





'''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__		(						__magic_name__  :   Optional[int]		,       __magic_name__  :   str=0.999		,       __magic_name__  :   Union[str, Any]="cosine"		,       )				->			Tuple:
 '''simple docstring'''






 if alpha_transform_type == "cosine":

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

 elif alpha_transform_type == "exp":

  def alpha_bar_fn(__magic_name__  :   int      ):
   return math.exp(t * -12.0      )

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

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





class 					__snake_case  (					__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE							):






   '''simple docstring'''





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

   @register_to_config
   def __init__(							self	,		__SCREAMING_SNAKE_CASE = 1_0_0_0	,		__SCREAMING_SNAKE_CASE = 0.0_0085	,		__SCREAMING_SNAKE_CASE = 0.012	,		__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	,		):
    if trained_betas is not None:
     snake_case__     :					List[Any]    =  torch.tensor(__SCREAMING_SNAKE_CASE	,		dtype=torch.floataa       )
    elif beta_schedule == "linear":
     snake_case__     :					Union[str, Any]    =  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.
     snake_case__     :					Dict    =  (
         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
     snake_case__     :					List[str]    =  betas_for_alpha_bar(__SCREAMING_SNAKE_CASE	,		alpha_transform_type="""cosine"""       )
    elif beta_schedule == "exp":
     snake_case__     :					List[Any]    =  betas_for_alpha_bar(__SCREAMING_SNAKE_CASE	,		alpha_transform_type="""exp"""       )
    else:
     raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"       )

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

    #  set all values
    self.set_timesteps(__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE       )
    snake_case__     :					Optional[Any]    =  use_karras_sigmas

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE=None       ):
    if schedule_timesteps is None:
     snake_case__     :					Union[str, Any]    =  self.timesteps

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

    return indices[pos].item()

   @property
   def 		__UpperCamelCase						(							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 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		):
    snake_case__     :					str    =  self.index_for_timestep(__SCREAMING_SNAKE_CASE       )

    snake_case__     :					Union[str, Any]    =  self.sigmas[step_index]
    snake_case__     :					Optional[Any]    =  sample / ((sigma**2 + 1) ** 0.5)
    return sample

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE = None	,		__SCREAMING_SNAKE_CASE = None	,		):
    snake_case__     :					str    =  num_inference_steps

    snake_case__     :					Optional[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":
     snake_case__     :					int    =  np.linspace(0	,		num_train_timesteps - 1	,		__SCREAMING_SNAKE_CASE	,		dtype=__SCREAMING_SNAKE_CASE       )[::-1].copy()
    elif self.config.timestep_spacing == "leading":
     snake_case__     :					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__     :					str    =  (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":
     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(__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'."       )

    snake_case__     :					Union[str, Any]    =  np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
    snake_case__     :					int    =  np.log(__SCREAMING_SNAKE_CASE       )
    snake_case__     :					List[str]    =  np.interp(__SCREAMING_SNAKE_CASE	,		np.arange(0	,		len(__SCREAMING_SNAKE_CASE       )       )	,		__SCREAMING_SNAKE_CASE       )

    if self.config.use_karras_sigmas:
     snake_case__     :					Any    =  self._convert_to_karras(in_sigmas=__SCREAMING_SNAKE_CASE	,		num_inference_steps=self.num_inference_steps       )
     snake_case__     :					Tuple    =  np.array([self._sigma_to_t(__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE       ) for sigma in sigmas]       )

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

    snake_case__     :					Dict    =  torch.from_numpy(__SCREAMING_SNAKE_CASE       )
    snake_case__     :					Dict    =  torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2       )]       )

    if str(__SCREAMING_SNAKE_CASE       ).startswith("""mps"""       ):
     # mps does not support float64
     snake_case__     :					List[str]    =  timesteps.to(__SCREAMING_SNAKE_CASE	,		dtype=torch.floataa       )
    else:
     snake_case__     :					Optional[Any]    =  timesteps.to(device=__SCREAMING_SNAKE_CASE       )

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

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

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE       ):
    # get log sigma
    snake_case__     :					int    =  np.log(__SCREAMING_SNAKE_CASE       )

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

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

    snake_case__     :					Any    =  log_sigmas[low_idx]
    snake_case__     :					List[Any]    =  log_sigmas[high_idx]

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

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

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE       ):
    snake_case__     :					float    =  in_sigmas[-1].item()
    snake_case__     :					float    =  in_sigmas[0].item()

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

   @property
   def 		__UpperCamelCase						(							self       ):
    return self.dt is None

   def 		__UpperCamelCase						(							self	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE = True	,		):
    snake_case__     :					str    =  self.index_for_timestep(__SCREAMING_SNAKE_CASE       )

    # advance index counter by 1
    snake_case__     :					List[str]    =  timestep.cpu().item() if torch.is_tensor(__SCREAMING_SNAKE_CASE       ) else timestep
    self._index_counter[timestep_int] += 1

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

     # store for 2nd order step
     snake_case__     :					List[Any]    =  derivative
     snake_case__     :					int    =  dt
     snake_case__     :					Optional[int]    =  sample
    else:
     # 2. 2nd order / Heun's method
     snake_case__     :					List[Any]    =  (sample - pred_original_sample) / sigma_next
     snake_case__     :					Dict    =  (self.prev_derivative + derivative) / 2

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

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

    snake_case__     :					List[Any]    =  sample + derivative * dt

    if not return_dict:
     return (prev_sample,)

    return SchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE       )

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

    snake_case__     :					Tuple    =  [self.index_for_timestep(__SCREAMING_SNAKE_CASE	,		__SCREAMING_SNAKE_CASE       ) for t in timesteps]

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

    snake_case__     :					str    =  original_samples + noise * sigma
    return noisy_samples


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









'''simple docstring'''





__a  			=						"Alexander Joslin"

import operator as op

from .stack import Stack





def 		__snake_case(							_lowerCAmelCase						)						->					int:
      snake_case__    :       str       		= {"""*""": op.mul, """/""": op.truediv, """+""": op.add, """-""": op.sub}

      snake_case__    :       Stack[int]       		= Stack()
      snake_case__    :       Stack[str]       		= Stack()

      for i in equation:
            if i.isdigit():
                  # RULE 1
                  operand_stack.push(int(_lowerCAmelCase						)						)
            elif i in operators:
                  # RULE 2
                  operator_stack.push(_lowerCAmelCase						)
            elif i == ")":
                  # RULE 4
                  snake_case__    :       Union[str, Any]       		= operator_stack.peek()
                  operator_stack.pop()
                  snake_case__    :       Any       		= operand_stack.peek()
                  operand_stack.pop()
                  snake_case__    :       str       		= operand_stack.peek()
                  operand_stack.pop()

                  snake_case__    :       Optional[Any]       		= operators[opr](_lowerCAmelCase	,  _lowerCAmelCase						)
                  operand_stack.push(_lowerCAmelCase						)

    # RULE 5
      return operand_stack.peek()


if __name__ == "__main__":
       __a  			=						"(5 + ((4 * 2) * (2 + 3)))"
       # answer = 45
       print(F"{equation} = {dijkstras_two_stack_algorithm(equation)}")
