


"""simple docstring"""



from __future__ import annotations







class _lowerCAmelCase       :







   def __init__(			self		,			UpperCamelCase__		)			->	None:

       '''simple docstring'''




       snake_case					:   Dict         =					order

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

       # x[n-1] ... x[n-k]
       snake_case					:   Dict         =					[0.0] * self.order
       # y[n-1] ... y[n-k]
       snake_case					:   Optional[int]         =					[0.0] * self.order







   def 				lowerCamelCase	(			self		,			UpperCamelCase__		,			UpperCamelCase__		)			->	None:

       '''simple docstring'''




       if len(UpperCamelCase__		) < self.order:
           snake_case					:   Optional[Any]         =					[1.0, *a_coeffs]

       if len(UpperCamelCase__		) != self.order + 1:
           snake_case					:   List[Any]         =					(
               F'Expected a_coeffs to have {self.order + 1} elements '
               F'for {self.order}-order filter, got {len(UpperCamelCase__		)}'
           )
           raise ValueError(UpperCamelCase__		)

       if len(UpperCamelCase__		) != self.order + 1:
           snake_case					:   Dict         =					(
               F'Expected b_coeffs to have {self.order + 1} elements '
               F'for {self.order}-order filter, got {len(UpperCamelCase__		)}'
           )
           raise ValueError(UpperCamelCase__		)

       snake_case					:   Optional[int]         =					a_coeffs
       snake_case					:   Optional[Any]         =					b_coeffs







   def 				lowerCamelCase	(			self		,			UpperCamelCase__		)			->	float:

       '''simple docstring'''




       snake_case					:   int         =					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]
           )

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

       snake_case					:   Optional[int]         =					self.input_history[:-1]
       snake_case					:   Dict         =					self.output_history[:-1]

       snake_case					:   Optional[Any]         =					sample
       snake_case					:   Union[str, Any]         =					result

       return result









"""simple docstring"""



from typing import Any







def 						__lowerCAmelCase		(		lowercase						:						list		,							lowercase						:						list		,							lowercase						:						dict		,							lowercase						:						dict		,							lowercase						:						dict		,							)			->		list:


    """simple docstring"""





    _validation(
        lowercase		,							lowercase		,							lowercase		,							lowercase		,							lowercase		,							)
    # Creates data structures and fill initial step
    snake_case					:   dict         =					{}
    snake_case					:   dict         =					{}
    for state in states_space:
        snake_case					:   int         =					observations_space[0]
        snake_case					:   Any         =					(
            initial_probabilities[state] * emission_probabilities[state][observation]
        )
        snake_case					:   Union[str, Any]         =					None

    # Fills the data structure with the probabilities of
    # different transitions and pointers to previous states
    for o in range(1		,							len(lowercase				)				):
        snake_case					:   Optional[Any]         =					observations_space[o]
        snake_case					:   str         =					observations_space[o - 1]
        for state in states_space:
            # Calculates the argmax for probability function
            snake_case					:   str         =					""
            snake_case					:   List[Any]         =					-1
            for k_state in states_space:
                snake_case					:   Tuple         =					(
                    probabilities[(k_state, prior_observation)]
                    * transition_probabilities[k_state][state]
                    * emission_probabilities[state][observation]
                )
                if probability > max_probability:
                    snake_case					:   Optional[Any]         =					probability
                    snake_case					:   int         =					k_state

            # Update probabilities and pointers dicts
            snake_case					:   List[str]         =					(
                probabilities[(arg_max, prior_observation)]
                * transition_probabilities[arg_max][state]
                * emission_probabilities[state][observation]
            )

            snake_case					:   List[Any]         =					arg_max

    # The final observation
    snake_case					:   Dict         =					observations_space[len(lowercase				) - 1]

    # argmax for given final observation
    snake_case					:   str         =					""
    snake_case					:   Optional[int]         =					-1
    for k_state in states_space:
        snake_case					:   int         =					probabilities[(k_state, final_observation)]
        if probability > max_probability:
            snake_case					:   Optional[int]         =					probability
            snake_case					:   List[Any]         =					k_state
    snake_case					:   str         =					arg_max

    # Process pointers backwards
    snake_case					:   List[str]         =					last_state
    snake_case					:   Optional[int]         =					[]
    for o in range(len(lowercase				) - 1		,							-1		,							-1				):
        result.append(lowercase				)
        snake_case					:   List[str]         =					pointers[previous, observations_space[o]]
    result.reverse()

    return result







def 						__lowerCAmelCase		(		lowercase						:						Any		,							lowercase						:						Any		,							lowercase						:						Any		,							lowercase						:						Any		,							lowercase						:						Any		,							)			->		None:


    """simple docstring"""





    _validate_not_empty(
        lowercase		,							lowercase		,							lowercase		,							lowercase		,							lowercase		,							)
    _validate_lists(lowercase		,							lowercase				)
    _validate_dicts(
        lowercase		,							lowercase		,							lowercase				)







def 						__lowerCAmelCase		(		lowercase						:						Any		,							lowercase						:						Any		,							lowercase						:						Any		,							lowercase						:						Any		,							lowercase						:						Any		,							)			->		None:


    """simple docstring"""





    if not all(
        [
            observations_space,
            states_space,
            initial_probabilities,
            transition_probabilities,
            emission_probabilities,
        ]				):
        raise ValueError("There's an empty parameter"				)







def 						__lowerCAmelCase		(		lowercase						:						Any		,							lowercase						:						Any				)			->		None:


    """simple docstring"""





    _validate_list(lowercase		,							"observations_space"				)
    _validate_list(lowercase		,							"states_space"				)







def 						__lowerCAmelCase		(		lowercase						:						Any		,							lowercase						:						str				)			->		None:


    """simple docstring"""





    if not isinstance(_object		,							lowercase				):
        snake_case					:   List[str]         =					F'{var_name} must be a list'
        raise ValueError(lowercase				)
    else:
        for x in _object:
            if not isinstance(lowercase		,							lowercase				):
                snake_case					:   Tuple         =					F'{var_name} must be a list of strings'
                raise ValueError(lowercase				)







def 						__lowerCAmelCase		(		lowercase						:						Any		,							lowercase						:						Any		,							lowercase						:						Any		,							)			->		None:


    """simple docstring"""





    _validate_dict(lowercase		,							"initial_probabilities"		,							lowercase				)
    _validate_nested_dict(lowercase		,							"transition_probabilities"				)
    _validate_nested_dict(lowercase		,							"emission_probabilities"				)







def 						__lowerCAmelCase		(		lowercase						:						Any		,							lowercase						:						str				)			->		None:


    """simple docstring"""





    _validate_dict(_object		,							lowercase		,							lowercase				)
    for x in _object.values():
        _validate_dict(lowercase		,							lowercase		,							lowercase		,							lowercase				)







def 						__lowerCAmelCase		(		lowercase						:						Any		,							lowercase						:						str		,							lowercase						:						type		,							lowercase						:						bool = False				)			->		None:


    """simple docstring"""





    if not isinstance(_object		,							lowercase				):
        snake_case					:   int         =					F'{var_name} must be a dict'
        raise ValueError(lowercase				)
    if not all(isinstance(lowercase		,							lowercase				) for x in _object				):
        snake_case					:   Optional[Any]         =					F'{var_name} all keys must be strings'
        raise ValueError(lowercase				)
    if not all(isinstance(lowercase		,							lowercase				) for x in _object.values()				):
        snake_case					:   Optional[int]         =					"nested dictionary " if nested else ""
        snake_case					:   int         =					F'{var_name} {nested_text}all values must be {value_type.__name__}'
        raise ValueError(lowercase				)


if __name__ == "__main__":
  from doctest import testmod

  testmod()





