





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 .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput



def 	A_       (  _lowerCAmelCase							,     _lowerCAmelCase=0.999							,     _lowerCAmelCase="cosine"							,     )		->				List[Any]:
 if alpha_transform_type == "cosine":

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

 elif alpha_transform_type == "exp":

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

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

 UpperCamelCase			:      str 			=     []
 for i in range(_lowerCAmelCase  ):
  UpperCamelCase			:      Optional[Any] 			=     i / num_diffusion_timesteps
  UpperCamelCase			:      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       A__     ( __snake_case ,     __snake_case    ):
      _UpperCAmelCase			:List[str]							=     [e.name for e in KarrasDiffusionSchedulers]
      _UpperCAmelCase			:List[Any]							=     2





      @register_to_config
      def __init__(				self ,							A_ = 1000 ,							A_ = 0.0_00_85 ,							A_ = 0.0_12 ,							A_ = "linear" ,							A_ = None ,							A_ = "epsilon" ,							A_ = False ,							A_ = False ,							A_ = 1.0 ,							A_ = "linspace" ,							A_ = 0 ,							):
       '''simple docstring'''




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

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

       #  set all values
       self.set_timesteps(A_ ,							A_ ,							A_     )
       UpperCamelCase			:      Union[str, Any] 			=     use_karras_sigmas





      def  __UpperCamelCase(				self ,							A_ ,							A_=None     ):
       '''simple docstring'''




       if schedule_timesteps is None:
        UpperCamelCase			:      Any 			=     self.timesteps

       UpperCamelCase			:      Dict 			=     (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:
        UpperCamelCase			:      Dict 			=     1 if len(A_     ) > 1 else 0
       else:
        UpperCamelCase			:      Optional[Any] 			=     timestep.cpu().item() if torch.is_tensor(A_     ) else timestep
        UpperCamelCase			:      Any 			=     self._index_counter[timestep_int]

       return indices[pos].item()





      @property
      def  __UpperCamelCase(				self     ):
       '''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 ,							A_ ,							A_ ,							):
       '''simple docstring'''




       UpperCamelCase			:      Optional[int] 			=     self.index_for_timestep(A_     )

       UpperCamelCase			:      Optional[Any] 			=     self.sigmas[step_index]
       UpperCamelCase			:      Any 			=     sample / ((sigma**2 + 1) ** 0.5)
       return sample





      def  __UpperCamelCase(				self ,							A_ ,							A_ = None ,							A_ = None ,							):
       '''simple docstring'''




       UpperCamelCase			:      Optional[int] 			=     num_inference_steps

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

       if self.config.use_karras_sigmas:
        UpperCamelCase			:      Tuple 			=     self._convert_to_karras(in_sigmas=A_ ,							num_inference_steps=self.num_inference_steps     )
        UpperCamelCase			:      Dict 			=     np.array([self._sigma_to_t(A_ ,							A_     ) for sigma in sigmas]     )

       UpperCamelCase			:      Any 			=     np.concatenate([sigmas, [0.0]]     ).astype(np.floataa     )
       UpperCamelCase			:      List[Any] 			=     torch.from_numpy(A_     ).to(device=A_     )
       UpperCamelCase			:      List[Any] 			=     torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2     ), sigmas[-1:]]     )

       UpperCamelCase			:      Optional[Any] 			=     torch.from_numpy(A_     )
       UpperCamelCase			:      Optional[Any] 			=     torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2     )]     )

       if str(A_     ).startswith("mps"     ):
        # mps does not support float64
        UpperCamelCase			:      str 			=     timesteps.to(A_ ,							dtype=torch.floataa     )
       else:
        UpperCamelCase			:      Any 			=     timesteps.to(device=A_     )

       # empty dt and derivative
       UpperCamelCase			:      Any 			=     None
       UpperCamelCase			:      Tuple 			=     None

       # for exp beta schedules, such as the one for `pipeline_shap_e.py`
       # we need an index counter
       UpperCamelCase			:      str 			=     defaultdict(A_     )





      def  __UpperCamelCase(				self ,							A_ ,							A_     ):
       '''simple docstring'''




       UpperCamelCase			:      Dict 			=     np.log(A_     )

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

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

       UpperCamelCase			:      int 			=     log_sigmas[low_idx]
       UpperCamelCase			:      int 			=     log_sigmas[high_idx]

       # interpolate sigmas
       UpperCamelCase			:      Tuple 			=     (low - log_sigma) / (low - high)
       UpperCamelCase			:      Dict 			=     np.clip(A_ ,							0 ,							1     )

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





      def  __UpperCamelCase(				self ,							A_ ,							A_     ):
       '''simple docstring'''




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

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





      @property
      def  __UpperCamelCase(				self     ):
       '''simple docstring'''




       return self.dt is None





      def  __UpperCamelCase(				self ,							A_ ,							A_ ,							A_ ,							A_ = True ,							):
       '''simple docstring'''




       UpperCamelCase			:      Optional[int] 			=     self.index_for_timestep(A_     )

       # advance index counter by 1
       UpperCamelCase			:      int 			=     timestep.cpu().item() if torch.is_tensor(A_     ) else timestep
       self._index_counter[timestep_int] += 1

       if self.state_in_first_order:
        UpperCamelCase			:      List[str] 			=     self.sigmas[step_index]
        UpperCamelCase			:      Union[str, Any] 			=     self.sigmas[step_index + 1]
       else:
        # 2nd order / Heun's method
        UpperCamelCase			:      int 			=     self.sigmas[step_index - 1]
        UpperCamelCase			:      Optional[int] 			=     self.sigmas[step_index]

       # 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
       UpperCamelCase			:      List[Any] 			=     0
       UpperCamelCase			:      Tuple 			=     sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

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

       if self.config.clip_sample:
        UpperCamelCase			:      Optional[Any] 			=     pred_original_sample.clamp(
            -self.config.clip_sample_range ,							self.config.clip_sample_range     )

       if self.state_in_first_order:
        # 2. Convert to an ODE derivative for 1st order
        UpperCamelCase			:      Optional[Any] 			=     (sample - pred_original_sample) / sigma_hat
        # 3. delta timestep
        UpperCamelCase			:      Optional[int] 			=     sigma_next - sigma_hat

        # store for 2nd order step
        UpperCamelCase			:      Any 			=     derivative
        UpperCamelCase			:      Any 			=     dt
        UpperCamelCase			:      int 			=     sample
       else:
        # 2. 2nd order / Heun's method
        UpperCamelCase			:      Dict 			=     (sample - pred_original_sample) / sigma_next
        UpperCamelCase			:      Union[str, Any] 			=     (self.prev_derivative + derivative) / 2

        # 3. take prev timestep & sample
        UpperCamelCase			:      Dict 			=     self.dt
        UpperCamelCase			:      Tuple 			=     self.sample

        # free dt and derivative
        # Note, this puts the scheduler in "first order mode"
        UpperCamelCase			:      Any 			=     None
        UpperCamelCase			:      List[Any] 			=     None
        UpperCamelCase			:      Any 			=     None

       UpperCamelCase			:      List[Any] 			=     sample + derivative * dt

       if not return_dict:
        return (prev_sample,)

       return SchedulerOutput(prev_sample=A_     )





      def  __UpperCamelCase(				self ,							A_ ,							A_ ,							A_ ,							):
       '''simple docstring'''




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

       UpperCamelCase			:      List[str] 			=     [self.index_for_timestep(A_ ,							A_     ) for t in timesteps]

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

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





      def __len__(				self     ):
       '''simple docstring'''




       return self.config.num_train_timesteps







from math import loga



def 	A_       (  _lowerCAmelCase  )		->				int:
 if a < 0:
  raise ValueError("Input value must be a positive integer"  )
 elif isinstance(_lowerCAmelCase							,     _lowerCAmelCase  ):
  raise TypeError("Input value must be a 'int' type"  )
 return 0 if (a == 0) else int(loga(a & -a  )  )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
