





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 					__magic_name__  (							lowerCamelCase__							):





     """simple docstring"""



     __UpperCamelCase					    =     42
     __UpperCamelCase					    =     None




def      __snake_case						(					_lowerCAmelCase : Any				,				_lowerCAmelCase : Any=0.9_99				,				_lowerCAmelCase : Dict="cosine"				,				) ->						List[str]:
   if alpha_transform_type == "cosine":

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

   elif alpha_transform_type == "exp":

      def alpha_bar_fn(_lowerCAmelCase : Optional[int]	):
         return math.exp(t * -12.0	)

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

   A_					:				Optional[int]          =			[]
   for i in range(_lowerCAmelCase	):
      A_					:				Optional[int]          =			i / num_diffusion_timesteps
      A_					:				Tuple          =			(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 					__magic_name__  (							lowerCamelCase__    ,				lowerCamelCase__							):





     """simple docstring"""



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



     @register_to_config
     def __init__(							self       :Optional[Any]			,      snake_case       :int = 1_000			,      snake_case       :float = 0.0001			,      snake_case       :float = 0.02			,      snake_case       :str = "linear"			,      snake_case       :Optional[Union[np.ndarray, List[float]]] = None			,      snake_case       :Optional[bool] = False			,      snake_case       :str = "epsilon"			,      snake_case       :str = "linspace"			,      snake_case       :int = 0			,      ):





        '''simple docstring'''




        if trained_betas is not None:
           A_					:				List[str]          =			torch.tensor(snake_case			,      dtype=torch.floataa  )
        elif beta_schedule == "linear":
           A_					:				str          =			torch.linspace(snake_case			,      snake_case			,      snake_case			,      dtype=torch.floataa  )
        elif beta_schedule == "scaled_linear":
           # this schedule is very specific to the latent diffusion model.
           A_					:				Union[str, Any]          =			(
               torch.linspace(beta_start**0.5			,      beta_end**0.5			,      snake_case			,      dtype=torch.floataa  ) ** 2
           )
        elif beta_schedule == "squaredcos_cap_v2":
           # Glide cosine schedule
           A_					:				Dict          =			betas_for_alpha_bar(snake_case  )
        else:
           raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"  )

        A_					:				List[str]          =			1.0 - self.betas
        A_					:				Any          =			torch.cumprod(self.alphas			,      dim=0  )

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

        # setable values
        A_					:				Union[str, Any]          =			None
        A_					:				int          =			use_karras_sigmas
        self.set_timesteps(snake_case			,      snake_case  )
        A_					:				Any          =			[]
        A_					:				Tuple          =			False



     @property
     def 						SCREAMING_SNAKE_CASE		(							self       :int  ):





        '''simple docstring'''




        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       :int			,      snake_case       :torch.FloatTensor			,      snake_case       :Union[float, torch.FloatTensor]  ):





        '''simple docstring'''




        if isinstance(snake_case			,      torch.Tensor  ):
           A_					:				List[str]          =			timestep.to(self.timesteps.device  )
        A_					:				Dict          =			(self.timesteps == timestep).nonzero().item()
        A_					:				List[str]          =			self.sigmas[step_index]
        A_					:				List[Any]          =			sample / ((sigma**2 + 1) ** 0.5)
        A_					:				Tuple          =			True
        return sample



     def 						SCREAMING_SNAKE_CASE		(							self       :int			,      snake_case       :int			,      snake_case       :List[str]			,      snake_case       :Dict  ):





        '''simple docstring'''




        def lms_derivative(snake_case       :Optional[int]  ):
           A_					:				Any          =			1.0
           for k in range(snake_case  ):
              if current_order == k:
                 continue
              prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
           return prod

        A_					:				List[Any]          =			integrate.quad(snake_case			,      self.sigmas[t]			,      self.sigmas[t + 1]			,      epsrel=1e-4  )[0]

        return integrated_coeff



     def 						SCREAMING_SNAKE_CASE		(							self       :Optional[int]			,      snake_case       :int			,      snake_case       :Union[str, torch.device] = None  ):





        '''simple docstring'''




        A_					:				List[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":
           A_					:				int          =			np.linspace(0			,      self.config.num_train_timesteps - 1			,      snake_case			,      dtype=snake_case  )[
               ::-1
           ].copy()
        elif self.config.timestep_spacing == "leading":
           A_					:				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
           A_					:				Tuple          =			(np.arange(0			,      snake_case  ) * step_ratio).round()[::-1].copy().astype(snake_case  )
           timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
           A_					:				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_					:				List[Any]          =			(np.arange(self.config.num_train_timesteps			,      0			,      -step_ratio  )).round().copy().astype(snake_case  )
           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_					:				List[str]          =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
        A_					:				Optional[int]          =			np.log(snake_case  )
        A_					:				Any          =			np.interp(snake_case			,      np.arange(0			,      len(snake_case  )  )			,      snake_case  )

        if self.use_karras_sigmas:
           A_					:				Union[str, Any]          =			self._convert_to_karras(in_sigmas=snake_case  )
           A_					:				List[Any]          =			np.array([self._sigma_to_t(snake_case			,      snake_case  ) for sigma in sigmas]  )

        A_					:				List[str]          =			np.concatenate([sigmas, [0.0]]  ).astype(np.floataa  )

        A_					:				Tuple          =			torch.from_numpy(snake_case  ).to(device=snake_case  )
        if str(snake_case  ).startswith("mps"  ):
           # mps does not support float64
           A_					:				Optional[int]          =			torch.from_numpy(snake_case  ).to(snake_case			,      dtype=torch.floataa  )
        else:
           A_					:				Optional[int]          =			torch.from_numpy(snake_case  ).to(device=snake_case  )

        A_					:				List[str]          =			[]



     def 						SCREAMING_SNAKE_CASE		(							self       :int			,      snake_case       :Tuple			,      snake_case       :str  ):





        '''simple docstring'''




        A_					:				Optional[int]          =			np.log(snake_case  )

        # get distribution
        A_					:				List[Any]          =			log_sigma - log_sigmas[:, np.newaxis]

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

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

        # interpolate sigmas
        A_					:				Union[str, Any]          =			(low - log_sigma) / (low - high)
        A_					:				Optional[Any]          =			np.clip(snake_case			,      0			,      1  )

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



     def 						SCREAMING_SNAKE_CASE		(							self       :str			,      snake_case       :torch.FloatTensor  ):





        '''simple docstring'''




        A_					:				float          =			in_sigmas[-1].item()
        A_					:				float          =			in_sigmas[0].item()

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



     def 						SCREAMING_SNAKE_CASE		(							self       :List[str]			,      snake_case       :torch.FloatTensor			,      snake_case       :Union[float, torch.FloatTensor]			,      snake_case       :torch.FloatTensor			,      snake_case       :int = 4			,      snake_case       :bool = 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(snake_case			,      torch.Tensor  ):
           A_					:				Tuple          =			timestep.to(self.timesteps.device  )
        A_					:				List[Any]          =			(self.timesteps == timestep).nonzero().item()
        A_					:				Union[str, Any]          =			self.sigmas[step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
           A_					:				Dict          =			sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
           # * c_out + input * c_skip
           A_					:				Optional[int]          =			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        elif self.config.prediction_type == "sample":
           A_					:				Dict          =			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
        A_					:				Tuple          =			(sample - pred_original_sample) / sigma
        self.derivatives.append(snake_case  )
        if len(self.derivatives  ) > order:
           self.derivatives.pop(0  )

        # 3. Compute linear multistep coefficients
        A_					:				Optional[int]          =			min(step_index + 1			,      snake_case  )
        A_					:				Optional[Any]          =			[self.get_lms_coefficient(snake_case			,      snake_case			,      snake_case  ) for curr_order in range(snake_case  )]

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

        if not return_dict:
           return (prev_sample,)

        return LMSDiscreteSchedulerOutput(prev_sample=snake_case			,      pred_original_sample=snake_case  )



     def 						SCREAMING_SNAKE_CASE		(							self       :Any			,      snake_case       :torch.FloatTensor			,      snake_case       :torch.FloatTensor			,      snake_case       :torch.FloatTensor			,      ):





        '''simple docstring'''




        A_					:				Optional[int]          =			self.sigmas.to(device=original_samples.device			,      dtype=original_samples.dtype  )
        if original_samples.device.type == "mps" and torch.is_floating_point(snake_case  ):
           # mps does not support float64
           A_					:				Optional[int]          =			self.timesteps.to(original_samples.device			,      dtype=torch.floataa  )
           A_					:				List[Any]          =			timesteps.to(original_samples.device			,      dtype=torch.floataa  )
        else:
           A_					:				Any          =			self.timesteps.to(original_samples.device  )
           A_					:				str          =			timesteps.to(original_samples.device  )

        A_					:				int          =			[(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_					:				Optional[int]          =			sigma.unsqueeze(-1  )

        A_					:				List[str]          =			original_samples + noise * sigma
        return noisy_samples





     def __len__(							self       :Optional[int]  ):





        '''simple docstring'''




        return self.config.num_train_timesteps







def      __snake_case						(					_lowerCAmelCase : int				,				_lowerCAmelCase : int = 1000	) ->						str:
   if (not isinstance(_lowerCAmelCase				,				_lowerCAmelCase	)) or (digit_position <= 0):
      raise ValueError("Digit position must be a positive integer"	)
   elif (not isinstance(_lowerCAmelCase				,				_lowerCAmelCase	)) or (precision < 0):
      raise ValueError("Precision must be a nonnegative integer"	)

   # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
   # accurate
   A_					:				List[str]          =			(
       4 * _subsum(_lowerCAmelCase				,				1				,				_lowerCAmelCase	)
       - 2 * _subsum(_lowerCAmelCase				,				4				,				_lowerCAmelCase	)
       - _subsum(_lowerCAmelCase				,				5				,				_lowerCAmelCase	)
       - _subsum(_lowerCAmelCase				,				6				,				_lowerCAmelCase	)
   )

   # return the first hex digit of the fractional part of the result
   return hex(int((sum_result % 1) * 16	)	)[2:]

def      __snake_case						(					_lowerCAmelCase : int				,				_lowerCAmelCase : int				,				_lowerCAmelCase : int	) ->						float:
   A_					:				int          =			0.0
   for sum_index in range(digit_pos_to_extract + precision	):
      A_					:				Optional[int]          =			8 * sum_index + denominator_addend
      if sum_index < digit_pos_to_extract:
         # if the exponential term is an integer and we mod it by the denominator
         # before dividing, only the integer part of the sum will change;
         # the fractional part will not
         A_					:				Optional[Any]          =			pow(
             16				,				digit_pos_to_extract - 1 - sum_index				,				_lowerCAmelCase	)
      else:
         A_					:				Tuple          =			pow(16				,				digit_pos_to_extract - 1 - sum_index	)
      total += exponential_term / denominator
   return total


if __name__ == "__main__":
 import doctest

 doctest.testmod()
