

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      snake_case__      (   SCREAMING_SNAKE_CASE_		:   Dict     ,					SCREAMING_SNAKE_CASE_		:   str=0.999     ,					SCREAMING_SNAKE_CASE_		:   Tuple="cosine"     ,					):



     '''simple docstring'''





     if alpha_transform_type == "cosine":

          def alpha_bar_fn(SCREAMING_SNAKE_CASE_		:   List[Any]      ):
               return math.cos((t + 0.008) / 1.008 * math.pi / 2      ) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(SCREAMING_SNAKE_CASE_		:   List[Any]      ):
               return math.exp(t * -12.0      )

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

     lowercase__   :       Any				=	[]
     for i in range(SCREAMING_SNAKE_CASE_      ):
          lowercase__   :       int				=	i / num_diffusion_timesteps
          lowercase__   :       Tuple				=	(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 				SCREAMING_SNAKE_CASE__ (__snake_case		,	__snake_case					):
    __lowerCamelCase						:	List[Any]														=					[e.name for e in KarrasDiffusionSchedulers]
    __lowerCamelCase						:	List[str]														=					2





    @register_to_config
    def __init__(				self						,       a = 1000						,       a = 0.00_085						,       a = 0.012						,       a = "linear"						,       a = None						,       a = "epsilon"						,       a = "linspace"						,       a = 0						,       ):
         if trained_betas is not None:
              lowercase__   :       List[Any]				=	torch.tensor(a						,       dtype=torch.floataa)
         elif beta_schedule == "linear":
              lowercase__   :       Any				=	torch.linspace(a						,       a						,       a						,       dtype=torch.floataa)
         elif beta_schedule == "scaled_linear":
              # this schedule is very specific to the latent diffusion model.
              lowercase__   :       Union[str, 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
              lowercase__   :       Optional[int]				=	betas_for_alpha_bar(a)
         else:
              raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}""")

         lowercase__   :       List[Any]				=	1.0 - self.betas
         lowercase__   :       Optional[Any]				=	torch.cumprod(self.alphas						,       dim=0)

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





    def 				snake_case_    (				self						,       a						,       a=None):
         if schedule_timesteps is None:
              lowercase__   :       Optional[Any]				=	self.timesteps

         lowercase__   :       Optional[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:
              lowercase__   :       str				=	1 if len(a) > 1 else 0
         else:
              lowercase__   :       Any				=	timestep.cpu().item() if torch.is_tensor(a) else timestep
              lowercase__   :       Optional[Any]				=	self._index_counter[timestep_int]

         return indices[pos].item()





    @property
    def 				snake_case_    (				self):
         # 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 				snake_case_    (				self						,       a						,       a						,       ):
         lowercase__   :       Dict				=	self.index_for_timestep(a)

         if self.state_in_first_order:
              lowercase__   :       List[Any]				=	self.sigmas[step_index]
         else:
              lowercase__   :       List[str]				=	self.sigmas_interpol[step_index]

         lowercase__   :       Tuple				=	sample / ((sigma**2 + 1) ** 0.5)
         return sample





    def 				snake_case_    (				self						,       a						,       a = None						,       a = None						,       ):
         lowercase__   :       str				=	num_inference_steps

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

         lowercase__   :       List[str]				=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
         lowercase__   :       List[str]				=	torch.from_numpy(np.log(a)).to(a)

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

         # interpolate sigmas
         lowercase__   :       Union[str, Any]				=	sigmas.log().lerp(sigmas.roll(1).log()						,       0.5).exp()

         lowercase__   :       Tuple				=	torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2), sigmas[-1:]])
         lowercase__   :       Union[str, 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
              lowercase__   :       List[Any]				=	torch.from_numpy(a).to(a						,       dtype=torch.floataa)
         else:
              lowercase__   :       Optional[Any]				=	torch.from_numpy(a).to(a)

         # interpolate timesteps
         lowercase__   :       List[Any]				=	self.sigma_to_t(a).to(a						,       dtype=timesteps.dtype)
         lowercase__   :       str				=	torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])						,       dim=-1).flatten()

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

         lowercase__   :       Any				=	None

         # for exp beta schedules, such as the one for `pipeline_shap_e.py`
         # we need an index counter
         lowercase__   :       List[str]				=	defaultdict(a)





    def 				snake_case_    (				self						,       a):
         # get log sigma
         lowercase__   :       str				=	sigma.log()

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

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

         lowercase__   :       Optional[Any]				=	self.log_sigmas[low_idx]
         lowercase__   :       int				=	self.log_sigmas[high_idx]

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

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





    @property
    def 				snake_case_    (				self):
         return self.sample is None





    def 				snake_case_    (				self						,       a						,       a						,       a						,       a = True						,       ):
         lowercase__   :       Union[str, Any]				=	self.index_for_timestep(a)

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

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

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

              # 3. delta timestep
              lowercase__   :       List[str]				=	sigma_next - sigma_hat

              lowercase__   :       int				=	self.sample
              lowercase__   :       Dict				=	None

         lowercase__   :       str				=	sample + derivative * dt

         if not return_dict:
              return (prev_sample,)

         return SchedulerOutput(prev_sample=a)





    def 				snake_case_    (				self						,       a						,       a						,       a						,       ):
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         lowercase__   :       List[str]				=	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
              lowercase__   :       Tuple				=	self.timesteps.to(original_samples.device						,       dtype=torch.floataa)
              lowercase__   :       List[Any]				=	timesteps.to(original_samples.device						,       dtype=torch.floataa)
         else:
              lowercase__   :       Any				=	self.timesteps.to(original_samples.device)
              lowercase__   :       List[Any]				=	timesteps.to(original_samples.device)

         lowercase__   :       Optional[int]				=	[self.index_for_timestep(a						,       a) for t in timesteps]

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

         lowercase__   :       Any				=	original_samples + noise * sigma
         return noisy_samples





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




def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   float      ):



     '''simple docstring'''





     if edge <= 0 or not isinstance(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_      ):
          raise ValueError('Length must be a positive.'      )
     return 3 * ((25 + 10 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)

def      snake_case__      (   SCREAMING_SNAKE_CASE_		:   float      ):



     '''simple docstring'''





     if edge <= 0 or not isinstance(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_      ):
          raise ValueError('Length must be a positive.'      )
     return ((15 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)


if __name__ == "__main__":
       import doctest

       doctest.testmod()

