





'''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 					a_     (				snake_case_       ):

    '''simple docstring'''
    UpperCamelCase     = 42
    UpperCamelCase     = 42
    UpperCamelCase     = None




class 					a_     (				snake_case_      ,    snake_case_       ):

    '''simple docstring'''
    UpperCamelCase     = 2


    @register_to_config
    def __init__(		self ,		A = 0.02 ,		A = 100 ,		A = 1.007 ,		A = 80 ,		A = 0.05 ,		A = 50 ,		)		->   Optional[Any]:
        # standard deviation of the initial noise distribution
        _SCREAMING_SNAKE_CASE									=			sigma_max

        # setable values
        _SCREAMING_SNAKE_CASE									=			None
        _SCREAMING_SNAKE_CASE									=			None
        _SCREAMING_SNAKE_CASE									=			None  # sigma(t_i)


    def 			snake_case_(		self ,		A ,		A = None       )		->   torch.FloatTensor:
        return sample


    def 			snake_case_(		self ,		A ,		A = None       )		->   List[Any]:
        _SCREAMING_SNAKE_CASE									=			num_inference_steps
        _SCREAMING_SNAKE_CASE									=			np.arange(0 ,		self.num_inference_steps       )[::-1].copy()
        _SCREAMING_SNAKE_CASE									=			torch.from_numpy(A       ).to(A       )
        _SCREAMING_SNAKE_CASE									=			[
            (
                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
        ]
        _SCREAMING_SNAKE_CASE									=			torch.tensor(A ,		dtype=torch.floataa ,		device=A       )


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

        # sample eps ~ N(0, S_noise^2 * I)
        _SCREAMING_SNAKE_CASE									=			self.config.s_noise * randn_tensor(sample.shape ,		generator=A       ).to(sample.device       )
        _SCREAMING_SNAKE_CASE									=			sigma + gamma * sigma
        _SCREAMING_SNAKE_CASE									=			sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

        return sample_hat, sigma_hat


    def 			snake_case_(		self ,		A ,		A ,		A ,		A ,		A = True ,		)		->   Union[KarrasVeOutput, Tuple]:
        _SCREAMING_SNAKE_CASE									=			sample_hat + sigma_hat * model_output
        _SCREAMING_SNAKE_CASE									=			(sample_hat - pred_original_sample) / sigma_hat
        _SCREAMING_SNAKE_CASE									=			sample_hat + (sigma_prev - sigma_hat) * derivative

        if not return_dict:
            return (sample_prev, derivative)

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


    def 			snake_case_(		self ,		A ,		A ,		A ,		A ,		A ,		A ,		A = True ,		)		->   Union[KarrasVeOutput, Tuple]:
        _SCREAMING_SNAKE_CASE									=			sample_prev + sigma_prev * model_output
        _SCREAMING_SNAKE_CASE									=			(sample_prev - pred_original_sample) / sigma_prev
        _SCREAMING_SNAKE_CASE									=			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=A ,		derivative=A ,		pred_original_sample=A       )





    def 			snake_case_(		self ,		A ,		A ,		A       )		->   List[Any]:
        raise NotImplementedError()





"""simple docstring"""





def 	__a     (		__lowerCamelCase = 3,		__lowerCamelCase = 7,		__lowerCamelCase = 100_0000  ):
   UpperCAmelCase_					:					Dict			     =    0
   UpperCAmelCase_					:					List[Any]			     =    1

   for current_denominator in range(1,		limit + 1  ):
      UpperCAmelCase_					:					Dict			     =    current_denominator * numerator // denominator
      if current_denominator % denominator == 0:
         current_numerator -= 1
      if current_numerator * max_denominator > current_denominator * max_numerator:
         UpperCAmelCase_					:					List[Any]			     =    current_numerator
         UpperCAmelCase_					:					Optional[int]			     =    current_denominator
   return max_numerator


if __name__ == "__main__":
    print(solution(numerator=3, denominator=7, limit=1_000_000))


