





"""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			(  _UpperCamelCase      ):







  '''simple docstring'''


  SCREAMING_SNAKE_CASE__							:Optional[Any]		   =    42
  SCREAMING_SNAKE_CASE__							:Dict		   =    None





def     lowercase__			(    lowercase_						,lowercase_=0.999						,lowercase_="cosine"						,)    ->						int:




      """simple docstring"""

      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

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

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

      _UpperCamelCase					:		List[Any]  =				[]
      for i in range(_UpperCAmelCase	):
            _UpperCamelCase					:		Dict  =				i / num_diffusion_timesteps
            _UpperCamelCase					:		Optional[int]  =				(i + 1) / num_diffusion_timesteps
            betas.append(min(1 - alpha_bar_fn(_UpperCAmelCase	) / alpha_bar_fn(_UpperCAmelCase	)						,_UpperCAmelCase	)	)
      return torch.tensor(_UpperCAmelCase						,dtype=torch.floataa	)



class    __SCREAMING_SNAKE_CASE			(  _UpperCamelCase						,     _UpperCamelCase      ):







  '''simple docstring'''


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

  @register_to_config
  def __init__(						self      :				List[Any]    ,      __a      :				Dict = 1000    ,      __a      :				str = 0.00_01    ,      __a      :				Any = 0.02    ,      __a      :				int = "linear"    ,      __a      :				int = None    ,      __a      :				str = False    ,      __a      :				Any = "epsilon"    ,      __a      :				Optional[Any] = "linspace"    ,      __a      :				Tuple = 0    ,      )						-> Dict:
        if trained_betas is not None:
              _UpperCamelCase					:		Optional[Any]  =				torch.tensor(UpperCAmelCase_    ,      dtype=torch.floataa		)
        elif beta_schedule == "linear":
              _UpperCamelCase					:		Dict  =				torch.linspace(UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_    ,      dtype=torch.floataa		)
        elif beta_schedule == "scaled_linear":
              # this schedule is very specific to the latent diffusion model.
              _UpperCamelCase					:		int  =				(
                  torch.linspace(beta_start**0.5    ,      beta_end**0.5    ,      UpperCAmelCase_    ,      dtype=torch.floataa		) ** 2
              )
        elif beta_schedule == "squaredcos_cap_v2":
              # Glide cosine schedule
              _UpperCamelCase					:		Dict  =				betas_for_alpha_bar(UpperCAmelCase_		)
        else:
              raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''		)

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

        _UpperCamelCase					:		Union[str, Any]  =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
        _UpperCamelCase					:		Dict  =				np.concatenate([sigmas[::-1], [0.0]]		).astype(np.floataa		)
        _UpperCamelCase					:		Dict  =				torch.from_numpy(UpperCAmelCase_		)

        # setable values
        _UpperCamelCase					:		List[str]  =				None
        _UpperCamelCase					:		Tuple  =				use_karras_sigmas
        self.set_timesteps(UpperCAmelCase_    ,      UpperCAmelCase_		)
        _UpperCamelCase					:		Tuple  =				[]
        _UpperCamelCase					:		Any  =				False

  @property
  def       __SCREAMING_SNAKE_CASE (						self      :				Optional[Any]		)						-> int:
        # 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      :				List[str]    ,      __a      :				List[str]    ,      __a      :				List[str]		)						-> List[str]:
        if isinstance(UpperCAmelCase_    ,      torch.Tensor		):
              _UpperCamelCase					:		Dict  =				timestep.to(self.timesteps.device		)
        _UpperCamelCase					:		Union[str, Any]  =				(self.timesteps == timestep).nonzero().item()
        _UpperCamelCase					:		Dict  =				self.sigmas[step_index]
        _UpperCamelCase					:		Tuple  =				sample / ((sigma**2 + 1) ** 0.5)
        _UpperCamelCase					:		List[Any]  =				True
        return sample

  def       __SCREAMING_SNAKE_CASE (						self      :				int    ,      __a      :				Optional[int]    ,      __a      :				List[str]    ,      __a      :				int		)						-> List[str]:

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

        _UpperCamelCase					:		List[str]  =				integrate.quad(UpperCAmelCase_    ,      self.sigmas[t]    ,      self.sigmas[t + 1]    ,      epsrel=1e-4		)[0]

        return integrated_coeff

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

        _UpperCamelCase					:		Optional[int]  =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
        _UpperCamelCase					:		Tuple  =				np.log(UpperCAmelCase_		)
        _UpperCamelCase					:		Optional[int]  =				np.interp(UpperCAmelCase_    ,      np.arange(0    ,      len(UpperCAmelCase_		)		)    ,      UpperCAmelCase_		)

        if self.use_karras_sigmas:
              _UpperCamelCase					:		Any  =				self._convert_to_karras(in_sigmas=UpperCAmelCase_		)
              _UpperCamelCase					:		Tuple  =				np.array([self._sigma_to_t(UpperCAmelCase_    ,      UpperCAmelCase_		) for sigma in sigmas]		)

        _UpperCamelCase					:		Dict  =				np.concatenate([sigmas, [0.0]]		).astype(np.floataa		)

        _UpperCamelCase					:		Optional[Any]  =				torch.from_numpy(UpperCAmelCase_		).to(device=UpperCAmelCase_		)
        if str(UpperCAmelCase_		).startswith("mps"		):
              # mps does not support float64
              _UpperCamelCase					:		str  =				torch.from_numpy(UpperCAmelCase_		).to(UpperCAmelCase_    ,      dtype=torch.floataa		)
        else:
              _UpperCamelCase					:		str  =				torch.from_numpy(UpperCAmelCase_		).to(device=UpperCAmelCase_		)

        _UpperCamelCase					:		Optional[int]  =				[]

  def       __SCREAMING_SNAKE_CASE (						self      :				List[Any]    ,      __a      :				List[Any]    ,      __a      :				List[Any]		)						-> Union[str, Any]:
        # get log sigma
        _UpperCamelCase					:		int  =				np.log(UpperCAmelCase_		)

        # get distribution
        _UpperCamelCase					:		Optional[int]  =				log_sigma - log_sigmas[:, np.newaxis]

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

        _UpperCamelCase					:		Dict  =				log_sigmas[low_idx]
        _UpperCamelCase					:		Tuple  =				log_sigmas[high_idx]

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

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

  def       __SCREAMING_SNAKE_CASE (						self      :				Any    ,      __a      :				List[Any]		)						-> Tuple:
        _UpperCamelCase					:		Dict  =				in_sigmas[-1].item()
        _UpperCamelCase					:		List[Any]  =				in_sigmas[0].item()

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

  def       __SCREAMING_SNAKE_CASE (						self      :				Tuple    ,      __a      :				List[Any]    ,      __a      :				List[Any]    ,      __a      :				int    ,      __a      :				Union[str, Any] = 4    ,      __a      :				int = True    ,      )						-> List[str]:
        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(UpperCAmelCase_    ,      torch.Tensor		):
              _UpperCamelCase					:		str  =				timestep.to(self.timesteps.device		)
        _UpperCamelCase					:		Tuple  =				(self.timesteps == timestep).nonzero().item()
        _UpperCamelCase					:		int  =				self.sigmas[step_index]

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

        # 3. Compute linear multistep coefficients
        _UpperCamelCase					:		int  =				min(step_index + 1    ,      UpperCAmelCase_		)
        _UpperCamelCase					:		str  =				[self.get_lms_coefficient(UpperCAmelCase_    ,      UpperCAmelCase_    ,      UpperCAmelCase_		) for curr_order in range(UpperCAmelCase_		)]

        # 4. Compute previous sample based on the derivatives path
        _UpperCamelCase					:		Optional[Any]  =				sample + sum(
            coeff * derivative for coeff, derivative in zip(UpperCAmelCase_    ,      reversed(self.derivatives		)		)		)

        if not return_dict:
              return (prev_sample,)

        return LMSDiscreteSchedulerOutput(prev_sample=UpperCAmelCase_    ,      pred_original_sample=UpperCAmelCase_		)

  def       __SCREAMING_SNAKE_CASE (						self      :				Union[str, Any]    ,      __a      :				Optional[int]    ,      __a      :				Optional[Any]    ,      __a      :				Dict    ,      )						-> Any:
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        _UpperCamelCase					:		Optional[Any]  =				self.sigmas.to(device=original_samples.device    ,      dtype=original_samples.dtype		)
        if original_samples.device.type == "mps" and torch.is_floating_point(UpperCAmelCase_		):
              # mps does not support float64
              _UpperCamelCase					:		str  =				self.timesteps.to(original_samples.device    ,      dtype=torch.floataa		)
              _UpperCamelCase					:		Any  =				timesteps.to(original_samples.device    ,      dtype=torch.floataa		)
        else:
              _UpperCamelCase					:		Union[str, Any]  =				self.timesteps.to(original_samples.device		)
              _UpperCamelCase					:		List[str]  =				timesteps.to(original_samples.device		)

        _UpperCamelCase					:		List[str]  =				[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

        _UpperCamelCase					:		Dict  =				original_samples + noise * sigma
        return noisy_samples


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







def    _lowercase    (  _UpperCAmelCase = 99_80_01 )  ->     int:

				# fetches the next number
				for number in range(n - 1	,					99_99	,					-1 ):
								lowerCamelCase		       =str(_UpperCAmelCase )

								# checks whether 'str_number' is a palindrome.
								if str_number == str_number[::-1]:
												lowerCamelCase		       =9_99

												# if 'number' is a product of two 3-digit numbers
												# then number is the answer otherwise fetch next number.
												while divisor != 99:
																if (number % divisor == 0) and (len(str(number // divisor ) ) == 3.0):
																				return number
																divisor -= 1
				raise ValueError("""That number is larger than our acceptable range.""" )


if __name__ == "__main__":
							print(F"{solution() = }")





