


'''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 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[str]      ,    UpperCAmelCase_    :				Tuple=0.999      ,    UpperCAmelCase_    :				str="cosine"      ,    )     ->		List[Any]:
     if alpha_transform_type == "cosine":

          def alpha_bar_fn(UpperCAmelCase_    :				Any							):
               return math.cos((t + 0.008) / 1.008 * math.pi / 2							) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(UpperCAmelCase_    :				Optional[int]							):
               return math.exp(t * -12.0							)

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

     __lowerCamelCase   :	str								=		[]
     for i in range(UpperCAmelCase_							):
          __lowerCamelCase   :	List[Any]								=		i / num_diffusion_timesteps
          __lowerCamelCase   :	List[str]								=		(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    UpperCAmelCase_  (_UpperCAmelCase					,		_UpperCAmelCase  ):





    """simple docstring"""






    lowerCamelCase  :					List[str]							     =			[e.name for e in KarrasDiffusionSchedulers]
    lowerCamelCase  :					Dict							     =			2







    @register_to_config
    def __init__(							self			,     SCREAMING_SNAKE_CASE_ = 10_00			,     SCREAMING_SNAKE_CASE_ = 0.0_0_0_8_5			,     SCREAMING_SNAKE_CASE_ = 0.0_1_2			,     SCREAMING_SNAKE_CASE_ = "linear"			,     SCREAMING_SNAKE_CASE_ = None			,     SCREAMING_SNAKE_CASE_ = "epsilon"			,     SCREAMING_SNAKE_CASE_ = False			,     SCREAMING_SNAKE_CASE_ = False			,     SCREAMING_SNAKE_CASE_ = 1.0			,     SCREAMING_SNAKE_CASE_ = "linspace"			,     SCREAMING_SNAKE_CASE_ = 0			,     )				->     int:
         if trained_betas is not None:
              __lowerCamelCase   :	str								=		torch.tensor(SCREAMING_SNAKE_CASE_			,     dtype=torch.floataa	)
         elif beta_schedule == "linear":
              __lowerCamelCase   :	Dict								=		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   :	Any								=		(
                  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   :	Dict								=		betas_for_alpha_bar(SCREAMING_SNAKE_CASE_			,     alpha_transform_type='cosine'	)
         elif beta_schedule == "exp":
              __lowerCamelCase   :	Dict								=		betas_for_alpha_bar(SCREAMING_SNAKE_CASE_			,     alpha_transform_type='exp'	)
         else:
              raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'	)

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

         #  set all values
         self.set_timesteps(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	str								=		use_karras_sigmas







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_=None	)				->     Dict:
         if schedule_timesteps is None:
              __lowerCamelCase   :	Tuple								=		self.timesteps

         __lowerCamelCase   :	Any								=		(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   :	List[Any]								=		1 if len(SCREAMING_SNAKE_CASE_	) > 1 else 0
         else:
              __lowerCamelCase   :	Union[str, Any]								=		timestep.cpu().item() if torch.is_tensor(SCREAMING_SNAKE_CASE_	) else timestep
              __lowerCamelCase   :	str								=		self._index_counter[timestep_int]

         return indices[pos].item()







    @property
    def       lowercase_				(							self	)				->     List[str]:
         # 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       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     )				->     torch.FloatTensor:
         __lowerCamelCase   :	str								=		self.index_for_timestep(SCREAMING_SNAKE_CASE_	)

         __lowerCamelCase   :	List[str]								=		self.sigmas[step_index]
         __lowerCamelCase   :	Any								=		sample / ((sigma**2 + 1) ** 0.5)
         return sample







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_ = None			,     SCREAMING_SNAKE_CASE_ = None			,     )				->     Tuple:
         __lowerCamelCase   :	Dict								=		num_inference_steps

         __lowerCamelCase   :	int								=		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   :	Union[str, Any]								=		np.linspace(0			,     num_train_timesteps - 1			,     SCREAMING_SNAKE_CASE_			,     dtype=SCREAMING_SNAKE_CASE_	)[::-1].copy()
         elif self.config.timestep_spacing == "leading":
              __lowerCamelCase   :	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
              __lowerCamelCase   :	Tuple								=		(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   :	Dict								=		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   :	Dict								=		(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   :	List[Any]								=		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5	)
         __lowerCamelCase   :	List[str]								=		np.log(SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	Optional[Any]								=		np.interp(SCREAMING_SNAKE_CASE_			,     np.arange(0			,     len(SCREAMING_SNAKE_CASE_	)	)			,     SCREAMING_SNAKE_CASE_	)

         if self.config.use_karras_sigmas:
              __lowerCamelCase   :	Dict								=		self._convert_to_karras(in_sigmas=SCREAMING_SNAKE_CASE_			,     num_inference_steps=self.num_inference_steps	)
              __lowerCamelCase   :	str								=		np.array([self._sigma_to_t(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	) for sigma in sigmas]	)

         __lowerCamelCase   :	List[str]								=		np.concatenate([sigmas, [0.0]]	).astype(np.floataa	)
         __lowerCamelCase   :	List[str]								=		torch.from_numpy(SCREAMING_SNAKE_CASE_	).to(device=SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	Union[str, Any]								=		torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2	), sigmas[-1:]]	)

         __lowerCamelCase   :	Optional[Any]								=		torch.from_numpy(SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	Optional[int]								=		torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2	)]	)

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

         # empty dt and derivative
         __lowerCamelCase   :	Union[str, Any]								=		None
         __lowerCamelCase   :	Any								=		None

         # for exp beta schedules, such as the one for `pipeline_shap_e.py`
         # we need an index counter
         __lowerCamelCase   :	Optional[Any]								=		defaultdict(SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     List[str]:
         # get log sigma
         __lowerCamelCase   :	int								=		np.log(SCREAMING_SNAKE_CASE_	)

         # get distribution
         __lowerCamelCase   :	List[Any]								=		log_sigma - log_sigmas[:, np.newaxis]

         # get sigmas range
         __lowerCamelCase   :	Optional[int]								=		np.cumsum((dists >= 0)			,     axis=0	).argmax(axis=0	).clip(max=log_sigmas.shape[0] - 2	)
         __lowerCamelCase   :	Union[str, Any]								=		low_idx + 1

         __lowerCamelCase   :	Union[str, Any]								=		log_sigmas[low_idx]
         __lowerCamelCase   :	Dict								=		log_sigmas[high_idx]

         # interpolate sigmas
         __lowerCamelCase   :	Optional[int]								=		(low - log_sigma) / (low - high)
         __lowerCamelCase   :	Optional[int]								=		np.clip(SCREAMING_SNAKE_CASE_			,     0			,     1	)

         # transform interpolation to time range
         __lowerCamelCase   :	Optional[Any]								=		(1 - w) * low_idx + w * high_idx
         __lowerCamelCase   :	Union[str, Any]								=		t.reshape(sigma.shape	)
         return t







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	)				->     torch.FloatTensor:
         __lowerCamelCase   :	float								=		in_sigmas[-1].item()
         __lowerCamelCase   :	float								=		in_sigmas[0].item()

         __lowerCamelCase   :	List[str]								=		7.0  # 7.0 is the value used in the paper
         __lowerCamelCase   :	List[Any]								=		np.linspace(0			,     1			,     SCREAMING_SNAKE_CASE_	)
         __lowerCamelCase   :	int								=		sigma_min ** (1 / rho)
         __lowerCamelCase   :	Any								=		sigma_max ** (1 / rho)
         __lowerCamelCase   :	Union[str, Any]								=		(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
         return sigmas







    @property
    def       lowercase_				(							self	)				->     Union[str, Any]:
         return self.dt is None







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_ = True			,     )				->     Union[SchedulerOutput, Tuple]:
         __lowerCamelCase   :	str								=		self.index_for_timestep(SCREAMING_SNAKE_CASE_	)

         # advance index counter by 1
         __lowerCamelCase   :	int								=		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   :	Optional[int]								=		self.sigmas[step_index]
              __lowerCamelCase   :	List[str]								=		self.sigmas[step_index + 1]
         else:
              # 2nd order / Heun's method
              __lowerCamelCase   :	str								=		self.sigmas[step_index - 1]
              __lowerCamelCase   :	Tuple								=		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
         __lowerCamelCase   :	str								=		0
         __lowerCamelCase   :	Dict								=		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":
              __lowerCamelCase   :	Union[str, Any]								=		sigma_hat if self.state_in_first_order else sigma_next
              __lowerCamelCase   :	Optional[int]								=		sample - sigma_input * model_output
         elif self.config.prediction_type == "v_prediction":
              __lowerCamelCase   :	Union[str, Any]								=		sigma_hat if self.state_in_first_order else sigma_next
              __lowerCamelCase   :	Union[str, Any]								=		model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
                  sample / (sigma_input**2 + 1)
              )
         elif self.config.prediction_type == "sample":
              __lowerCamelCase   :	Optional[int]								=		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:
              __lowerCamelCase   :	str								=		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
              __lowerCamelCase   :	Union[str, Any]								=		(sample - pred_original_sample) / sigma_hat
              # 3. delta timestep
              __lowerCamelCase   :	Any								=		sigma_next - sigma_hat

              # store for 2nd order step
              __lowerCamelCase   :	Union[str, Any]								=		derivative
              __lowerCamelCase   :	Union[str, Any]								=		dt
              __lowerCamelCase   :	Union[str, Any]								=		sample
         else:
              # 2. 2nd order / Heun's method
              __lowerCamelCase   :	Tuple								=		(sample - pred_original_sample) / sigma_next
              __lowerCamelCase   :	Any								=		(self.prev_derivative + derivative) / 2

              # 3. take prev timestep & sample
              __lowerCamelCase   :	Any								=		self.dt
              __lowerCamelCase   :	Optional[int]								=		self.sample

              # free dt and derivative
              # Note, this puts the scheduler in "first order mode"
              __lowerCamelCase   :	str								=		None
              __lowerCamelCase   :	Dict								=		None
              __lowerCamelCase   :	List[str]								=		None

         __lowerCamelCase   :	List[str]								=		sample + derivative * dt

         if not return_dict:
              return (prev_sample,)

         return SchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_	)







    def       lowercase_				(							self			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_			,     )				->     torch.FloatTensor:
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         __lowerCamelCase   :	Union[str, Any]								=		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   :	Tuple								=		self.timesteps.to(original_samples.device			,     dtype=torch.floataa	)
              __lowerCamelCase   :	Tuple								=		timesteps.to(original_samples.device			,     dtype=torch.floataa	)
         else:
              __lowerCamelCase   :	Optional[int]								=		self.timesteps.to(original_samples.device	)
              __lowerCamelCase   :	Any								=		timesteps.to(original_samples.device	)

         __lowerCamelCase   :	Union[str, Any]								=		[self.index_for_timestep(SCREAMING_SNAKE_CASE_			,     SCREAMING_SNAKE_CASE_	) for t in timesteps]

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

         __lowerCamelCase   :	str								=		original_samples + noise * sigma
         return noisy_samples







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










'''simple docstring'''



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]							)     ->		str:
     __lowerCamelCase   :	Tuple								=		0
     __lowerCamelCase   :	Optional[int]								=		len(UpperCAmelCase_							)

     for i in range(n - 1							):
          for j in range(i + 1      ,    UpperCAmelCase_							):
               if arr[i] > arr[j]:
                    num_inversions += 1

     return num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				str							)     ->		Optional[int]:
     if len(UpperCAmelCase_							) <= 1:
          return arr, 0
     __lowerCamelCase   :	str								=		len(UpperCAmelCase_							) // 2
     __lowerCamelCase   :	List[Any]								=		arr[0:mid]
     __lowerCamelCase   :	List[str]								=		arr[mid:]

     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Optional[Any]								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Any								=		_count_cross_inversions(UpperCAmelCase_      ,    UpperCAmelCase_							)

     __lowerCamelCase   :	Optional[int]								=		inversion_p + inversions_q + cross_inversions
     return c, num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]      ,    UpperCAmelCase_    :				List[str]							)     ->		Optional[Any]:
     __lowerCamelCase   :	List[str]								=		[]
     __lowerCamelCase   :	Optional[int]								=		0
     while i < len(UpperCAmelCase_							) and j < len(UpperCAmelCase_							):
          if p[i] > q[j]:
               # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
               # These are all inversions. The claim emerges from the
               # property that P is sorted.
               num_inversion += len(UpperCAmelCase_							) - i
               r.append(q[j]							)
               j += 1
          else:
               r.append(p[i]							)
               i += 1

     if i < len(UpperCAmelCase_							):
          r.extend(p[i:]							)
     else:
          r.extend(q[j:]							)

     return r, num_inversion



def 			UpperCAmelCase__					(	)     ->		List[str]:
     __lowerCamelCase   :	Any								=		[10, 2, 1, 5, 5, 2, 11]

     # this arr has 8 inversions:
     # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Dict								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 8

     print('number of inversions = '      ,    UpperCAmelCase_							)

     # testing an array with zero inversion (a sorted arr_1)

     arr_a.sort()
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)

     # an empty list should also have zero inversions
     __lowerCamelCase   :	Dict								=		[]
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Union[str, Any]								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)


if __name__ == "__main__":
      main()






