





from typing import Any

import numpy as np

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:np.ndarray  )   ->    bool:
  return np.array_equal(snake_case__      ,				matrix.conjugate().T  )

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:np.ndarray      ,				snake_case__	:np.ndarray  )   ->    Any:
  _lowercase						    =			v.conjugate().T
  _lowercase						    =			v_star.dot(snake_case__  )
  assert isinstance(snake_case__      ,				np.ndarray  )
  return (v_star_dot.dot(snake_case__  )) / (v_star.dot(snake_case__  ))

def 				SCREAMING_SNAKE_CASE__							(	)   ->    None:
  _lowercase						    =			np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]  )
  _lowercase						    =			np.array([[1], [2], [3]]  )
  assert is_hermitian(snake_case__  ), F"""{a} is not hermitian."""
  print(rayleigh_quotient(snake_case__      ,				snake_case__  )  )

  _lowercase						    =			np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]  )
  assert is_hermitian(snake_case__  ), F"""{a} is not hermitian."""
  assert rayleigh_quotient(snake_case__      ,				snake_case__  ) == float(3  )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      tests()







"""simple docstring"""
from typing import List, Optional, Union

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


lowerCamelCase_							      = logging.get_logger(__name__)

lowerCamelCase_							      = {
    '''huggingface/informer-tourism-monthly''': (
        '''https://huggingface.co/huggingface/informer-tourism-monthly/resolve/main/config.json'''
    ),
    # See all Informer models at https://huggingface.co/models?filter=informer
}







class      UpperCamelCase_			(__A	):
	__magic_name__       =							'''informer'''
	__magic_name__       =							{
	    '''hidden_size''': '''d_model''',
	    '''num_attention_heads''': '''encoder_attention_heads''',
	    '''num_hidden_layers''': '''encoder_layers''',
	}





	def __init__( self   :					Optional[Any]      ,      lowerCAmelCase_   :					Optional[int] = None      ,      lowerCAmelCase_   :					Optional[int] = None      ,      lowerCAmelCase_   :					str = "student_t"      ,      lowerCAmelCase_   :					str = "nll"      ,      lowerCAmelCase_   :					int = 1      ,      lowerCAmelCase_   :					List[int] = None      ,      lowerCAmelCase_   :					Optional[Union[str, bool]] = "mean"      ,      lowerCAmelCase_   :					int = 0      ,      lowerCAmelCase_   :					int = 0      ,      lowerCAmelCase_   :					int = 0      ,      lowerCAmelCase_   :					int = 0      ,      lowerCAmelCase_   :					Optional[List[int]] = None      ,      lowerCAmelCase_   :					Optional[List[int]] = None      ,      lowerCAmelCase_   :					int = 64      ,      lowerCAmelCase_   :					int = 32      ,      lowerCAmelCase_   :					int = 32      ,      lowerCAmelCase_   :					int = 2      ,      lowerCAmelCase_   :					int = 2      ,      lowerCAmelCase_   :					int = 2      ,      lowerCAmelCase_   :					int = 2      ,      lowerCAmelCase_   :					bool = True      ,      lowerCAmelCase_   :					str = "gelu"      ,      lowerCAmelCase_   :					float = 0.0_5      ,      lowerCAmelCase_   :					float = 0.1      ,      lowerCAmelCase_   :					float = 0.1      ,      lowerCAmelCase_   :					float = 0.1      ,      lowerCAmelCase_   :					float = 0.1      ,      lowerCAmelCase_   :					int = 100      ,      lowerCAmelCase_   :					float = 0.0_2      ,      lowerCAmelCase_   :					List[Any]=True      ,      lowerCAmelCase_   :					str = "prob"      ,      lowerCAmelCase_   :					int = 5      ,      lowerCAmelCase_   :					bool = True      ,      **lowerCAmelCase_   :					Tuple      ,      )		->     Tuple:
				# time series specific configuration
				UpperCAmelCase_	:					str     	=   prediction_length
				UpperCAmelCase_	:					Tuple     	=   context_length or prediction_length
				UpperCAmelCase_	:					Any     	=   distribution_output
				UpperCAmelCase_	:					Union[str, Any]     	=   loss
				UpperCAmelCase_	:					Any     	=   input_size
				UpperCAmelCase_	:					int     	=   num_time_features
				UpperCAmelCase_	:					Union[str, Any]     	=   lags_sequence if lags_sequence is not None else [1, 2, 3, 4, 5, 6, 7]
				UpperCAmelCase_	:					List[Any]     	=   scaling
				UpperCAmelCase_	:					List[str]     	=   num_dynamic_real_features
				UpperCAmelCase_	:					int     	=   num_static_real_features
				UpperCAmelCase_	:					Any     	=   num_static_categorical_features

				# set cardinality
				if cardinality 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_	:					Optional[Any]     	=   cardinality
				else:
							UpperCAmelCase_	:					Optional[int]     	=   [0]

				# set embedding_dimension
				if embedding_dimension 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_	:					Any     	=   embedding_dimension
				else:
							UpperCAmelCase_	:					Optional[Any]     	=   [min(50      ,      (cat + 1) // 2		) for cat in self.cardinality]

				UpperCAmelCase_	:					Dict     	=   num_parallel_samples

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

				UpperCAmelCase_	:					List[str]     	=   dropout
				UpperCAmelCase_	:					Optional[Any]     	=   attention_dropout
				UpperCAmelCase_	:					Any     	=   activation_dropout
				UpperCAmelCase_	:					Union[str, Any]     	=   encoder_layerdrop
				UpperCAmelCase_	:					Optional[int]     	=   decoder_layerdrop

				UpperCAmelCase_	:					Union[str, Any]     	=   activation_function
				UpperCAmelCase_	:					int     	=   init_std

				UpperCAmelCase_	:					Optional[Any]     	=   use_cache

				# Informer
				UpperCAmelCase_	:					int     	=   attention_type
				UpperCAmelCase_	:					List[str]     	=   sampling_factor
				UpperCAmelCase_	:					Union[str, Any]     	=   distil

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





	@property
	def 	_SCREAMING_SNAKE_CASE ( self   :					List[Any]		)		->     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
				)



