





"""simple docstring"""




import colorsys

from PIL import Image  # type: ignore






def    _SCREAMING_SNAKE_CASE	(			_lowercase		:					float					, _lowercase		:					float					, _lowercase		:					int      )				->float:






	'''simple docstring'''






	a   :	Tuple			=       x
	a   :	Union[str, Any]			=       y
	for step in range(_lowercase      ):  # noqa: B007
		a   :	Any			=       a * a - b * b + x
		a   :	str			=       2 * a * b + y
		a   :	Dict			=       a_new

		# divergence happens for all complex number with an absolute value
		# greater than 4
		if a * a + b * b > 4:
			break
	return step / (max_step - 1)






def    _SCREAMING_SNAKE_CASE	(			_lowercase		:					float      )				->tuple:






	'''simple docstring'''






	if distance == 1:
		return (0, 0, 0)
	else:
		return (255, 255, 255)






def    _SCREAMING_SNAKE_CASE	(			_lowercase		:					float      )				->tuple:






	'''simple docstring'''






	if distance == 1:
		return (0, 0, 0)
	else:
		return tuple(round(i * 255      ) for i in colorsys.hsv_to_rgb(_lowercase					, 1					, 1      )      )






def    _SCREAMING_SNAKE_CASE	(			_lowercase		:					int = 800					, _lowercase		:					int = 600					, _lowercase		:					float = -0.6					, _lowercase		:					float = 0					, _lowercase		:					float = 3.2					, _lowercase		:					int = 50					, _lowercase		:					bool = True					, )				->Image.Image:






	'''simple docstring'''






	a   :	List[str]			=       Image.new("RGB"					, (image_width, image_height)      )
	a   :	Union[str, Any]			=       img.load()

	# loop through the image-coordinates
	for image_x in range(_lowercase      ):
		for image_y in range(_lowercase      ):
			# determine the figure-coordinates based on the image-coordinates
			a   :	List[Any]			=       figure_width / image_width * image_height
			a   :	Any			=       figure_center_x + (image_x / image_width - 0.5) * figure_width
			a   :	List[Any]			=       figure_center_y + (image_y / image_height - 0.5) * figure_height

			a   :	Union[str, Any]			=       get_distance(_lowercase					, _lowercase					, _lowercase      )

			# color the corresponding pixel based on the selected coloring-function
			if use_distance_color_coding:
				a   :	List[Any]			=       get_color_coded_rgb(_lowercase      )
			else:
				a   :	List[Any]			=       get_black_and_white_rgb(_lowercase      )

	return img


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		# colored version, full figure
		a		:				Union[str, Any]  			=    get_image()

		# uncomment for colored version, different section, zoomed in
		# img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
		# figure_width = 0.8)

		# uncomment for black and white version, full figure
		# img = get_image(use_distance_color_coding = False)

		# uncomment to save the image
		# img.save("mandelbrot.png")

		img.show()









"""simple docstring"""




from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin


@dataclass
class  __UpperCamelCase       (		a__		):
							lowerCamelCase     :      torch.FloatTensor
							lowerCamelCase     :      torch.FloatTensor
							lowerCamelCase     :      Optional[torch.FloatTensor]         =None


class  __UpperCamelCase       (		a__	, a__		):
							lowerCamelCase     :      Tuple         =2






							@register_to_config
							def __init__(     self   ,      lowerCAmelCase__ = 0.02   ,      lowerCAmelCase__ = 100   ,      lowerCAmelCase__ = 1.007   ,      lowerCAmelCase__ = 80   ,      lowerCAmelCase__ = 0.05   ,      lowerCAmelCase__ = 50   ,      )			->				Union[str, Any]:
								# standard deviation of the initial noise distribution
								a   :	Tuple			=       sigma_max

								# setable values
								a   :	int			=       None
								a   :	np.IntTensor			=       None
								a   :	torch.FloatTensor			=       None  # sigma(t_i)






							def 					__a     (     self   ,      lowerCAmelCase__   ,      lowerCAmelCase__ = None   )			->				torch.FloatTensor:
								return sample






							def 					__a     (     self   ,      lowerCAmelCase__   ,      lowerCAmelCase__ = None   )			->				List[str]:
								a   :	List[Any]			=       num_inference_steps
								a   :	List[str]			=       np.arange(0   ,      self.num_inference_steps   )[::-1].copy()
								a   :	int			=       torch.from_numpy(lowerCAmelCase__   ).to(lowerCAmelCase__   )
								a   :	List[str]			=       [
								    (
								        self.config.sigma_max**2
								        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
								    )
								    for i in self.timesteps
								]
								a   :	Any			=       torch.tensor(lowerCAmelCase__   ,      dtype=torch.floataa   ,      device=lowerCAmelCase__   )






							def 					__a     (     self   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__ = None   )			->				Tuple[torch.FloatTensor, float]:
								if self.config.s_min <= sigma <= self.config.s_max:
									a   :	str			=       min(self.config.s_churn / self.num_inference_steps   ,      2**0.5 - 1   )
								else:
									a   :	Dict			=       0

								# sample eps ~ N(0, S_noise^2 * I)
								a   :	Union[str, Any]			=       self.config.s_noise * randn_tensor(sample.shape   ,      generator=lowerCAmelCase__   ).to(sample.device   )
								a   :	Any			=       sigma + gamma * sigma
								a   :	Tuple			=       sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

								return sample_hat, sigma_hat






							def 					__a     (     self   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__ = True   ,      )			->				Union[KarrasVeOutput, Tuple]:
								a   :	Union[str, Any]			=       sample_hat + sigma_hat * model_output
								a   :	Tuple			=       (sample_hat - pred_original_sample) / sigma_hat
								a   :	List[Any]			=       sample_hat + (sigma_prev - sigma_hat) * derivative

								if not return_dict:
									return (sample_prev, derivative)

								return KarrasVeOutput(
								    prev_sample=lowerCAmelCase__   ,      derivative=lowerCAmelCase__   ,      pred_original_sample=lowerCAmelCase__   )






							def 					__a     (     self   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__ = True   ,      )			->				Union[KarrasVeOutput, Tuple]:
								a   :	Optional[int]			=       sample_prev + sigma_prev * model_output
								a   :	str			=       (sample_prev - pred_original_sample) / sigma_prev
								a   :	Dict			=       sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

								if not return_dict:
									return (sample_prev, derivative)

								return KarrasVeOutput(
								    prev_sample=lowerCAmelCase__   ,      derivative=lowerCAmelCase__   ,      pred_original_sample=lowerCAmelCase__   )






							def 					__a     (     self   ,      lowerCAmelCase__   ,      lowerCAmelCase__   ,      lowerCAmelCase__   )			->				str:
								raise NotImplementedError()


