






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	(							snake_case__  : List[Any]						,snake_case__  : str=0.9_9_9						,snake_case__  : Any="cosine"						,):




     '''simple docstring'''






     if alpha_transform_type == "cosine":

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

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

     __snake_case      :Tuple 							=    []
     for i in range(snake_case__	):
          __snake_case      :Dict 							=    i / num_diffusion_timesteps
          __snake_case      :Union[str, Any] 							=    (i + 1) / num_diffusion_timesteps
          betas.append(min(1 - alpha_bar_fn(snake_case__	) / alpha_bar_fn(snake_case__	)						,snake_case__	)	)
     return torch.tensor(snake_case__						,dtype=torch.floataa	)




class       snake_case__ (				lowercase_						,     lowercase_):

       '''simple docstring'''
       lowerCamelCase				:					Dict								=			[e.name for e in KarrasDiffusionSchedulers]
       lowerCamelCase				:					Tuple								=			2



       @register_to_config
       def __init__(				self      ,    a__ = 10_00      ,    a__ = 0.0_00_85      ,    a__ = 0.0_12      ,    a__ = "linear"      ,    a__ = None      ,    a__ = "epsilon"      ,    a__ = "linspace"      ,    a__ = 0      ,    )			->   str:






            '''simple docstring'''





            if trained_betas is not None:
                 __snake_case      :Dict 							=    torch.tensor(a__      ,    dtype=torch.floataa     )
            elif beta_schedule == "linear":
                 __snake_case      :Optional[int] 							=    torch.linspace(a__      ,    a__      ,    a__      ,    dtype=torch.floataa     )
            elif beta_schedule == "scaled_linear":
                 # this schedule is very specific to the latent diffusion model.
                 __snake_case      :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
                 __snake_case      :List[str] 							=    betas_for_alpha_bar(a__     )
            else:
                 raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''     )

            __snake_case      :str 							=    1.0 - self.betas
            __snake_case      :Union[str, Any] 							=    torch.cumprod(self.alphas      ,    dim=0     )

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



       def        __lowercase    (				self      ,    a__      ,    a__=None     )			->   Dict:






            '''simple docstring'''





            if schedule_timesteps is None:
                 __snake_case      :List[str] 							=    self.timesteps

            __snake_case      :List[str] 							=    (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      :Any 							=    1 if len(a__     ) > 1 else 0
            else:
                 __snake_case      :int 							=    timestep.cpu().item() if torch.is_tensor(a__     ) else timestep
                 __snake_case      :Dict 							=    self._index_counter[timestep_int]

            return indices[pos].item()



       @property
       def        __lowercase    (				self     )			->   Dict:






            '''simple docstring'''





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

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



       def        __lowercase    (				self      ,    a__      ,    a__      ,    )			->   torch.FloatTensor:






            '''simple docstring'''





            __snake_case      :List[str] 							=    self.index_for_timestep(a__     )

            if self.state_in_first_order:
                 __snake_case      :List[Any] 							=    self.sigmas[step_index]
            else:
                 __snake_case      :Tuple 							=    self.sigmas_interpol[step_index]

            __snake_case      :int 							=    sample / ((sigma**2 + 1) ** 0.5)
            return sample



       def        __lowercase    (				self      ,    a__      ,    a__ = None      ,    a__ = None      ,    )			->   Dict:






            '''simple docstring'''





            __snake_case      :Tuple 							=    num_inference_steps

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

            __snake_case      :List[str] 							=    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5     )
            __snake_case      :Optional[Any] 							=    torch.from_numpy(np.log(a__     )     ).to(a__     )

            __snake_case      :Optional[Any] 							=    np.interp(a__      ,    np.arange(0      ,    len(a__     )     )      ,    a__     )
            __snake_case      :Any 							=    np.concatenate([sigmas, [0.0]]     ).astype(np.floataa     )
            __snake_case      :Optional[int] 							=    torch.from_numpy(a__     ).to(device=a__     )

            # interpolate sigmas
            __snake_case      :Any 							=    sigmas.log().lerp(sigmas.roll(1     ).log()      ,    0.5     ).exp()

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

            if str(a__     ).startswith("""mps"""     ):
                 # mps does not support float64
                 __snake_case      :str 							=    torch.from_numpy(a__     ).to(a__      ,    dtype=torch.floataa     )
            else:
                 __snake_case      :Optional[int] 							=    torch.from_numpy(a__     ).to(a__     )

            # interpolate timesteps
            __snake_case      :Union[str, Any] 							=    self.sigma_to_t(a__     ).to(a__      ,    dtype=timesteps.dtype     )
            __snake_case      :Dict 							=    torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])      ,    dim=-1     ).flatten()

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

            __snake_case      :Optional[Any] 							=    None

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



       def        __lowercase    (				self      ,    a__     )			->   List[str]:






            '''simple docstring'''





            __snake_case      :List[str] 							=    sigma.log()

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

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

            __snake_case      :List[str] 							=    self.log_sigmas[low_idx]
            __snake_case      :int 							=    self.log_sigmas[high_idx]

            # interpolate sigmas
            __snake_case      :str 							=    (low - log_sigma) / (low - high)
            __snake_case      :List[Any] 							=    w.clamp(0      ,    1     )

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



       @property
       def        __lowercase    (				self     )			->   Dict:






            '''simple docstring'''





            return self.sample is None



       def        __lowercase    (				self      ,    a__      ,    a__      ,    a__      ,    a__ = True      ,    )			->   Union[SchedulerOutput, Tuple]:






            '''simple docstring'''





            __snake_case      :List[str] 							=    self.index_for_timestep(a__     )

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

            if self.state_in_first_order:
                 __snake_case      :int 							=    self.sigmas[step_index]
                 __snake_case      :Tuple 							=    self.sigmas_interpol[step_index + 1]
                 __snake_case      :str 							=    self.sigmas[step_index + 1]
            else:
                 # 2nd order / KDPM2's method
                 __snake_case      :str 							=    self.sigmas[step_index - 1]
                 __snake_case      :int 							=    self.sigmas_interpol[step_index]
                 __snake_case      :Dict 							=    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
            __snake_case      :str 							=    0
            __snake_case      :List[Any] 							=    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":
                 __snake_case      :Tuple 							=    sigma_hat if self.state_in_first_order else sigma_interpol
                 __snake_case      :str 							=    sample - sigma_input * model_output
            elif self.config.prediction_type == "v_prediction":
                 __snake_case      :List[Any] 							=    sigma_hat if self.state_in_first_order else sigma_interpol
                 __snake_case      :str 							=    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      :Dict 							=    (sample - pred_original_sample) / sigma_hat
                 # 3. delta timestep
                 __snake_case      :Dict 							=    sigma_interpol - sigma_hat

                 # store for 2nd order step
                 __snake_case      :Optional[Any] 							=    sample
            else:
                 # DPM-Solver-2
                 # 2. Convert to an ODE derivative for 2nd order
                 __snake_case      :Union[str, Any] 							=    (sample - pred_original_sample) / sigma_interpol

                 # 3. delta timestep
                 __snake_case      :Optional[Any] 							=    sigma_next - sigma_hat

                 __snake_case      :Tuple 							=    self.sample
                 __snake_case      :List[str] 							=    None

            __snake_case      :Any 							=    sample + derivative * dt

            if not return_dict:
                 return (prev_sample,)

            return SchedulerOutput(prev_sample=a__     )



       def        __lowercase    (				self      ,    a__      ,    a__      ,    a__      ,    )			->   torch.FloatTensor:






            '''simple docstring'''





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

            __snake_case      :Dict 							=    [self.index_for_timestep(a__      ,    a__     ) for t in timesteps]

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

            __snake_case      :Union[str, Any] 							=    original_samples + noise * sigma
            return noisy_samples



       def __len__(				self     )			->   List[Any]:






            '''simple docstring'''





            return self.config.num_train_timesteps










def 	UpperCamelCase	(							snake_case__  : int	):




     '''simple docstring'''






     __snake_case      :List[Any] 							=    0
     while num > 0:
          digit_sum += num % 10
          num //= 10
     return digit_sum






def 	UpperCamelCase	(							snake_case__  : int = 100	):




     '''simple docstring'''






     __snake_case      :Tuple 							=    1
     __snake_case      :Dict 							=    2

     for i in range(2						,max_n + 1	):
          __snake_case      :Optional[int] 							=    pre_numerator
          __snake_case      :List[Any] 							=    2 * i // 3 if i % 3 == 0 else 1
          __snake_case      :Dict 							=    cur_numerator
          __snake_case      :Optional[Any] 							=    e_cont * pre_numerator + temp

     return sum_digits(snake_case__	)


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


