
"""simple docstring"""



from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					float = 1 / sqrt(2						)						):






							"""simple docstring"""



							_lowerCAmelCase  	=			tau * frequency / samplerate
							_lowerCAmelCase  	=			sin(snake_case_						)
							_lowerCAmelCase  	=			cos(snake_case_						)
							_lowerCAmelCase  	=			_sin / (2 * q_factor)

							_lowerCAmelCase  	=			(1 - _cos) / 2
							_lowerCAmelCase  	=			1 - _cos

							_lowerCAmelCase  	=			1 + alpha
							_lowerCAmelCase  	=			-2 * _cos
							_lowerCAmelCase  	=			1 - alpha

							_lowerCAmelCase  	=			IIRFilter(2						)
							filt.set_coefficients([aa, aa, aa]     ,  [ba, ba, ba]						)
							return filt






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					float = 1 / sqrt(2						)						):






							"""simple docstring"""



							_lowerCAmelCase  	=			tau * frequency / samplerate
							_lowerCAmelCase  	=			sin(snake_case_						)
							_lowerCAmelCase  	=			cos(snake_case_						)
							_lowerCAmelCase  	=			_sin / (2 * q_factor)

							_lowerCAmelCase  	=			(1 + _cos) / 2
							_lowerCAmelCase  	=			-1 - _cos

							_lowerCAmelCase  	=			1 + alpha
							_lowerCAmelCase  	=			-2 * _cos
							_lowerCAmelCase  	=			1 - alpha

							_lowerCAmelCase  	=			IIRFilter(2						)
							filt.set_coefficients([aa, aa, aa]     ,  [ba, ba, ba]						)
							return filt






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					float = 1 / sqrt(2						)						):






							"""simple docstring"""



							_lowerCAmelCase  	=			tau * frequency / samplerate
							_lowerCAmelCase  	=			sin(snake_case_						)
							_lowerCAmelCase  	=			cos(snake_case_						)
							_lowerCAmelCase  	=			_sin / (2 * q_factor)

							_lowerCAmelCase  	=			_sin / 2
							_lowerCAmelCase  	=			0
							_lowerCAmelCase  	=			-ba

							_lowerCAmelCase  	=			1 + alpha
							_lowerCAmelCase  	=			-2 * _cos
							_lowerCAmelCase  	=			1 - alpha

							_lowerCAmelCase  	=			IIRFilter(2						)
							filt.set_coefficients([aa, aa, aa]     ,  [ba, ba, ba]						)
							return filt






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					float = 1 / sqrt(2						)						):






							"""simple docstring"""



							_lowerCAmelCase  	=			tau * frequency / samplerate
							_lowerCAmelCase  	=			sin(snake_case_						)
							_lowerCAmelCase  	=			cos(snake_case_						)
							_lowerCAmelCase  	=			_sin / (2 * q_factor)

							_lowerCAmelCase  	=			1 - alpha
							_lowerCAmelCase  	=			-2 * _cos
							_lowerCAmelCase  	=			1 + alpha

							_lowerCAmelCase  	=			IIRFilter(2						)
							filt.set_coefficients([ba, ba, ba]     ,  [ba, ba, ba]						)
							return filt






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					float     ,  SCREAMING_SNAKE_CASE:					float = 1 / sqrt(2						)     ,  ):






							"""simple docstring"""



							_lowerCAmelCase  	=			tau * frequency / samplerate
							_lowerCAmelCase  	=			sin(snake_case_						)
							_lowerCAmelCase  	=			cos(snake_case_						)
							_lowerCAmelCase  	=			_sin / (2 * q_factor)
							_lowerCAmelCase  	=			10 ** (gain_db / 40)

							_lowerCAmelCase  	=			1 + alpha * big_a
							_lowerCAmelCase  	=			-2 * _cos
							_lowerCAmelCase  	=			1 - alpha * big_a
							_lowerCAmelCase  	=			1 + alpha / big_a
							_lowerCAmelCase  	=			-2 * _cos
							_lowerCAmelCase  	=			1 - alpha / big_a

							_lowerCAmelCase  	=			IIRFilter(2						)
							filt.set_coefficients([aa, aa, aa]     ,  [ba, ba, ba]						)
							return filt






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					float     ,  SCREAMING_SNAKE_CASE:					float = 1 / sqrt(2						)     ,  ):






							"""simple docstring"""



							_lowerCAmelCase  	=			tau * frequency / samplerate
							_lowerCAmelCase  	=			sin(snake_case_						)
							_lowerCAmelCase  	=			cos(snake_case_						)
							_lowerCAmelCase  	=			_sin / (2 * q_factor)
							_lowerCAmelCase  	=			10 ** (gain_db / 40)
							_lowerCAmelCase  	=			(big_a + 1) - (big_a - 1) * _cos
							_lowerCAmelCase  	=			(big_a + 1) + (big_a - 1) * _cos
							_lowerCAmelCase  	=			(big_a - 1) - (big_a + 1) * _cos
							_lowerCAmelCase  	=			(big_a - 1) + (big_a + 1) * _cos
							_lowerCAmelCase  	=			2 * sqrt(snake_case_						) * alpha

							_lowerCAmelCase  	=			big_a * (pmc + aaa)
							_lowerCAmelCase  	=			2 * big_a * mpc
							_lowerCAmelCase  	=			big_a * (pmc - aaa)
							_lowerCAmelCase  	=			ppmc + aaa
							_lowerCAmelCase  	=			-2 * pmpc
							_lowerCAmelCase  	=			ppmc - aaa

							_lowerCAmelCase  	=			IIRFilter(2						)
							filt.set_coefficients([aa, aa, aa]     ,  [ba, ba, ba]						)
							return filt






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					int     ,  SCREAMING_SNAKE_CASE:					float     ,  SCREAMING_SNAKE_CASE:					float = 1 / sqrt(2						)     ,  ):






							"""simple docstring"""



							_lowerCAmelCase  	=			tau * frequency / samplerate
							_lowerCAmelCase  	=			sin(snake_case_						)
							_lowerCAmelCase  	=			cos(snake_case_						)
							_lowerCAmelCase  	=			_sin / (2 * q_factor)
							_lowerCAmelCase  	=			10 ** (gain_db / 40)
							_lowerCAmelCase  	=			(big_a + 1) - (big_a - 1) * _cos
							_lowerCAmelCase  	=			(big_a + 1) + (big_a - 1) * _cos
							_lowerCAmelCase  	=			(big_a - 1) - (big_a + 1) * _cos
							_lowerCAmelCase  	=			(big_a - 1) + (big_a + 1) * _cos
							_lowerCAmelCase  	=			2 * sqrt(snake_case_						) * alpha

							_lowerCAmelCase  	=			big_a * (ppmc + aaa)
							_lowerCAmelCase  	=			-2 * big_a * pmpc
							_lowerCAmelCase  	=			big_a * (ppmc - aaa)
							_lowerCAmelCase  	=			pmc + aaa
							_lowerCAmelCase  	=			2 * mpc
							_lowerCAmelCase  	=			pmc - aaa

							_lowerCAmelCase  	=			IIRFilter(2						)
							filt.set_coefficients([aa, aa, aa]     ,  [ba, ba, ba]						)
							return filt








"""simple docstring"""



def 	__snake_case  (    SCREAMING_SNAKE_CASE:					list[int]						):






							"""simple docstring"""



							_lowerCAmelCase  	=			[]
							if len(SCREAMING_SNAKE_CASE						) == 1:
														return [nums.copy()]
							for _ in range(len(SCREAMING_SNAKE_CASE						)						):
														_lowerCAmelCase  	=			nums.pop(0						)
														_lowerCAmelCase  	=			permute(SCREAMING_SNAKE_CASE						)
														for perm in permutations:
																					perm.append(SCREAMING_SNAKE_CASE						)
														result.extend(SCREAMING_SNAKE_CASE						)
														nums.append(SCREAMING_SNAKE_CASE						)
							return result






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					Any						):






							"""simple docstring"""



							def backtrack(SCREAMING_SNAKE_CASE:					Tuple						):
														if start == len(SCREAMING_SNAKE_CASE						) - 1:
																					output.append(nums[:]						)
														else:
																					for i in range(SCREAMING_SNAKE_CASE     ,  len(SCREAMING_SNAKE_CASE						)						):
																												_lowerCAmelCase	,		_lowerCAmelCase  	=			nums[i], nums[start]
																												backtrack(start + 1						)
																												_lowerCAmelCase	,		_lowerCAmelCase  	=			nums[i], nums[start]  # backtrack

							_lowerCAmelCase  	=			[]
							backtrack(0						)
							return output


if __name__ == "__main__":
	import doctest

	# use res to print the data in permute2 function
	_snake_case          =						permutea([1, 2, 3])
	print(res)
	doctest.testmod()






