new_contents: def test_parameterized_expectations_direct():
  
      from dolo import yaml_import
      from dolo.algos.dtcscc.parameterized_expectations import  parameterized_expectations_direct
      from dolo.algos.dtcscc.time_iteration import time_iteration_direct
  
      model = yaml_import("examples/models/rbc_full.yaml")
  
      dr_ti = time_iteration_direct(model)
      dr_pea = parameterized_expectations_direct(model)
  
      x_ti  = dr_ti(dr_ti.grid)
      x_pea = dr_pea(dr_ti.grid)
  
      print(abs(x_ti - x_pea).max()<1e-5)
  
  
  if __name__ =='__main__':
      test_parameterized_expectations_direct()
  
subject: add a test for the parameterized expectations algorithm