


'''simple docstring'''





from math import factorial




class 				UpperCAmelCase			:


 def __init__(      self							:	Optional[int]			,       __lowerCamelCase							:	Any			,       __lowerCamelCase							:	Any ):
    UpperCAmelCase__	:Tuple      =      real
    if isinstance(__lowerCamelCase			,       __lowerCamelCase ):
       UpperCAmelCase__	:int      =      [1] * rank
    else:
       UpperCAmelCase__	:int      =      rank


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


 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[int] ):
    UpperCAmelCase__	:int      =      self.duals.copy()
    while cur[-1] == 0:
       cur.pop(-1 )
    return Dual(self.real			,       __lowerCamelCase )


 def __add__(      self							:	Union[str, Any]			,       __lowerCamelCase							:	Optional[Any] ):
    if not isinstance(__lowerCamelCase			,       __lowerCamelCase ):
       return Dual(self.real + other			,       self.duals )
    UpperCAmelCase__	:Tuple      =      self.duals.copy()
    UpperCAmelCase__	:str      =      other.duals.copy()
    if len(__lowerCamelCase ) > len(__lowerCamelCase ):
       o_dual.extend([1] * (len(__lowerCamelCase ) - len(__lowerCamelCase )) )
    elif len(__lowerCamelCase ) < len(__lowerCamelCase ):
       s_dual.extend([1] * (len(__lowerCamelCase ) - len(__lowerCamelCase )) )
    UpperCAmelCase__	:str      =      []
    for i in range(len(__lowerCamelCase ) ):
       new_duals.append(s_dual[i] + o_dual[i] )
    return Dual(self.real + other.real			,       __lowerCamelCase )

 UpperCAmelCase				=					__add__


 def __sub__(      self							:	str			,       __lowerCamelCase							:	Optional[Any] ):
    return self + other * -1


 def __mul__(      self							:	List[str]			,       __lowerCamelCase							:	Dict ):
    if not isinstance(__lowerCamelCase			,       __lowerCamelCase ):
       UpperCAmelCase__	:Tuple      =      []
       for i in self.duals:
          new_duals.append(i * other )
       return Dual(self.real * other			,       __lowerCamelCase )
    UpperCAmelCase__	:int      =      [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			,       __lowerCamelCase )

 UpperCAmelCase				=					__mul__


 def __truediv__(      self							:	Tuple			,       __lowerCamelCase							:	Dict ):
    if not isinstance(__lowerCamelCase			,       __lowerCamelCase ):
       UpperCAmelCase__	:Union[str, Any]      =      []
       for i in self.duals:
          new_duals.append(i / other )
       return Dual(self.real / other			,       __lowerCamelCase )
    raise ValueError


 def __floordiv__(      self							:	Union[str, Any]			,       __lowerCamelCase							:	Any ):
    if not isinstance(__lowerCamelCase			,       __lowerCamelCase ):
       UpperCAmelCase__	:Any      =      []
       for i in self.duals:
          new_duals.append(i // other )
       return Dual(self.real // other			,       __lowerCamelCase )
    raise ValueError





 def __pow__(      self							:	List[Any]			,       __lowerCamelCase							:	str ):
    if n < 0 or isinstance(__lowerCamelCase			,       __lowerCamelCase ):
       raise ValueError('''power must be a positive integer''' )
    if n == 0:
       return 1
    if n == 1:
       return self
    UpperCAmelCase__	:Any      =      self
    for _ in range(n - 1 ):
       x *= self
    return x


def        a__     (					UpperCamelCase_						:      Union[str, Any],   UpperCamelCase_						:      Optional[Any],   UpperCamelCase_						:      Dict						):
   if not callable(UpperCamelCase_						):
      raise ValueError('''differentiate() requires a function as input for func'''						)
   if not isinstance(UpperCamelCase_,   (float, int)						):
      raise ValueError('''differentiate() requires a float as input for position'''						)
   if not isinstance(UpperCamelCase_,   UpperCamelCase_						):
      raise ValueError('''differentiate() requires an int as input for order'''						)
   UpperCAmelCase__	:Tuple      =      Dual(UpperCamelCase_,   1						)
   UpperCAmelCase__	:Tuple      =      func(UpperCamelCase_						)
   if order == 0:
      return result.real
   return result.duals[order - 1] * factorial(UpperCamelCase_						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()


    def        a__     (					UpperCamelCase_						:      Any						):
       return y**2 * y**4


    print(differentiate(f, 9, 2))







'''simple docstring'''





from typing import List, Optional

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


__lowerCamelCase												=						logging.get_logger(__name__)

__lowerCamelCase												=						{
    '''huggingface/autoformer-tourism-monthly''': '''https://huggingface.co/huggingface/autoformer-tourism-monthly/resolve/main/config.json''',
}




class 				UpperCAmelCase			(			_snake_case						):
 UpperCAmelCase				=					"autoformer"
 UpperCAmelCase				=					{
     "hidden_size": "d_model",
     "num_attention_heads": "encoder_attention_heads",
     "num_hidden_layers": "encoder_layers",
 }


 def __init__(      self							:	List[str]			,       __lowerCamelCase							:	Optional[int] = None			,       __lowerCamelCase							:	Optional[int] = None			,       __lowerCamelCase							:	str = "student_t"			,       __lowerCamelCase							:	str = "nll"			,       __lowerCamelCase							:	int = 1			,       __lowerCamelCase							:	List[int] = [1, 2, 3, 4, 5, 6, 7]			,       __lowerCamelCase							:	bool = True			,       __lowerCamelCase							:	int = 0			,       __lowerCamelCase							:	int = 0			,       __lowerCamelCase							:	int = 0			,       __lowerCamelCase							:	int = 0			,       __lowerCamelCase							:	Optional[List[int]] = None			,       __lowerCamelCase							:	Optional[List[int]] = None			,       __lowerCamelCase							:	int = 6_4			,       __lowerCamelCase							:	int = 2			,       __lowerCamelCase							:	int = 2			,       __lowerCamelCase							:	int = 2			,       __lowerCamelCase							:	int = 2			,       __lowerCamelCase							:	int = 3_2			,       __lowerCamelCase							:	int = 3_2			,       __lowerCamelCase							:	str = "gelu"			,       __lowerCamelCase							:	float = 0.1			,       __lowerCamelCase							:	float = 0.1			,       __lowerCamelCase							:	float = 0.1			,       __lowerCamelCase							:	float = 0.1			,       __lowerCamelCase							:	float = 0.1			,       __lowerCamelCase							:	int = 1_0_0			,       __lowerCamelCase							:	float = 0.02			,       __lowerCamelCase							:	bool = True			,       __lowerCamelCase							:	Optional[int]=True			,       __lowerCamelCase							:	int = 1_0			,       __lowerCamelCase							:	int = 2_5			,       __lowerCamelCase							:	int = 3			,       **__lowerCamelCase							:	int			,       ):
    # time series specific configuration
    UpperCAmelCase__	:Any      =      prediction_length
    UpperCAmelCase__	:Optional[int]      =      context_length if context_length is not None else prediction_length
    UpperCAmelCase__	:int      =      distribution_output
    UpperCAmelCase__	:str      =      loss
    UpperCAmelCase__	:Tuple      =      input_size
    UpperCAmelCase__	:Optional[int]      =      num_time_features
    UpperCAmelCase__	:List[Any]      =      lags_sequence
    UpperCAmelCase__	:Any      =      scaling
    UpperCAmelCase__	:Union[str, Any]      =      num_dynamic_real_features
    UpperCAmelCase__	:Dict      =      num_static_real_features
    UpperCAmelCase__	:Optional[int]      =      num_static_categorical_features
    if cardinality is not None and num_static_categorical_features > 0:
       if len(__lowerCamelCase ) != num_static_categorical_features:
          raise ValueError(
              '''The cardinality should be a list of the same length as `num_static_categorical_features`''' )
       UpperCAmelCase__	:Any      =      cardinality
    else:
       UpperCAmelCase__	:Dict      =      [0]
    if embedding_dimension is not None and num_static_categorical_features > 0:
       if len(__lowerCamelCase ) != num_static_categorical_features:
          raise ValueError(
              '''The embedding dimension should be a list of the same length as `num_static_categorical_features`''' )
       UpperCAmelCase__	:List[str]      =      embedding_dimension
    else:
       UpperCAmelCase__	:int      =      [min(5_0			,       (cat + 1) // 2 ) for cat in self.cardinality]
    UpperCAmelCase__	:Optional[Any]      =      num_parallel_samples

    # Transformer architecture configuration
    UpperCAmelCase__	:Optional[Any]      =      input_size * len(self.lags_sequence ) + self._number_of_features
    UpperCAmelCase__	:Optional[Any]      =      d_model
    UpperCAmelCase__	:Any      =      encoder_attention_heads
    UpperCAmelCase__	:Any      =      decoder_attention_heads
    UpperCAmelCase__	:int      =      encoder_ffn_dim
    UpperCAmelCase__	:Union[str, Any]      =      decoder_ffn_dim
    UpperCAmelCase__	:Optional[Any]      =      encoder_layers
    UpperCAmelCase__	:str      =      decoder_layers

    UpperCAmelCase__	:Optional[Any]      =      dropout
    UpperCAmelCase__	:str      =      attention_dropout
    UpperCAmelCase__	:int      =      activation_dropout
    UpperCAmelCase__	:Optional[Any]      =      encoder_layerdrop
    UpperCAmelCase__	:Dict      =      decoder_layerdrop

    UpperCAmelCase__	:Union[str, Any]      =      activation_function
    UpperCAmelCase__	:List[Any]      =      init_std

    UpperCAmelCase__	:List[str]      =      use_cache

    # Autoformer
    UpperCAmelCase__	:List[str]      =      label_length
    UpperCAmelCase__	:Dict      =      moving_average
    UpperCAmelCase__	:str      =      autocorrelation_factor

    super().__init__(is_encoder_decoder=__lowerCamelCase			,       **__lowerCamelCase )





 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	int ):
    return (
        sum(self.embedding_dimension )
        + self.num_dynamic_real_features
        + self.num_time_features
        + self.num_static_real_features
        + self.input_size * 2  # the log1p(abs(loc)) and log(scale) features
    )



