts for an untrained model with different retrain values.
code: def test_retrain(self):
      """test historical_forecasts for an untrained model with different retrain values."""
  
      def helper_hist_forecasts(retrain_val, start):
          model = LinearRegressionModel(lags=4, output_chunk_length=4)
          return model.historical_forecasts(
              self.ts_passengers,
              start=start,
              retrain=retrain_val,
              verbose=False,
          )
  
      def retrain_f_invalid(
          counter,
          pred_time,
          train_series,
          past_covariates,
          future_covariates,
      ):
          return False
  
      def retrain_f_missing_arg(
          counter, train_series, past_covariates, future_covariates
      ):
          if len(train_series) % 2 == 0:
              return True
          else:
              return False
  
      def retrain_f_invalid_ouput_int(
          counter,
          pred_time,
          train_series,
          past_covariates,
          future_covariates,
      ):
          return 1
  
      def retrain_f_invalid_ouput_str(
          counter,
          pred_time,
          train_series,
          past_covariates,
          future_covariates,
      ):
          return "True"
  
      def retrain_f_valid(
          counter,
          pred_time,
          train_series,
          past_covariates,
          future_covariates,
      ):
          # only retrain once in first iteration
          if pred_time == pd.Timestamp("1959-09-01 00:00:00"):
              return True
          else:
              return False
  
      def retrain_f_delayed_true(
          counter,
          pred_time,
          train_series,
          past_covariates,
          future_covariates,
      ):
          if counter > 1:
              return True
          else:
              return False
  
      # test callable
      helper_hist_forecasts(retrain_f_valid, 0.9)
      # missing the `pred_time` positional argument
      expected_msg = "the Callable `retrain` must have a signature/arguments matching the following positional"
      with pytest.raises(ValueError) as error_msg:
          helper_hist_forecasts(retrain_f_missing_arg, 0.9)
      assert str(error_msg.value).startswith(expected_msg)
      # returning a non-bool value (int)
      expected_msg = "Return value of `retrain` must be bool, received <class 'int'>"
      with pytest.raises(ValueError) as error_msg:
          helper_hist_forecasts(retrain_f_invalid_ouput_int, 0.9)
      assert str(error_msg.value).startswith(expected_msg)
      # returning a non-bool value (str)
      expected_msg = "Return value of `retrain` must be bool, received <class 'str'>"
      with pytest.raises(ValueError) as error_msg:
          helper_hist_forecasts(retrain_f_invalid_ouput_str, 0.9)
      assert str(error_msg.value).startswith(expected_msg)
      # predict fails but model could have been trained before the predict round
      expected_msg = "`retrain` is `False` in the first train iteration at prediction point (in time)"
      with pytest.raises(ValueError) as error_msg:
          helper_hist_forecasts(retrain_f_delayed_true, 0.9)
      assert str(error_msg.value).startswith(expected_msg)
      # always returns False, treated slightly different than `retrain=False` and `retrain=0`
      with pytest.raises(ValueError) as error_msg:
          helper_hist_forecasts(retrain_f_invalid, 0.9)
      assert str(error_msg.value).startswith(expected_msg)
  
      # test int
      helper_hist_forecasts(10, 0.9)
      expected_msg = "Model has not been fit yet."
      # `retrain=0` with not-trained model, encountering directly a predictable time index
      with pytest.raises(ValueError) as error_msg:
          helper_hist_forecasts(0, 0.9)
      assert str(error_msg.value).startswith(expected_msg), str(
          error_msg.value
      )
  
      # test bool
      helper_hist_forecasts(True, 0.9)
      # `retrain=False` with not-trained model, encountering directly a predictable time index
      expected_msg = "The model has not been fitted yet, and `retrain` is ``False``."
      with pytest.raises(ValueError) as error_msg:
          helper_hist_forecasts(False, 0.9)
      assert str(error_msg.value).startswith(expected_msg)
  
      expected_start = pd.Timestamp("1949-10-01 00:00:00")
      # start before first trainable time index should still work
      res = helper_hist_forecasts(
          True, pd.Timestamp("1949-09-01 00:00:00")
      )
      assert res.time_index[0] == expected_start
      # start at first trainable time index should still work
      res = helper_hist_forecasts(True, expected_start)
      assert res.time_index[0] == expected_start
      # start at last trainable time index should still work
      expected_end = pd.Timestamp("1960-12-01 00:00:00")
      res = helper_hist_forecasts(True, expected_end)
      assert res.time_index[0] == expected_end
  
imports: import itertools
  from itertools import product
  import numpy
  import pandas
  import pytest
  import darts
  from darts import TimeSeries, concatenate
  from darts.dataprocessing.transformers import Scaler
  from darts.datasets import AirPassengersDataset
  from darts.logging import get_logger
  from darts.models import ARIMA, AutoARIMA, CatBoostModel, LightGBMModel, LinearRegressionModel, NaiveSeasonal, NotImportedModule
  from darts.tests.conftest import tfm_kwargs
  from darts.utils import timeseries_generation
label_desc: Use image node_id 21 for calling the TestHistoricalforecast obj's underlying member method code with example usage: obj.test_retrain() and returns: model, False, int, str, True, False, True, False, True, False