
'''simple docstring'''



import math


def A				(__lowerCamelCase				:float			,     __lowerCamelCase				:float		):

						if initial_intensity < 0:
												raise ValueError("""The value of intensity cannot be negative"""		)
												# handling of negative values of initial intensity
						if angle < 0 or angle > 360:
												raise ValueError("""In Malus Law, the angle is in the range 0-360 degrees"""		)
												# handling of values out of allowed range
						return initial_intensity * (math.cos(math.radians(__lowerCamelCase		)		) ** 2)


if __name__ == "__main__":
						import doctest

						doctest.testmod(name="""malus_law""")


'''simple docstring'''



from __future__ import annotations




class   UpperCAmelCase_					:






						'''simple docstring'''






						def __init__( self   ,       _lowercase				):

												"""simple docstring"""



												_lowerCAmelCase  						=			order

												# a_{0} ... a_{k}
												_lowerCAmelCase  						=			[1.0] + [0.0] * order
												# b_{0} ... b_{k}
												_lowerCAmelCase  						=			[1.0] + [0.0] * order

												# x[n-1] ... x[n-k]
												_lowerCAmelCase  						=			[0.0] * self.order
												# y[n-1] ... y[n-k]
												_lowerCAmelCase  						=			[0.0] * self.order




						def  _lowercase     ( self   ,       _lowercase   ,       _lowercase				):

												"""simple docstring"""



												if len(_lowercase				) < self.order:
																		_lowerCAmelCase  						=			[1.0, *a_coeffs]

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

												_lowerCAmelCase  						=			a_coeffs
												_lowerCAmelCase  						=			b_coeffs




						def  _lowercase     ( self   ,       _lowercase				):

												"""simple docstring"""



												_lowerCAmelCase  						=			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  						=			(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

												_lowerCAmelCase  						=			self.input_history[:-1]
												_lowerCAmelCase  						=			self.output_history[:-1]

												_lowerCAmelCase  						=			sample
												_lowerCAmelCase  						=			result

												return result
