




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

import numpy as np
import torch
from scipy import integrate

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






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class      A     (						_lowerCAmelCase						):
     """simple docstring"""

     _snake_case:		torch.FloatTensor
     _snake_case:		Optional[torch.FloatTensor]       =None

def      lowerCAmelCase_     (					lowerCamelCase:    List[Any]       ,			lowerCamelCase:    Tuple=0.999       ,			lowerCamelCase:    Optional[int]="cosine"       ,			)   ->     int:


      '''simple docstring'''




      if alpha_transform_type == "cosine":

            def alpha_bar_fn(lowerCamelCase:    Optional[Any]  ):
                  return math.cos((t + 0.008) / 1.008 * math.pi / 2  ) ** 2

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(lowerCamelCase:    Any  ):
                  return math.exp(t * -12.0  )

      else:
            raise ValueError(f"""Unsupported alpha_tranform_type: {alpha_transform_type}"""  )

      lowerCamelCase__ 					=			[]
      for i in range(lowerCamelCase  ):
            lowerCamelCase__ 					=			i / num_diffusion_timesteps
            lowerCamelCase__ 					=			(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      A     (						_lowerCAmelCase     ,  _lowerCAmelCase						):
     """simple docstring"""

     _snake_case:		List[str]       =[e.name for e in KarrasDiffusionSchedulers]
     _snake_case:		int       =1




     @register_to_config
     def __init__(      self					:				Tuple		,					A__					:				int = 1_0_0_0		,					A__					:				float = 0.0001		,					A__					:				float = 0.02		,					A__					:				str = "linear"		,					A__					:				Optional[Union[np.ndarray, List[float]]] = None		,					A__					:				Optional[bool] = False		,					A__					:				str = "epsilon"		,					A__					:				str = "linspace"		,					A__					:				int = 0		,					)			->    Union[str, Any]:
           if trained_betas is not None:
                 lowerCamelCase__ 					=			torch.tensor(A__		,					dtype=torch.floataa     )
           elif beta_schedule == "linear":
                 lowerCamelCase__ 					=			torch.linspace(A__		,					A__		,					A__		,					dtype=torch.floataa     )
           elif beta_schedule == "scaled_linear":
                 # this schedule is very specific to the latent diffusion model.
                 lowerCamelCase__ 					=			(
                     torch.linspace(beta_start**0.5		,					beta_end**0.5		,					A__		,					dtype=torch.floataa     ) ** 2
                 )
           elif beta_schedule == "squaredcos_cap_v2":
                 # Glide cosine schedule
                 lowerCamelCase__ 					=			betas_for_alpha_bar(A__     )
           else:
                 raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""     )

           lowerCamelCase__ 					=			1.0 - self.betas
           lowerCamelCase__ 					=			torch.cumprod(self.alphas		,					dim=0     )

           lowerCamelCase__ 					=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5     )
           lowerCamelCase__ 					=			np.concatenate([sigmas[::-1], [0.0]]     ).astype(np.floataa     )
           lowerCamelCase__ 					=			torch.from_numpy(A__     )

           # setable values
           lowerCamelCase__ 					=			None
           lowerCamelCase__ 					=			use_karras_sigmas
           self.set_timesteps(A__		,					A__     )
           lowerCamelCase__ 					=			[]
           lowerCamelCase__ 					=			False




     @property
     def 	__snake_case				(      self					:				Optional[int]     )			->    Any:
           # 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					:				Optional[int]		,					A__					:				torch.FloatTensor		,					A__					:				Union[float, torch.FloatTensor]     )			->    torch.FloatTensor:
           if isinstance(A__		,					torch.Tensor     ):
                 lowerCamelCase__ 					=			timestep.to(self.timesteps.device     )
           lowerCamelCase__ 					=			(self.timesteps == timestep).nonzero().item()
           lowerCamelCase__ 					=			self.sigmas[step_index]
           lowerCamelCase__ 					=			sample / ((sigma**2 + 1) ** 0.5)
           lowerCamelCase__ 					=			True
           return sample




     def 	__snake_case				(      self					:				Dict		,					A__					:				int		,					A__					:				Tuple		,					A__					:				Optional[Any]     )			->    int:

           def lms_derivative(A__					:				Union[str, Any]     ):
                 lowerCamelCase__ 					=			1.0
                 for k in range(A__     ):
                       if current_order == k:
                             continue
                       prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
                 return prod

           lowerCamelCase__ 					=			integrate.quad(A__		,					self.sigmas[t]		,					self.sigmas[t + 1]		,					epsrel=1E-4     )[0]

           return integrated_coeff




     def 	__snake_case				(      self					:				Union[str, Any]		,					A__					:				int		,					A__					:				Union[str, torch.device] = None     )			->    Union[str, Any]:
           lowerCamelCase__ 					=			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":
                 lowerCamelCase__ 					=			np.linspace(0		,					self.config.num_train_timesteps - 1		,					A__		,					dtype=A__     )[
                     ::-1
                 ].copy()
           elif self.config.timestep_spacing == "leading":
                 lowerCamelCase__ 					=			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
                 lowerCamelCase__ 					=			(np.arange(0		,					A__     ) * step_ratio).round()[::-1].copy().astype(A__     )
                 timesteps += self.config.steps_offset
           elif self.config.timestep_spacing == "trailing":
                 lowerCamelCase__ 					=			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
                 lowerCamelCase__ 					=			(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'."""     )

           lowerCamelCase__ 					=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5     )
           lowerCamelCase__ 					=			np.log(A__     )
           lowerCamelCase__ 					=			np.interp(A__		,					np.arange(0		,					len(A__     )     )		,					A__     )

           if self.use_karras_sigmas:
                 lowerCamelCase__ 					=			self._convert_to_karras(in_sigmas=A__     )
                 lowerCamelCase__ 					=			np.array([self._sigma_to_t(A__		,					A__     ) for sigma in sigmas]     )

           lowerCamelCase__ 					=			np.concatenate([sigmas, [0.0]]     ).astype(np.floataa     )

           lowerCamelCase__ 					=			torch.from_numpy(A__     ).to(device=A__     )
           if str(A__     ).startswith('mps'     ):
                 # mps does not support float64
                 lowerCamelCase__ 					=			torch.from_numpy(A__     ).to(A__		,					dtype=torch.floataa     )
           else:
                 lowerCamelCase__ 					=			torch.from_numpy(A__     ).to(device=A__     )

           lowerCamelCase__ 					=			[]




     def 	__snake_case				(      self					:				int		,					A__					:				str		,					A__					:				Dict     )			->    int:
           # get log sigma
           lowerCamelCase__ 					=			np.log(A__     )

           # get distribution
           lowerCamelCase__ 					=			log_sigma - log_sigmas[:, np.newaxis]

           # get sigmas range
           lowerCamelCase__ 					=			np.cumsum((dists >= 0)		,					axis=0     ).argmax(axis=0     ).clip(max=log_sigmas.shape[0] - 2     )
           lowerCamelCase__ 					=			low_idx + 1

           lowerCamelCase__ 					=			log_sigmas[low_idx]
           lowerCamelCase__ 					=			log_sigmas[high_idx]

           # interpolate sigmas
           lowerCamelCase__ 					=			(low - log_sigma) / (low - high)
           lowerCamelCase__ 					=			np.clip(A__		,					0		,					1     )

           # transform interpolation to time range
           lowerCamelCase__ 					=			(1 - w) * low_idx + w * high_idx
           lowerCamelCase__ 					=			t.reshape(sigma.shape     )
           return t




     def 	__snake_case				(      self					:				Any		,					A__					:				torch.FloatTensor     )			->    torch.FloatTensor:
           lowerCamelCase__ 					=			in_sigmas[-1].item()
           lowerCamelCase__ 					=			in_sigmas[0].item()

           lowerCamelCase__ 					=			7.0  # 7.0 is the value used in the paper
           lowerCamelCase__ 					=			np.linspace(0		,					1		,					self.num_inference_steps     )
           lowerCamelCase__ 					=			sigma_min ** (1 / rho)
           lowerCamelCase__ 					=			sigma_max ** (1 / rho)
           lowerCamelCase__ 					=			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
           return sigmas




     def 	__snake_case				(      self					:				int		,					A__					:				torch.FloatTensor		,					A__					:				Union[float, torch.FloatTensor]		,					A__					:				torch.FloatTensor		,					A__					:				int = 4		,					A__					:				bool = True		,					)			->    Union[LMSDiscreteSchedulerOutput, Tuple]:
           if not self.is_scale_input_called:
                 warnings.warn(
                     '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     ):
                 lowerCamelCase__ 					=			timestep.to(self.timesteps.device     )
           lowerCamelCase__ 					=			(self.timesteps == timestep).nonzero().item()
           lowerCamelCase__ 					=			self.sigmas[step_index]

           # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
           if self.config.prediction_type == "epsilon":
                 lowerCamelCase__ 					=			sample - sigma * model_output
           elif self.config.prediction_type == "v_prediction":
                 # * c_out + input * c_skip
                 lowerCamelCase__ 					=			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
           elif self.config.prediction_type == "sample":
                 lowerCamelCase__ 					=			model_output
           else:
                 raise ValueError(
                     F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"""     )

           # 2. Convert to an ODE derivative
           lowerCamelCase__ 					=			(sample - pred_original_sample) / sigma
           self.derivatives.append(A__     )
           if len(self.derivatives     ) > order:
                 self.derivatives.pop(0     )

           # 3. Compute linear multistep coefficients
           lowerCamelCase__ 					=			min(step_index + 1		,					A__     )
           lowerCamelCase__ 					=			[self.get_lms_coefficient(A__		,					A__		,					A__     ) for curr_order in range(A__     )]

           # 4. Compute previous sample based on the derivatives path
           lowerCamelCase__ 					=			sample + sum(
               coeff * derivative for coeff, derivative in zip(A__		,					reversed(self.derivatives     )     )     )

           if not return_dict:
                 return (prev_sample,)

           return LMSDiscreteSchedulerOutput(prev_sample=A__		,					pred_original_sample=A__     )




     def 	__snake_case				(      self					:				Dict		,					A__					:				torch.FloatTensor		,					A__					:				torch.FloatTensor		,					A__					:				torch.FloatTensor		,					)			->    torch.FloatTensor:
           # Make sure sigmas and timesteps have the same device and dtype as original_samples
           lowerCamelCase__ 					=			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
                 lowerCamelCase__ 					=			self.timesteps.to(original_samples.device		,					dtype=torch.floataa     )
                 lowerCamelCase__ 					=			timesteps.to(original_samples.device		,					dtype=torch.floataa     )
           else:
                 lowerCamelCase__ 					=			self.timesteps.to(original_samples.device     )
                 lowerCamelCase__ 					=			timesteps.to(original_samples.device     )

           lowerCamelCase__ 					=			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

           lowerCamelCase__ 					=			sigmas[step_indices].flatten()
           while len(sigma.shape     ) < len(original_samples.shape     ):
                 lowerCamelCase__ 					=			sigma.unsqueeze(-1     )

           lowerCamelCase__ 					=			original_samples + noise * sigma
           return noisy_samples




     def __len__(      self					:				Union[str, Any]     )			->    int:
           return self.config.num_train_timesteps





def      lowerCAmelCase_     (					lowerCamelCase:    Optional[int]  )   ->     Union[str, Any]:


      '''simple docstring'''




      lowerCamelCase__ 					=			[7_01, 3_01, 1_32, 57, 23, 10, 4, 1]
      for gap in gaps:
            for i in range(lowerCamelCase       ,			len(lowerCamelCase  )  ):
                  lowerCamelCase__ 					=			collection[i]
                  lowerCamelCase__ 					=			i
                  while j >= gap and collection[j - gap] > insert_value:
                        lowerCamelCase__ 					=			collection[j - gap]
                        j -= gap
                  if j != i:
                        lowerCamelCase__ 					=			insert_value
      return collection


if __name__ == "__main__":
      from doctest import testmod

      testmod()
      __SCREAMING_SNAKE_CASE      :				List[Any]				      =input("""Enter numbers separated by a comma:\n""").strip()
      __SCREAMING_SNAKE_CASE      :				Dict				      =[int(item) for item in user_input.split(""",""")]
      print(shell_sort(unsorted))