






import math
from typing import Callable, List, Optional, Union

import numpy as np
import PIL
import torch
from PIL import Image
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers.models import AutoencoderKL, UNetaDConditionModel
from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion_upscale import StableDiffusionUpscalePipeline
from diffusers.schedulers import DDIMScheduler, DDPMScheduler, LMSDiscreteScheduler, PNDMScheduler




def 					lowercase__				(					__snake_case   :							Any					,	__snake_case   :							Tuple					,	__snake_case   :							List[Any]=[]  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Dict						=						size[0] - overlap_pixels * 2
					UpperCAmelCase_   :				List[Any]						=						size[1] - overlap_pixels * 2
					for letter in ["l", "r"]:
										if letter in remove_borders:
															size_x += overlap_pixels
					for letter in ["t", "b"]:
										if letter in remove_borders:
															size_y += overlap_pixels
					UpperCAmelCase_   :				Tuple						=						np.ones((size_y, size_x)					,	dtype=np.uinta  ) * 255
					UpperCAmelCase_   :				List[str]						=						np.pad(__snake_case					,	mode='linear_ramp'					,	pad_width=__snake_case					,	end_values=0  )

					if "l" in remove_borders:
										UpperCAmelCase_   :				Optional[int]						=						mask[:, overlap_pixels : mask.shape[1]]
					if "r" in remove_borders:
										UpperCAmelCase_   :				List[Any]						=						mask[:, 0 : mask.shape[1] - overlap_pixels]
					if "t" in remove_borders:
										UpperCAmelCase_   :				int						=						mask[overlap_pixels : mask.shape[0], :]
					if "b" in remove_borders:
										UpperCAmelCase_   :				Dict						=						mask[0 : mask.shape[0] - overlap_pixels, :]
					return mask




def 					lowercase__				(					__snake_case   :							Dict					,	__snake_case   :							Optional[Any]					,	__snake_case   :							Optional[int]  ):


					'''simple docstring'''


					return max(__snake_case					,	min(__snake_case					,	__snake_case  )  )




def 					lowercase__				(					__snake_case   :							[int]					,	__snake_case   :							[int]					,	__snake_case   :							[int]  ):


					'''simple docstring'''


					return (
					    clamp(rect[0]					,	min[0]					,	max[0]  ),
					    clamp(rect[1]					,	min[1]					,	max[1]  ),
					    clamp(rect[2]					,	min[0]					,	max[0]  ),
					    clamp(rect[3]					,	min[1]					,	max[1]  ),
					)




def 					lowercase__				(					__snake_case   :							[int]					,	__snake_case   :							int					,	__snake_case   :							[int]  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Union[str, Any]						=						list(__snake_case  )
					rect[0] -= overlap
					rect[1] -= overlap
					rect[2] += overlap
					rect[3] += overlap
					UpperCAmelCase_   :				int						=						clamp_rect(__snake_case					,	[0, 0]					,	[image_size[0], image_size[1]]  )
					return rect




def 					lowercase__				(					__snake_case   :							List[str]					,	__snake_case   :							str					,	__snake_case   :							Union[str, Any]					,	__snake_case   :							Any  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Tuple						=						Image.new('RGB'					,	(tile.size[0] + original_slice, tile.size[1])  )
					result.paste(
					    original_image.resize((tile.size[0], tile.size[1])					,	Image.BICUBIC  ).crop(
					        (slice_x, 0, slice_x + original_slice, tile.size[1])  )					,	(0, 0)					,	)
					result.paste(__snake_case					,	(original_slice, 0)  )
					return result




def 					lowercase__				(					__snake_case   :							Union[str, Any]					,	__snake_case   :							str  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Optional[int]						=						(original_image_slice * 4, 0, tile.size[0], tile.size[1])
					UpperCAmelCase_   :				List[Any]						=						tile.crop(__snake_case  )
					return tile




def 					lowercase__				(					__snake_case   :							Optional[Any]					,	__snake_case   :							List[str]  ):


					'''simple docstring'''


					UpperCAmelCase_   :				str						=						n % d
					return n - divisor



class   lowerCamelCase				(_snake_case      ):







		'''simple docstring'''



		def __init__(							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = 3_5_0    ,		)     ->							List[Any]:
							super().__init__(
							    vae=_UpperCamelCase    ,		text_encoder=_UpperCamelCase    ,		tokenizer=_UpperCamelCase    ,		unet=_UpperCamelCase    ,		low_res_scheduler=_UpperCamelCase    ,		scheduler=_UpperCamelCase    ,		max_noise_level=_UpperCamelCase    ,		)



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		**_UpperCamelCase       )     ->							List[Any]:
							torch.manual_seed(0       )
							UpperCAmelCase_   :				Tuple						=						(
							    min(image.size[0] - (tile_size + original_image_slice)    ,		x * tile_size       ),
							    min(image.size[1] - (tile_size + original_image_slice)    ,		y * tile_size       ),
							    min(image.size[0]    ,		(x + 1) * tile_size       ),
							    min(image.size[1]    ,		(y + 1) * tile_size       ),
							)
							UpperCAmelCase_   :				List[str]						=						add_overlap_rect(_UpperCamelCase    ,		_UpperCamelCase    ,		image.size       )
							UpperCAmelCase_   :				Optional[int]						=						image.crop(_UpperCamelCase       )
							UpperCAmelCase_   :				List[Any]						=						((crop_rect[0] + ((crop_rect[2] - crop_rect[0]) / 2)) / image.size[0]) * tile.size[0]
							UpperCAmelCase_   :				int						=						translated_slice_x - (original_image_slice / 2)
							UpperCAmelCase_   :				str						=						max(0    ,		_UpperCamelCase       )
							UpperCAmelCase_   :				Union[str, Any]						=						squeeze_tile(_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase       )
							UpperCAmelCase_   :				Optional[int]						=						to_input.size
							UpperCAmelCase_   :				Union[str, Any]						=						to_input.resize((tile_size, tile_size)    ,		Image.BICUBIC       )
							UpperCAmelCase_   :				str						=						super(_UpperCamelCase    ,		self       ).__call__(image=_UpperCamelCase    ,		**_UpperCamelCase       ).images[0]
							UpperCAmelCase_   :				Any						=						upscaled_tile.resize((orig_input_size[0] * 4, orig_input_size[1] * 4)    ,		Image.BICUBIC       )
							UpperCAmelCase_   :				Optional[Any]						=						unsqueeze_tile(_UpperCamelCase    ,		_UpperCamelCase       )
							UpperCAmelCase_   :				int						=						upscaled_tile.resize((tile.size[0] * 4, tile.size[1] * 4)    ,		Image.BICUBIC       )
							UpperCAmelCase_   :				List[str]						=						[]
							if x == 0:
												remove_borders.append('l'       )
							elif crop_rect[2] == image.size[0]:
												remove_borders.append('r'       )
							if y == 0:
												remove_borders.append('t'       )
							elif crop_rect[3] == image.size[1]:
												remove_borders.append('b'       )
							UpperCAmelCase_   :				Optional[Any]						=						Image.fromarray(
							    make_transparency_mask(
							        (upscaled_tile.size[0], upscaled_tile.size[1])    ,		tile_border * 4    ,		remove_borders=_UpperCamelCase       )    ,		mode='L'    ,		)
							final_image.paste(
							    _UpperCamelCase    ,		(crop_rect_with_overlap[0] * 4, crop_rect_with_overlap[1] * 4)    ,		_UpperCamelCase       )



		@torch.no_grad()
		def __call__(							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = 7_5    ,		_UpperCamelCase = 9.0    ,		_UpperCamelCase = 5_0    ,		_UpperCamelCase = None    ,		_UpperCamelCase = 1    ,		_UpperCamelCase = 0.0    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = 1    ,		_UpperCamelCase = 1_2_8    ,		_UpperCamelCase = 3_2    ,		_UpperCamelCase = 3_2    ,		)     ->							Optional[int]:
							UpperCAmelCase_   :				str						=						Image.new('RGB'    ,		(image.size[0] * 4, image.size[1] * 4)       )
							UpperCAmelCase_   :				str						=						math.ceil(image.size[0] / tile_size       )
							UpperCAmelCase_   :				str						=						math.ceil(image.size[1] / tile_size       )
							UpperCAmelCase_   :				Optional[Any]						=						tcx * tcy
							UpperCAmelCase_   :				str						=						0
							for y in range(_UpperCamelCase       ):
												for x in range(_UpperCamelCase       ):
																	self._process_tile(
																	    _UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		prompt=_UpperCamelCase    ,		num_inference_steps=_UpperCamelCase    ,		guidance_scale=_UpperCamelCase    ,		noise_level=_UpperCamelCase    ,		negative_prompt=_UpperCamelCase    ,		num_images_per_prompt=_UpperCamelCase    ,		eta=_UpperCamelCase    ,		generator=_UpperCamelCase    ,		latents=_UpperCamelCase    ,		)
																	current_count += 1
																	if callback is not None:
																						callback({'progress': current_count / total_tile_count, 'image': final_image}       )
							return final_image





def 					lowercase__				(					):


					'''simple docstring'''


					UpperCAmelCase_   :				List[Any]						=						'stabilityai/stable-diffusion-x4-upscaler'
					UpperCAmelCase_   :				int						=						StableDiffusionTiledUpscalePipeline.from_pretrained(__snake_case					,	revision='fp16'					,	torch_dtype=torch.floataa  )
					UpperCAmelCase_   :				Union[str, Any]						=						pipe.to('cuda'  )
					UpperCAmelCase_   :				List[str]						=						Image.open('../../docs/source/imgs/diffusers_library.jpg'  )

					def callback(__snake_case   :							Optional[Any]  ):
										print(F"progress: {obj['progress']:.4f}"  )
										obj["image"].save('diffusers_library_progress.jpg'  )

					UpperCAmelCase_   :				Optional[int]						=						pipe(image=__snake_case					,	prompt='Black font, white background, vector'					,	noise_level=40					,	callback=__snake_case  )
					final_image.save('diffusers_library.jpg'  )


if __name__ == "__main__":
		main()














from __future__ import annotations

from collections.abc import Callable

__UpperCAmelCase     							=						list[list[float | int]]




def 					lowercase__				(					__snake_case   :							Matrix					,	__snake_case   :							Matrix  ):


					'''simple docstring'''


					UpperCAmelCase_   :				int						=						len(__snake_case  )
					UpperCAmelCase_   :				Matrix						=						[[0 for _ in range(size + 1  )] for _ in range(__snake_case  )]
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				float

					for row in range(__snake_case  ):
										for col in range(__snake_case  ):
															UpperCAmelCase_   :				Dict						=						matrix[row][col]

										UpperCAmelCase_   :				Union[str, Any]						=						vector[row][0]

					UpperCAmelCase_   :				Union[str, Any]						=						0
					UpperCAmelCase_   :				Union[str, Any]						=						0
					while row < size and col < size:
										# pivoting
										UpperCAmelCase_   :				Optional[Any]						=						max((abs(augmented[rowa][col]  ), rowa) for rowa in range(__snake_case					,	__snake_case  )  )[
										    1
										]
										if augmented[pivot_row][col] == 0:
															col += 1
															continue
										else:
															UpperCAmelCase_	,  UpperCAmelCase_   :				Tuple						=						augmented[pivot_row], augmented[row]

										for rowa in range(row + 1					,	__snake_case  ):
															UpperCAmelCase_   :				Optional[int]						=						augmented[rowa][col] / augmented[row][col]
															UpperCAmelCase_   :				List[str]						=						0
															for cola in range(col + 1					,	size + 1  ):
																				augmented[rowa][cola] -= augmented[row][cola] * ratio

										row += 1
										col += 1

					# back substitution
					for col in range(1					,	__snake_case  ):
										for row in range(__snake_case  ):
															UpperCAmelCase_   :				Union[str, Any]						=						augmented[row][col] / augmented[col][col]
															for cola in range(__snake_case					,	size + 1  ):
																				augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
					return [
					    [round(augmented[row][size] / augmented[row][row]					,	10  )] for row in range(__snake_case  )
					]




def 					lowercase__				(					__snake_case   :							list[int]  ):


					'''simple docstring'''


					UpperCAmelCase_   :				int						=						len(__snake_case  )
					UpperCAmelCase_   :				Matrix						=						[[0 for _ in range(__snake_case  )] for _ in range(__snake_case  )]
					UpperCAmelCase_   :				Matrix						=						[[0] for _ in range(__snake_case  )]
					UpperCAmelCase_   :				Matrix
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int
					UpperCAmelCase_   :				int

					for x_val, y_val in enumerate(__snake_case  ):
										for col in range(__snake_case  ):
															UpperCAmelCase_   :				int						=						(x_val + 1) ** (size - col - 1)
										UpperCAmelCase_   :				int						=						y_val

					UpperCAmelCase_   :				List[str]						=						solve(__snake_case					,	__snake_case  )

					def interpolated_func(__snake_case   :							int  ) -> int:
										return sum(
										    round(coeffs[x_val][0]  ) * (var ** (size - x_val - 1))
										    for x_val in range(__snake_case  )  )

					return interpolated_func




def 					lowercase__				(					__snake_case   :							int  ):


					'''simple docstring'''


					return (
					    1
					    - variable
					    + variable**2
					    - variable**3
					    + variable**4
					    - variable**5
					    + variable**6
					    - variable**7
					    + variable**8
					    - variable**9
					    + variable**10
					)




def 					lowercase__				(					__snake_case   :							Callable[[int], int] = question_function					,	__snake_case   :							int = 10  ):


					'''simple docstring'''


					UpperCAmelCase_   :				list[int]						=						[func(__snake_case  ) for x_val in range(1					,	order + 1  )]

					UpperCAmelCase_   :				list[Callable[[int], int]]						=						[
					    interpolate(data_points[:max_coeff]  ) for max_coeff in range(1					,	order + 1  )
					]

					UpperCAmelCase_   :				int						=						0
					UpperCAmelCase_   :				Callable[[int], int]
					UpperCAmelCase_   :				int

					for poly in polynomials:
										UpperCAmelCase_   :				Optional[int]						=						1
										while func(__snake_case  ) == poly(__snake_case  ):
															x_val += 1

										ret += poly(__snake_case  )

					return ret


if __name__ == "__main__":
		print(F'{solution() = }')






