



"""simple docstring"""







import math







class  UpperCamelCase__  :




      """simple docstring"""




      def __init__( self							: Any       ,     SCREAMING_SNAKE_CASE_							: int       ,     SCREAMING_SNAKE_CASE_							: int       ,     SCREAMING_SNAKE_CASE_							: int       ,     SCREAMING_SNAKE_CASE_							: List[Any]			):
        lowerCAmelCase_  :							Any								=					x
        lowerCAmelCase_  :							int								=					y
        lowerCAmelCase_  :							List[str]								=					step_size
        lowerCAmelCase_  :							int								=					function_to_optimize



      def 	SCREAMING_SNAKE_CASE__					( self							: Optional[Any]			):
        return self.function(self.x       ,     self.y			)



      def 	SCREAMING_SNAKE_CASE__					( self							: Dict			):
        lowerCAmelCase_  :							str								=					self.step_size
        return [
            SearchProblem(SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_       ,     self.function			)
            for x, y in (
                (self.x - step_size, self.y - step_size),
                (self.x - step_size, self.y),
                (self.x - step_size, self.y + step_size),
                (self.x, self.y - step_size),
                (self.x, self.y + step_size),
                (self.x + step_size, self.y - step_size),
                (self.x + step_size, self.y),
                (self.x + step_size, self.y + step_size),
            )
        ]



      def __hash__( self							: int			):
        return hash(str(self			)			)



      def __eq__( self							: Union[str, Any]       ,     SCREAMING_SNAKE_CASE_							: Any			):
        if isinstance(SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_			):
          return hash(str(self			)			) == hash(str(SCREAMING_SNAKE_CASE_			)			)
        return False





      def __str__( self							: Dict			):
        return F"x: {self.x} y: {self.y}"




def 							UpperCamelCase_       (       lowerCAmelCase__ :							int       ,  lowerCAmelCase__ :							bool = True       ,  lowerCAmelCase__ :							float = math.inf       ,  lowerCAmelCase__ :							float = -math.inf       ,  lowerCAmelCase__ :							float = math.inf       ,  lowerCAmelCase__ :							float = -math.inf       ,  lowerCAmelCase__ :							bool = False       ,  lowerCAmelCase__ :							int = 1_0000       ,  )		->  SearchProblem:

  """simple docstring"""




  lowerCAmelCase_  :							Union[str, Any]								=					search_prob
  lowerCAmelCase_  :							Dict								=					[]  # list to store the current score at each iteration
  lowerCAmelCase_  :							int								=					0
  lowerCAmelCase_  :							Any								=					False
  lowerCAmelCase_  :							int								=					set()
  while not solution_found and iterations < max_iter:
    visited.add(lowerCAmelCase__		)
    iterations += 1
    lowerCAmelCase_  :							List[Any]								=					current_state.score()
    scores.append(lowerCAmelCase__		)
    lowerCAmelCase_  :							Optional[int]								=					current_state.get_neighbors()
    lowerCAmelCase_  :							Any								=					-math.inf
    lowerCAmelCase_  :							str								=					math.inf
    lowerCAmelCase_  :							List[Any]								=					None  # to hold the next best neighbor
    for neighbor in neighbors:
      if neighbor in visited:
        continue  # do not want to visit the same state again
      if (
          neighbor.x > max_x
          or neighbor.x < min_x
          or neighbor.y > max_y
          or neighbor.y < min_y
      ):
        continue  # neighbor outside our bounds
      lowerCAmelCase_  :							int								=					neighbor.score() - current_score
      if find_max:  # finding max
        # going to direction with greatest ascent
        if change > max_change and change > 0:
          lowerCAmelCase_  :							int								=					change
          lowerCAmelCase_  :							Any								=					neighbor
      else:  # finding min
        # to direction with greatest descent
        if change < min_change and change < 0:
          lowerCAmelCase_  :							List[Any]								=					change
          lowerCAmelCase_  :							List[Any]								=					neighbor
    if next_state is not None:
      # we found at least one neighbor which improved the current state
      lowerCAmelCase_  :							Union[str, Any]								=					next_state
    else:
      # since we have no neighbor that improves the solution we stop the search
      lowerCAmelCase_  :							Optional[int]								=					True

  if visualization:
    from matplotlib import pyplot as plt

    plt.plot(range(lowerCAmelCase__		)       ,  lowerCAmelCase__		)
    plt.xlabel('Iterations'		)
    plt.ylabel('Function values'		)
    plt.show()

  return current_state


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     def 							UpperCamelCase_       (       lowerCAmelCase__ :							Tuple       ,  lowerCAmelCase__ :							List[Any]		)		->  Any:

       """simple docstring"""




       return (x**2) + (y**2)

     # starting the problem with initial coordinates (3, 4)
     lowercase__						:							Optional[Any]        =      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     lowercase__						:							int        =      hill_climbing(prob, find_max=False)
     print(
         """The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: """
         f'{local_min.score()}'
     )

     # starting the problem with initial coordinates (12, 47)
     lowercase__						:							Tuple        =      SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
     lowercase__						:							str        =      hill_climbing(
         prob, find_max=False, max_x=1_0_0, min_x=5, max_y=5_0, min_y=-5, visualization=True
     )
     print(
         """The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 """
         f'and 50 > y > - 5 found via hill climbing: {local_min.score()}'
     )

     def 							UpperCamelCase_       (       lowerCAmelCase__ :							Dict       ,  lowerCAmelCase__ :							Optional[int]		)		->  Union[str, Any]:

       """simple docstring"""




       return (3 * x**2) - (6 * y)

     lowercase__						:							List[str]        =      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
     lowercase__						:							Optional[Any]        =      hill_climbing(prob, find_max=True)
     print(
         """The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: """
         f'{local_min.score()}'
     )










"""simple docstring"""







import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


lowercase__						:							Any        =      logging.get_logger(__name__)  # pylint: disable=invalid-name







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class  UpperCamelCase__  (      lowercase_    ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE    							=	42
      _SCREAMING_SNAKE_CASE    							=	None




def 							UpperCamelCase_       (       lowerCAmelCase__ :							List[Any]       ,  lowerCAmelCase__ :							Optional[Any]=0.999       ,  lowerCAmelCase__ :							Optional[int]="cosine"       ,  )		->  Optional[Any]:

  """simple docstring"""




  if alpha_transform_type == "cosine":

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

  elif alpha_transform_type == "exp":

    def alpha_bar_fn(lowerCAmelCase__ :							Union[str, Any]		):
      return math.exp(t * -12.0		)

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

  lowerCAmelCase_  :							List[str]								=					[]
  for i in range(lowerCAmelCase__		):
    lowerCAmelCase_  :							str								=					i / num_diffusion_timesteps
    lowerCAmelCase_  :							Optional[int]								=					(i + 1) / num_diffusion_timesteps
    betas.append(min(1 - alpha_bar_fn(lowerCAmelCase__		) / alpha_bar_fn(lowerCAmelCase__		)       ,  lowerCAmelCase__		)		)
  return torch.tensor(lowerCAmelCase__       ,  dtype=torch.floataa		)







class  UpperCamelCase__  (      lowercase_,   lowercase_    ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE    							=	[e.name for e in KarrasDiffusionSchedulers]
      _SCREAMING_SNAKE_CASE    							=	1



      @register_to_config
      def __init__( self							: str       ,     SCREAMING_SNAKE_CASE_							: int = 1_0_0_0       ,     SCREAMING_SNAKE_CASE_							: float = 0.00_01       ,     SCREAMING_SNAKE_CASE_							: float = 0.02       ,     SCREAMING_SNAKE_CASE_							: str = "linear"       ,     SCREAMING_SNAKE_CASE_							: Optional[Union[np.ndarray, List[float]]] = None       ,     SCREAMING_SNAKE_CASE_							: str = "epsilon"       ,     SCREAMING_SNAKE_CASE_							: str = "linspace"       ,     SCREAMING_SNAKE_CASE_							: int = 0       ,     ):
        if trained_betas is not None:
          lowerCAmelCase_  :							int								=					torch.tensor(SCREAMING_SNAKE_CASE_       ,     dtype=torch.floataa			)
        elif beta_schedule == "linear":
          lowerCAmelCase_  :							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.
          lowerCAmelCase_  :							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
          lowerCAmelCase_  :							Optional[int]								=					betas_for_alpha_bar(SCREAMING_SNAKE_CASE_			)
        else:
          raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"			)

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

        lowerCAmelCase_  :							Dict								=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
        lowerCAmelCase_  :							Optional[int]								=					np.concatenate([sigmas[::-1], [0.0]]			).astype(np.floataa			)
        lowerCAmelCase_  :							Optional[int]								=					torch.from_numpy(SCREAMING_SNAKE_CASE_			)

        # setable values
        lowerCAmelCase_  :							Union[str, Any]								=					None
        lowerCAmelCase_  :							List[Any]								=					np.linspace(0       ,     num_train_timesteps - 1       ,     SCREAMING_SNAKE_CASE_       ,     dtype=SCREAMING_SNAKE_CASE_			)[::-1].copy()
        lowerCAmelCase_  :							int								=					torch.from_numpy(SCREAMING_SNAKE_CASE_			)
        lowerCAmelCase_  :							List[str]								=					False



      @property
      def 	SCREAMING_SNAKE_CASE__					( self							: Tuple			):
        # 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 	SCREAMING_SNAKE_CASE__					( self							: int       ,     SCREAMING_SNAKE_CASE_							: torch.FloatTensor       ,     SCREAMING_SNAKE_CASE_							: Union[float, torch.FloatTensor]			):
        if isinstance(SCREAMING_SNAKE_CASE_       ,     torch.Tensor			):
          lowerCAmelCase_  :							List[Any]								=					timestep.to(self.timesteps.device			)
        lowerCAmelCase_  :							Any								=					(self.timesteps == timestep).nonzero().item()
        lowerCAmelCase_  :							List[str]								=					self.sigmas[step_index]
        lowerCAmelCase_  :							Optional[int]								=					sample / ((sigma**2 + 1) ** 0.5)
        lowerCAmelCase_  :							Dict								=					True
        return sample



      def 	SCREAMING_SNAKE_CASE__					( self							: str       ,     SCREAMING_SNAKE_CASE_							: int       ,     SCREAMING_SNAKE_CASE_							: Union[str, torch.device] = None			):
        lowerCAmelCase_  :							Optional[int]								=					num_inference_steps

        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
          lowerCAmelCase_  :							Any								=					np.linspace(0       ,     self.config.num_train_timesteps - 1       ,     SCREAMING_SNAKE_CASE_       ,     dtype=SCREAMING_SNAKE_CASE_			)[
              ::-1
          ].copy()
        elif self.config.timestep_spacing == "leading":
          lowerCAmelCase_  :							int								=					self.config.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_  :							List[Any]								=					(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_  :							List[Any]								=					self.config.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_  :							int								=					(np.arange(self.config.num_train_timesteps       ,     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_  :							Optional[int]								=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
        lowerCAmelCase_  :							List[str]								=					np.interp(SCREAMING_SNAKE_CASE_       ,     np.arange(0       ,     len(SCREAMING_SNAKE_CASE_			)			)       ,     SCREAMING_SNAKE_CASE_			)
        lowerCAmelCase_  :							Union[str, Any]								=					np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
        lowerCAmelCase_  :							List[str]								=					torch.from_numpy(SCREAMING_SNAKE_CASE_			).to(device=SCREAMING_SNAKE_CASE_			)
        if str(SCREAMING_SNAKE_CASE_			).startswith('mps'			):
          # mps does not support float64
          lowerCAmelCase_  :							List[str]								=					torch.from_numpy(SCREAMING_SNAKE_CASE_			).to(SCREAMING_SNAKE_CASE_       ,     dtype=torch.floataa			)
        else:
          lowerCAmelCase_  :							List[Any]								=					torch.from_numpy(SCREAMING_SNAKE_CASE_			).to(device=SCREAMING_SNAKE_CASE_			)



      def 	SCREAMING_SNAKE_CASE__					( self							: Tuple       ,     SCREAMING_SNAKE_CASE_							: torch.FloatTensor       ,     SCREAMING_SNAKE_CASE_							: Union[float, torch.FloatTensor]       ,     SCREAMING_SNAKE_CASE_							: torch.FloatTensor       ,     SCREAMING_SNAKE_CASE_							: Optional[torch.Generator] = None       ,     SCREAMING_SNAKE_CASE_							: bool = True       ,     ):

        if (
            isinstance(SCREAMING_SNAKE_CASE_       ,     SCREAMING_SNAKE_CASE_			)
            or isinstance(SCREAMING_SNAKE_CASE_       ,     torch.IntTensor			)
            or isinstance(SCREAMING_SNAKE_CASE_       ,     torch.LongTensor			)
        ):
          raise ValueError(
              (
                  'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
                  ' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'
                  ' one of the `scheduler.timesteps` as a timestep.'
              )       ,     )

        if not self.is_scale_input_called:
          logger.warning(
              'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
              'See `StableDiffusionPipeline` for a usage example.'			)

        if isinstance(SCREAMING_SNAKE_CASE_       ,     torch.Tensor			):
          lowerCAmelCase_  :							Union[str, Any]								=					timestep.to(self.timesteps.device			)

        lowerCAmelCase_  :							Optional[int]								=					(self.timesteps == timestep).nonzero().item()
        lowerCAmelCase_  :							Dict								=					self.sigmas[step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
          lowerCAmelCase_  :							List[str]								=					sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
          # * c_out + input * c_skip
          lowerCAmelCase_  :							Tuple								=					model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**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`"			)

        lowerCAmelCase_  :							Any								=					self.sigmas[step_index]
        lowerCAmelCase_  :							Union[str, Any]								=					self.sigmas[step_index + 1]
        lowerCAmelCase_  :							List[str]								=					(sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
        lowerCAmelCase_  :							Dict								=					(sigma_to**2 - sigma_up**2) ** 0.5

        # 2. Convert to an ODE derivative
        lowerCAmelCase_  :							Dict								=					(sample - pred_original_sample) / sigma

        lowerCAmelCase_  :							Tuple								=					sigma_down - sigma

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

        lowerCAmelCase_  :							Any								=					model_output.device
        lowerCAmelCase_  :							Optional[int]								=					randn_tensor(model_output.shape       ,     dtype=model_output.dtype       ,     device=SCREAMING_SNAKE_CASE_       ,     generator=SCREAMING_SNAKE_CASE_			)

        lowerCAmelCase_  :							Optional[Any]								=					prev_sample + noise * sigma_up

        if not return_dict:
          return (prev_sample,)

        return EulerAncestralDiscreteSchedulerOutput(
            prev_sample=SCREAMING_SNAKE_CASE_       ,     pred_original_sample=SCREAMING_SNAKE_CASE_			)



      def 	SCREAMING_SNAKE_CASE__					( self							: Dict       ,     SCREAMING_SNAKE_CASE_							: torch.FloatTensor       ,     SCREAMING_SNAKE_CASE_							: torch.FloatTensor       ,     SCREAMING_SNAKE_CASE_							: torch.FloatTensor       ,     ):
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        lowerCAmelCase_  :							int								=					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_  :							Any								=					self.timesteps.to(original_samples.device       ,     dtype=torch.floataa			)
          lowerCAmelCase_  :							str								=					timesteps.to(original_samples.device       ,     dtype=torch.floataa			)
        else:
          lowerCAmelCase_  :							Dict								=					self.timesteps.to(original_samples.device			)
          lowerCAmelCase_  :							List[str]								=					timesteps.to(original_samples.device			)

        lowerCAmelCase_  :							Any								=					[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

        lowerCAmelCase_  :							List[str]								=					original_samples + noise * sigma
        return noisy_samples





      def __len__( self							: List[Any]			):
        return self.config.num_train_timesteps





