'''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    lowerCamelCase__  (   __snake_case     ):
   __UpperCAmelCase           =						42
   __UpperCAmelCase           =						None




def  _lowerCAmelCase				(				__a			,      __a=0.9_99			,      __a="cosine"			,      )  ->      List[Any]:
     '''simple docstring'''







     if alpha_transform_type == "cosine":

          def alpha_bar_fn(__a      ):
               return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2      ) ** 2

     elif alpha_transform_type == "exp":

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

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

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




class    lowerCamelCase__  (   __snake_case       ,				__snake_case     ):
   __UpperCAmelCase           =						[e.name for e in KarrasDiffusionSchedulers]
   __UpperCAmelCase           =						1



   @register_to_config
   def __init__(    self					,      lowerCAmelCase__ = 1_000					,      lowerCAmelCase__ = 0.0001					,      lowerCAmelCase__ = 0.02					,      lowerCAmelCase__ = "linear"					,      lowerCAmelCase__ = None					,      lowerCAmelCase__ = False					,      lowerCAmelCase__ = "epsilon"					,      lowerCAmelCase__ = "linspace"					,      lowerCAmelCase__ = 0					,      )				->     Dict:
        """simple docstring"""





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

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

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

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



   @property
   def  _UpperCamelCase		(    self     )				->     str:
        """simple docstring"""





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

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



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__     )				->     torch.FloatTensor:
        """simple docstring"""





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



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__     )				->     List[Any]:
        """simple docstring"""





        def lms_derivative(lowerCAmelCase__     ):
             _UpperCamelCase  :Dict       =1.0
             for k in range(lowerCAmelCase__     ):
                  if current_order == k:
                       continue
                  prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
             return prod

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

        return integrated_coeff



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__ = None     )				->     Tuple:
        """simple docstring"""





        _UpperCamelCase  :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":
             _UpperCamelCase  :str       =np.linspace(0					,      self.config.num_train_timesteps - 1					,      lowerCAmelCase__					,      dtype=lowerCAmelCase__     )[
                 ::-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  :Optional[int]       =(np.arange(0					,      lowerCAmelCase__     ) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__     )
             timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
             _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  :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\'.'''     )

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

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

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

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

        _UpperCamelCase  :Union[str, Any]       =[]



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__     )				->     List[Any]:
        """simple docstring"""





        _UpperCamelCase  :Optional[int]       =np.log(lowerCAmelCase__     )

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

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

        _UpperCamelCase  :str       =log_sigmas[low_idx]
        _UpperCamelCase  :Union[str, Any]       =log_sigmas[high_idx]

        # interpolate sigmas
        _UpperCamelCase  :int       =(low - log_sigma) / (low - high)
        _UpperCamelCase  :Union[str, Any]       =np.clip(lowerCAmelCase__					,      0					,      1     )

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



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__     )				->     torch.FloatTensor:
        """simple docstring"""





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

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



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__ = 4					,      lowerCAmelCase__ = True					,      )				->     Union[LMSDiscreteSchedulerOutput, Tuple]:
        """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(lowerCAmelCase__					,      torch.Tensor     ):
             _UpperCamelCase  :Tuple       =timestep.to(self.timesteps.device     )
        _UpperCamelCase  :int       =(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  :List[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  :List[str]       =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  :List[str]       =(sample - pred_original_sample) / sigma
        self.derivatives.append(lowerCAmelCase__     )
        if len(self.derivatives     ) > order:
             self.derivatives.pop(0     )

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

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

        if not return_dict:
             return (prev_sample,)

        return LMSDiscreteSchedulerOutput(prev_sample=lowerCAmelCase__					,      pred_original_sample=lowerCAmelCase__     )



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__					,      lowerCAmelCase__					,      lowerCAmelCase__					,      )				->     torch.FloatTensor:
        """simple docstring"""





        _UpperCamelCase  :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
             _UpperCamelCase  :Tuple       =self.timesteps.to(original_samples.device					,      dtype=torch.floataa     )
             _UpperCamelCase  :Union[str, Any]       =timesteps.to(original_samples.device					,      dtype=torch.floataa     )
        else:
             _UpperCamelCase  :Optional[Any]       =self.timesteps.to(original_samples.device     )
             _UpperCamelCase  :Any       =timesteps.to(original_samples.device     )

        _UpperCamelCase  :Optional[int]       =[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

        _UpperCamelCase  :List[Any]       =original_samples + noise * sigma
        return noisy_samples




   def __len__(    self     )				->     Optional[int]:
        """simple docstring"""





        return self.config.num_train_timesteps
'''simple docstring'''

from __future__ import annotations

_lowerCamelCase :				Optional[int]														= """Alexander Joslin"""



def  _lowerCAmelCase				(				__a      )  ->      int:
     '''simple docstring'''







     if number <= 0:
          _UpperCamelCase  :Optional[Any]       =F'''n must be greater than 0. Got n = {number}'''
          raise ValueError(__a      )

     _UpperCamelCase  :Optional[Any]       =[number + 1] * (number + 1)

     # starting position
     _UpperCamelCase  :int       =0
     for i in range(1			,      __a      ):
          _UpperCamelCase  :List[str]       =min(table[i + 1]			,      table[i] + 1      )
          # check if out of bounds
          if i * 2 <= number:
               _UpperCamelCase  :int       =min(table[i * 2]			,      table[i] + 1      )
          # check if out of bounds
          if i * 3 <= number:
               _UpperCamelCase  :Tuple       =min(table[i * 3]			,      table[i] + 1      )
     return table[number]


if __name__ == "__main__":
      import doctest

      doctest.testmod()