





"""simple docstring"""





from __future__ import annotations
class 		SCREAMING_SNAKE_CASE_				:
				"""simple docstring"""




				def __init__(  self	:Dict    ,     __lowercase	:int      ):
											__lowerCamelCase   :   Optional[int]       =order

											# a_{0} ... a_{k}
											__lowerCamelCase   :   List[str]       =[1.0] + [0.0] * order
											# b_{0} ... b_{k}
											__lowerCamelCase   :   str       =[1.0] + [0.0] * order

											# x[n-1] ... x[n-k]
											__lowerCamelCase   :   Any       =[0.0] * self.order
											# y[n-1] ... y[n-k]
											__lowerCamelCase   :   Union[str, Any]       =[0.0] * self.order




				def        __lowercase	(  self	:Optional[int]    ,     __lowercase	:list[float]    ,     __lowercase	:list[float]      ):
											if len(__lowercase      ) < self.order:
																		__lowerCamelCase   :   Union[str, Any]       =[1.0, *a_coeffs]

											if len(__lowercase      ) != self.order + 1:
																		__lowerCamelCase   :   List[str]       =(
																		    f'Expected a_coeffs to have {self.order + 1} elements '
																		    f'for {self.order}-order filter, got {len(__lowercase      )}'
																		)
																		raise ValueError(__lowercase      )

											if len(__lowercase      ) != self.order + 1:
																		__lowerCamelCase   :   Any       =(
																		    f'Expected b_coeffs to have {self.order + 1} elements '
																		    f'for {self.order}-order filter, got {len(__lowercase      )}'
																		)
																		raise ValueError(__lowercase      )

											__lowerCamelCase   :   int       =a_coeffs
											__lowerCamelCase   :   Tuple       =b_coeffs




				def        __lowercase	(  self	:Optional[int]    ,     __lowercase	:float      ):
											__lowerCamelCase   :   Any       =0.0

											# Start at index 1 and do index 0 at the end.
											for i in range(1    ,     self.order + 1      ):
																		result += (
																		    self.b_coeffs[i] * self.input_history[i - 1]
																		    - self.a_coeffs[i] * self.output_history[i - 1]
																		)

											__lowerCamelCase   :   str       =(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

											__lowerCamelCase   :   Dict       =self.input_history[:-1]
											__lowerCamelCase   :   str       =self.output_history[:-1]

											__lowerCamelCase   :   Tuple       =sample
											__lowerCamelCase   :   str       =result

											return result











"""simple docstring"""





import numpy as np



def 					lowerCAmelCase_      (   SCREAMING_SNAKE_CASE							:				np.array ):


							'''simple docstring'''







							return 1 / (1 + np.exp(-vector ))


if __name__ == "__main__":
							import doctest

							doctest.testmod()




