'''simple docstring'''

def 					UpperCAmelCase__      (							_lowerCAmelCase						: Any)						->		str:



						"""simple docstring"""

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

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

						snake_case   :					Tuple							=						{x for x, _ in coordinates}
						if len(__lowerCamelCase) == 1:
												return f"""x={coordinates[0][0]}"""

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

						snake_case   :					Tuple							=						len(__lowerCamelCase)

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

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

						snake_case   :					Optional[Any]							=						0

						while count < x:
												snake_case   :					Optional[int]							=						0
												while zahlen < x:
																		if count == zahlen:
																								zahlen += 1
																		if zahlen == x:
																								break
																		snake_case   :					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

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

						snake_case   :					Union[str, Any]							=						0
						snake_case   :					Tuple							=						"""f(x)="""

						while count < x:
												snake_case   :					list[str]							=						solution[count].split("E")
												if len(__lowerCamelCase) > 1:
																		snake_case   :					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]]))






'''simple docstring'''

from typing import List, Optional, Union

import numpy as np
import PIL
import torch
from PIL import Image

from ...models import UNetaDConditionModel, VQModel
from ...pipelines import DiffusionPipeline
from ...pipelines.pipeline_utils import ImagePipelineOutput
from ...schedulers import DDPMScheduler
from ...utils import (
    is_accelerate_available,
    is_accelerate_version,
    logging,
    randn_tensor,
    replace_example_docstring,
)


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

A_        =   "\n    Examples:\n        ```py\n        >>> import torch\n        >>> import numpy as np\n\n        >>> from diffusers import KandinskyV22PriorEmb2EmbPipeline, KandinskyV22ControlnetImg2ImgPipeline\n        >>> from transformers import pipeline\n        >>> from diffusers.utils import load_image\n\n\n        >>> def make_hint(image, depth_estimator):\n        ...     image = depth_estimator(image)[\"depth\"]\n        ...     image = np.array(image)\n        ...     image = image[:, :, None]\n        ...     image = np.concatenate([image, image, image], axis=2)\n        ...     detected_map = torch.from_numpy(image).float() / 255.0\n        ...     hint = detected_map.permute(2, 0, 1)\n        ...     return hint\n\n\n        >>> depth_estimator = pipeline(\"depth-estimation\")\n\n        >>> pipe_prior = KandinskyV22PriorEmb2EmbPipeline.from_pretrained(\n        ...     \"kandinsky-community/kandinsky-2-2-prior\", torch_dtype=torch.float16\n        ... )\n        >>> pipe_prior = pipe_prior.to(\"cuda\")\n\n        >>> pipe = KandinskyV22ControlnetImg2ImgPipeline.from_pretrained(\n        ...     \"kandinsky-community/kandinsky-2-2-controlnet-depth\", torch_dtype=torch.float16\n        ... )\n        >>> pipe = pipe.to(\"cuda\")\n\n        >>> img = load_image(\n        ...     \"https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main\"\n        ...     \"/kandinsky/cat.png\"\n        ... ).resize((768, 768))\n\n\n        >>> hint = make_hint(img, depth_estimator).unsqueeze(0).half().to(\"cuda\")\n\n        >>> prompt = \"A robot, 4k photo\"\n        >>> negative_prior_prompt = \"lowres, text, error, cropped, worst quality, low quality, jpeg artifacts, ugly, duplicate, morbid, mutilated, out of frame, extra fingers, mutated hands, poorly drawn hands, poorly drawn face, mutation, deformed, blurry, dehydrated, bad anatomy, bad proportions, extra limbs, cloned face, disfigured, gross proportions, malformed limbs, missing arms, missing legs, extra arms, extra legs, fused fingers, too many fingers, long neck, username, watermark, signature\"\n\n        >>> generator = torch.Generator(device=\"cuda\").manual_seed(43)\n\n        >>> img_emb = pipe_prior(prompt=prompt, image=img, strength=0.85, generator=generator)\n        >>> negative_emb = pipe_prior(prompt=negative_prior_prompt, image=img, strength=1, generator=generator)\n\n        >>> images = pipe(\n        ...     image=img,\n        ...     strength=0.5,\n        ...     image_embeds=img_emb.image_embeds,\n        ...     negative_image_embeds=negative_emb.image_embeds,\n        ...     hint=hint,\n        ...     num_inference_steps=50,\n        ...     generator=generator,\n        ...     height=768,\n        ...     width=768,\n        ... ).images\n\n        >>> images[0].save(\"robot_cat.png\")\n        ```\n"


def 					UpperCAmelCase__      (							_lowerCAmelCase						: int,			_lowerCAmelCase						: Any,			_lowerCAmelCase						: Optional[Any]=8)						->		Optional[int]:



						"""simple docstring"""

						snake_case   :					Any							=						height // scale_factor**2
						if height % scale_factor**2 != 0:
												new_height += 1
						snake_case   :					Tuple							=						width // scale_factor**2
						if width % scale_factor**2 != 0:
												new_width += 1
						return new_height * scale_factor, new_width * scale_factor


def 					UpperCAmelCase__      (							_lowerCAmelCase						: Tuple,			_lowerCAmelCase						: List[Any]=512,			_lowerCAmelCase						: int=512)						->		Any:



						"""simple docstring"""

						snake_case   :					str							=						pil_image.resize((w, h),			resample=Image.BICUBIC,			reducing_gap=1)
						snake_case   :					List[Any]							=						np.array(pil_image.convert("RGB"))
						snake_case   :					Optional[Any]							=						arr.astype(np.floataa) / 127.5 - 1
						snake_case   :					int							=						np.transpose(_lowerCAmelCase,			[2, 0, 1])
						snake_case   :					str							=						torch.from_numpy(_lowerCAmelCase).unsqueeze(0)
						return image




class 		SCREAMING_SNAKE_CASE_				(_UpperCAmelCase			):



			"""simple docstring"""






			def __init__(       self							, snake_case_							, snake_case_							, snake_case_							, ):
									super().__init__()

									self.register_modules(
									    unet=snake_case_							, scheduler=snake_case_							, movq=snake_case_							, )
									snake_case   :					Union[str, Any]							=						2 ** (len(self.movq.config.block_out_channels				) - 1)



			def      lowerCamelCase   (       self							, snake_case_							, snake_case_							, snake_case_				):
									# get the original timestep using init_timestep
									snake_case   :					List[Any]							=						min(int(num_inference_steps * strength				)							, snake_case_				)

									snake_case   :					Optional[int]							=						max(num_inference_steps - init_timestep							, 0				)
									snake_case   :					int							=						self.scheduler.timesteps[t_start:]

									return timesteps, num_inference_steps - t_start



			def      lowerCamelCase   (       self							, snake_case_							, snake_case_							, snake_case_							, snake_case_							, snake_case_							, snake_case_							, snake_case_=None				):
									if not isinstance(snake_case_							, (torch.Tensor, PIL.Image.Image, list)				):
															raise ValueError(
															    F"""`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(snake_case_				)}"""				)

									snake_case   :					Union[str, Any]							=						image.to(device=snake_case_							, dtype=snake_case_				)

									snake_case   :					str							=						batch_size * num_images_per_prompt

									if image.shape[1] == 4:
															snake_case   :					Dict							=						image

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

															elif isinstance(snake_case_							, snake_case_				):
																					snake_case   :					Optional[Any]							=						[
																					    self.movq.encode(image[i : i + 1]				).latent_dist.sample(generator[i]				) for i in range(snake_case_				)
																					]
																					snake_case   :					Optional[Any]							=						torch.cat(snake_case_							, dim=0				)
															else:
																					snake_case   :					List[Any]							=						self.movq.encode(snake_case_				).latent_dist.sample(snake_case_				)

															snake_case   :					List[str]							=						self.movq.config.scaling_factor * init_latents

									snake_case   :					int							=						torch.cat([init_latents]							, dim=0				)

									snake_case   :					str							=						init_latents.shape
									snake_case   :					Dict							=						randn_tensor(snake_case_							, generator=snake_case_							, device=snake_case_							, dtype=snake_case_				)

									# get latents
									snake_case   :					int							=						self.scheduler.add_noise(snake_case_							, snake_case_							, snake_case_				)

									snake_case   :					Optional[int]							=						init_latents

									return latents



			def      lowerCamelCase   (       self							, snake_case_=0				):
									if is_accelerate_available():
															from accelerate import cpu_offload
									else:
															raise ImportError("Please install accelerate via `pip install accelerate`"				)

									snake_case   :					Dict							=						torch.device(F"""cuda:{gpu_id}"""				)

									snake_case   :					List[str]							=						[
									    self.unet,
									    self.movq,
									]
									for cpu_offloaded_model in models:
															if cpu_offloaded_model is not None:
																					cpu_offload(snake_case_							, snake_case_				)



			def      lowerCamelCase   (       self							, snake_case_=0				):
									if is_accelerate_available() and is_accelerate_version(">="							, "0.17.0.dev0"				):
															from accelerate import cpu_offload_with_hook
									else:
															raise ImportError("`enable_model_cpu_offload` requires `accelerate v0.17.0` or higher."				)

									snake_case   :					Dict							=						torch.device(F"""cuda:{gpu_id}"""				)

									if self.device.type != "cpu":
															self.to("cpu"							, silence_dtype_warnings=snake_case_				)
															torch.cuda.empty_cache()  # otherwise we don't see the memory savings (but they probably exist)

									snake_case   :					Any							=						None
									for cpu_offloaded_model in [self.unet, self.movq]:
															snake_case							,				snake_case   :					Tuple							=						cpu_offload_with_hook(snake_case_							, snake_case_							, prev_module_hook=snake_case_				)

									# We'll offload the last model manually.
									snake_case   :					Union[str, Any]							=						hook



			@property
			# Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
			def      lowerCamelCase   (       self				):
									if not hasattr(self.unet							, "_hf_hook"				):
															return self.device
									for module in self.unet.modules():
															if (
															    hasattr(snake_case_							, "_hf_hook"				)
															    and hasattr(module._hf_hook							, "execution_device"				)
															    and module._hf_hook.execution_device is not None
															):
																					return torch.device(module._hf_hook.execution_device				)
									return self.device






			@torch.no_grad()
			@replace_example_docstring(snake_case_				)
			def __call__(       self							, snake_case_							, snake_case_							, snake_case_							, snake_case_							, snake_case_ = 512							, snake_case_ = 512							, snake_case_ = 100							, snake_case_ = 4.0							, snake_case_ = 0.3							, snake_case_ = 1							, snake_case_ = None							, snake_case_ = "pil"							, snake_case_ = True							, ):
									snake_case   :					List[Any]							=						self._execution_device

									snake_case   :					int							=						guidance_scale > 1.0

									if isinstance(snake_case_							, snake_case_				):
															snake_case   :					Optional[Any]							=						torch.cat(snake_case_							, dim=0				)
									if isinstance(snake_case_							, snake_case_				):
															snake_case   :					int							=						torch.cat(snake_case_							, dim=0				)
									if isinstance(snake_case_							, snake_case_				):
															snake_case   :					List[Any]							=						torch.cat(snake_case_							, dim=0				)

									snake_case   :					Tuple							=						image_embeds.shape[0]

									if do_classifier_free_guidance:
															snake_case   :					Union[str, Any]							=						image_embeds.repeat_interleave(snake_case_							, dim=0				)
															snake_case   :					str							=						negative_image_embeds.repeat_interleave(snake_case_							, dim=0				)
															snake_case   :					Dict							=						hint.repeat_interleave(snake_case_							, dim=0				)

									snake_case   :					int							=						torch.cat([negative_image_embeds, image_embeds]							, dim=0				).to(dtype=self.unet.dtype							, device=snake_case_				)
									snake_case   :					Optional[Any]							=						torch.cat([hint, hint]							, dim=0				).to(dtype=self.unet.dtype							, device=snake_case_				)

									if not isinstance(snake_case_							, snake_case_				):
															snake_case   :					Dict							=						[image]
									if not all(isinstance(snake_case_							, (PIL.Image.Image, torch.Tensor)				) for i in image				):
															raise ValueError(
															    F"""Input is in incorrect format: {[type(snake_case_				) for i in image]}. Currently, we only support  PIL image and pytorch tensor"""				)

									snake_case   :					Union[str, Any]							=						torch.cat([prepare_image(snake_case_							, snake_case_							, snake_case_				) for i in image]							, dim=0				)
									snake_case   :					List[Any]							=						image.to(dtype=image_embeds.dtype							, device=snake_case_				)

									snake_case   :					int							=						self.movq.encode(snake_case_				)["latents"]
									snake_case   :					Tuple							=						latents.repeat_interleave(snake_case_							, dim=0				)
									self.scheduler.set_timesteps(snake_case_							, device=snake_case_				)
									snake_case							,				snake_case   :					str							=						self.get_timesteps(snake_case_							, snake_case_							, snake_case_				)
									snake_case   :					Dict							=						timesteps[:1].repeat(batch_size * num_images_per_prompt				)
									snake_case							,				snake_case   :					Union[str, Any]							=						downscale_height_and_width(snake_case_							, snake_case_							, self.movq_scale_factor				)
									snake_case   :					List[Any]							=						self.prepare_latents(
									    snake_case_							, snake_case_							, snake_case_							, snake_case_							, image_embeds.dtype							, snake_case_							, snake_case_				)
									for i, t in enumerate(self.progress_bar(snake_case_				)				):
															# expand the latents if we are doing classifier free guidance
															snake_case   :					Union[str, Any]							=						torch.cat([latents] * 2				) if do_classifier_free_guidance else latents

															snake_case   :					Any							=						{"image_embeds": image_embeds, "hint": hint}
															snake_case   :					List[str]							=						self.unet(
															    sample=snake_case_							, timestep=snake_case_							, encoder_hidden_states=snake_case_							, added_cond_kwargs=snake_case_							, return_dict=snake_case_							, )[0]

															if do_classifier_free_guidance:
																					snake_case							,				snake_case   :					List[str]							=						noise_pred.split(latents.shape[1]							, dim=1				)
																					snake_case							,				snake_case   :					Optional[Any]							=						noise_pred.chunk(2				)
																					snake_case							,				snake_case   :					Tuple							=						variance_pred.chunk(2				)
																					snake_case   :					Optional[Any]							=						noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
																					snake_case   :					Any							=						torch.cat([noise_pred, variance_pred_text]							, dim=1				)

															if not (
															    hasattr(self.scheduler.config							, "variance_type"				)
															    and self.scheduler.config.variance_type in ["learned", "learned_range"]
															):
																					snake_case							,				snake_case   :					Optional[Any]							=						noise_pred.split(latents.shape[1]							, dim=1				)

															# compute the previous noisy sample x_t -> x_t-1

															snake_case   :					Union[str, Any]							=						self.scheduler.step(
															    snake_case_							, snake_case_							, snake_case_							, generator=snake_case_							, )[0]

									# post-processing
									snake_case   :					Dict							=						self.movq.decode(snake_case_							, force_not_quantize=snake_case_				)["sample"]

									if output_type not in ["pt", "np", "pil"]:
															raise ValueError(F"""Only the output types `pt`, `pil` and `np` are supported not output_type={output_type}"""				)

									if output_type in ["np", "pil"]:
															snake_case   :					Any							=						image * 0.5 + 0.5
															snake_case   :					List[str]							=						image.clamp(0							, 1				)
															snake_case   :					List[str]							=						image.cpu().permute(0							, 2							, 3							, 1				).float().numpy()

									if output_type == "pil":
															snake_case   :					str							=						self.numpy_to_pil(snake_case_				)

									if not return_dict:
															return (image,)

									return ImagePipelineOutput(images=snake_case_				)





