





'''simple docstring'''

import mpmath  # for roots of unity
import numpy as np
class     __lowerCAmelCase					:






       """simple docstring"""





       def __init__(							self       :		Tuple	,			lowerCAmelCase__       :		Dict=None	,			lowerCAmelCase__       :		Union[str, Any]=None					)   ->					Optional[Any]:

            '''simple docstring'''




            _UpperCamelCase       =	list(poly_a or [0]					)[:]
            _UpperCamelCase       =	list(poly_b or [0]					)[:]

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

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

            # Add 0 to make lengths equal a power of 2
            _UpperCamelCase       =	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
            _UpperCamelCase       =	complex(mpmath.root(x=1	,			n=self.c_max_length	,			k=1					)					)

            # The product
            _UpperCamelCase       =	self.__multiply()





       def snake_case__						(							self       :		Optional[int]	,			lowerCAmelCase__       :		str					)   ->					List[str]:

            '''simple docstring'''




            _UpperCamelCase       =	[[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]
            #
            _UpperCamelCase       =	self.c_max_length // 2
            while next_ncol > 0:
                 _UpperCamelCase       =	[[] for i in range(__lowerCAmelCase					)]
                 _UpperCamelCase       =	self.root**next_ncol

                 # First half of next step
                 _UpperCamelCase       =	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
                 _UpperCamelCase       =	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
                 _UpperCamelCase       =	new_dft
                 _UpperCamelCase       =	next_ncol // 2
            return dft[0]





       def snake_case__						(							self       :		Tuple					)   ->					Any:

            '''simple docstring'''




            _UpperCamelCase       =	self.__dft('''A'''					)
            _UpperCamelCase       =	self.__dft('''B'''					)
            _UpperCamelCase       =	[[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
            _UpperCamelCase       =	2
            while next_ncol <= self.c_max_length:
                 _UpperCamelCase       =	[[] for i in range(__lowerCAmelCase					)]
                 _UpperCamelCase       =	self.root ** (next_ncol // 2)
                 _UpperCamelCase       =	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
                 _UpperCamelCase       =	new_inverse_c
                 next_ncol *= 2
            # Unpack
            _UpperCamelCase       =	[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       :		Dict					)   ->					Tuple:

            '''simple docstring'''




            _UpperCamelCase       =	'''A = ''' + ''' + '''.join(
                f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]					)					)
            _UpperCamelCase       =	'''B = ''' + ''' + '''.join(
                f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]					)					)
            _UpperCamelCase       =	'''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 unittest

from transformers.utils.backbone_utils import (
    BackboneMixin,
    get_aligned_output_features_output_indices,
    verify_out_features_out_indices,
)
class     __lowerCAmelCase					(   unittest.TestCase			):






       """simple docstring"""





       def snake_case__						(							self       :		Optional[Any]					)   ->					List[str]:

            '''simple docstring'''




            _UpperCamelCase       =	['''a''', '''b''', '''c''']

            # Defaults to last layer if both are None
            _UpperCamelCase   ,    _UpperCamelCase       =	get_aligned_output_features_output_indices(lowerCAmelCase__	,			lowerCAmelCase__	,			lowerCAmelCase__					)
            self.assertEqual(lowerCAmelCase__	,			['''c''']					)
            self.assertEqual(lowerCAmelCase__	,			[2]					)

            # Out indices set to match out features
            _UpperCamelCase   ,    _UpperCamelCase       =	get_aligned_output_features_output_indices(['''a''', '''c''']	,			lowerCAmelCase__	,			lowerCAmelCase__					)
            self.assertEqual(lowerCAmelCase__	,			['''a''', '''c''']					)
            self.assertEqual(lowerCAmelCase__	,			[0, 2]					)

            # Out features set to match out indices
            _UpperCamelCase   ,    _UpperCamelCase       =	get_aligned_output_features_output_indices(lowerCAmelCase__	,			[0, 2]	,			lowerCAmelCase__					)
            self.assertEqual(lowerCAmelCase__	,			['''a''', '''c''']					)
            self.assertEqual(lowerCAmelCase__	,			[0, 2]					)

            # Out features selected from negative indices
            _UpperCamelCase   ,    _UpperCamelCase       =	get_aligned_output_features_output_indices(lowerCAmelCase__	,			[-3, -1]	,			lowerCAmelCase__					)
            self.assertEqual(lowerCAmelCase__	,			['''a''', '''c''']					)
            self.assertEqual(lowerCAmelCase__	,			[-3, -1]					)





       def snake_case__						(							self       :		Any					)   ->					Union[str, Any]:

            '''simple docstring'''




            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(['''a''', '''b''']	,			(0, 1)	,			lowerCAmelCase__					)

            # Out features must be a list
            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(('''a''', '''b''')	,			(0, 1)	,			['''a''', '''b''']					)

            # Out features must be a subset of stage names
            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(['''a''', '''b''']	,			(0, 1)	,			['''a''']					)

            # Out indices must be a list or tuple
            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(lowerCAmelCase__	,			0	,			['''a''', '''b''']					)

            # Out indices must be a subset of stage names
            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(lowerCAmelCase__	,			(0, 1)	,			['''a''']					)

            # Out features and out indices must be the same length
            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(['''a''', '''b''']	,			(0,)	,			['''a''', '''b''', '''c''']					)

            # Out features should match out indices
            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(['''a''', '''b''']	,			(0, 2)	,			['''a''', '''b''', '''c''']					)

            # Out features and out indices should be in order
            with self.assertRaises(lowerCAmelCase__					):
                 verify_out_features_out_indices(['''b''', '''a''']	,			(0, 1)	,			['''a''', '''b''']					)

            # Check passes with valid inputs
            verify_out_features_out_indices(['''a''', '''b''', '''d''']	,			(0, 1, -1)	,			['''a''', '''b''', '''c''', '''d''']					)







       def snake_case__						(							self       :		Any					)   ->					str:

            '''simple docstring'''




            _UpperCamelCase       =	BackboneMixin()

            _UpperCamelCase       =	['''a''', '''b''', '''c''']
            _UpperCamelCase       =	['''a''', '''c''']
            _UpperCamelCase       =	[0, 2]

            # Check that the output features and indices are set correctly
            self.assertEqual(backbone.out_features	,			['''a''', '''c''']					)
            self.assertEqual(backbone.out_indices	,			[0, 2]					)

            # Check out features and indices are updated correctly
            _UpperCamelCase       =	['''a''', '''b''']
            self.assertEqual(backbone.out_features	,			['''a''', '''b''']					)
            self.assertEqual(backbone.out_indices	,			[0, 1]					)

            _UpperCamelCase       =	[-3, -1]
            self.assertEqual(backbone.out_features	,			['''a''', '''c''']					)
            self.assertEqual(backbone.out_indices	,			[-3, -1]					)



