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







class  __A				:
 def __init__(   self			:    Union[str, Any]				,   lowerCamelCase			:    List[Any]=None				,   lowerCamelCase			:    Optional[Any]=None       ):



   """simple docstring"""





   __A		:     Optional[int]												=		list(poly_a or [0]       )[:]
   __A		:     Optional[Any]												=		list(poly_b or [0]       )[:]

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

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

   # Add 0 to make lengths equal a power of 2
   __A		:     int												=		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
   __A		:     Union[str, Any]												=		complex(mpmath.root(x=1				,   n=self.c_max_length				,   k=1       )       )

   # The product
   __A		:     Tuple												=		self.__multiply()
 def 		lowercase_(   self			:    Union[str, Any]				,   lowerCamelCase			:    Tuple       ):



   """simple docstring"""





   __A		:     Union[str, Any]												=		[[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
   # Corner case
   if len(UpperCAmelCase__       ) <= 1:
     return dft[0]
   #
   __A		:     Any												=		self.c_max_length // 2
   while next_ncol > 0:
     __A		:     Optional[int]												=		[[] for i in range(UpperCAmelCase__       )]
     __A		:     Tuple												=		self.root**next_ncol

     # First half of next step
     __A		:     str												=		1
     for j in range(self.c_max_length // (next_ncol * 2)       ):
       for i in range(UpperCAmelCase__       ):
         new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]       )
       current_root *= root
     # Second half of next step
     __A		:     int												=		1
     for j in range(self.c_max_length // (next_ncol * 2)       ):
       for i in range(UpperCAmelCase__       ):
         new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]       )
       current_root *= root
     # Update
     __A		:     Dict												=		new_dft
     __A		:     Tuple												=		next_ncol // 2
   return dft[0]
 def 		lowercase_(   self			:    List[Any]       ):



   """simple docstring"""





   __A		:     Any												=		self.__dft("""A"""       )
   __A		:     Any												=		self.__dft("""B"""       )
   __A		:     Optional[int]												=		[[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
   __A		:     Optional[int]												=		2
   while next_ncol <= self.c_max_length:
     __A		:     Optional[int]												=		[[] for i in range(UpperCAmelCase__       )]
     __A		:     List[str]												=		self.root ** (next_ncol // 2)
     __A		:     Optional[int]												=		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
     __A		:     List[Any]												=		new_inverse_c
     next_ncol *= 2
   # Unpack
   __A		:     Tuple												=		[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			:    Any       ):



   """simple docstring"""





   __A		:     Any												=		'''A = ''' + ''' + '''.join(
       f"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A]       )       )
   __A		:     Tuple												=		'''B = ''' + ''' + '''.join(
       f"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B]       )       )
   __A		:     List[str]												=		'''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'''
A__   :		List[Any] 		=[
    'Audio',
    'Array2D',
    'Array3D',
    'Array4D',
    'Array5D',
    'ClassLabel',
    'Features',
    'Sequence',
    'Value',
    'Image',
    'Translation',
    'TranslationVariableLanguages',
]
from .audio import Audio
from .features import ArrayaD, ArrayaD, ArrayaD, ArrayaD, ClassLabel, Features, Sequence, Value
from .image import Image
from .translation import Translation, TranslationVariableLanguages



