

'''simple docstring'''





import mpmath  # for roots of unity
import numpy as np





class 		__SCREAMING_SNAKE_CASE       :







				def __init__(					self    :		Union[str, Any]		,				UpperCAmelCase__    :		List[Any]=None		,				UpperCAmelCase__    :		Optional[Any]=None      ):
										'''simple docstring'''
										# Input as list
										lowercase   :       Optional[int]								=list(poly_a or [0]      )[:]
										lowercase   :       Optional[Any]								=list(poly_b or [0]      )[:]

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

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

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

										# The product
										lowercase   :       Tuple								=self.__multiply()







				def    lowerCamelCase_  (					self    :		Union[str, Any]		,				UpperCAmelCase__    :		Tuple      ):
										'''simple docstring'''
										lowercase   :       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]
										#
										lowercase   :       Any								=self.c_max_length // 2
										while next_ncol > 0:
																lowercase   :       Optional[int]								=[[] for i in range(UpperCAmelCase__      )]
																lowercase   :       Tuple								=self.root**next_ncol

																# First half of next step
																lowercase   :       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
																lowercase   :       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
																lowercase   :       Dict								=new_dft
																lowercase   :       Tuple								=next_ncol // 2
										return dft[0]







				def    lowerCamelCase_  (					self    :		List[Any]      ):
										'''simple docstring'''
										lowercase   :       Any								=self.__dft('''A'''      )
										lowercase   :       Any								=self.__dft('''B'''      )
										lowercase   :       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
										lowercase   :       Optional[int]								=2
										while next_ncol <= self.c_max_length:
																lowercase   :       Optional[int]								=[[] for i in range(UpperCAmelCase__      )]
																lowercase   :       List[str]								=self.root ** (next_ncol // 2)
																lowercase   :       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
																lowercase   :       List[Any]								=new_inverse_c
																next_ncol *= 2
										# Unpack
										lowercase   :       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'''
										lowercase   :       Any								='''A = ''' + ''' + '''.join(
										    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]      )      )
										lowercase   :       Tuple								='''B = ''' + ''' + '''.join(
										    F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]      )      )
										lowercase   :       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'''





from typing import List, Optional, Tuple, Union

import torch

from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput





class 		__SCREAMING_SNAKE_CASE       ( lowercase__			):







				def __init__(					self    :		Optional[Any]		,				UpperCAmelCase__    :		Optional[int]		,				UpperCAmelCase__    :		int      ):
										'''simple docstring'''
										super().__init__()

										# make sure scheduler can always be converted to DDIM
										lowercase   :       Any								=DDIMScheduler.from_config(scheduler.config      )

										self.register_modules(unet=UpperCAmelCase__		,				scheduler=UpperCAmelCase__      )







				@torch.no_grad()
				def __call__(					self    :		List[Any]		,				UpperCAmelCase__    :		int = 1		,				UpperCAmelCase__    :		Optional[Union[torch.Generator, List[torch.Generator]]] = None		,				UpperCAmelCase__    :		float = 0.0		,				UpperCAmelCase__    :		int = 50		,				UpperCAmelCase__    :		Optional[bool] = None		,				UpperCAmelCase__    :		Optional[str] = "pil"		,				UpperCAmelCase__    :		bool = True		,				):
										'''simple docstring'''

										# Sample gaussian noise to begin loop
										if isinstance(self.unet.config.sample_size		,				UpperCAmelCase__      ):
																lowercase   :       Optional[int]								=(
																    batch_size,
																    self.unet.config.in_channels,
																    self.unet.config.sample_size,
																    self.unet.config.sample_size,
																)
										else:
																lowercase   :       Optional[int]								=(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

										if isinstance(UpperCAmelCase__		,				UpperCAmelCase__      ) and len(UpperCAmelCase__      ) != batch_size:
																raise ValueError(
																    F'''You have passed a list of generators of length {len(UpperCAmelCase__      )}, but requested an effective batch'''
																    F''' size of {batch_size}. Make sure the batch size matches the length of the generators.'''      )

										lowercase   :       str								=randn_tensor(UpperCAmelCase__		,				generator=UpperCAmelCase__		,				device=self.device		,				dtype=self.unet.dtype      )

										# set step values
										self.scheduler.set_timesteps(UpperCAmelCase__      )

										for t in self.progress_bar(self.scheduler.timesteps      ):
																# 1. predict noise model_output
																lowercase   :       Dict								=self.unet(UpperCAmelCase__		,				UpperCAmelCase__      ).sample

																# 2. predict previous mean of image x_t-1 and add variance depending on eta
																# eta corresponds to η in paper and should be between [0, 1]
																# do x_t -> x_t-1
																lowercase   :       Dict								=self.scheduler.step(
																    UpperCAmelCase__		,				UpperCAmelCase__		,				UpperCAmelCase__		,				eta=UpperCAmelCase__		,				use_clipped_model_output=UpperCAmelCase__		,				generator=UpperCAmelCase__      ).prev_sample

										lowercase   :       Optional[Any]								=(image / 2 + 0.5).clamp(0		,				1      )
										lowercase   :       Optional[Any]								=image.cpu().permute(0		,				2		,				3		,				1      ).numpy()
										if output_type == "pil":
																lowercase   :       List[str]								=self.numpy_to_pil(UpperCAmelCase__      )

										if not return_dict:
																return (image,)

										return ImagePipelineOutput(images=UpperCAmelCase__      )





