
"""simple docstring"""

from math import factorial
class      _UpperCAmelCase							:




      def __init__(							self   ,       lowercase_   ,       lowercase_							)						->					List[Any]:
          UpperCAmelCase									=					real
          if isinstance(lowercase_   ,       lowercase_							):
              UpperCAmelCase									=					[1] * rank
          else:
              UpperCAmelCase									=					rank




      def __repr__(							self							)						->					List[str]:
          return (
              F"{self.real}+"
              F"{'+'.join(str(lowercase_							)+'E'+str(n+1							)for n,dual in enumerate(self.duals							)							)}"
          )




      def     a_      (							self							)						->					int:
          UpperCAmelCase									=					self.duals.copy()
          while cur[-1] == 0:
              cur.pop(-1							)
          return Dual(self.real   ,       lowercase_							)




      def __add__(							self   ,       lowercase_							)						->					Dict:
          if not isinstance(lowercase_   ,       lowercase_							):
              return Dual(self.real + other   ,       self.duals							)
          UpperCAmelCase									=					self.duals.copy()
          UpperCAmelCase									=					other.duals.copy()
          if len(lowercase_							) > len(lowercase_							):
              o_dual.extend([1] * (len(lowercase_							) - len(lowercase_							))							)
          elif len(lowercase_							) < len(lowercase_							):
              s_dual.extend([1] * (len(lowercase_							) - len(lowercase_							))							)
          UpperCAmelCase									=					[]
          for i in range(len(lowercase_							)							):
              new_duals.append(s_dual[i] + o_dual[i]							)
          return Dual(self.real + other.real   ,       lowercase_							)

      __SCREAMING_SNAKE_CASE   :							List[str]							      =	__add__




      def __sub__(							self   ,       lowercase_							)						->					List[Any]:
          return self + other * -1




      def __mul__(							self   ,       lowercase_							)						->					Any:
          if not isinstance(lowercase_   ,       lowercase_							):
              UpperCAmelCase									=					[]
              for i in self.duals:
                  new_duals.append(i * other							)
              return Dual(self.real * other   ,       lowercase_							)
          UpperCAmelCase									=					[0] * (len(self.duals							) + len(other.duals							) + 1)
          for i, item in enumerate(self.duals							):
              for j, jtem in enumerate(other.duals							):
                  new_duals[i + j + 1] += item * jtem
          for k in range(len(self.duals							)							):
              new_duals[k] += self.duals[k] * other.real
          for index in range(len(other.duals							)							):
              new_duals[index] += other.duals[index] * self.real
          return Dual(self.real * other.real   ,       lowercase_							)

      __SCREAMING_SNAKE_CASE   :							Union[str, Any]							      =	__mul__




      def __truediv__(							self   ,       lowercase_							)						->					Optional[int]:
          if not isinstance(lowercase_   ,       lowercase_							):
              UpperCAmelCase									=					[]
              for i in self.duals:
                  new_duals.append(i / other							)
              return Dual(self.real / other   ,       lowercase_							)
          raise ValueError




      def __floordiv__(							self   ,       lowercase_							)						->					int:
          if not isinstance(lowercase_   ,       lowercase_							):
              UpperCAmelCase									=					[]
              for i in self.duals:
                  new_duals.append(i // other							)
              return Dual(self.real // other   ,       lowercase_							)
          raise ValueError




      def __pow__(							self   ,       lowercase_							)						->					Dict:
          if n < 0 or isinstance(lowercase_   ,       lowercase_							):
              raise ValueError('power must be a positive integer'							)
          if n == 0:
              return 1
          if n == 1:
              return self
          UpperCAmelCase									=					self
          for _ in range(n - 1							):
              x *= self
          return x




def     lowercase__						(					lowerCAmelCase ,				lowerCAmelCase ,				lowerCAmelCase ) ->      Union[str, Any]:






    """simple docstring"""




    if not callable(__snake_case ):
        raise ValueError('differentiate() requires a function as input for func' )
    if not isinstance(__snake_case ,				(float, int) ):
        raise ValueError('differentiate() requires a float as input for position' )
    if not isinstance(__snake_case ,				__snake_case ):
        raise ValueError('differentiate() requires an int as input for order' )
    UpperCAmelCase									=					Dual(__snake_case ,				1 )
    UpperCAmelCase									=					func(__snake_case )
    if order == 0:
        return result.real
    return result.duals[order - 1] * factorial(__snake_case )


if __name__ == "__main__":
   import doctest

   doctest.testmod()




   def     lowercase__						(					lowerCAmelCase ) ->      Optional[int]:






       """simple docstring"""




       return y**2 * y**4







   print(differentiate(f, 9, 2))





"""simple docstring"""

import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


SCREAMING_SNAKE_CASE_    					=						logging.get_logger(__name__)
class      _UpperCAmelCase							(		SCREAMING_SNAKE_CASE_							):
      __SCREAMING_SNAKE_CASE   :							Union[str, Any]							      =	"encoder-decoder"
      __SCREAMING_SNAKE_CASE   :							Any							      =	True




      def __init__(							self   ,       **lowercase_							)						->					str:
          super().__init__(**lowercase_							)
          assert (
              "encoder" in kwargs and "decoder" in kwargs
          ), "Config has to be initialized with encoder and decoder config"
          UpperCAmelCase									=					kwargs.pop('encoder'							)
          UpperCAmelCase									=					encoder_config.pop('model_type'							)
          UpperCAmelCase									=					kwargs.pop('decoder'							)
          UpperCAmelCase									=					decoder_config.pop('model_type'							)

          from ..auto.configuration_auto import AutoConfig

          UpperCAmelCase									=					AutoConfig.for_model(lowercase_   ,       **lowercase_							)
          UpperCAmelCase									=					AutoConfig.for_model(lowercase_   ,       **lowercase_							)
          UpperCAmelCase									=					True




      @classmethod
      def     a_      (							cls   ,       lowercase_   ,       lowercase_   ,       **lowercase_							)						->					PretrainedConfig:
          logger.info('Set `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config'							)
          UpperCAmelCase									=					True
          UpperCAmelCase									=					True

          return cls(encoder=encoder_config.to_dict()   ,       decoder=decoder_config.to_dict()   ,       **lowercase_							)




      def     a_      (							self							)						->					Optional[int]:
          UpperCAmelCase									=					copy.deepcopy(self.__dict__							)
          UpperCAmelCase									=					self.encoder.to_dict()
          UpperCAmelCase									=					self.decoder.to_dict()
          UpperCAmelCase									=					self.__class__.model_type
          return output



