code: def test_int_double_time_type(dates_df):
      dates_df.ww.init(
          name="dates_table",
          index="backwards_order",
          time_index="random_order",
          logical_types={
              "random_order": "Integer",
              "special": "Double",
          },
      )
      es = EntitySet("es")
  
      # Both random_order and special are numeric, but they are different logical types
      es.add_dataframe(
          dates_df,
          secondary_time_index={"special": ["dates_backwards"]},
      )
  
      assert isinstance(
          es["dates_table"].ww.logical_types["random_order"], Integer
      )
      assert isinstance(
          es["dates_table"].ww.logical_types["special"], Double
      )
  
      assert es["dates_table"].ww.time_index == "random_order"
      assert (
          "special"
          in es["dates_table"].ww.metadata["secondary_time_index"]
      )
  
imports: from datetime import datetime
  import numpy
  import pandas
  import pytest
  from woodwork.exceptions import TypeConversionError
  from woodwork.logical_types import Boolean, Categorical, Datetime, Double, Integer, NaturalLanguage
  from featuretools.entityset.entityset import LTI_COLUMN_NAME, EntitySet
  from featuretools.tests.testing_utils import to_pandas
  from featuretools.utils.gen_utils import Library, import_or_none, is_instance
label_desc: Use image node_id 19 for calling a global function with example usage: test_int_double_time_type(dates_df) without return types