
import mpmath  # for roots of unity
import numpy as np
class 			UpperCamelCase      :
     def __init__(     self  ,     snake_case__=None  ,     snake_case__=None				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				Any							    = list(poly_a or [0]				)[:]
       _SCREAMING_SNAKE_CASE   :				Dict							    = list(poly_b or [0]				)[:]

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

       while self.polyB[-1] == 0:
         self.polyB.pop()
       _SCREAMING_SNAKE_CASE   :				List[str]							    = len(self.polyB				)

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

       # The product
       _SCREAMING_SNAKE_CASE   :				str							    = self.__multiply()
     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__				):




       """simple docstring"""


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

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




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				List[Any]							    = self.__dft("A"				)
       _SCREAMING_SNAKE_CASE   :				Union[str, Any]							    = self.__dft("B"				)
       _SCREAMING_SNAKE_CASE   :				Any							    = [[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
       _SCREAMING_SNAKE_CASE   :				Tuple							    = 2
       while next_ncol <= self.c_max_length:
         _SCREAMING_SNAKE_CASE   :				Tuple							    = [[] for i in range(snake_case__				)]
         _SCREAMING_SNAKE_CASE   :				Tuple							    = self.root ** (next_ncol // 2)
         _SCREAMING_SNAKE_CASE   :				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
         _SCREAMING_SNAKE_CASE   :				List[Any]							    = new_inverse_c
         next_ncol *= 2
       # Unpack
       _SCREAMING_SNAKE_CASE   :				List[str]							    = [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				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = '''A = ''' + ''' + '''.join(
           F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]				)				)
       _SCREAMING_SNAKE_CASE   :				List[str]							    = '''B = ''' + ''' + '''.join(
           F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]				)				)
       _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = '''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"""
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch
import torch.nn as nn

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, apply_forward_hook
from .modeling_utils import ModelMixin
from .vae import Decoder, DecoderOutput, Encoder, VectorQuantizer
@dataclass
class 			UpperCamelCase      (							__SCREAMING_SNAKE_CASE  ):
     A__      =			42
class 			UpperCamelCase      (							__SCREAMING_SNAKE_CASE      ,       __SCREAMING_SNAKE_CASE  ):
     @register_to_config
     def __init__(     self  ,     snake_case__ = 3  ,     snake_case__ = 3  ,     snake_case__ = ("DownEncoderBlock2D",)  ,     snake_case__ = ("UpDecoderBlock2D",)  ,     snake_case__ = (64,)  ,     snake_case__ = 1  ,     snake_case__ = "silu"  ,     snake_case__ = 3  ,     snake_case__ = 32  ,     snake_case__ = 256  ,     snake_case__ = 32  ,     snake_case__ = None  ,     snake_case__ = 0.18_215  ,     snake_case__ = "group"  ,     ):




       """simple docstring"""


       super().__init__()

       # pass init params to Encoder
       _SCREAMING_SNAKE_CASE   :				Optional[Any]							    = Encoder(
           in_channels=snake_case__  ,     out_channels=snake_case__  ,     down_block_types=snake_case__  ,     block_out_channels=snake_case__  ,     layers_per_block=snake_case__  ,     act_fn=snake_case__  ,     norm_num_groups=snake_case__  ,     double_z=snake_case__  ,     )

       _SCREAMING_SNAKE_CASE   :				Dict							    = vq_embed_dim if vq_embed_dim is not None else latent_channels

       _SCREAMING_SNAKE_CASE   :				Tuple							    = nn.Convad(snake_case__  ,     snake_case__  ,     1				)
       _SCREAMING_SNAKE_CASE   :				Optional[int]							    = VectorQuantizer(snake_case__  ,     snake_case__  ,     beta=0.25  ,     remap=snake_case__  ,     sane_index_shape=snake_case__				)
       _SCREAMING_SNAKE_CASE   :				List[str]							    = nn.Convad(snake_case__  ,     snake_case__  ,     1				)

       # pass init params to Decoder
       _SCREAMING_SNAKE_CASE   :				Optional[int]							    = Decoder(
           in_channels=snake_case__  ,     out_channels=snake_case__  ,     up_block_types=snake_case__  ,     block_out_channels=snake_case__  ,     layers_per_block=snake_case__  ,     act_fn=snake_case__  ,     norm_num_groups=snake_case__  ,     norm_type=snake_case__  ,     )
     @apply_forward_hook
     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__  ,     snake_case__ = True				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				List[str]							    = self.encoder(snake_case__				)
       _SCREAMING_SNAKE_CASE   :				Dict							    = self.quant_conv(snake_case__				)

       if not return_dict:
         return (h,)

       return VQEncoderOutput(latents=snake_case__				)
     @apply_forward_hook
     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__  ,     snake_case__ = False  ,     snake_case__ = True				):




       """simple docstring"""


       if not force_not_quantize:
         _SCREAMING_SNAKE_CASE    ,		_SCREAMING_SNAKE_CASE    ,		_SCREAMING_SNAKE_CASE   :				int							    = self.quantize(snake_case__				)
       else:
         _SCREAMING_SNAKE_CASE   :				int							    = h
       _SCREAMING_SNAKE_CASE   :				Dict							    = self.post_quant_conv(snake_case__				)
       _SCREAMING_SNAKE_CASE   :				int							    = self.decoder(snake_case__  ,     quant if self.config.norm_type == "spatial" else None				)

       if not return_dict:
         return (dec,)

       return DecoderOutput(sample=snake_case__				)




     def 				__SCREAMING_SNAKE_CASE							(     self  ,     snake_case__  ,     snake_case__ = True				):




       """simple docstring"""


       _SCREAMING_SNAKE_CASE   :				Tuple							    = sample
       _SCREAMING_SNAKE_CASE   :				Union[str, Any]							    = self.encode(snake_case__				).latents
       _SCREAMING_SNAKE_CASE   :				Any							    = self.decode(snake_case__				).sample

       if not return_dict:
         return (dec,)

       return DecoderOutput(sample=snake_case__				)



