

"""simple docstring"""




def   __SCREAMING_SNAKE_CASE		(		lowercase__ = 30 ):
					"""simple docstring"""
					A     =   exponent + 2
					A     =   (1 + 5**0.5) / 2
					A     =   (phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

					return int(lowercase__ )


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






"""simple docstring"""







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 ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput



def       A__    (	lowercase_     :	Any      , lowercase_     :	int=0.9_9_9      , lowercase_     :	Dict="cosine"      , )  ->							Optional[int]:
   if alpha_transform_type == "cosine":

      def alpha_bar_fn(lowercase_     :	List[str]						):
         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(lowercase_     :	Union[str, Any]						):
         return math.exp(t * -1_2.0						)

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

   __lowerCamelCase    		=					[]
   for i in range(lowercase_						):
      __lowerCamelCase    		=					i / num_diffusion_timesteps
      __lowerCamelCase    		=					(i + 1) / num_diffusion_timesteps
      betas.append(min(1 - alpha_bar_fn(lowercase_						) / alpha_bar_fn(lowercase_						)      , lowercase_						)						)
   return torch.tensor(lowercase_      , dtype=torch.floataa						)






class      _SCREAMING_SNAKE_CASE							(			UpperCAmelCase    ,				UpperCAmelCase				):



   '''simple docstring'''



   __UpperCAmelCase	:							int    =    [e.name for e in KarrasDiffusionSchedulers]
   __UpperCAmelCase	:							Tuple    =    2







   @register_to_config
   def __init__(	self ,				_SCREAMING_SNAKE_CASE = 1000 ,				_SCREAMING_SNAKE_CASE = 0.0_0085 ,				_SCREAMING_SNAKE_CASE = 0.012 ,				_SCREAMING_SNAKE_CASE = "linear" ,				_SCREAMING_SNAKE_CASE = None ,				_SCREAMING_SNAKE_CASE = "epsilon" ,				_SCREAMING_SNAKE_CASE = "linspace" ,				_SCREAMING_SNAKE_CASE = 0 ,				):


      '''simple docstring'''

      if trained_betas is not None:
         __lowerCamelCase    		=					torch.tensor(_SCREAMING_SNAKE_CASE ,				dtype=torch.floataa	)
      elif beta_schedule == "linear":
         __lowerCamelCase    		=					torch.linspace(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				dtype=torch.floataa	)
      elif beta_schedule == "scaled_linear":
         # this schedule is very specific to the latent diffusion model.
         __lowerCamelCase    		=					(
             torch.linspace(beta_start**0.5 ,				beta_end**0.5 ,				_SCREAMING_SNAKE_CASE ,				dtype=torch.floataa	) ** 2
         )
      elif beta_schedule == "squaredcos_cap_v2":
         # Glide cosine schedule
         __lowerCamelCase    		=					betas_for_alpha_bar(_SCREAMING_SNAKE_CASE	)
      else:
         raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''	)

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

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







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE=None	):


      '''simple docstring'''

      if schedule_timesteps is None:
         __lowerCamelCase    		=					self.timesteps

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

      return indices[pos].item()







   @property
   def    _A				(	self	):


      '''simple docstring'''

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

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







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					self.index_for_timestep(_SCREAMING_SNAKE_CASE	)

      if self.state_in_first_order:
         __lowerCamelCase    		=					self.sigmas[step_index]
      else:
         __lowerCamelCase    		=					self.sigmas_interpol[step_index - 1]

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







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = None ,				_SCREAMING_SNAKE_CASE = None ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					num_inference_steps

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

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

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

      # compute up and down sigmas
      __lowerCamelCase    		=					sigmas.roll(-1	)
      __lowerCamelCase    		=					0.0
      __lowerCamelCase    		=					(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
      __lowerCamelCase    		=					(sigmas_next**2 - sigmas_up**2) ** 0.5
      __lowerCamelCase    		=					0.0

      # compute interpolated sigmas
      __lowerCamelCase    		=					sigmas.log().lerp(sigmas_down.log() ,				0.5	).exp()
      __lowerCamelCase    		=					0.0

      # set sigmas
      __lowerCamelCase    		=					torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2	), sigmas[-1:]]	)
      __lowerCamelCase    		=					torch.cat(
          [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2	), sigmas_interpol[-1:]]	)
      __lowerCamelCase    		=					torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2	), sigmas_up[-1:]]	)
      __lowerCamelCase    		=					torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2	), sigmas_down[-1:]]	)

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

      __lowerCamelCase    		=					self.sigma_to_t(_SCREAMING_SNAKE_CASE	).to(_SCREAMING_SNAKE_CASE ,				dtype=timesteps.dtype	)
      __lowerCamelCase    		=					torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None]) ,				dim=-1	).flatten()

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

      __lowerCamelCase    		=					None

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







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE	):


      '''simple docstring'''

      __lowerCamelCase    		=					sigma.log()

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

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

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

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

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







   @property
   def    _A				(	self	):


      '''simple docstring'''

      return self.sample is None







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE = None ,				_SCREAMING_SNAKE_CASE = True ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					self.index_for_timestep(_SCREAMING_SNAKE_CASE	)

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

      if self.state_in_first_order:
         __lowerCamelCase    		=					self.sigmas[step_index]
         __lowerCamelCase    		=					self.sigmas_interpol[step_index]
         __lowerCamelCase    		=					self.sigmas_up[step_index]
         __lowerCamelCase    		=					self.sigmas_down[step_index - 1]
      else:
         # 2nd order / KPDM2's method
         __lowerCamelCase    		=					self.sigmas[step_index - 1]
         __lowerCamelCase    		=					self.sigmas_interpol[step_index - 1]
         __lowerCamelCase    		=					self.sigmas_up[step_index - 1]
         __lowerCamelCase    		=					self.sigmas_down[step_index - 1]

      # 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
      __lowerCamelCase    		=					0
      __lowerCamelCase    		=					sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

      __lowerCamelCase    		=					model_output.device
      __lowerCamelCase    		=					randn_tensor(model_output.shape ,				dtype=model_output.dtype ,				device=_SCREAMING_SNAKE_CASE ,				generator=_SCREAMING_SNAKE_CASE	)

      # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
      if self.config.prediction_type == "epsilon":
         __lowerCamelCase    		=					sigma_hat if self.state_in_first_order else sigma_interpol
         __lowerCamelCase    		=					sample - sigma_input * model_output
      elif self.config.prediction_type == "v_prediction":
         __lowerCamelCase    		=					sigma_hat if self.state_in_first_order else sigma_interpol
         __lowerCamelCase    		=					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
         __lowerCamelCase    		=					(sample - pred_original_sample) / sigma_hat
         # 3. delta timestep
         __lowerCamelCase    		=					sigma_interpol - sigma_hat

         # store for 2nd order step
         __lowerCamelCase    		=					sample
         __lowerCamelCase    		=					dt
         __lowerCamelCase    		=					sample + derivative * dt
      else:
         # DPM-Solver-2
         # 2. Convert to an ODE derivative for 2nd order
         __lowerCamelCase    		=					(sample - pred_original_sample) / sigma_interpol
         # 3. delta timestep
         __lowerCamelCase    		=					sigma_down - sigma_hat

         __lowerCamelCase    		=					self.sample
         __lowerCamelCase    		=					None

         __lowerCamelCase    		=					sample + derivative * dt
         __lowerCamelCase    		=					prev_sample + noise * sigma_up

      if not return_dict:
         return (prev_sample,)

      return SchedulerOutput(prev_sample=_SCREAMING_SNAKE_CASE	)







   def    _A				(	self ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE ,				):


      '''simple docstring'''

      __lowerCamelCase    		=					self.sigmas.to(device=original_samples.device ,				dtype=original_samples.dtype	)
      if original_samples.device.type == "mps" and torch.is_floating_point(_SCREAMING_SNAKE_CASE	):
         # mps does not support float64
         __lowerCamelCase    		=					self.timesteps.to(original_samples.device ,				dtype=torch.floataa	)
         __lowerCamelCase    		=					timesteps.to(original_samples.device ,				dtype=torch.floataa	)
      else:
         __lowerCamelCase    		=					self.timesteps.to(original_samples.device	)
         __lowerCamelCase    		=					timesteps.to(original_samples.device	)

      __lowerCamelCase    		=					[self.index_for_timestep(_SCREAMING_SNAKE_CASE ,				_SCREAMING_SNAKE_CASE	) for t in timesteps]

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

      __lowerCamelCase    		=					original_samples + noise * sigma
      return noisy_samples







   def __len__(	self	):


      '''simple docstring'''

      return self.config.num_train_timesteps






