




# limitations under the License.


from typing import Optional, Tuple, Union

import torch

from diffusers import DiffusionPipeline, ImagePipelineOutput



class       a_       (     SCREAMING_SNAKE_CASE__     ):





	def __init__(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					Tuple:




				"""simple docstring"""



				super().__init__()
				self.register_modules(unet=SCREAMING_SNAKE_CASE      ,     scheduler=SCREAMING_SNAKE_CASE      )





	@torch.no_grad()
	def __call__(							self      ,     SCREAMING_SNAKE_CASE = 1      ,     SCREAMING_SNAKE_CASE = None      ,     SCREAMING_SNAKE_CASE = 50      ,     SCREAMING_SNAKE_CASE = "pil"      ,     SCREAMING_SNAKE_CASE = True      ,     **SCREAMING_SNAKE_CASE      ,     )  ->					Union[ImagePipelineOutput, Tuple]:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						torch.randn(
				    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)      ,     generator=SCREAMING_SNAKE_CASE      ,     )
				SCREAMING_SNAKE_CASE_								=						image.to(self.device      )

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

				for t in self.progress_bar(self.scheduler.timesteps      ):
							# 1. predict noise model_output
							SCREAMING_SNAKE_CASE_								=						self.unet(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      ).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
							SCREAMING_SNAKE_CASE_								=						self.scheduler.step(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      ).prev_sample

				SCREAMING_SNAKE_CASE_								=						(image / 2 + 0.5).clamp(0      ,     1      )
				SCREAMING_SNAKE_CASE_								=						image.cpu().permute(0      ,     2      ,     3      ,     1      ).numpy()
				if output_type == "pil":
							SCREAMING_SNAKE_CASE_								=						self.numpy_to_pil(SCREAMING_SNAKE_CASE      )

				if not return_dict:
							return (image,), "This is a local test"

				return ImagePipelineOutput(images=SCREAMING_SNAKE_CASE      ), "This is a local test"






from __future__ import annotations

from collections.abc import MutableSequence



class       a_       :





	def __init__(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					None:




				"""simple docstring"""



				if len(SCREAMING_SNAKE_CASE      ) != degree + 1:
							raise ValueError(
							    'The number of coefficients should be equal to the degree + 1.'      )

				SCREAMING_SNAKE_CASE_								=						list(SCREAMING_SNAKE_CASE      )
				SCREAMING_SNAKE_CASE_								=						degree





	def __add__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				if self.degree > polynomial_a.degree:
							SCREAMING_SNAKE_CASE_								=						self.coefficients[:]
							for i in range(polynomial_a.degree + 1      ):
										coefficients[i] += polynomial_a.coefficients[i]
							return Polynomial(self.degree      ,     SCREAMING_SNAKE_CASE      )
				else:
							SCREAMING_SNAKE_CASE_								=						polynomial_a.coefficients[:]
							for i in range(self.degree + 1      ):
										coefficients[i] += self.coefficients[i]
							return Polynomial(polynomial_a.degree      ,     SCREAMING_SNAKE_CASE      )





	def __sub__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				return self + polynomial_a * Polynomial(0      ,     [-1]      )





	def __neg__(							self      )  ->					Polynomial:




				"""simple docstring"""



				return Polynomial(self.degree      ,     [-c for c in self.coefficients]      )





	def __mul__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * (self.degree + polynomial_a.degree + 1)
				for i in range(self.degree + 1      ):
							for j in range(polynomial_a.degree + 1      ):
										coefficients[i + j] += (
										    self.coefficients[i] * polynomial_a.coefficients[j]
										)

				return Polynomial(self.degree + polynomial_a.degree      ,     SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					int | float:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						0
				for i in range(self.degree + 1      ):
							result += self.coefficients[i] * (substitution**i)
				return result





	def __str__(							self      )  ->					str:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						''
				for i in range(self.degree      ,     -1      ,     -1      ):
							if self.coefficients[i] == 0:
										continue
							elif self.coefficients[i] > 0:
										if polynomial:
													polynomial += " + "
							else:
										polynomial += " - "

							if i == 0:
										polynomial += str(abs(self.coefficients[i]      )      )
							elif i == 1:
										polynomial += str(abs(self.coefficients[i]      )      ) + "x"
							else:
										polynomial += str(abs(self.coefficients[i]      )      ) + "x^" + str(SCREAMING_SNAKE_CASE      )

				return polynomial





	def __repr__(							self      )  ->					str:




				"""simple docstring"""



				return self.__str__()





	def 						A_(							self      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * self.degree
				for i in range(self.degree      ):
							SCREAMING_SNAKE_CASE_								=						self.coefficients[i + 1] * (i + 1)
				return Polynomial(self.degree - 1      ,     SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE = 0      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * (self.degree + 2)
				SCREAMING_SNAKE_CASE_								=						constant
				for i in range(self.degree + 1      ):
							SCREAMING_SNAKE_CASE_								=						self.coefficients[i] / (i + 1)
				return Polynomial(self.degree + 1      ,     SCREAMING_SNAKE_CASE      )





	def __eq__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				if not isinstance(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      ):
							return False

				if self.degree != polynomial_a.degree:
							return False

				for i in range(self.degree + 1      ):
							if self.coefficients[i] != polynomial_a.coefficients[i]:
										return False

				return True





	def __ne__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				return not self.__eq__(SCREAMING_SNAKE_CASE      )
