


def  __SCREAMING_SNAKE_CASE       (				lowercase__  :list[list[int]]				)       ->  str:
						if len(lowercase__				) == 0 or not all(len(lowercase__				) == 2 for pair in coordinates				):
												raise ValueError('The program cannot work out a fitting polynomial.'				)

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

						__magic_name__				:							Optional[int]				=      {x for x, _ in coordinates}
						if len(lowercase__				) == 1:
												return f"x={coordinates[0][0]}"

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

						__magic_name__				:							List[str]				=      len(lowercase__				)

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

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

						__magic_name__				:							List[Any]				=      0

						while count < x:
												__magic_name__				:							Tuple				=      0
												while zahlen < x:
																		if count == zahlen:
																								zahlen += 1
																		if zahlen == x:
																								break
																		__magic_name__				:							List[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

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

						__magic_name__				:							Tuple				=      0
						__magic_name__				:							Tuple				=      'f(x)='

						while count < x:
												__magic_name__				:							list[str]				=      solution[count].split('E'				)
												if len(lowercase__				) > 1:
																		__magic_name__				:							int				=      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]]))






import numpy as np
import torch
import torch.nn as nn
from transformers import CLIPConfig, CLIPVisionModel, PreTrainedModel

from ...utils import logging


snake_case__     							= logging.get_logger(__name__)
def  __SCREAMING_SNAKE_CASE       (				lowercase__  :Optional[Any]      ,						lowercase__  :List[str]				)       ->  Tuple:
						__magic_name__				:							List[str]				=      nn.functional.normalize(lowercase__				)
						__magic_name__				:							Union[str, Any]				=      nn.functional.normalize(lowercase__				)
						return torch.mm(lowercase__      ,						normalized_text_embeds.t()				)



class     snake_case__  (      _A  ):
				__lowerCAmelCase		=      CLIPConfig

				__lowerCAmelCase		=      ['''CLIPEncoderLayer''']
				def __init__(  self     ,      _UpperCAmelCase      ):




										"""simple docstring"""




										super().__init__(_UpperCAmelCase      )

										__magic_name__				:							List[Any]				=      CLIPVisionModel(config.vision_config      )
										__magic_name__				:							Tuple				=      nn.Linear(config.vision_config.hidden_size     ,      config.projection_dim     ,      bias=_UpperCAmelCase      )

										__magic_name__				:							str				=      nn.Parameter(torch.ones(17     ,      config.projection_dim      )     ,      requires_grad=_UpperCAmelCase      )
										__magic_name__				:							Optional[Any]				=      nn.Parameter(torch.ones(3     ,      config.projection_dim      )     ,      requires_grad=_UpperCAmelCase      )

										__magic_name__				:							Optional[Any]				=      nn.Parameter(torch.ones(17      )     ,      requires_grad=_UpperCAmelCase      )
										__magic_name__				:							str				=      nn.Parameter(torch.ones(3      )     ,      requires_grad=_UpperCAmelCase      )
				@torch.no_grad()
				def  UpperCamelCase_						(  self     ,      _UpperCAmelCase     ,      _UpperCAmelCase      ):




										"""simple docstring"""




										__magic_name__				:							Union[str, Any]				=      self.vision_model(_UpperCAmelCase      )[1]  # pooled_output
										__magic_name__				:							Any				=      self.visual_projection(_UpperCAmelCase      )

										# we always cast to float32 as this does not cause significant overhead and is compatible with bfloat16
										__magic_name__				:							Union[str, Any]				=      cosine_distance(_UpperCAmelCase     ,      self.special_care_embeds      ).cpu().float().numpy()
										__magic_name__				:							int				=      cosine_distance(_UpperCAmelCase     ,      self.concept_embeds      ).cpu().float().numpy()

										__magic_name__				:							str				=      []
										__magic_name__				:							List[Any]				=      image_embeds.shape[0]
										for i in range(_UpperCAmelCase      ):
																__magic_name__				:							Optional[Any]				=      {'special_scores': {}, 'special_care': [], 'concept_scores': {}, 'bad_concepts': []}

																# increase this value to create a stronger `nfsw` filter
																# at the cost of increasing the possibility of filtering benign images
																__magic_name__				:							Optional[int]				=      0.0

																for concept_idx in range(len(special_cos_dist[0]      )      ):
																						__magic_name__				:							Any				=      special_cos_dist[i][concept_idx]
																						__magic_name__				:							Tuple				=      self.special_care_embeds_weights[concept_idx].item()
																						__magic_name__				:							Dict				=      round(concept_cos - concept_threshold + adjustment     ,      3      )
																						if result_img["special_scores"][concept_idx] > 0:
																												result_img["special_care"].append({concept_idx, result_img['special_scores'][concept_idx]}      )
																												__magic_name__				:							str				=      0.01

																for concept_idx in range(len(cos_dist[0]      )      ):
																						__magic_name__				:							Optional[Any]				=      cos_dist[i][concept_idx]
																						__magic_name__				:							Tuple				=      self.concept_embeds_weights[concept_idx].item()
																						__magic_name__				:							Optional[int]				=      round(concept_cos - concept_threshold + adjustment     ,      3      )
																						if result_img["concept_scores"][concept_idx] > 0:
																												result_img["bad_concepts"].append(_UpperCAmelCase      )

																result.append(_UpperCAmelCase      )

										__magic_name__				:							Union[str, Any]				=      [len(res['bad_concepts']      ) > 0 for res in result]

										for idx, has_nsfw_concept in enumerate(_UpperCAmelCase      ):
																if has_nsfw_concept:
																						if torch.is_tensor(_UpperCAmelCase      ) or torch.is_tensor(images[0]      ):
																												__magic_name__				:							Union[str, Any]				=      torch.zeros_like(images[idx]      )  # black image
																						else:
																												__magic_name__				:							Optional[int]				=      np.zeros(images[idx].shape      )  # black image

										if any(_UpperCAmelCase      ):
																logger.warning(
																    'Potential NSFW content was detected in one or more images. A black image will be returned instead.'
																    ' Try again with a different prompt and/or seed.'      )

										return images, has_nsfw_concepts





				@torch.no_grad()
				def  UpperCamelCase_						(  self     ,      _UpperCAmelCase     ,      _UpperCAmelCase      ):




										"""simple docstring"""




										__magic_name__				:							List[str]				=      self.vision_model(_UpperCAmelCase      )[1]  # pooled_output
										__magic_name__				:							List[str]				=      self.visual_projection(_UpperCAmelCase      )

										__magic_name__				:							Union[str, Any]				=      cosine_distance(_UpperCAmelCase     ,      self.special_care_embeds      )
										__magic_name__				:							Optional[int]				=      cosine_distance(_UpperCAmelCase     ,      self.concept_embeds      )

										# increase this value to create a stronger `nsfw` filter
										# at the cost of increasing the possibility of filtering benign images
										__magic_name__				:							int				=      0.0

										__magic_name__				:							Optional[int]				=      special_cos_dist - self.special_care_embeds_weights + adjustment
										# special_scores = special_scores.round(decimals=3)
										__magic_name__				:							int				=      torch.any(special_scores > 0     ,      dim=1      )
										__magic_name__				:							Optional[Any]				=      special_care * 0.01
										__magic_name__				:							Any				=      special_adjustment.unsqueeze(1      ).expand(-1     ,      cos_dist.shape[1]      )

										__magic_name__				:							Optional[int]				=      (cos_dist - self.concept_embeds_weights) + special_adjustment
										# concept_scores = concept_scores.round(decimals=3)
										__magic_name__				:							Union[str, Any]				=      torch.any(concept_scores > 0     ,      dim=1      )

										__magic_name__				:							Dict				=      0.0  # black image

										return images, has_nsfw_concepts


