


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


lowerCAmelCase__						=			logging.get_logger(__name__)  # pylint: disable=invalid-name







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class 					lowerCAmelCase__    (    lowercase__):




     '''simple docstring'''
     __SCREAMING_SNAKE_CASE        =			42
     __SCREAMING_SNAKE_CASE        =			None




def 							_UpperCAmelCase    (UpperCamelCase__					:  Tuple    ,							UpperCamelCase__					:  List[str]=0.9_99    ,							UpperCamelCase__					:  Optional[int]="cosine"    ,							):

       if alpha_transform_type == "cosine":

              def alpha_bar_fn(UpperCamelCase__					:  Optional[Any]						):
                     return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2						) ** 2

       elif alpha_transform_type == "exp":

              def alpha_bar_fn(UpperCamelCase__					:  Dict						):
                     return math.exp(t * -12.0						)

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

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







class 					lowerCAmelCase__    (    lowercase__					,   lowercase__):




     '''simple docstring'''
     __SCREAMING_SNAKE_CASE        =			[e.name for e in KarrasDiffusionSchedulers]
     __SCREAMING_SNAKE_CASE        =			1


     @register_to_config
     def __init__(						self			,						__lowerCamelCase = 1_0_0_0			,						__lowerCamelCase = 0.0_0_0_1			,						__lowerCamelCase = 0.0_2			,						__lowerCamelCase = "linear"			,						__lowerCamelCase = None			,						__lowerCamelCase = "epsilon"			,						__lowerCamelCase = "linear"			,						__lowerCamelCase = False			,						__lowerCamelCase = "linspace"			,						__lowerCamelCase = 0			,						)      ->    Optional[Any]:
            if trained_betas is not None:
                   _A				:	Dict       =			torch.tensor(lowerCAmelCase__			,						dtype=torch.floataa)
            elif beta_schedule == "linear":
                   _A				:	Optional[int]       =			torch.linspace(lowerCAmelCase__			,						lowerCAmelCase__			,						lowerCAmelCase__			,						dtype=torch.floataa)
            elif beta_schedule == "scaled_linear":
                   # this schedule is very specific to the latent diffusion model.
                   _A				:	List[str]       =			(
                       torch.linspace(beta_start**0.5			,						beta_end**0.5			,						lowerCAmelCase__			,						dtype=torch.floataa) ** 2
                   )
            elif beta_schedule == "squaredcos_cap_v2":
                   # Glide cosine schedule
                   _A				:	Union[str, Any]       =			betas_for_alpha_bar(lowerCAmelCase__)
            else:
                   raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}")

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

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

            # setable values
            _A				:	List[str]       =			None
            _A				:	Any       =			np.linspace(0			,						num_train_timesteps - 1			,						lowerCAmelCase__			,						dtype=lowerCAmelCase__)[::-1].copy()
            _A				:	Tuple       =			torch.from_numpy(lowerCAmelCase__)
            _A				:	str       =			False
            _A				:	Any       =			use_karras_sigmas


     @property
     def 			_lowerCamelCase			(						self)      ->    List[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 			_lowerCamelCase			(						self			,						__lowerCamelCase			,						__lowerCamelCase)      ->    torch.FloatTensor:
            if isinstance(lowerCAmelCase__			,						torch.Tensor):
                   _A				:	Optional[Any]       =			timestep.to(self.timesteps.device)
            _A				:	Tuple       =			(self.timesteps == timestep).nonzero().item()
            _A				:	str       =			self.sigmas[step_index]

            _A				:	Dict       =			sample / ((sigma**2 + 1) ** 0.5)

            _A				:	Any       =			True
            return sample


     def 			_lowerCamelCase			(						self			,						__lowerCamelCase			,						__lowerCamelCase = None)      ->    List[str]:
            _A				:	Optional[int]       =			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":
                   _A				:	Any       =			np.linspace(0			,						self.config.num_train_timesteps - 1			,						lowerCAmelCase__			,						dtype=lowerCAmelCase__)[
                       ::-1
                   ].copy()
            elif self.config.timestep_spacing == "leading":
                   _A				:	Optional[int]       =			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
                   _A				:	int       =			(np.arange(0			,						lowerCAmelCase__) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__)
                   timesteps += self.config.steps_offset
            elif self.config.timestep_spacing == "trailing":
                   _A				:	Tuple       =			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
                   _A				:	List[str]       =			(np.arange(self.config.num_train_timesteps			,						0			,						-step_ratio)).round().copy().astype(lowerCAmelCase__)
                   timesteps -= 1
            else:
                   raise ValueError(
                       F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.")

            _A				:	int       =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
            _A				:	Union[str, Any]       =			np.log(lowerCAmelCase__)

            if self.config.interpolation_type == "linear":
                   _A				:	List[str]       =			np.interp(lowerCAmelCase__			,						np.arange(0			,						len(lowerCAmelCase__))			,						lowerCAmelCase__)
            elif self.config.interpolation_type == "log_linear":
                   _A				:	Optional[Any]       =			torch.linspace(np.log(sigmas[-1])			,						np.log(sigmas[0])			,						num_inference_steps + 1).exp()
            else:
                   raise ValueError(
                       F"{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"
                       " \'linear\' or \'log_linear\'")

            if self.use_karras_sigmas:
                   _A				:	Tuple       =			self._convert_to_karras(in_sigmas=lowerCAmelCase__			,						num_inference_steps=self.num_inference_steps)
                   _A				:	Optional[int]       =			np.array([self._sigma_to_t(lowerCAmelCase__			,						lowerCAmelCase__) for sigma in sigmas])

            _A				:	List[Any]       =			np.concatenate([sigmas, [0.0]]).astype(np.floataa)
            _A				:	Dict       =			torch.from_numpy(lowerCAmelCase__).to(device=lowerCAmelCase__)
            if str(lowerCAmelCase__).startswith("mps"):
                   # mps does not support float64
                   _A				:	Any       =			torch.from_numpy(lowerCAmelCase__).to(lowerCAmelCase__			,						dtype=torch.floataa)
            else:
                   _A				:	List[str]       =			torch.from_numpy(lowerCAmelCase__).to(device=lowerCAmelCase__)


     def 			_lowerCamelCase			(						self			,						__lowerCamelCase			,						__lowerCamelCase)      ->    Optional[Any]:
            _A				:	str       =			np.log(lowerCAmelCase__)

            # get distribution
            _A				:	List[str]       =			log_sigma - log_sigmas[:, np.newaxis]

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

            _A				:	List[str]       =			log_sigmas[low_idx]
            _A				:	Union[str, Any]       =			log_sigmas[high_idx]

            # interpolate sigmas
            _A				:	Optional[Any]       =			(low - log_sigma) / (low - high)
            _A				:	List[Any]       =			np.clip(lowerCAmelCase__			,						0			,						1)

            # transform interpolation to time range
            _A				:	int       =			(1 - w) * low_idx + w * high_idx
            _A				:	Union[str, Any]       =			t.reshape(sigma.shape)
            return t


     def 			_lowerCamelCase			(						self			,						__lowerCamelCase			,						__lowerCamelCase)      ->    torch.FloatTensor:
            _A				:	Tuple       =			in_sigmas[-1].item()
            _A				:	Optional[Any]       =			in_sigmas[0].item()

            _A				:	List[str]       =			7.0  # 7.0 is the value used in the paper
            _A				:	int       =			np.linspace(0			,						1			,						lowerCAmelCase__)
            _A				:	Union[str, Any]       =			sigma_min ** (1 / rho)
            _A				:	Optional[Any]       =			sigma_max ** (1 / rho)
            _A				:	Union[str, Any]       =			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
            return sigmas


     def 			_lowerCamelCase			(						self			,						__lowerCamelCase			,						__lowerCamelCase			,						__lowerCamelCase			,						__lowerCamelCase = 0.0			,						__lowerCamelCase = 0.0			,						__lowerCamelCase = float("inf")			,						__lowerCamelCase = 1.0			,						__lowerCamelCase = None			,						__lowerCamelCase = True			,						)      ->    Union[EulerDiscreteSchedulerOutput, Tuple]:

            if (
                isinstance(lowerCAmelCase__			,						lowerCAmelCase__)
                or isinstance(lowerCAmelCase__			,						torch.IntTensor)
                or isinstance(lowerCAmelCase__			,						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(lowerCAmelCase__			,						torch.Tensor):
                   _A				:	Optional[int]       =			timestep.to(self.timesteps.device)

            _A				:	Tuple       =			(self.timesteps == timestep).nonzero().item()
            _A				:	Union[str, Any]       =			self.sigmas[step_index]

            _A				:	Dict       =			min(s_churn / (len(self.sigmas) - 1)			,						2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0

            _A				:	List[Any]       =			randn_tensor(
                model_output.shape			,						dtype=model_output.dtype			,						device=model_output.device			,						generator=lowerCAmelCase__)

            _A				:	Optional[int]       =			noise * s_noise
            _A				:	List[str]       =			sigma * (gamma + 1)

            if gamma > 0:
                   _A				:	Tuple       =			sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

            # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
            # NOTE: "original_sample" should not be an expected prediction_type but is left in for
            # backwards compatibility
            if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
                   _A				:	Union[str, Any]       =			model_output
            elif self.config.prediction_type == "epsilon":
                   _A				:	List[str]       =			sample - sigma_hat * model_output
            elif self.config.prediction_type == "v_prediction":
                   # * c_out + input * c_skip
                   _A				:	Optional[Any]       =			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
            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
            _A				:	Optional[Any]       =			(sample - pred_original_sample) / sigma_hat

            _A				:	Tuple       =			self.sigmas[step_index + 1] - sigma_hat

            _A				:	str       =			sample + derivative * dt

            if not return_dict:
                   return (prev_sample,)

            return EulerDiscreteSchedulerOutput(prev_sample=lowerCAmelCase__			,						pred_original_sample=lowerCAmelCase__)


     def 			_lowerCamelCase			(						self			,						__lowerCamelCase			,						__lowerCamelCase			,						__lowerCamelCase			,						)      ->    torch.FloatTensor:
            _A				:	Dict       =			self.sigmas.to(device=original_samples.device			,						dtype=original_samples.dtype)
            if original_samples.device.type == "mps" and torch.is_floating_point(lowerCAmelCase__):
                   # mps does not support float64
                   _A				:	str       =			self.timesteps.to(original_samples.device			,						dtype=torch.floataa)
                   _A				:	str       =			timesteps.to(original_samples.device			,						dtype=torch.floataa)
            else:
                   _A				:	str       =			self.timesteps.to(original_samples.device)
                   _A				:	Optional[int]       =			timesteps.to(original_samples.device)

            _A				:	Tuple       =			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

            _A				:	Optional[Any]       =			sigmas[step_indices].flatten()
            while len(sigma.shape) < len(original_samples.shape):
                   _A				:	Union[str, Any]       =			sigma.unsqueeze(-1)

            _A				:	Union[str, Any]       =			original_samples + noise * sigma
            return noisy_samples


     def __len__(						self)      ->    str:
            return self.config.num_train_timesteps




def 							_UpperCAmelCase    (UpperCamelCase__					:  list    ,							UpperCamelCase__					:  int    ,							UpperCamelCase__					:  int						):
       if right <= left:
              return
       _A				:	str       =			left
       _A				:	List[str]       =			right
       _A				:	Union[str, Any]       =			sorting[left]
       while i <= b:
              if sorting[i] < pivot:
                     _A   ,      _A				:	Union[str, Any]       =			sorting[i], sorting[a]
                     a += 1
                     i += 1
              elif sorting[i] > pivot:
                     _A   ,      _A				:	str       =			sorting[i], sorting[b]
                     b -= 1
              else:
                     i += 1
       quick_sort_apartition(UpperCamelCase__    ,							UpperCamelCase__    ,							a - 1						)
       quick_sort_apartition(UpperCamelCase__    ,							b + 1    ,							UpperCamelCase__						)
def 							_UpperCAmelCase    (UpperCamelCase__					:  list    ,							UpperCamelCase__					:  int    ,							UpperCamelCase__					:  int						):
       if left < right:
              _A				:	Tuple       =			lomuto_partition(UpperCamelCase__    ,							UpperCamelCase__    ,							UpperCamelCase__						)
              quick_sort_lomuto_partition(UpperCamelCase__    ,							UpperCamelCase__    ,							pivot_index - 1						)
              quick_sort_lomuto_partition(UpperCamelCase__    ,							pivot_index + 1    ,							UpperCamelCase__						)
def 							_UpperCAmelCase    (UpperCamelCase__					:  list    ,							UpperCamelCase__					:  int    ,							UpperCamelCase__					:  int						):
       _A				:	Tuple       =			sorting[right]
       _A				:	Tuple       =			left
       for i in range(UpperCamelCase__    ,							UpperCamelCase__						):
              if sorting[i] < pivot:
                     _A   ,      _A				:	int       =			sorting[i], sorting[store_index]
                     store_index += 1
       _A   ,      _A				:	Dict       =			sorting[store_index], sorting[right]
       return store_index
def 							_UpperCAmelCase    (UpperCamelCase__					:  list						):
       if len(UpperCamelCase__						) <= 1:
              return sorting
       return (
           three_way_radix_quicksort([i for i in sorting if i < sorting[0]]						)
           + [i for i in sorting if i == sorting[0]]
           + three_way_radix_quicksort([i for i in sorting if i > sorting[0]]						)
       )


if __name__ == "__main__":
    import doctest

    doctest.testmod(verbose=True)

    lowerCAmelCase__						=			input('Enter numbers separated by a comma:\n').strip()
    lowerCAmelCase__						=			[int(item) for item in user_input.split(',')]
    quick_sort_apartition(unsorted, 0, len(unsorted) - 1)
    print(unsorted)
