






"""simple docstring"""




def  _lowerCAmelCase		(		_UpperCamelCase ,				_UpperCamelCase						):






  """simple docstring"""



  _lowercase:			Union[str, Any]       =     len(_snake_case						) + 1
  _lowercase:			List[Any]       =     len(_snake_case						) + 1

  # dp is a 2d matrix where dp[i][j] denotes whether prefix string of
  # length i of input_string matches with prefix string of length j of
  # given pattern.
  # "dp" stands for dynamic programming.
  _lowercase:			List[Any]       =     [[0 for i in range(_snake_case						)] for j in range(_snake_case						)]

  # since string of zero length match pattern of zero length
  _lowercase:			Dict       =     1

  # since pattern of zero length will never match with string of non-zero length
  for i in range(1 ,				_snake_case						):
    _lowercase:			str       =     0

  # since string of zero length will match with pattern where there
  # is at least one * alternatively
  for j in range(1 ,				_snake_case						):
    _lowercase:			List[str]       =     dp[0][j - 2] if pattern[j - 1] == '''*''' else 0

  # now using bottom-up approach to find for all remaining lengths
  for i in range(1 ,				_snake_case						):
    for j in range(1 ,				_snake_case						):
      if input_string[i - 1] == pattern[j - 1] or pattern[j - 1] == ".":
        _lowercase:			Optional[int]       =     dp[i - 1][j - 1]

      elif pattern[j - 1] == "*":
        if dp[i][j - 2] == 1:
          _lowercase:			Any       =     1
        elif pattern[j - 2] in (input_string[i - 1], "."):
          _lowercase:			Union[str, Any]       =     dp[i - 1][j]
        else:
          _lowercase:			Dict       =     0
      else:
        _lowercase:			List[str]       =     0

  return bool(dp[-1][-1]						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  # inputing the strings
  # input_string = input("input a string :")
  # pattern = input("input a pattern :")

  A__   :					Tuple							=   'aab'
  A__   :					List[str]							=   'c*a*b'

  # using function to check whether given string matches the given pattern
  if match_pattern(input_string, pattern):
    print(f"""{input_string} matches the given pattern {pattern}""")
  else:
    print(f"""{input_string} does not match with the given pattern {pattern}""")


"""simple docstring"""




import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest


class 			__magic_name__       (       SCREAMING_SNAKE_CASE__ ):
       UpperCamelCase_   =		(KDPMaDiscreteScheduler,)
       UpperCamelCase_   =		10
       def 							lowercase_							(     self ,				**A_       )     ->	List[Any]:





         """simple docstring"""




         _lowercase:			Tuple       =     {
             '''num_train_timesteps''': 1100,
             '''beta_start''': 0.00_01,
             '''beta_end''': 0.02,
             '''beta_schedule''': '''linear''',
         }

         config.update(**A_       )
         return config
       def 							lowercase_							(     self       )     ->	List[str]:





         """simple docstring"""




         for timesteps in [10, 50, 100, 1000]:
           self.check_over_configs(num_train_timesteps=A_       )
       def 							lowercase_							(     self       )     ->	Tuple:





         """simple docstring"""




         for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01] ,				[0.00_02, 0.0_02, 0.02]       ):
           self.check_over_configs(beta_start=A_ ,				beta_end=A_       )
       def 							lowercase_							(     self       )     ->	int:





         """simple docstring"""




         for schedule in ["linear", "scaled_linear"]:
           self.check_over_configs(beta_schedule=A_       )
       def 							lowercase_							(     self       )     ->	str:





         """simple docstring"""




         for prediction_type in ["epsilon", "v_prediction"]:
           self.check_over_configs(prediction_type=A_       )
       def 							lowercase_							(     self       )     ->	Tuple:





         """simple docstring"""




         _lowercase:			Optional[int]       =     self.scheduler_classes[0]
         _lowercase:			List[str]       =     self.get_scheduler_config(prediction_type='''v_prediction'''       )
         _lowercase:			List[Any]       =     scheduler_class(**A_       )

         scheduler.set_timesteps(self.num_inference_steps       )

         _lowercase:			List[str]       =     self.dummy_model()
         _lowercase:			Dict       =     self.dummy_sample_deter * scheduler.init_noise_sigma
         _lowercase:			List[Any]       =     sample.to(A_       )

         for i, t in enumerate(scheduler.timesteps       ):
           _lowercase:			Optional[int]       =     scheduler.scale_model_input(A_ ,				A_       )

           _lowercase:			Optional[Any]       =     model(A_ ,				A_       )

           _lowercase:			List[str]       =     scheduler.step(A_ ,				A_ ,				A_       )
           _lowercase:			str       =     output.prev_sample

         _lowercase:			Dict       =     torch.sum(torch.abs(A_       )       )
         _lowercase:			Optional[int]       =     torch.mean(torch.abs(A_       )       )

         if torch_device in ["cpu", "mps"]:
           assert abs(result_sum.item() - 4.69_34E-07       ) < 1E-2
           assert abs(result_mean.item() - 6.11_12E-10       ) < 1E-3
         else:
           # CUDA
           assert abs(result_sum.item() - 4.6_93_42_86_50_17_09_72E-07       ) < 1E-2
           assert abs(result_mean.item() - 0.00_02       ) < 1E-3
       def 							lowercase_							(     self       )     ->	str:





         """simple docstring"""




         if torch_device == "mps":
           return
         _lowercase:			List[str]       =     self.scheduler_classes[0]
         _lowercase:			Optional[int]       =     self.get_scheduler_config()
         _lowercase:			int       =     scheduler_class(**A_       )

         scheduler.set_timesteps(self.num_inference_steps       )

         _lowercase:			Tuple       =     self.dummy_model()
         _lowercase:			Tuple       =     self.dummy_sample_deter * scheduler.init_noise_sigma
         _lowercase:			Any       =     sample.to(A_       )

         for i, t in enumerate(scheduler.timesteps       ):
           _lowercase:			Any       =     scheduler.scale_model_input(A_ ,				A_       )

           _lowercase:			List[Any]       =     model(A_ ,				A_       )

           _lowercase:			Any       =     scheduler.step(A_ ,				A_ ,				A_       )
           _lowercase:			List[Any]       =     output.prev_sample

         _lowercase:			Optional[Any]       =     torch.sum(torch.abs(A_       )       )
         _lowercase:			Tuple       =     torch.mean(torch.abs(A_       )       )

         if torch_device in ["cpu", "mps"]:
           assert abs(result_sum.item() - 20.41_25       ) < 1E-2
           assert abs(result_mean.item() - 0.02_66       ) < 1E-3
         else:
           # CUDA
           assert abs(result_sum.item() - 20.41_25       ) < 1E-2
           assert abs(result_mean.item() - 0.02_66       ) < 1E-3



       def 							lowercase_							(     self       )     ->	Any:





         """simple docstring"""




         if torch_device == "mps":
           return
         _lowercase:			int       =     self.scheduler_classes[0]
         _lowercase:			Union[str, Any]       =     self.get_scheduler_config()
         _lowercase:			Optional[Any]       =     scheduler_class(**A_       )

         scheduler.set_timesteps(self.num_inference_steps ,				device=A_       )

         _lowercase:			List[str]       =     self.dummy_model()
         _lowercase:			Union[str, Any]       =     self.dummy_sample_deter.to(A_       ) * scheduler.init_noise_sigma

         for t in scheduler.timesteps:
           _lowercase:			Optional[Any]       =     scheduler.scale_model_input(A_ ,				A_       )

           _lowercase:			int       =     model(A_ ,				A_       )

           _lowercase:			Tuple       =     scheduler.step(A_ ,				A_ ,				A_       )
           _lowercase:			int       =     output.prev_sample

         _lowercase:			Union[str, Any]       =     torch.sum(torch.abs(A_       )       )
         _lowercase:			Dict       =     torch.mean(torch.abs(A_       )       )

         if str(A_       ).startswith('''cpu'''       ):
           # The following sum varies between 148 and 156 on mps. Why?
           assert abs(result_sum.item() - 20.41_25       ) < 1E-2
           assert abs(result_mean.item() - 0.02_66       ) < 1E-3
         else:
           # CUDA
           assert abs(result_sum.item() - 20.41_25       ) < 1E-2
           assert abs(result_mean.item() - 0.02_66       ) < 1E-3
