


def     __SCREAMING_SNAKE_CASE							(       lowercase_      )		->     list[int]:




						'''simple docstring'''







						__UpperCAmelCase			:							Tuple	    =	[0 for i in range(len(lowercase_      )      )]

						# initialize interval's left pointer and right pointer
						__UpperCAmelCase    ,      __UpperCAmelCase			:							str	    =	0, 0

						for i in range(1      ,       len(lowercase_      )      ):
												# case when current index is inside the interval
												if i <= right_pointer:
																		__UpperCAmelCase			:							List[str]	    =	min(right_pointer - i + 1      ,       z_result[i - left_pointer]      )
																		__UpperCAmelCase			:							List[Any]	    =	min_edge

												while go_next(lowercase_      ,       lowercase_      ,       lowercase_      ):
																		z_result[i] += 1

												# if new index's result gives us more right interval,
												# we've to update left_pointer and right_pointer
												if i + z_result[i] - 1 > right_pointer:
																		__UpperCAmelCase    ,      __UpperCAmelCase			:							List[str]	    =	i, i + z_result[i] - 1

						return z_result




def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_      ,       lowercase_      )		->     bool:




						'''simple docstring'''







						return i + z_result[i] < len(lowercase_      ) and s[z_result[i]] == s[i + z_result[i]]




def     __SCREAMING_SNAKE_CASE							(       lowercase_      ,       lowercase_      )		->     int:




						'''simple docstring'''







						__UpperCAmelCase			:							List[Any]	    =	0
						# concatenate 'pattern' and 'input_str' and call z_function
						# with concatenated string
						__UpperCAmelCase			:							List[Any]	    =	z_function(pattern + input_str      )

						for val in z_result:
												# if value is greater then length of the pattern string
												# that means this index is starting position of substring
												# which is equal to pattern string
												if val >= len(lowercase_      ):
																		answer += 1

						return answer


if __name__ == "__main__":
				import doctest

				doctest.testmod()





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 							lowerCamelCase   (  _UpperCamelCase ):
	_lowerCAmelCase     :		torch.FloatTensor
	_lowerCAmelCase     :		torch.FloatTensor
	_lowerCAmelCase     :		Optional[torch.FloatTensor]										=						None






class 							lowerCamelCase   (  _UpperCamelCase							,						_UpperCamelCase ):
	_lowerCAmelCase     :		Tuple										=						2


	@register_to_config
	def __init__(    self				,     lowercase__ = 0.0_2				,     lowercase__ = 1_0_0				,     lowercase__ = 1.0_0_7				,     lowercase__ = 8_0				,     lowercase__ = 0.0_5				,     lowercase__ = 5_0				,     ):
							# standard deviation of the initial noise distribution
							__UpperCAmelCase			:							Union[str, Any]	    =	sigma_max

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


	def  A(    self				,     lowercase__				,     lowercase__ = None):
							return sample


	def  A(    self				,     lowercase__				,     lowercase__ = None):
							__UpperCAmelCase			:							int	    =	num_inference_steps
							__UpperCAmelCase			:							List[str]	    =	np.arange(0				,     self.num_inference_steps)[::-1].copy()
							__UpperCAmelCase			:							Any	    =	torch.from_numpy(lowercase__).to(lowercase__)
							__UpperCAmelCase			:							Union[str, Any]	    =	[
							    (
							        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
							]
							__UpperCAmelCase			:							Tuple	    =	torch.tensor(lowercase__				,     dtype=torch.floataa				,     device=lowercase__)


	def  A(    self				,     lowercase__				,     lowercase__				,     lowercase__ = None):
							if self.config.s_min <= sigma <= self.config.s_max:
													__UpperCAmelCase			:							int	    =	min(self.config.s_churn / self.num_inference_steps				,     2**0.5 - 1)
							else:
													__UpperCAmelCase			:							int	    =	0

							# sample eps ~ N(0, S_noise^2 * I)
							__UpperCAmelCase			:							List[str]	    =	self.config.s_noise * randn_tensor(sample.shape				,     generator=lowercase__).to(sample.device)
							__UpperCAmelCase			:							Optional[int]	    =	sigma + gamma * sigma
							__UpperCAmelCase			:							List[Any]	    =	sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

							return sample_hat, sigma_hat


	def  A(    self				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__ = True				,     ):
							__UpperCAmelCase			:							str	    =	sample_hat + sigma_hat * model_output
							__UpperCAmelCase			:							Tuple	    =	(sample_hat - pred_original_sample) / sigma_hat
							__UpperCAmelCase			:							str	    =	sample_hat + (sigma_prev - sigma_hat) * derivative

							if not return_dict:
													return (sample_prev, derivative)

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


	def  A(    self				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__				,     lowercase__ = True				,     ):
							__UpperCAmelCase			:							Any	    =	sample_prev + sigma_prev * model_output
							__UpperCAmelCase			:							List[str]	    =	(sample_prev - pred_original_sample) / sigma_prev
							__UpperCAmelCase			:							Union[str, Any]	    =	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=lowercase__				,     derivative=lowercase__				,     pred_original_sample=lowercase__)


	def  A(    self				,     lowercase__				,     lowercase__				,     lowercase__):
							raise NotImplementedError()

