





'''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 .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
def 				lowercase__   (   __lowercase						:  Tuple				,  __lowercase						:  Union[str, Any]=0.9_9_9				,  __lowercase						:  List[Any]="cosine"				,  ) ->      List[Any]:



       """simple docstring"""






       if alpha_transform_type == "cosine":

              def alpha_bar_fn(__lowercase						:  Optional[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(__lowercase						:  str     ):
                     return math.exp(t * -1_2.0     )

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

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


class      snake_case     (    __lowerCamelCase			,       __lowerCamelCase       ):




 """simple docstring"""



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






 @register_to_config
 def __init__(       self       :							Tuple							,	__A       :							Optional[int] = 1_0_0_0							,	__A       :							int = 0.0_0085							,	__A       :							Optional[Any] = 0.012							,	__A       :							Dict = "linear"							,	__A       :							List[Any] = None							,	__A       :							Optional[int] = "epsilon"							,	__A       :							Union[str, Any] = False							,	__A       :							int = False							,	__A       :							Optional[int] = 1.0							,	__A       :							Optional[int] = "linspace"							,	__A       :							int = 0							,	):







        if trained_betas is not None:
               __UpperCamelCase       =  torch.tensor(__A							,	dtype=torch.floataa	)
        elif beta_schedule == "linear":
               __UpperCamelCase       =  torch.linspace(__A							,	__A							,	__A							,	dtype=torch.floataa	)
        elif beta_schedule == "scaled_linear":
               # this schedule is very specific to the latent diffusion model.
               __UpperCamelCase       =  (
                   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       =  betas_for_alpha_bar(__A							,	alpha_transform_type='cosine'	)
        elif beta_schedule == "exp":
               __UpperCamelCase       =  betas_for_alpha_bar(__A							,	alpha_transform_type='exp'	)
        else:
               raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''	)

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

        #  set all values
        self.set_timesteps(__A							,	__A							,	__A	)
        __UpperCamelCase       =  use_karras_sigmas






 def        _lowerCamelCase					(       self       :							List[Any]							,	__A       :							List[Any]							,	__A       :							Any=None	):







        if schedule_timesteps is None:
               __UpperCamelCase       =  self.timesteps

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

        return indices[pos].item()






 @property
 def        _lowerCamelCase					(       self       :							List[Any]	):







        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]							,	__A       :							List[str]							,	__A       :							Tuple							,	):
        __UpperCamelCase       =  self.index_for_timestep(__A	)

        __UpperCamelCase       =  self.sigmas[step_index]
        __UpperCamelCase       =  sample / ((sigma**2 + 1) ** 0.5)
        return sample






 def        _lowerCamelCase					(       self       :							Any							,	__A       :							Dict							,	__A       :							List[str] = None							,	__A       :							Union[str, Any] = None							,	):
        __UpperCamelCase       =  num_inference_steps

        __UpperCamelCase       =  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       =  np.linspace(0							,	num_train_timesteps - 1							,	__A							,	dtype=__A	)[::-1].copy()
        elif self.config.timestep_spacing == "leading":
               __UpperCamelCase       =  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       =  (np.arange(0							,	__A	) * step_ratio).round()[::-1].copy().astype(__A	)
               timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
               __UpperCamelCase       =  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       =  (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       =  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5	)
        __UpperCamelCase       =  np.log(__A	)
        __UpperCamelCase       =  np.interp(__A							,	np.arange(0							,	len(__A	)	)							,	__A	)

        if self.config.use_karras_sigmas:
               __UpperCamelCase       =  self._convert_to_karras(in_sigmas=__A							,	num_inference_steps=self.num_inference_steps	)
               __UpperCamelCase       =  np.array([self._sigma_to_t(__A							,	__A	) for sigma in sigmas]	)

        __UpperCamelCase       =  np.concatenate([sigmas, [0.0]]	).astype(np.floataa	)
        __UpperCamelCase       =  torch.from_numpy(__A	).to(device=__A	)
        __UpperCamelCase       =  torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2	), sigmas[-1:]]	)

        __UpperCamelCase       =  torch.from_numpy(__A	)
        __UpperCamelCase       =  torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2	)]	)

        if str(__A	).startswith('mps'	):
               # mps does not support float64
               __UpperCamelCase       =  timesteps.to(__A							,	dtype=torch.floataa	)
        else:
               __UpperCamelCase       =  timesteps.to(device=__A	)

        # empty dt and derivative
        __UpperCamelCase       =  None
        __UpperCamelCase       =  None

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






 def        _lowerCamelCase					(       self       :							Tuple							,	__A       :							Any							,	__A       :							Tuple	):
        __UpperCamelCase       =  np.log(__A	)

        # get distribution
        __UpperCamelCase       =  log_sigma - log_sigmas[:, np.newaxis]

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

        __UpperCamelCase       =  log_sigmas[low_idx]
        __UpperCamelCase       =  log_sigmas[high_idx]

        # interpolate sigmas
        __UpperCamelCase       =  (low - log_sigma) / (low - high)
        __UpperCamelCase       =  np.clip(__A							,	0							,	1	)

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






 def        _lowerCamelCase					(       self       :							Tuple							,	__A       :							str							,	__A       :							Dict	):
        __UpperCamelCase       =  in_sigmas[-1].item()
        __UpperCamelCase       =  in_sigmas[0].item()

        __UpperCamelCase       =  7.0  # 7.0 is the value used in the paper
        __UpperCamelCase       =  np.linspace(0							,	1							,	__A	)
        __UpperCamelCase       =  sigma_min ** (1 / rho)
        __UpperCamelCase       =  sigma_max ** (1 / rho)
        __UpperCamelCase       =  (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
        return sigmas






 @property
 def        _lowerCamelCase					(       self       :							Optional[Any]	):
        return self.dt is None






 def        _lowerCamelCase					(       self       :							Optional[int]							,	__A       :							List[Any]							,	__A       :							Optional[int]							,	__A       :							Tuple							,	__A       :							List[str] = True							,	):
        __UpperCamelCase       =  self.index_for_timestep(__A	)

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

        if self.state_in_first_order:
               __UpperCamelCase       =  self.sigmas[step_index]
               __UpperCamelCase       =  self.sigmas[step_index + 1]
        else:
               # 2nd order / Heun's method
               __UpperCamelCase       =  self.sigmas[step_index - 1]
               __UpperCamelCase       =  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       =  0
        __UpperCamelCase       =  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       =  sigma_hat if self.state_in_first_order else sigma_next
               __UpperCamelCase       =  sample - sigma_input * model_output
        elif self.config.prediction_type == "v_prediction":
               __UpperCamelCase       =  sigma_hat if self.state_in_first_order else sigma_next
               __UpperCamelCase       =  model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
                   sample / (sigma_input**2 + 1)
               )
        elif self.config.prediction_type == "sample":
               __UpperCamelCase       =  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       =  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       =  (sample - pred_original_sample) / sigma_hat
               # 3. delta timestep
               __UpperCamelCase       =  sigma_next - sigma_hat

               # store for 2nd order step
               __UpperCamelCase       =  derivative
               __UpperCamelCase       =  dt
               __UpperCamelCase       =  sample
        else:
               # 2. 2nd order / Heun's method
               __UpperCamelCase       =  (sample - pred_original_sample) / sigma_next
               __UpperCamelCase       =  (self.prev_derivative + derivative) / 2

               # 3. take prev timestep & sample
               __UpperCamelCase       =  self.dt
               __UpperCamelCase       =  self.sample

               # free dt and derivative
               # Note, this puts the scheduler in "first order mode"
               __UpperCamelCase       =  None
               __UpperCamelCase       =  None
               __UpperCamelCase       =  None

        __UpperCamelCase       =  sample + derivative * dt

        if not return_dict:
               return (prev_sample,)

        return SchedulerOutput(prev_sample=__A	)






 def        _lowerCamelCase					(       self       :							int							,	__A       :							Any							,	__A       :							Dict							,	__A       :							Union[str, Any]							,	):
        __UpperCamelCase       =  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       =  self.timesteps.to(original_samples.device							,	dtype=torch.floataa	)
               __UpperCamelCase       =  timesteps.to(original_samples.device							,	dtype=torch.floataa	)
        else:
               __UpperCamelCase       =  self.timesteps.to(original_samples.device	)
               __UpperCamelCase       =  timesteps.to(original_samples.device	)

        __UpperCamelCase       =  [self.index_for_timestep(__A							,	__A	) for t in timesteps]

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

        __UpperCamelCase       =  original_samples + noise * sigma
        return noisy_samples






 def __len__(       self       :							Tuple	):
        return self.config.num_train_timesteps


def 						_snake_case(  SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) ->    List[str]:
       if index == r:
              for j in range(SCREAMING_SNAKE_CASE__				):
                     print(data[j]					,	end=""" """				)
              print(""" """				)
              return
       #  When no more elements are there to put in data[]
       if i >= n:
              return
       # current is included, put next at next location
       lowercase							:     Tuple       	=      arr[i]
       combination_util(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	index + 1					,	SCREAMING_SNAKE_CASE__					,	i + 1				)
       # current is excluded, replace it with
       # next (Note that i+1 is passed, but
       # index is not changed)
       combination_util(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	i + 1				)
       # The main function that prints all combinations
       # of size r in arr[] of size n. This function
       # mainly uses combinationUtil()







def 						_snake_case(  SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				) ->    List[str]:
       # A temporary array to store all combination one by one
       lowercase							:     Optional[int]       	=      [0] * r
       # Print all combination using temporary array 'data[]'
       combination_util(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__					,	0					,	SCREAMING_SNAKE_CASE__					,	0				)


if __name__ == "__main__":
  # Driver code to check the function above
  lowercase  :					int						    =							[10, 20, 30, 40, 50]
  print_combination(arr, len(arr), 3)
  # This code is contributed by Ambuj sahu
