"""simple docstring"""







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      _SCREAMING_SNAKE_CASE							(			lowercase__				):



   '''simple docstring'''



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



def       A__    (	lowercase_     :	Tuple      , lowercase_     :	Tuple=0.9_9_9      , lowercase_     :	List[Any]="cosine"      , )  ->							int:
   if alpha_transform_type == "cosine":

      def alpha_bar_fn(lowercase_     :	int						):
         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(lowercase_     :	str						):
         return math.exp(t * -1_2.0						)

   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      _SCREAMING_SNAKE_CASE							(			lowercase__    ,				lowercase__				):



   '''simple docstring'''



   __UpperCAmelCase	:							Optional[Any]    =    [e.name for e in KarrasDiffusionSchedulers]
   __UpperCAmelCase	:							int    =    1







   @register_to_config
   def __init__(	self ,				_SCREAMING_SNAKE_CASE = 1000 ,				_SCREAMING_SNAKE_CASE = 0.0001 ,				_SCREAMING_SNAKE_CASE = 0.02 ,				_SCREAMING_SNAKE_CASE = "linear" ,				_SCREAMING_SNAKE_CASE = None ,				_SCREAMING_SNAKE_CASE = False ,				_SCREAMING_SNAKE_CASE = "epsilon" ,				_SCREAMING_SNAKE_CASE = "linspace" ,				_SCREAMING_SNAKE_CASE = 0 ,				):


      '''simple docstring'''

      if trained_betas is not None:
         __lowerCamelCase    		=					torch.tensor(lowercase_ ,				dtype=torch.floataa	)
      elif beta_schedule == "linear":
         __lowerCamelCase    		=					torch.linspace(lowercase_ ,				lowercase_ ,				lowercase_ ,				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 ,				lowercase_ ,				dtype=torch.floataa	) ** 2
         )
      elif beta_schedule == "squaredcos_cap_v2":
         # Glide cosine schedule
         __lowerCamelCase    		=					betas_for_alpha_bar(lowercase_	)
      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(lowercase_	)

      # setable values
      __lowerCamelCase    		=					None
      __lowerCamelCase    		=					use_karras_sigmas
      self.set_timesteps(lowercase_ ,				lowercase_	)
      __lowerCamelCase    		=					[]
      __lowerCamelCase    		=					False







   @property
   def    _A				(	self	):


      '''simple docstring'''

      if self.config.timestep_spacing in ["linspace", "trailing"]:
         return self.sigmas.max()

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







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      if isinstance(lowercase_ ,				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    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      def lms_derivative(_SCREAMING_SNAKE_CASE	):
         __lowerCamelCase    		=					1.0
         for k in range(lowercase_	):
            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(lowercase_ ,				self.sigmas[t] ,				self.sigmas[t + 1] ,				epsrel=1E-4	)[0]

      return integrated_coeff







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = None	):


      '''simple docstring'''

      __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 ,				lowercase_ ,				dtype=lowercase_	)[
             ::-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 ,				lowercase_	) * step_ratio).round()[::-1].copy().astype(lowercase_	)
         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(lowercase_	)
         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(lowercase_	)
      __lowerCamelCase    		=					np.interp(lowercase_ ,				np.arange(0 ,				len(lowercase_	)	) ,				lowercase_	)

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

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

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

      __lowerCamelCase    		=					[]







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __lowerCamelCase    		=					np.log(lowercase_	)

      # 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(lowercase_ ,				0 ,				1	)

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







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __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    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = 4 ,				_SCREAMING_SNAKE_CASE = True ,				):


      '''simple docstring'''

      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(lowercase_ ,				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(lowercase_	)
      if len(self.derivatives	) > order:
         self.derivatives.pop(0	)

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

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

      if not return_dict:
         return (prev_sample,)

      return LMSDiscreteSchedulerOutput(prev_sample=lowercase_ ,				pred_original_sample=lowercase_	)







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					self.sigmas.to(device=original_samples.device ,				dtype=original_samples.dtype	)
      if original_samples.device.type == "mps" and torch.is_floating_point(lowercase_	):
         # 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	):


      '''simple docstring'''

      return self.config.num_train_timesteps








"""simple docstring"""





class A_      :




  '''simple docstring'''







  def __init__(						self							,  lowercase_    ):

     """simple docstring"""
     UpperCAmelCase_   :   str     	=       data
     UpperCAmelCase_   :   str     	=       None
     UpperCAmelCase_   :   List[Any]     	=       None







  def __str__(						self    ):

     """simple docstring"""
     return F"""{self.data}"""




class A_      :




  '''simple docstring'''







  def __init__(						self    ):

     """simple docstring"""
     UpperCAmelCase_   :   Tuple     	=       None
     UpperCAmelCase_   :   List[str]     	=       None







  def __iter__(						self    ):

     """simple docstring"""
     UpperCAmelCase_   :   Optional[int]     	=       self.head
     while node:
        yield node.data
        UpperCAmelCase_   :   Optional[Any]     	=       node.next







  def __str__(						self    ):

     """simple docstring"""
     return "->".join([str(lowercase_    ) for item in self]    )







  def __len__(						self    ):

     """simple docstring"""
     return sum(1 for _ in self    )







  def 			UpperCamelCase__   (						self							,  lowercase_    ):

     """simple docstring"""
     self.insert_at_nth(0							,  lowercase_    )







  def 			UpperCamelCase__   (						self							,  lowercase_    ):

     """simple docstring"""
     self.insert_at_nth(len(self    )							,  lowercase_    )







  def 			UpperCamelCase__   (						self							,  lowercase_							,  lowercase_    ):

     """simple docstring"""
     UpperCAmelCase_   :   int     	=       len(self    )

     if not 0 <= index <= length:
        raise IndexError("list index out of range"    )
     UpperCAmelCase_   :   Tuple     	=       Node(lowercase_    )
     if self.head is None:
        UpperCAmelCase_   :   List[str]     	=       new_node
     elif index == 0:
        UpperCAmelCase_   :   int     	=       new_node
        UpperCAmelCase_   :   Optional[Any]     	=       self.head
        UpperCAmelCase_   :   Optional[int]     	=       new_node
     elif index == length:
        UpperCAmelCase_   :   Union[str, Any]     	=       new_node
        UpperCAmelCase_   :   Optional[Any]     	=       self.tail
        UpperCAmelCase_   :   Tuple     	=       new_node
     else:
        UpperCAmelCase_   :   Dict     	=       self.head
        for _ in range(0							,  lowercase_    ):
           UpperCAmelCase_   :   str     	=       temp.next
        UpperCAmelCase_   :   int     	=       new_node
        UpperCAmelCase_   :   Tuple     	=       temp.previous
        UpperCAmelCase_   :   Union[str, Any]     	=       temp
        UpperCAmelCase_   :   int     	=       new_node







  def 			UpperCamelCase__   (						self    ):

     """simple docstring"""
     return self.delete_at_nth(0    )







  def 			UpperCamelCase__   (						self    ):

     """simple docstring"""
     return self.delete_at_nth(len(self    ) - 1    )







  def 			UpperCamelCase__   (						self							,  lowercase_    ):

     """simple docstring"""
     UpperCAmelCase_   :   int     	=       len(self    )

     if not 0 <= index <= length - 1:
        raise IndexError("list index out of range"    )
     UpperCAmelCase_   :   Optional[int]     	=       self.head  # default first node
     if length == 1:
        UpperCAmelCase_   :   Union[str, Any]     	=       None
     elif index == 0:
        UpperCAmelCase_   :   List[Any]     	=       self.head.next
        UpperCAmelCase_   :   str     	=       None
     elif index == length - 1:
        UpperCAmelCase_   :   str     	=       self.tail
        UpperCAmelCase_   :   Optional[Any]     	=       self.tail.previous
        UpperCAmelCase_   :   Any     	=       None
     else:
        UpperCAmelCase_   :   List[Any]     	=       self.head
        for _ in range(0							,  lowercase_    ):
           UpperCAmelCase_   :   str     	=       temp.next
        UpperCAmelCase_   :   Dict     	=       temp
        UpperCAmelCase_   :   Optional[Any]     	=       temp.previous
        UpperCAmelCase_   :   int     	=       temp.next
     return delete_node.data







  def 			UpperCamelCase__   (						self							,  lowercase_    ):

     """simple docstring"""
     UpperCAmelCase_   :   Tuple     	=       self.head

     while current.data != data:  # Find the position to delete
        if current.next:
           UpperCAmelCase_   :   List[str]     	=       current.next
        else:  # We have reached the end an no value matches
           raise ValueError("No data matching given value"    )

     if current == self.head:
        self.delete_head()

     elif current == self.tail:
        self.delete_tail()

     else:  # Before: 1 <--> 2(current) <--> 3
        UpperCAmelCase_   :   str     	=       current.next  # 1 --> 3
        UpperCAmelCase_   :   Optional[Any]     	=       current.previous  # 1 <--> 3
     return data







  def 			UpperCamelCase__   (						self    ):

     """simple docstring"""
     return len(self    ) == 0







def       __a	(						):
   UpperCAmelCase_   :   Dict     	=       DoublyLinkedList()
   assert linked_list.is_empty() is True
   assert str(__lowerCamelCase    ) == ""

   try:
      linked_list.delete_head()
      raise AssertionError  # This should not happen.
   except IndexError:
      assert True  # This should happen.

   try:
      linked_list.delete_tail()
      raise AssertionError  # This should not happen.
   except IndexError:
      assert True  # This should happen.

   for i in range(10    ):
      assert len(__lowerCamelCase    ) == i
      linked_list.insert_at_nth(__lowerCamelCase,						i + 1    )
   assert str(__lowerCamelCase    ) == "->".join(str(__lowerCamelCase    ) for i in range(1,						11    )    )

   linked_list.insert_at_head(0    )
   linked_list.insert_at_tail(11    )
   assert str(__lowerCamelCase    ) == "->".join(str(__lowerCamelCase    ) for i in range(0,						12    )    )

   assert linked_list.delete_head() == 0
   assert linked_list.delete_at_nth(9    ) == 10
   assert linked_list.delete_tail() == 11
   assert len(__lowerCamelCase    ) == 9
   assert str(__lowerCamelCase    ) == "->".join(str(__lowerCamelCase    ) for i in range(1,						10    )    )


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

    testmod()


