




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 					UpperCAmelCase_							(      __UpperCAmelCase						:	Any			,			__UpperCAmelCase						:	Union[str, Any]=0.9_9_9			,			__UpperCAmelCase						:	str="cosine"			,			)					-> List[str]:
      if alpha_transform_type == "cosine":

            def alpha_bar_fn(__UpperCAmelCase						:	Any							):
                  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(__UpperCAmelCase						:	Any							):
                  return math.exp(t * -1_2.0							)

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

      SCREAMING_SNAKE_CASE_							=			[]
      for i in range(__UpperCamelCase							):
            SCREAMING_SNAKE_CASE_							=			i / num_diffusion_timesteps
            SCREAMING_SNAKE_CASE_							=			(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        lowerCamelCase_							(      SCREAMING_SNAKE_CASE__       ,   SCREAMING_SNAKE_CASE__					):


 '''simple docstring'''







 lowercase_				    =    [e.name for e in KarrasDiffusionSchedulers]
 lowercase_				    =    2



 @register_to_config
 def __init__(							self  :		str				,				_lowerCAmelCase  :		int = 1_000				,				_lowerCAmelCase  :		float = 0.0_0085				,				_lowerCAmelCase  :		float = 0.012				,				_lowerCAmelCase  :		str = "linear"				,				_lowerCAmelCase  :		Optional[Union[np.ndarray, List[float]]] = None				,				_lowerCAmelCase  :		str = "epsilon"				,				_lowerCAmelCase  :		str = "linspace"				,				_lowerCAmelCase  :		int = 0				,				):
       if trained_betas is not None:
             SCREAMING_SNAKE_CASE_							=			torch.tensor(_lowerCAmelCase				,				dtype=torch.floataa						)
       elif beta_schedule == "linear":
             SCREAMING_SNAKE_CASE_							=			torch.linspace(_lowerCAmelCase				,				_lowerCAmelCase				,				_lowerCAmelCase				,				dtype=torch.floataa						)
       elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
             SCREAMING_SNAKE_CASE_							=			(
                 torch.linspace(beta_start**0.5				,				beta_end**0.5				,				_lowerCAmelCase				,				dtype=torch.floataa						) ** 2
             )
       elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             SCREAMING_SNAKE_CASE_							=			betas_for_alpha_bar(_lowerCAmelCase						)
       else:
             raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"						)

       SCREAMING_SNAKE_CASE_							=			1.0 - self.betas
       SCREAMING_SNAKE_CASE_							=			torch.cumprod(self.alphas				,				dim=0						)

       #  set all values
       self.set_timesteps(_lowerCAmelCase				,				_lowerCAmelCase				,				_lowerCAmelCase						)



 def       lowerCAmelCase_  (							self  :		str				,				_lowerCAmelCase  :		Any				,				_lowerCAmelCase  :		Dict=None						):
       if schedule_timesteps is None:
             SCREAMING_SNAKE_CASE_							=			self.timesteps

       SCREAMING_SNAKE_CASE_							=			(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:
             SCREAMING_SNAKE_CASE_							=			1 if len(_lowerCAmelCase						) > 1 else 0
       else:
             SCREAMING_SNAKE_CASE_							=			timestep.cpu().item() if torch.is_tensor(_lowerCAmelCase						) else timestep
             SCREAMING_SNAKE_CASE_							=			self._index_counter[timestep_int]

       return indices[pos].item()



 @property
 def       lowerCAmelCase_  (							self  :		Any						):
       # 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       lowerCAmelCase_  (							self  :		Union[str, Any]				,				_lowerCAmelCase  :		torch.FloatTensor				,				_lowerCAmelCase  :		Union[float, torch.FloatTensor]				,				):
       SCREAMING_SNAKE_CASE_							=			self.index_for_timestep(_lowerCAmelCase						)

       if self.state_in_first_order:
             SCREAMING_SNAKE_CASE_							=			self.sigmas[step_index]
       else:
             SCREAMING_SNAKE_CASE_							=			self.sigmas_interpol[step_index]

       SCREAMING_SNAKE_CASE_							=			sample / ((sigma**2 + 1) ** 0.5)
       return sample



 def       lowerCAmelCase_  (							self  :		Dict				,				_lowerCAmelCase  :		int				,				_lowerCAmelCase  :		Union[str, torch.device] = None				,				_lowerCAmelCase  :		Optional[int] = None				,				):
       SCREAMING_SNAKE_CASE_							=			num_inference_steps

       SCREAMING_SNAKE_CASE_							=			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":
             SCREAMING_SNAKE_CASE_							=			np.linspace(0				,				num_train_timesteps - 1				,				_lowerCAmelCase				,				dtype=_lowerCAmelCase						)[::-1].copy()
       elif self.config.timestep_spacing == "leading":
             SCREAMING_SNAKE_CASE_							=			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
             SCREAMING_SNAKE_CASE_							=			(np.arange(0				,				_lowerCAmelCase						) * step_ratio).round()[::-1].copy().astype(_lowerCAmelCase						)
             timesteps += self.config.steps_offset
       elif self.config.timestep_spacing == "trailing":
             SCREAMING_SNAKE_CASE_							=			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
             SCREAMING_SNAKE_CASE_							=			(np.arange(_lowerCAmelCase				,				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\'."						)

       SCREAMING_SNAKE_CASE_							=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5						)
       SCREAMING_SNAKE_CASE_							=			torch.from_numpy(np.log(_lowerCAmelCase						)						).to(_lowerCAmelCase						)

       SCREAMING_SNAKE_CASE_							=			np.interp(_lowerCAmelCase				,				np.arange(0				,				len(_lowerCAmelCase						)						)				,				_lowerCAmelCase						)
       SCREAMING_SNAKE_CASE_							=			np.concatenate([sigmas, [0.0]]						).astype(np.floataa						)
       SCREAMING_SNAKE_CASE_							=			torch.from_numpy(_lowerCAmelCase						).to(device=_lowerCAmelCase						)

       # interpolate sigmas
       SCREAMING_SNAKE_CASE_							=			sigmas.log().lerp(sigmas.roll(1						).log()				,				0.5						).exp()

       SCREAMING_SNAKE_CASE_							=			torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2						), sigmas[-1:]]						)
       SCREAMING_SNAKE_CASE_							=			torch.cat(
           [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2						), sigmas_interpol[-1:]]						)

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

       # interpolate timesteps
       SCREAMING_SNAKE_CASE_							=			self.sigma_to_t(_lowerCAmelCase						).to(_lowerCAmelCase				,				dtype=timesteps.dtype						)
       SCREAMING_SNAKE_CASE_							=			torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])				,				dim=-1						).flatten()

       SCREAMING_SNAKE_CASE_							=			torch.cat([timesteps[:1], interleaved_timesteps]						)

       SCREAMING_SNAKE_CASE_							=			None

       # for exp beta schedules, such as the one for `pipeline_shap_e.py`
       # we need an index counter
       SCREAMING_SNAKE_CASE_							=			defaultdict(_lowerCAmelCase						)



 def       lowerCAmelCase_  (							self  :		Optional[int]				,				_lowerCAmelCase  :		int						):
       # get log sigma
       SCREAMING_SNAKE_CASE_							=			sigma.log()

       # get distribution
       SCREAMING_SNAKE_CASE_							=			log_sigma - self.log_sigmas[:, None]

       # get sigmas range
       SCREAMING_SNAKE_CASE_							=			dists.ge(0						).cumsum(dim=0						).argmax(dim=0						).clamp(max=self.log_sigmas.shape[0] - 2						)
       SCREAMING_SNAKE_CASE_							=			low_idx + 1

       SCREAMING_SNAKE_CASE_							=			self.log_sigmas[low_idx]
       SCREAMING_SNAKE_CASE_							=			self.log_sigmas[high_idx]

       # interpolate sigmas
       SCREAMING_SNAKE_CASE_							=			(low - log_sigma) / (low - high)
       SCREAMING_SNAKE_CASE_							=			w.clamp(0				,				1						)

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



 @property
 def       lowerCAmelCase_  (							self  :		List[Any]						):
       return self.sample is None



 def       lowerCAmelCase_  (							self  :		Dict				,				_lowerCAmelCase  :		Union[torch.FloatTensor, np.ndarray]				,				_lowerCAmelCase  :		Union[float, torch.FloatTensor]				,				_lowerCAmelCase  :		Union[torch.FloatTensor, np.ndarray]				,				_lowerCAmelCase  :		bool = True				,				):
       SCREAMING_SNAKE_CASE_							=			self.index_for_timestep(_lowerCAmelCase						)

       # advance index counter by 1
       SCREAMING_SNAKE_CASE_							=			timestep.cpu().item() if torch.is_tensor(_lowerCAmelCase						) else timestep
       self._index_counter[timestep_int] += 1

       if self.state_in_first_order:
             SCREAMING_SNAKE_CASE_							=			self.sigmas[step_index]
             SCREAMING_SNAKE_CASE_							=			self.sigmas_interpol[step_index + 1]
             SCREAMING_SNAKE_CASE_							=			self.sigmas[step_index + 1]
       else:
             # 2nd order / KDPM2's method
             SCREAMING_SNAKE_CASE_							=			self.sigmas[step_index - 1]
             SCREAMING_SNAKE_CASE_							=			self.sigmas_interpol[step_index]
             SCREAMING_SNAKE_CASE_							=			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
       SCREAMING_SNAKE_CASE_							=			0
       SCREAMING_SNAKE_CASE_							=			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":
             SCREAMING_SNAKE_CASE_							=			sigma_hat if self.state_in_first_order else sigma_interpol
             SCREAMING_SNAKE_CASE_							=			sample - sigma_input * model_output
       elif self.config.prediction_type == "v_prediction":
             SCREAMING_SNAKE_CASE_							=			sigma_hat if self.state_in_first_order else sigma_interpol
             SCREAMING_SNAKE_CASE_							=			model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
                 sample / (sigma_input**2 + 1)
             )
       elif self.config.prediction_type == "sample":
             raise NotImplementedError('prediction_type not implemented yet: sample'						)
       else:
             raise ValueError(
                 F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"						)

       if self.state_in_first_order:
             # 2. Convert to an ODE derivative for 1st order
             SCREAMING_SNAKE_CASE_							=			(sample - pred_original_sample) / sigma_hat
             # 3. delta timestep
             SCREAMING_SNAKE_CASE_							=			sigma_interpol - sigma_hat

             # store for 2nd order step
             SCREAMING_SNAKE_CASE_							=			sample
       else:
             # DPM-Solver-2
             # 2. Convert to an ODE derivative for 2nd order
             SCREAMING_SNAKE_CASE_							=			(sample - pred_original_sample) / sigma_interpol

             # 3. delta timestep
             SCREAMING_SNAKE_CASE_							=			sigma_next - sigma_hat

             SCREAMING_SNAKE_CASE_							=			self.sample
             SCREAMING_SNAKE_CASE_							=			None

       SCREAMING_SNAKE_CASE_							=			sample + derivative * dt

       if not return_dict:
             return (prev_sample,)

       return SchedulerOutput(prev_sample=_lowerCAmelCase						)



 def       lowerCAmelCase_  (							self  :		Any				,				_lowerCAmelCase  :		torch.FloatTensor				,				_lowerCAmelCase  :		torch.FloatTensor				,				_lowerCAmelCase  :		torch.FloatTensor				,				):
       # Make sure sigmas and timesteps have the same device and dtype as original_samples
       SCREAMING_SNAKE_CASE_							=			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
             SCREAMING_SNAKE_CASE_							=			self.timesteps.to(original_samples.device				,				dtype=torch.floataa						)
             SCREAMING_SNAKE_CASE_							=			timesteps.to(original_samples.device				,				dtype=torch.floataa						)
       else:
             SCREAMING_SNAKE_CASE_							=			self.timesteps.to(original_samples.device						)
             SCREAMING_SNAKE_CASE_							=			timesteps.to(original_samples.device						)

       SCREAMING_SNAKE_CASE_							=			[self.index_for_timestep(_lowerCAmelCase				,				_lowerCAmelCase						) for t in timesteps]

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

       SCREAMING_SNAKE_CASE_							=			original_samples + noise * sigma
       return noisy_samples




 def __len__(							self  :		int						):
       return self.config.num_train_timesteps
from functools import lru_cache


@lru_cache
def    a__       (						__UpperCamelCase ):
      if num < 0:
            raise ValueError("Number should not be negative." )

      return 1 if num in (0, 1) else num * factorial(num - 1 )


if __name__ == "__main__":
      import doctest

      doctest.testmod()


