





"""simple docstring"""





import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

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




def 		lowerCAmelCase_     (  lowercase_       :							str			,				lowercase_       :							List[str]=0.999			,				lowercase_       :							Any="cosine"			,				):

 '''simple docstring'''






 if alpha_transform_type == "cosine":

  def alpha_bar_fn(lowercase_       :							int		):
   return math.cos((t + 0.008) / 1.008 * math.pi / 2		) ** 2

 elif alpha_transform_type == "exp":

  def alpha_bar_fn(lowercase_       :							List[str]		):
   return math.exp(t * -12.0		)

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

 __SCREAMING_SNAKE_CASE			:      str 							=	[]
 for i in range(lowercase_		):
  __SCREAMING_SNAKE_CASE			:      Any 							=	i / num_diffusion_timesteps
  __SCREAMING_SNAKE_CASE			:      Dict 							=	(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       snake_case		(       __UpperCAmelCase			,					__UpperCAmelCase       ):
      lowerCamelCase__      =			[e.name for e in KarrasDiffusionSchedulers]
      lowerCamelCase__      =			2

      @register_to_config
      def __init__(      self       :Any						,							_lowerCamelCase       :int = 1_0_0_0						,							_lowerCamelCase       :float = 0.0_0_0_8_5						,							_lowerCamelCase       :float = 0.0_1_2						,							_lowerCamelCase       :str = "linear"						,							_lowerCamelCase       :Optional[Union[np.ndarray, List[float]]] = None						,							_lowerCamelCase       :str = "epsilon"						,							_lowerCamelCase       :str = "linspace"						,							_lowerCamelCase       :int = 0						,							):
       if trained_betas is not None:
        __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	torch.tensor(_lowerCamelCase						,							dtype=torch.floataa						)
       elif beta_schedule == "linear":
        __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	torch.linspace(_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						,							dtype=torch.floataa						)
       elif beta_schedule == "scaled_linear":
        # this schedule is very specific to the latent diffusion model.
        __SCREAMING_SNAKE_CASE			:      Tuple 							=	(
            torch.linspace(beta_start**0.5						,							beta_end**0.5						,							_lowerCamelCase						,							dtype=torch.floataa						) ** 2
        )
       elif beta_schedule == "squaredcos_cap_v2":
        # Glide cosine schedule
        __SCREAMING_SNAKE_CASE			:      List[Any] 							=	betas_for_alpha_bar(_lowerCamelCase						)
       else:
        raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''						)

       __SCREAMING_SNAKE_CASE			:      Dict 							=	1.0 - self.betas
       __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	torch.cumprod(self.alphas						,							dim=0						)

       #  set all values
       self.set_timesteps(_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase						)

      def 						SCREAMING_SNAKE_CASE_      (      self       :Optional[Any]						,							_lowerCamelCase       :Optional[Any]						,							_lowerCamelCase       :Union[str, Any]=None						):
       if schedule_timesteps is None:
        __SCREAMING_SNAKE_CASE			:      int 							=	self.timesteps

       __SCREAMING_SNAKE_CASE			:      str 							=	(schedule_timesteps == timestep).nonzero()

       # The sigma index that is taken for the **very** first `step`
       # is always the second index (or the last index if there is only 1)
       # This way we can ensure we don't accidentally skip a sigma in
       # case we start in the middle of the denoising schedule (e.g. for image-to-image)
       if len(self._index_counter						) == 0:
        __SCREAMING_SNAKE_CASE			:      Dict 							=	1 if len(_lowerCamelCase						) > 1 else 0
       else:
        __SCREAMING_SNAKE_CASE			:      Dict 							=	timestep.cpu().item() if torch.is_tensor(_lowerCamelCase						) else timestep
        __SCREAMING_SNAKE_CASE			:      Tuple 							=	self._index_counter[timestep_int]

       return indices[pos].item()

      @property
      def 						SCREAMING_SNAKE_CASE_      (      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 						SCREAMING_SNAKE_CASE_      (      self       :Dict						,							_lowerCamelCase       :torch.FloatTensor						,							_lowerCamelCase       :Union[float, torch.FloatTensor]						,							):
       __SCREAMING_SNAKE_CASE			:      List[str] 							=	self.index_for_timestep(_lowerCamelCase						)

       if self.state_in_first_order:
        __SCREAMING_SNAKE_CASE			:      Any 							=	self.sigmas[step_index]
       else:
        __SCREAMING_SNAKE_CASE			:      Any 							=	self.sigmas_interpol[step_index - 1]

       __SCREAMING_SNAKE_CASE			:      Any 							=	sample / ((sigma**2 + 1) ** 0.5)
       return sample

      def 						SCREAMING_SNAKE_CASE_      (      self       :Optional[Any]						,							_lowerCamelCase       :int						,							_lowerCamelCase       :Union[str, torch.device] = None						,							_lowerCamelCase       :Optional[int] = None						,							):
       __SCREAMING_SNAKE_CASE			:      int 							=	num_inference_steps

       __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	num_train_timesteps or self.config.num_train_timesteps

       # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
       if self.config.timestep_spacing == "linspace":
        __SCREAMING_SNAKE_CASE			:      Tuple 							=	np.linspace(0						,							num_train_timesteps - 1						,							_lowerCamelCase						,							dtype=_lowerCamelCase						)[::-1].copy()
       elif self.config.timestep_spacing == "leading":
        __SCREAMING_SNAKE_CASE			:      Any 							=	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
        __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	(np.arange(0						,							_lowerCamelCase						) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase						)
        timesteps += self.config.steps_offset
       elif self.config.timestep_spacing == "trailing":
        __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	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
        __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	(np.arange(_lowerCamelCase						,							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\'.'''						)

       __SCREAMING_SNAKE_CASE			:      int 							=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
       __SCREAMING_SNAKE_CASE			:      int 							=	torch.from_numpy(np.log(_lowerCamelCase						)						).to(_lowerCamelCase						)

       __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	np.interp(_lowerCamelCase						,							np.arange(0						,							len(_lowerCamelCase						)						)						,							_lowerCamelCase						)
       __SCREAMING_SNAKE_CASE			:      List[str] 							=	np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
       __SCREAMING_SNAKE_CASE			:      List[Any] 							=	torch.from_numpy(_lowerCamelCase						).to(device=_lowerCamelCase						)

       # compute up and down sigmas
       __SCREAMING_SNAKE_CASE			:      Tuple 							=	sigmas.roll(-1						)
       __SCREAMING_SNAKE_CASE			:      Dict 							=	0.0
       __SCREAMING_SNAKE_CASE			:      Dict 							=	(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
       __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	(sigmas_next**2 - sigmas_up**2) ** 0.5
       __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	0.0

       # compute interpolated sigmas
       __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	sigmas.log().lerp(sigmas_down.log()						,							0.5						).exp()
       __SCREAMING_SNAKE_CASE			:      int 							=	0.0

       # set sigmas
       __SCREAMING_SNAKE_CASE			:      List[Any] 							=	torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2						), sigmas[-1:]]						)
       __SCREAMING_SNAKE_CASE			:      Any 							=	torch.cat(
           [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2						), sigmas_interpol[-1:]]						)
       __SCREAMING_SNAKE_CASE			:      List[str] 							=	torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2						), sigmas_up[-1:]]						)
       __SCREAMING_SNAKE_CASE			:      List[str] 							=	torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2						), sigmas_down[-1:]]						)

       if str(_lowerCamelCase						).startswith('''mps'''						):
        # mps does not support float64
        __SCREAMING_SNAKE_CASE			:      Dict 							=	torch.from_numpy(_lowerCamelCase						).to(_lowerCamelCase						,							dtype=torch.floataa						)
       else:
        __SCREAMING_SNAKE_CASE			:      int 							=	torch.from_numpy(_lowerCamelCase						).to(_lowerCamelCase						)

       __SCREAMING_SNAKE_CASE			:      List[Any] 							=	self.sigma_to_t(_lowerCamelCase						).to(_lowerCamelCase						,							dtype=timesteps.dtype						)
       __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])						,							dim=-1						).flatten()

       __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	torch.cat([timesteps[:1], interleaved_timesteps]						)

       __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	None

       # for exp beta schedules, such as the one for `pipeline_shap_e.py`
       # we need an index counter
       __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	defaultdict(_lowerCamelCase						)

      def 						SCREAMING_SNAKE_CASE_      (      self       :str						,							_lowerCamelCase       :List[Any]						):
       # get log sigma
       __SCREAMING_SNAKE_CASE			:      int 							=	sigma.log()

       # get distribution
       __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	log_sigma - self.log_sigmas[:, None]

       # get sigmas range
       __SCREAMING_SNAKE_CASE			:      str 							=	dists.ge(0						).cumsum(dim=0						).argmax(dim=0						).clamp(max=self.log_sigmas.shape[0] - 2						)
       __SCREAMING_SNAKE_CASE			:      List[Any] 							=	low_idx + 1

       __SCREAMING_SNAKE_CASE			:      List[str] 							=	self.log_sigmas[low_idx]
       __SCREAMING_SNAKE_CASE			:      int 							=	self.log_sigmas[high_idx]

       # interpolate sigmas
       __SCREAMING_SNAKE_CASE			:      Any 							=	(low - log_sigma) / (low - high)
       __SCREAMING_SNAKE_CASE			:      Tuple 							=	w.clamp(0						,							1						)

       # transform interpolation to time range
       __SCREAMING_SNAKE_CASE			:      List[Any] 							=	(1 - w) * low_idx + w * high_idx
       __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	t.view(sigma.shape						)
       return t

      @property
      def 						SCREAMING_SNAKE_CASE_      (      self       :int						):
       return self.sample is None

      def 						SCREAMING_SNAKE_CASE_      (      self       :List[Any]						,							_lowerCamelCase       :Union[torch.FloatTensor, np.ndarray]						,							_lowerCamelCase       :Union[float, torch.FloatTensor]						,							_lowerCamelCase       :Union[torch.FloatTensor, np.ndarray]						,							_lowerCamelCase       :Optional[torch.Generator] = None						,							_lowerCamelCase       :bool = True						,							):
       __SCREAMING_SNAKE_CASE			:      Tuple 							=	self.index_for_timestep(_lowerCamelCase						)

       # advance index counter by 1
       __SCREAMING_SNAKE_CASE			:      List[Any] 							=	timestep.cpu().item() if torch.is_tensor(_lowerCamelCase						) else timestep
       self._index_counter[timestep_int] += 1

       if self.state_in_first_order:
        __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	self.sigmas[step_index]
        __SCREAMING_SNAKE_CASE			:      int 							=	self.sigmas_interpol[step_index]
        __SCREAMING_SNAKE_CASE			:      Tuple 							=	self.sigmas_up[step_index]
        __SCREAMING_SNAKE_CASE			:      List[Any] 							=	self.sigmas_down[step_index - 1]
       else:
        # 2nd order / KPDM2's method
        __SCREAMING_SNAKE_CASE			:      str 							=	self.sigmas[step_index - 1]
        __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	self.sigmas_interpol[step_index - 1]
        __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	self.sigmas_up[step_index - 1]
        __SCREAMING_SNAKE_CASE			:      str 							=	self.sigmas_down[step_index - 1]

       # currently only gamma=0 is supported. This usually works best anyways.
       # We can support gamma in the future but then need to scale the timestep before
       # passing it to the model which requires a change in API
       __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	0
       __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

       __SCREAMING_SNAKE_CASE			:      int 							=	model_output.device
       __SCREAMING_SNAKE_CASE			:      List[str] 							=	randn_tensor(model_output.shape						,							dtype=model_output.dtype						,							device=_lowerCamelCase						,							generator=_lowerCamelCase						)

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       if self.config.prediction_type == "epsilon":
        __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	sigma_hat if self.state_in_first_order else sigma_interpol
        __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	sample - sigma_input * model_output
       elif self.config.prediction_type == "v_prediction":
        __SCREAMING_SNAKE_CASE			:      List[str] 							=	sigma_hat if self.state_in_first_order else sigma_interpol
        __SCREAMING_SNAKE_CASE			:      List[str] 							=	model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
            sample / (sigma_input**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`'''						)

       if self.state_in_first_order:
        # 2. Convert to an ODE derivative for 1st order
        __SCREAMING_SNAKE_CASE			:      Dict 							=	(sample - pred_original_sample) / sigma_hat
        # 3. delta timestep
        __SCREAMING_SNAKE_CASE			:      Dict 							=	sigma_interpol - sigma_hat

        # store for 2nd order step
        __SCREAMING_SNAKE_CASE			:      str 							=	sample
        __SCREAMING_SNAKE_CASE			:      List[Any] 							=	dt
        __SCREAMING_SNAKE_CASE			:      Any 							=	sample + derivative * dt
       else:
        # DPM-Solver-2
        # 2. Convert to an ODE derivative for 2nd order
        __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	(sample - pred_original_sample) / sigma_interpol
        # 3. delta timestep
        __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	sigma_down - sigma_hat

        __SCREAMING_SNAKE_CASE			:      List[str] 							=	self.sample
        __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	None

        __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	sample + derivative * dt
        __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	prev_sample + noise * sigma_up

       if not return_dict:
        return (prev_sample,)

       return SchedulerOutput(prev_sample=_lowerCamelCase						)

      def 						SCREAMING_SNAKE_CASE_      (      self       :List[Any]						,							_lowerCamelCase       :torch.FloatTensor						,							_lowerCamelCase       :torch.FloatTensor						,							_lowerCamelCase       :torch.FloatTensor						,							):
       # Make sure sigmas and timesteps have the same device and dtype as original_samples
       __SCREAMING_SNAKE_CASE			:      List[str] 							=	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
        __SCREAMING_SNAKE_CASE			:      str 							=	self.timesteps.to(original_samples.device						,							dtype=torch.floataa						)
        __SCREAMING_SNAKE_CASE			:      Any 							=	timesteps.to(original_samples.device						,							dtype=torch.floataa						)
       else:
        __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	self.timesteps.to(original_samples.device						)
        __SCREAMING_SNAKE_CASE			:      Tuple 							=	timesteps.to(original_samples.device						)

       __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	[self.index_for_timestep(_lowerCamelCase						,							_lowerCamelCase						) for t in timesteps]

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

       __SCREAMING_SNAKE_CASE			:      int 							=	original_samples + noise * sigma
       return noisy_samples



      def __len__(      self       :Tuple						):
       return self.config.num_train_timesteps








"""simple docstring"""





def 		lowerCAmelCase_     (  lowercase_       :							Tuple			,				lowercase_       :							Any			,				lowercase_       :							List[str]		):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE			:      Any 							=	index
 __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	2 * index + 1
 __SCREAMING_SNAKE_CASE			:      Any 							=	2 * index + 2
 if left_index < heap_size and unsorted[left_index] > unsorted[largest]:
  __SCREAMING_SNAKE_CASE			:      str 							=	left_index

 if right_index < heap_size and unsorted[right_index] > unsorted[largest]:
  __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	right_index

 if largest != index:
  __SCREAMING_SNAKE_CASE							,				__SCREAMING_SNAKE_CASE			:      List[str] 							=	unsorted[index], unsorted[largest]
  heapify(lowercase_			,				lowercase_			,				lowercase_		)




def 		lowerCAmelCase_     (  lowercase_       :							List[Any]		):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE			:      Dict 							=	len(lowercase_		)
 for i in range(n // 2 - 1			,				-1			,				-1		):
  heapify(lowercase_			,				lowercase_			,				lowercase_		)
 for i in range(n - 1			,				0			,				-1		):
  __SCREAMING_SNAKE_CASE							,				__SCREAMING_SNAKE_CASE			:      List[Any] 							=	unsorted[i], unsorted[0]
  heapify(lowercase_			,				0			,				lowercase_		)
 return unsorted


if __name__ == "__main__":
    _lowerCamelCase  					=     input('''Enter numbers separated by a comma:\n''').strip()
    _lowerCamelCase  					=     [int(item) for item in user_input.split(''',''')]
    print(heap_sort(unsorted))

