



'''simple docstring'''






def 					snake_case_      (  lowerCAmelCase_ ,     lowerCAmelCase_	)->	int:





       '''simple docstring'''


       for index, item in enumerate(lowerCAmelCase_	):
              if item == target:
                     return index
       return -1




def 					snake_case_      (  lowerCAmelCase_ ,     lowerCAmelCase_ ,     lowerCAmelCase_ ,     lowerCAmelCase_	)->	int:





       '''simple docstring'''


       if not (0 <= high < len(lowerCAmelCase_	) and 0 <= low < len(lowerCAmelCase_	)):
              raise Exception("""Invalid upper or lower bound!"""	)
       if high < low:
              return -1
       if sequence[low] == target:
              return low
       if sequence[high] == target:
              return high
       return rec_linear_search(lowerCAmelCase_ ,     low + 1 ,     high - 1 ,     lowerCAmelCase_	)


if __name__ == "__main__":
   A_							:				Dict						=			input("""Enter numbers separated by comma:\n""").strip()
   A_							:				Any						=			[int(item.strip()) for item in user_input.split(""",""")]

   A_							:				Union[str, Any]						=			int(input("""Enter a single number to be found in the list:\n""").strip())
   A_							:				Dict						=			linear_search(sequence, target)
   if result != -1:
      print(f"""linear_search({sequence}, {target}) = {result}""")
   else:
      print(f"""{target} was not found in {sequence}""")








'''simple docstring'''






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

import numpy as np
import torch

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


A_							:				Optional[Any]						=			logging.get_logger(__name__)  # pylint: disable=invalid-name



@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 							lowercase (						_lowerCamelCase       ):


 """simple docstring"""


 UpperCAmelCase					=						42
 UpperCAmelCase					=						None







def 					snake_case_      (  lowerCAmelCase_ ,     lowerCAmelCase_=0.9_9_9 ,     lowerCAmelCase_="cosine" ,     )->	Any:





       '''simple docstring'''


       if alpha_transform_type == "cosine":

              def alpha_bar_fn(lowerCAmelCase_	):
                     return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2	) ** 2

       elif alpha_transform_type == "exp":

              def alpha_bar_fn(lowerCAmelCase_	):
                     return math.exp(t * -1_2.0	)

       else:
              raise ValueError(F'''Unsupported alpha_tranform_type: {alpha_transform_type}'''	)

       _UpperCAmelCase						:		int      =				[]
       for i in range(lowerCAmelCase_	):
              _UpperCAmelCase						:		Union[str, Any]      =				i / num_diffusion_timesteps
              _UpperCAmelCase						:		Union[str, Any]      =				(i + 1) / num_diffusion_timesteps
              betas.append(min(1 - alpha_bar_fn(lowerCAmelCase_	) / alpha_bar_fn(lowerCAmelCase_	) ,     lowerCAmelCase_	)	)
       return torch.tensor(lowerCAmelCase_ ,     dtype=torch.floataa	)



class 							lowercase (						_lowerCamelCase      ,      _lowerCamelCase       ):


 """simple docstring"""


 UpperCAmelCase					=						[e.name for e in KarrasDiffusionSchedulers]
 UpperCAmelCase					=						1







 @register_to_config
 def __init__(							self						,a_ = 1_000						,a_ = 0.0001						,a_ = 0.02						,a_ = "linear"						,a_ = None						,a_ = "epsilon"						,a_ = "linspace"						,a_ = 0						,)	->     Optional[Any]:
        if trained_betas is not None:
               _UpperCAmelCase						:		List[str]      =				torch.tensor(a_						,dtype=torch.floataa							)
        elif beta_schedule == "linear":
               _UpperCAmelCase						:		int      =				torch.linspace(a_						,a_						,a_						,dtype=torch.floataa							)
        elif beta_schedule == "scaled_linear":
               # this schedule is very specific to the latent diffusion model.
               _UpperCAmelCase						:		Optional[int]      =				(
                   torch.linspace(beta_start**0.5						,beta_end**0.5						,a_						,dtype=torch.floataa							) ** 2
               )
        elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               _UpperCAmelCase						:		int      =				betas_for_alpha_bar(a_							)
        else:
               raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''							)

        _UpperCAmelCase						:		Tuple      =				1.0 - self.betas
        _UpperCAmelCase						:		Tuple      =				torch.cumprod(self.alphas						,dim=0							)

        _UpperCAmelCase						:		List[str]      =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
        _UpperCAmelCase						:		List[Any]      =				np.concatenate([sigmas[::-1], [0.0]]							).astype(np.floataa							)
        _UpperCAmelCase						:		Optional[Any]      =				torch.from_numpy(a_							)

        # setable values
        _UpperCAmelCase						:		Tuple      =				None
        _UpperCAmelCase						:		int      =				np.linspace(0						,num_train_timesteps - 1						,a_						,dtype=a_							)[::-1].copy()
        _UpperCAmelCase						:		Dict      =				torch.from_numpy(a_							)
        _UpperCAmelCase						:		Optional[int]      =				False







 @property
 def _snake_case				(							self							)	->     List[str]:
        # standard deviation of the initial noise distribution
        if self.config.timestep_spacing in ["linspace", "trailing"]:
               return self.sigmas.max()

        return (self.sigmas.max() ** 2 + 1) ** 0.5







 def _snake_case				(							self						,a_						,a_							)	->     torch.FloatTensor:
        if isinstance(a_						,torch.Tensor							):
               _UpperCAmelCase						:		Optional[int]      =				timestep.to(self.timesteps.device							)
        _UpperCAmelCase						:		Any      =				(self.timesteps == timestep).nonzero().item()
        _UpperCAmelCase						:		Dict      =				self.sigmas[step_index]
        _UpperCAmelCase						:		List[str]      =				sample / ((sigma**2 + 1) ** 0.5)
        _UpperCAmelCase						:		str      =				True
        return sample







 def _snake_case				(							self						,a_						,a_ = None							)	->     Optional[Any]:
        _UpperCAmelCase						:		str      =				num_inference_steps

        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
               _UpperCAmelCase						:		Optional[int]      =				np.linspace(0						,self.config.num_train_timesteps - 1						,a_						,dtype=a_							)[
                   ::-1
               ].copy()
        elif self.config.timestep_spacing == "leading":
               _UpperCAmelCase						:		str      =				self.config.num_train_timesteps // self.num_inference_steps
               # creates integer timesteps by multiplying by ratio
               # casting to int to avoid issues when num_inference_step is power of 3
               _UpperCAmelCase						:		int      =				(np.arange(0						,a_							) * step_ratio).round()[::-1].copy().astype(a_							)
               timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
               _UpperCAmelCase						:		List[str]      =				self.config.num_train_timesteps / self.num_inference_steps
               # creates integer timesteps by multiplying by ratio
               # casting to int to avoid issues when num_inference_step is power of 3
               _UpperCAmelCase						:		Union[str, Any]      =				(np.arange(self.config.num_train_timesteps						,0						,-step_ratio							)).round().copy().astype(a_							)
               timesteps -= 1
        else:
               raise ValueError(
                   f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''							)

        _UpperCAmelCase						:		Optional[int]      =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
        _UpperCAmelCase						:		Optional[int]      =				np.interp(a_						,np.arange(0						,len(a_							)							)						,a_							)
        _UpperCAmelCase						:		Any      =				np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
        _UpperCAmelCase						:		Optional[Any]      =				torch.from_numpy(a_							).to(device=a_							)
        if str(a_							).startswith("""mps"""							):
               # mps does not support float64
               _UpperCAmelCase						:		Optional[Any]      =				torch.from_numpy(a_							).to(a_						,dtype=torch.floataa							)
        else:
               _UpperCAmelCase						:		Union[str, Any]      =				torch.from_numpy(a_							).to(device=a_							)







 def _snake_case				(							self						,a_						,a_						,a_						,a_ = None						,a_ = True						,)	->     Union[EulerAncestralDiscreteSchedulerOutput, Tuple]:

        if (
            isinstance(a_						,a_							)
            or isinstance(a_						,torch.IntTensor							)
            or isinstance(a_						,torch.LongTensor							)
        ):
               raise ValueError(
                   (
                       """Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"""
                       """ `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"""
                       """ one of the `scheduler.timesteps` as a timestep."""
                   )						,)

        if not self.is_scale_input_called:
               logger.warning(
                   """The `scale_model_input` function should be called before `step` to ensure correct denoising. """
                   """See `StableDiffusionPipeline` for a usage example."""							)

        if isinstance(a_						,torch.Tensor							):
               _UpperCAmelCase						:		Union[str, Any]      =				timestep.to(self.timesteps.device							)

        _UpperCAmelCase						:		List[str]      =				(self.timesteps == timestep).nonzero().item()
        _UpperCAmelCase						:		Any      =				self.sigmas[step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
               _UpperCAmelCase						:		Optional[int]      =				sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
               # * c_out + input * c_skip
               _UpperCAmelCase						:		Union[str, Any]      =				model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        elif self.config.prediction_type == "sample":
               raise NotImplementedError("""prediction_type not implemented yet: sample"""							)
        else:
               raise ValueError(
                   f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''							)

        _UpperCAmelCase						:		List[Any]      =				self.sigmas[step_index]
        _UpperCAmelCase						:		List[Any]      =				self.sigmas[step_index + 1]
        _UpperCAmelCase						:		List[str]      =				(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
        _UpperCAmelCase						:		Any      =				(sigma_to**2 - sigma_up**2) ** 0.5

        # 2. Convert to an ODE derivative
        _UpperCAmelCase						:		Any      =				(sample - pred_original_sample) / sigma

        _UpperCAmelCase						:		List[str]      =				sigma_down - sigma

        _UpperCAmelCase						:		List[str]      =				sample + derivative * dt

        _UpperCAmelCase						:		Optional[int]      =				model_output.device
        _UpperCAmelCase						:		Union[str, Any]      =				randn_tensor(model_output.shape						,dtype=model_output.dtype						,device=a_						,generator=a_							)

        _UpperCAmelCase						:		Optional[int]      =				prev_sample + noise * sigma_up

        if not return_dict:
               return (prev_sample,)

        return EulerAncestralDiscreteSchedulerOutput(
            prev_sample=a_						,pred_original_sample=a_							)







 def _snake_case				(							self						,a_						,a_						,a_						,)	->     torch.FloatTensor:
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        _UpperCAmelCase						:		Dict      =				self.sigmas.to(device=original_samples.device						,dtype=original_samples.dtype							)
        if original_samples.device.type == "mps" and torch.is_floating_point(a_							):
               # mps does not support float64
               _UpperCAmelCase						:		Tuple      =				self.timesteps.to(original_samples.device						,dtype=torch.floataa							)
               _UpperCAmelCase						:		Optional[Any]      =				timesteps.to(original_samples.device						,dtype=torch.floataa							)
        else:
               _UpperCAmelCase						:		Optional[Any]      =				self.timesteps.to(original_samples.device							)
               _UpperCAmelCase						:		int      =				timesteps.to(original_samples.device							)

        _UpperCAmelCase						:		Any      =				[(schedule_timesteps == t).nonzero().item() for t in timesteps]

        _UpperCAmelCase						:		Optional[int]      =				sigmas[step_indices].flatten()
        while len(sigma.shape							) < len(original_samples.shape							):
               _UpperCAmelCase						:		List[Any]      =				sigma.unsqueeze(-1							)

        _UpperCAmelCase						:		int      =				original_samples + noise * sigma
        return noisy_samples







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



