
'''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 	snake_case_							(				_a  :				str			,       _a  :				Dict=0.9_9_9			,       _a  :				Optional[int]="cosine"			,       ):
      if alpha_transform_type == "cosine":

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

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

      snake_case_    							=				[]
      for i in range(_a      ):
            snake_case_    							=				i / num_diffusion_timesteps
            snake_case_    							=				(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__ (							UpperCamelCase       ,				UpperCamelCase							):



  '''simple docstring'''






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

  @register_to_config
  def __init__(self	:			Tuple						,			lowerCAmelCase_	:			int = 10_00						,			lowerCAmelCase_	:			float = 0.00_085						,			lowerCAmelCase_	:			float = 0.012						,			lowerCAmelCase_	:			str = "linear"						,			lowerCAmelCase_	:			Optional[Union[np.ndarray, List[float]]] = None						,			lowerCAmelCase_	:			str = "epsilon"						,			lowerCAmelCase_	:			str = "linspace"						,			lowerCAmelCase_	:			int = 0						,			) ->							Union[str, Any]:
        if trained_betas is not None:
              snake_case_    							=				torch.tensor(lowerCAmelCase_						,			dtype=torch.floataa     )
        elif beta_schedule == "linear":
              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.
              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
              snake_case_    							=				betas_for_alpha_bar(lowerCAmelCase_     )
        else:
              raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''     )

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

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

  def 		_lowerCamelCase						(self	:			Optional[Any]						,			lowerCAmelCase_	:			Any						,			lowerCAmelCase_	:			List[str]=None     ) ->							Any:
        if schedule_timesteps is None:
              snake_case_    							=				self.timesteps

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

        return indices[pos].item()

  @property
  def 		_lowerCamelCase						(self	:			Dict     ) ->							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	:			Optional[int]						,			lowerCAmelCase_	:			torch.FloatTensor						,			lowerCAmelCase_	:			Union[float, torch.FloatTensor]						,			) ->							torch.FloatTensor:
        snake_case_    							=				self.index_for_timestep(lowerCAmelCase_     )

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

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

  def 		_lowerCamelCase						(self	:			List[str]						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			Union[str, torch.device] = None						,			lowerCAmelCase_	:			Optional[int] = None						,			) ->							Any:
        snake_case_    							=				num_inference_steps

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

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

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

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

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

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

        if str(lowerCAmelCase_     ).startswith("mps"     ):
              # mps does not support float64
              snake_case_    							=				torch.from_numpy(lowerCAmelCase_     ).to(lowerCAmelCase_						,			dtype=torch.floataa     )
        else:
              snake_case_    							=				torch.from_numpy(lowerCAmelCase_     ).to(lowerCAmelCase_     )

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

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

        snake_case_    							=				None

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

  def 		_lowerCamelCase						(self	:			Any						,			lowerCAmelCase_	:			Optional[Any]     ) ->							Optional[int]:
        # get log sigma
        snake_case_    							=				sigma.log()

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

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

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

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

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

  @property
  def 		_lowerCamelCase						(self	:			List[str]     ) ->							Any:
        return self.sample is None

  def 		_lowerCamelCase						(self	:			List[Any]						,			lowerCAmelCase_	:			Union[torch.FloatTensor, np.ndarray]						,			lowerCAmelCase_	:			Union[float, torch.FloatTensor]						,			lowerCAmelCase_	:			Union[torch.FloatTensor, np.ndarray]						,			lowerCAmelCase_	:			Optional[torch.Generator] = None						,			lowerCAmelCase_	:			bool = True						,			) ->							Union[SchedulerOutput, Tuple]:
        snake_case_    							=				self.index_for_timestep(lowerCAmelCase_     )

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

        if self.state_in_first_order:
              snake_case_    							=				self.sigmas[step_index]
              snake_case_    							=				self.sigmas_interpol[step_index]
              snake_case_    							=				self.sigmas_up[step_index]
              snake_case_    							=				self.sigmas_down[step_index - 1]
        else:
              # 2nd order / KPDM2's method
              snake_case_    							=				self.sigmas[step_index - 1]
              snake_case_    							=				self.sigmas_interpol[step_index - 1]
              snake_case_    							=				self.sigmas_up[step_index - 1]
              snake_case_    							=				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
        snake_case_    							=				0
        snake_case_    							=				sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

        snake_case_    							=				model_output.device
        snake_case_    							=				randn_tensor(model_output.shape						,			dtype=model_output.dtype						,			device=lowerCAmelCase_						,			generator=lowerCAmelCase_     )

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

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

              snake_case_    							=				self.sample
              snake_case_    							=				None

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

        if not return_dict:
              return (prev_sample,)

        return SchedulerOutput(prev_sample=lowerCAmelCase_     )

  def 		_lowerCamelCase						(self	:			int						,			lowerCAmelCase_	:			torch.FloatTensor						,			lowerCAmelCase_	:			torch.FloatTensor						,			lowerCAmelCase_	:			torch.FloatTensor						,			) ->							torch.FloatTensor:
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        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
              snake_case_    							=				self.timesteps.to(original_samples.device						,			dtype=torch.floataa     )
              snake_case_    							=				timesteps.to(original_samples.device						,			dtype=torch.floataa     )
        else:
              snake_case_    							=				self.timesteps.to(original_samples.device     )
              snake_case_    							=				timesteps.to(original_samples.device     )

        snake_case_    							=				[self.index_for_timestep(lowerCAmelCase_						,			lowerCAmelCase_     ) for t in timesteps]

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

        snake_case_    							=				original_samples + noise * sigma
        return noisy_samples


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





'''simple docstring'''







import itertools







def _UpperCamelCase			(	__A = 1000000       )				->						int:


      '''simple docstring'''



      UpperCamelCase__      =							[1]

      for i in itertools.count(len(__A       )       ):
            UpperCamelCase__      =							0
            for j in itertools.count(1       ):
                  UpperCamelCase__      =							-1 if j % 2 == 0 else +1
                  UpperCamelCase__      =							(j * j * 3 - j) // 2
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number
                  index += j
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number

            if item == 0:
                  return i
            partitions.append(__A       )

      return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(F"""{solution() = }""")





