



"""simple docstring"""
import mpmath  # for roots of unity
import numpy as np


class 							lowerCamelCase_:





					'''simple docstring'''



					def __init__(    self				,       lowerCamelCase__=None				,       lowerCamelCase__=None   ):
									# Input as list
									_lowerCamelCase        =				list(poly_a or [0]   )[:]
									_lowerCamelCase        =				list(poly_b or [0]   )[:]

									# Remove leading zero coefficients
									while self.polyA[-1] == 0:
													self.polyA.pop()
									_lowerCamelCase        =				len(self.polyA   )

									while self.polyB[-1] == 0:
													self.polyB.pop()
									_lowerCamelCase        =				len(self.polyB   )

									# Add 0 to make lengths equal a power of 2
									_lowerCamelCase        =				int(
									    2 ** np.ceil(np.loga(len(self.polyA   ) + len(self.polyB   ) - 1   )   )   )

									while len(self.polyA   ) < self.c_max_length:
													self.polyA.append(0   )
									while len(self.polyB   ) < self.c_max_length:
													self.polyB.append(0   )
									# A complex root used for the fourier transform
									_lowerCamelCase        =				complex(mpmath.root(x=1				,       n=self.c_max_length				,       k=1   )   )

									# The product
									_lowerCamelCase        =				self.__multiply()

					def 			snake_case__      (    self				,       lowerCamelCase__   ):
									_lowerCamelCase        =				[[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
									# Corner case
									if len(lowerCamelCase__   ) <= 1:
													return dft[0]
									#
									_lowerCamelCase        =				self.c_max_length // 2
									while next_ncol > 0:
													_lowerCamelCase        =				[[] for i in range(lowerCamelCase__   )]
													_lowerCamelCase        =				self.root**next_ncol

													# First half of next step
													_lowerCamelCase        =				1
													for j in range(self.c_max_length // (next_ncol * 2)   ):
																	for i in range(lowerCamelCase__   ):
																					new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]   )
																	current_root *= root
													# Second half of next step
													_lowerCamelCase        =				1
													for j in range(self.c_max_length // (next_ncol * 2)   ):
																	for i in range(lowerCamelCase__   ):
																					new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]   )
																	current_root *= root
													# Update
													_lowerCamelCase        =				new_dft
													_lowerCamelCase        =				next_ncol // 2
									return dft[0]

					def 			snake_case__      (    self   ):
									_lowerCamelCase        =				self.__dft('''A'''   )
									_lowerCamelCase        =				self.__dft('''B'''   )
									_lowerCamelCase        =				[[dft_a[i] * dft_b[i] for i in range(self.c_max_length   )]]
									del dft_a
									del dft_b

									# Corner Case
									if len(inverce_c[0]   ) <= 1:
													return inverce_c[0]
									# Inverse DFT
									_lowerCamelCase        =				2
									while next_ncol <= self.c_max_length:
													_lowerCamelCase        =				[[] for i in range(lowerCamelCase__   )]
													_lowerCamelCase        =				self.root ** (next_ncol // 2)
													_lowerCamelCase        =				1
													# First half of next step
													for j in range(self.c_max_length // next_ncol   ):
																	for i in range(next_ncol // 2   ):
																					# Even positions
																					new_inverse_c[i].append(
																					    (
																					        inverce_c[i][j]
																					        + inverce_c[i][j + self.c_max_length // next_ncol]
																					    )
																					    / 2   )
																					# Odd positions
																					new_inverse_c[i + next_ncol // 2].append(
																					    (
																					        inverce_c[i][j]
																					        - inverce_c[i][j + self.c_max_length // next_ncol]
																					    )
																					    / (2 * current_root)   )
																	current_root *= root
													# Update
													_lowerCamelCase        =				new_inverse_c
													next_ncol *= 2
									# Unpack
									_lowerCamelCase        =				[round(x[0].real				,       8   ) + round(x[0].imag				,       8   ) * 1j for x in inverce_c]

									# Remove leading 0's
									while inverce_c[-1] == 0:
													inverce_c.pop()
									return inverce_c





					def __str__(    self   ):
									_lowerCamelCase        =				'''A = ''' + ''' + '''.join(
									    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]   )   )
									_lowerCamelCase        =				'''B = ''' + ''' + '''.join(
									    F"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]   )   )
									_lowerCamelCase        =				'''A*B = ''' + ''' + '''.join(
									    F"""{coef}*x^{i}""" for coef, i in enumerate(self.product   )   )

									return F"""{a}\n{b}\n{c}"""


# Unit tests
if __name__ == "__main__":
			import doctest

			doctest.testmod()





"""simple docstring"""
import numpy as np



def        lowerCAmelCase_(   lowercase_     :							np.array							)	->       np.array:
				return 1 / (1 + np.exp(-vector							))



def        lowerCAmelCase_(   lowercase_     :							np.array							)	->       np.array:
				return vector * sigmoid(1.7_0_2 * vector							)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
