




"""simple docstring"""

from typing import Any, Callable, Dict, List, Optional, Union

import PIL.Image
import torch
from transformers import CLIPImageProcessor, CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    LMSDiscreteScheduler,
    PNDMScheduler,
    StableDiffusionImgaImgPipeline,
    StableDiffusionInpaintPipelineLegacy,
    StableDiffusionPipeline,
    UNetaDConditionModel,
)
from diffusers.configuration_utils import FrozenDict
from diffusers.pipelines.stable_diffusion.safety_checker import StableDiffusionSafetyChecker
from diffusers.utils import deprecate, logging


__lowerCamelCase								=						logging.get_logger(__name__)  # pylint: disable=invalid-name



class  _snake_case				(							A__       ):

				'''simple docstring'''




				UpperCamelCase__		     =["""safety_checker""", """feature_extractor"""]





				def __init__(							self      :  Tuple					,							snake_case      :  AutoencoderKL					,							snake_case      :  CLIPTextModel					,							snake_case      :  CLIPTokenizer					,							snake_case      :  UNetaDConditionModel					,							snake_case      :  Union[DDIMScheduler, PNDMScheduler, LMSDiscreteScheduler]					,							snake_case      :  StableDiffusionSafetyChecker					,							snake_case      :  CLIPImageProcessor					,							snake_case      :  bool = True					,							):
								super().__init__()
								if hasattr(scheduler.config					,							'''steps_offset'''     ) and scheduler.config.steps_offset != 1:
												UpperCAmelCase_					:Optional[int]      			=      (
												    f'The configuration file of this scheduler: {scheduler} is outdated. `steps_offset`'
												    f' should be set to 1 instead of {scheduler.config.steps_offset}. Please make sure '
												    '''to update the config accordingly as leaving `steps_offset` might led to incorrect results'''
												    ''' in future versions. If you have downloaded this checkpoint from the Hugging Face Hub,'''
												    ''' it would be very nice if you could open a Pull request for the `scheduler/scheduler_config.json`'''
												    ''' file'''
												)
												deprecate('''steps_offset!=1'''					,							'''1.0.0'''					,							snake_case					,							standard_warn=snake_case     )
												UpperCAmelCase_					:Dict      			=      dict(scheduler.config     )
												UpperCAmelCase_					:Optional[Any]      			=      1
												UpperCAmelCase_					:List[Any]      			=      FrozenDict(snake_case     )

								self.register_modules(
								    vae=snake_case					,							text_encoder=snake_case					,							tokenizer=snake_case					,							unet=snake_case					,							scheduler=snake_case					,							safety_checker=snake_case					,							feature_extractor=snake_case					,							)
								self.register_to_config(requires_safety_checker=snake_case     )





				@property
				def 				snake_case_ (							self      :  int     ):
								return {k: getattr(self					,							snake_case     ) for k in self.config.keys() if not k.startswith('''_'''     )}





				def 				snake_case_ (							self      :  Union[str, Any]					,							snake_case      :  Optional[Union[str, int]] = "auto"     ):
								if slice_size == "auto":
												# half the attention head size is usually a good trade-off between
												# speed and memory
												UpperCAmelCase_					:str      			=      self.unet.config.attention_head_dim // 2
								self.unet.set_attention_slice(snake_case     )





				def 				snake_case_ (							self      :  Optional[int]     ):
								self.enable_attention_slicing(snake_case     )





				@torch.no_grad()
				def 				snake_case_ (							self      :  Any					,							snake_case      :  Union[str, List[str]]					,							snake_case      :  Union[torch.FloatTensor, PIL.Image.Image]					,							snake_case      :  Union[torch.FloatTensor, PIL.Image.Image]					,							snake_case      :  float = 0.8					,							snake_case      :  Optional[int] = 50					,							snake_case      :  Optional[float] = 7.5					,							snake_case      :  Optional[Union[str, List[str]]] = None					,							snake_case      :  Optional[int] = 1					,							snake_case      :  Optional[float] = 0.0					,							snake_case      :  Optional[torch.Generator] = None					,							snake_case      :  Optional[str] = "pil"					,							snake_case      :  bool = True					,							snake_case      :  Optional[Callable[[int, int, torch.FloatTensor], None]] = None					,							snake_case      :  int = 1					,							):
								# For more information on how this function works, please see: https://huggingface.co/docs/diffusers/api/pipelines/stable_diffusion#diffusers.StableDiffusionImg2ImgPipeline
								return StableDiffusionInpaintPipelineLegacy(**self.components     )(
								    prompt=snake_case					,							image=snake_case					,							mask_image=snake_case					,							strength=snake_case					,							num_inference_steps=snake_case					,							guidance_scale=snake_case					,							negative_prompt=snake_case					,							num_images_per_prompt=snake_case					,							eta=snake_case					,							generator=snake_case					,							output_type=snake_case					,							return_dict=snake_case					,							callback=snake_case					,							)





				@torch.no_grad()
				def 				snake_case_ (							self      :  List[str]					,							snake_case      :  Union[str, List[str]]					,							snake_case      :  Union[torch.FloatTensor, PIL.Image.Image]					,							snake_case      :  float = 0.8					,							snake_case      :  Optional[int] = 50					,							snake_case      :  Optional[float] = 7.5					,							snake_case      :  Optional[Union[str, List[str]]] = None					,							snake_case      :  Optional[int] = 1					,							snake_case      :  Optional[float] = 0.0					,							snake_case      :  Optional[torch.Generator] = None					,							snake_case      :  Optional[str] = "pil"					,							snake_case      :  bool = True					,							snake_case      :  Optional[Callable[[int, int, torch.FloatTensor], None]] = None					,							snake_case      :  int = 1					,							**snake_case      :  int					,							):
								# For more information on how this function works, please see: https://huggingface.co/docs/diffusers/api/pipelines/stable_diffusion#diffusers.StableDiffusionImg2ImgPipeline
								return StableDiffusionImgaImgPipeline(**self.components     )(
								    prompt=snake_case					,							image=snake_case					,							strength=snake_case					,							num_inference_steps=snake_case					,							guidance_scale=snake_case					,							negative_prompt=snake_case					,							num_images_per_prompt=snake_case					,							eta=snake_case					,							generator=snake_case					,							output_type=snake_case					,							return_dict=snake_case					,							callback=snake_case					,							callback_steps=snake_case					,							)





				@torch.no_grad()
				def 				snake_case_ (							self      :  Tuple					,							snake_case      :  Union[str, List[str]]					,							snake_case      :  int = 512					,							snake_case      :  int = 512					,							snake_case      :  int = 50					,							snake_case      :  float = 7.5					,							snake_case      :  Optional[Union[str, List[str]]] = None					,							snake_case      :  Optional[int] = 1					,							snake_case      :  float = 0.0					,							snake_case      :  Optional[torch.Generator] = None					,							snake_case      :  Optional[torch.FloatTensor] = None					,							snake_case      :  Optional[str] = "pil"					,							snake_case      :  bool = True					,							snake_case      :  Optional[Callable[[int, int, torch.FloatTensor], None]] = None					,							snake_case      :  int = 1					,							):
								# For more information on how this function https://huggingface.co/docs/diffusers/api/pipelines/stable_diffusion#diffusers.StableDiffusionPipeline
								return StableDiffusionPipeline(**self.components     )(
								    prompt=snake_case					,							height=snake_case					,							width=snake_case					,							num_inference_steps=snake_case					,							guidance_scale=snake_case					,							negative_prompt=snake_case					,							num_images_per_prompt=snake_case					,							eta=snake_case					,							generator=snake_case					,							latents=snake_case					,							output_type=snake_case					,							return_dict=snake_case					,							callback=snake_case					,							callback_steps=snake_case					,							)








"""simple docstring"""

def 				a (						__snake_case     :				list[list[int]]  ):



				'''simple docstring'''





				if len(__snake_case  ) == 0 or not all(len(__snake_case  ) == 2 for pair in coordinates  ):
								raise ValueError('''The program cannot work out a fitting polynomial.'''  )

				if len({tuple(__snake_case  ) for pair in coordinates}  ) != len(__snake_case  ):
								raise ValueError('''The program cannot work out a fitting polynomial.'''  )

				UpperCAmelCase_					:Optional[Any]      			=      {x for x, _ in coordinates}
				if len(__snake_case  ) == 1:
								return f'x={coordinates[0][0]}'

				if len(__snake_case  ) != len(__snake_case  ):
								raise ValueError('''The program cannot work out a fitting polynomial.'''  )

				UpperCAmelCase_					:List[Any]      			=      len(__snake_case  )

				UpperCAmelCase_					:str      			=      0
				UpperCAmelCase_					:list[list[float]]      			=      []
				# put the x and x to the power values in a matrix
				while count_of_line < x:
								UpperCAmelCase_					:str      			=      0
								UpperCAmelCase_					:Optional[int]      			=      coordinates[count_of_line][0]
								UpperCAmelCase_					:list[float]      			=      []
								while count_in_line < x:
												count_line.append(a ** (x - (count_in_line + 1))  )
												count_in_line += 1
								matrix.append(__snake_case  )
								count_of_line += 1

				UpperCAmelCase_					:Dict      			=      0
				# put the y values into a vector
				UpperCAmelCase_					:list[float]      			=      []
				while count_of_line < x:
								vector.append(coordinates[count_of_line][1]  )
								count_of_line += 1

				UpperCAmelCase_					:Dict      			=      0

				while count < x:
								UpperCAmelCase_					:Any      			=      0
								while zahlen < x:
												if count == zahlen:
																zahlen += 1
												if zahlen == x:
																break
												UpperCAmelCase_					:str      			=      matrix[zahlen][count] / matrix[count][count]
												for counting_columns, item in enumerate(matrix[count]  ):
																# manipulating all the values in the matrix
																matrix[zahlen][counting_columns] -= item * bruch
												# manipulating the values in the vector
												vector[zahlen] -= vector[count] * bruch
												zahlen += 1
								count += 1

				UpperCAmelCase_					:Tuple      			=      0
				# make solutions
				UpperCAmelCase_					:list[str]      			=      []
				while count < x:
								solution.append(str(vector[count] / matrix[count][count]  )  )
								count += 1

				UpperCAmelCase_					:Optional[int]      			=      0
				UpperCAmelCase_					:Optional[Any]      			=      '''f(x)='''

				while count < x:
								UpperCAmelCase_					:list[str]      			=      solution[count].split('''E'''  )
								if len(__snake_case  ) > 1:
												UpperCAmelCase_					:List[Any]      			=      f'{remove_e[0]}*10^{remove_e[1]}'
								solved += f'x^{x - (count + 1)}*{solution[count]}'
								if count + 1 != x:
												solved += "+"
								count += 1

				return solved


if __name__ == "__main__":
						print(points_to_polynomial([]))
						print(points_to_polynomial([[]]))
						print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
						print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
						print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
						print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
						print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
						print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))


