"""simple docstring"""







# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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

import torch

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

@dataclass
class 	UpperCamelCase    (					UpperCAmelCase__		):
    UpperCAmelCase       :   List[str]					=	42
    UpperCAmelCase       :   Optional[Any]					=	42







class 	UpperCamelCase    (					UpperCAmelCase__   ,			UpperCAmelCase__		):
    UpperCAmelCase       :   Optional[int]					=	1



    @register_to_config
    def __init__(self       :   List[Any]			,						_A       :   int = 20_00			,						_A       :   float = 0.15			,						_A       :   float = 0.01			,						_A       :   float = 13_48.0			,						_A       :   float = 1E-5			,						_A       :   int = 1			,						)					->			Optional[Any]:
     __snake_case    :							Optional[Any]   	=				sigma_max

     # setable values
     __snake_case    :							int   	=				None

     self.set_sigmas(__lowerCAmelCase			,						__lowerCAmelCase			,						__lowerCAmelCase			,						__lowerCAmelCase)



    def       _lowercase  (self       :   int			,						_A       :   torch.FloatTensor			,						_A       :   Optional[int] = None)					->			torch.FloatTensor:
     return sample



    def       _lowercase  (self       :   Tuple			,						_A       :   int			,						_A       :   float = None			,						_A       :   Union[str, torch.device] = None)					->			Optional[Any]:
     __snake_case    :							Tuple   	=				sampling_eps if sampling_eps is not None else self.config.sampling_eps

     __snake_case    :							str   	=				torch.linspace(1			,						__lowerCAmelCase			,						__lowerCAmelCase			,						device=__lowerCAmelCase)



    def       _lowercase  (self       :   Optional[Any]			,						_A       :   int			,						_A       :   float = None			,						_A       :   float = None			,						_A       :   float = None)					->			Union[str, Any]:
     __snake_case    :							Optional[int]   	=				sigma_min if sigma_min is not None else self.config.sigma_min
     __snake_case    :							int   	=				sigma_max if sigma_max is not None else self.config.sigma_max
     __snake_case    :							Union[str, Any]   	=				sampling_eps if sampling_eps is not None else self.config.sampling_eps
     if self.timesteps is None:
      self.set_timesteps(__lowerCAmelCase			,						__lowerCAmelCase)

     __snake_case    :							Optional[Any]   	=				sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
     __snake_case    :							int   	=				torch.exp(torch.linspace(math.log(__lowerCAmelCase)			,						math.log(__lowerCAmelCase)			,						__lowerCAmelCase))
     __snake_case    :							Optional[int]   	=				torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps])



    def       _lowercase  (self       :   List[str]			,						_A       :   Optional[int]			,						_A       :   Optional[Any])					->			str:
     return torch.where(
         timesteps == 0			,						torch.zeros_like(t.to(timesteps.device))			,						self.discrete_sigmas[timesteps - 1].to(timesteps.device)			,						)



    def       _lowercase  (self       :   List[str]			,						_A       :   torch.FloatTensor			,						_A       :   int			,						_A       :   torch.FloatTensor			,						_A       :   Optional[torch.Generator] = None			,						_A       :   bool = True			,						)					->			Union[SdeVeOutput, Tuple]:






     if self.timesteps is None:
      raise ValueError(
          '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler')

     __snake_case    :							Dict   	=				timestep * torch.ones(
         sample.shape[0]			,						device=sample.device)  # torch.repeat_interleave(timestep, sample.shape[0])
     __snake_case    :							Union[str, Any]   	=				(timestep * (len(self.timesteps) - 1)).long()

     # mps requires indices to be in the same device, so we use cpu as is the default with cuda
     __snake_case    :							List[Any]   	=				timesteps.to(self.discrete_sigmas.device)

     __snake_case    :							Any   	=				self.discrete_sigmas[timesteps].to(sample.device)
     __snake_case    :							Union[str, Any]   	=				self.get_adjacent_sigma(__lowerCAmelCase			,						__lowerCAmelCase).to(sample.device)
     __snake_case    :							Union[str, Any]   	=				torch.zeros_like(__lowerCAmelCase)
     __snake_case    :							Any   	=				(sigma**2 - adjacent_sigma**2) ** 0.5

     # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
     # also equation 47 shows the analog from SDE models to ancestral sampling methods
     __snake_case    :							Optional[Any]   	=				diffusion.flatten()
     while len(diffusion.shape) < len(sample.shape):
      __snake_case    :							List[Any]   	=				diffusion.unsqueeze(-1)
     __snake_case    :							Tuple   	=				drift - diffusion**2 * model_output

     #  equation 6: sample noise for the diffusion term of
     __snake_case    :							Union[str, Any]   	=				randn_tensor(
         sample.shape			,						layout=sample.layout			,						generator=__lowerCAmelCase			,						device=sample.device			,						dtype=sample.dtype)
     __snake_case    :							Union[str, Any]   	=				sample - drift  # subtract because `dt` is a small negative timestep
     # TODO is the variable diffusion the correct scaling term for the noise?
     __snake_case    :							List[str]   	=				prev_sample_mean + diffusion * noise  # add impact of diffusion field g

     if not return_dict:
      return (prev_sample, prev_sample_mean)

     return SdeVeOutput(prev_sample=__lowerCAmelCase			,						prev_sample_mean=__lowerCAmelCase)



    def       _lowercase  (self       :   Optional[Any]			,						_A       :   torch.FloatTensor			,						_A       :   torch.FloatTensor			,						_A       :   Optional[torch.Generator] = None			,						_A       :   bool = True			,						)					->			Union[SchedulerOutput, Tuple]:






     if self.timesteps is None:
      raise ValueError(
          '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler')

     # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
     # sample noise for correction
     __snake_case    :							Any   	=				randn_tensor(sample.shape			,						layout=sample.layout			,						generator=__lowerCAmelCase).to(sample.device)

     # compute step size from the model_output, the noise, and the snr
     __snake_case    :							Optional[Any]   	=				torch.norm(model_output.reshape(model_output.shape[0]			,						-1)			,						dim=-1).mean()
     __snake_case    :							Optional[int]   	=				torch.norm(noise.reshape(noise.shape[0]			,						-1)			,						dim=-1).mean()
     __snake_case    :							Any   	=				(self.config.snr * noise_norm / grad_norm) ** 2 * 2
     __snake_case    :							str   	=				step_size * torch.ones(sample.shape[0]).to(sample.device)
     # self.repeat_scalar(step_size, sample.shape[0])

     # compute corrected sample: model_output term and noise term
     __snake_case    :							Union[str, Any]   	=				step_size.flatten()
     while len(step_size.shape) < len(sample.shape):
      __snake_case    :							Dict   	=				step_size.unsqueeze(-1)
     __snake_case    :							str   	=				sample + step_size * model_output
     __snake_case    :							int   	=				prev_sample_mean + ((step_size * 2) ** 0.5) * noise

     if not return_dict:
      return (prev_sample,)

     return SchedulerOutput(prev_sample=__lowerCAmelCase)



    def       _lowercase  (self       :   List[str]			,						_A       :   torch.FloatTensor			,						_A       :   torch.FloatTensor			,						_A       :   torch.FloatTensor			,						)					->			torch.FloatTensor:
     __snake_case    :							str   	=				timesteps.to(original_samples.device)
     __snake_case    :							Dict   	=				self.discrete_sigmas.to(original_samples.device)[timesteps]
     __snake_case    :							Tuple   	=				(
         noise * sigmas[:, None, None, None]
         if noise is not None
         else torch.randn_like(__lowerCAmelCase) * sigmas[:, None, None, None]
     )
     __snake_case    :							Union[str, Any]   	=				noise + original_samples
     return noisy_samples






    def __len__(self       :   List[Any])					->			Optional[int]:
     return self.config.num_train_timesteps






"""simple docstring"""







import math
def 						__UpperCAmelCase       (					UpperCAmelCase_					:       list    ,							UpperCAmelCase_					:       int						)							->    int:

	'''simple docstring'''





	__snake_case    :							List[str]   	=				len(UpperCAmelCase_						)
	__snake_case    :							List[Any]   	=				int(math.floor(math.sqrt(UpperCAmelCase_						)						)						)
	__snake_case    :							Any   	=				0
	while arr[min(UpperCAmelCase_    ,							UpperCAmelCase_						) - 1] < x:
		__snake_case    :							Tuple   	=				step
		step += int(math.floor(math.sqrt(UpperCAmelCase_						)						)						)
		if prev >= n:
			return -1

	while arr[prev] < x:
		__snake_case    :							Union[str, Any]   	=				prev + 1
		if prev == min(UpperCAmelCase_    ,							UpperCAmelCase_						):
			return -1
	if arr[prev] == x:
		return prev
	return -1


if __name__ == "__main__":
	_a  :  str=				input("Enter numbers separated by a comma:\n").strip()
	_a  :  int=				[int(item) for item in user_input.split(",")]
	_a  :  Optional[Any]=				int(input("Enter the number to be searched:\n"))
	_a  :  Tuple=				jump_search(arr, x)
	if res == -1:
		print("Number not found!")
	else:
		print(f'''Number {x} is at index {res}''')





