



'''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 ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput

def 	a_					(							_lowerCAmelCase	,_lowerCAmelCase=0.999	,_lowerCAmelCase="cosine"	,)				->				Tuple:
  if alpha_transform_type == "cosine":

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

  elif alpha_transform_type == "exp":

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

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

  __lowerCamelCase	:	Union[str, Any]   	=			[]
  for i in range(_lowerCAmelCase	):
    __lowerCamelCase	:	int   	=			i / num_diffusion_timesteps
    __lowerCamelCase	:	Optional[Any]   	=			(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  lowerCamelCase_   (    SCREAMING_SNAKE_CASE_       ,       SCREAMING_SNAKE_CASE_					):
  """simple docstring"""




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




  @register_to_config
  def __init__(			self				:     Optional[Any]      ,     _a				:     int = 1000      ,     _a				:     float = 0.00085      ,     _a				:     float = 0.012      ,     _a				:     str = "linear"      ,     _a				:     Optional[Union[np.ndarray, List[float]]] = None      ,     _a				:     str = "epsilon"      ,     _a				:     str = "linspace"      ,     _a				:     int = 0      ,     ) -> str:
    if trained_betas is not None:
      __lowerCamelCase	:	Optional[int]   	=			torch.tensor(_a      ,     dtype=torch.floataa       )
    elif beta_schedule == "linear":
      __lowerCamelCase	:	Union[str, Any]   	=			torch.linspace(_a      ,     _a      ,     _a      ,     dtype=torch.floataa       )
    elif beta_schedule == "scaled_linear":
      # this schedule is very specific to the latent diffusion model.
      __lowerCamelCase	:	Optional[int]   	=			(
          torch.linspace(beta_start**0.5      ,     beta_end**0.5      ,     _a      ,     dtype=torch.floataa       ) ** 2
      )
    elif beta_schedule == "squaredcos_cap_v2":
      # Glide cosine schedule
      __lowerCamelCase	:	Optional[Any]   	=			betas_for_alpha_bar(_a       )
    else:
      raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'       )

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

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




  def 						_lowercase					(			self				:     Dict      ,     _a				:     Tuple      ,     _a				:     Any=None       ) -> Optional[int]:
    if schedule_timesteps is None:
      __lowerCamelCase	:	Optional[Any]   	=			self.timesteps

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

    return indices[pos].item()




  @property
  def 						_lowercase					(			self				:     Optional[Any]       ) -> Optional[Any]:
    # 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				:     Tuple      ,     _a				:     torch.FloatTensor      ,     _a				:     Union[float, torch.FloatTensor]      ,     ) -> torch.FloatTensor:
    __lowerCamelCase	:	Union[str, Any]   	=			self.index_for_timestep(_a       )

    if self.state_in_first_order:
      __lowerCamelCase	:	Optional[Any]   	=			self.sigmas[step_index]
    else:
      __lowerCamelCase	:	Dict   	=			self.sigmas_interpol[step_index - 1]

    __lowerCamelCase	:	List[str]   	=			sample / ((sigma**2 + 1) ** 0.5)
    return sample




  def 						_lowercase					(			self				:     int      ,     _a				:     int      ,     _a				:     Union[str, torch.device] = None      ,     _a				:     Optional[int] = None      ,     ) -> int:
    __lowerCamelCase	:	List[str]   	=			num_inference_steps

    __lowerCamelCase	:	str   	=			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	:	List[str]   	=			np.linspace(0      ,     num_train_timesteps - 1      ,     _a      ,     dtype=_a       )[::-1].copy()
    elif self.config.timestep_spacing == "leading":
      __lowerCamelCase	:	Tuple   	=			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(0      ,     _a       ) * step_ratio).round()[::-1].copy().astype(_a       )
      timesteps += self.config.steps_offset
    elif self.config.timestep_spacing == "trailing":
      __lowerCamelCase	:	List[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
      __lowerCamelCase	:	Dict   	=			(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\'.'       )

    __lowerCamelCase	:	Optional[int]   	=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
    __lowerCamelCase	:	Optional[Any]   	=			torch.from_numpy(np.log(_a       )       ).to(_a       )

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

    # compute up and down sigmas
    __lowerCamelCase	:	Union[str, Any]   	=			sigmas.roll(-1       )
    __lowerCamelCase	:	Any   	=			0.0
    __lowerCamelCase	:	Tuple   	=			(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
    __lowerCamelCase	:	str   	=			(sigmas_next**2 - sigmas_up**2) ** 0.5
    __lowerCamelCase	:	List[Any]   	=			0.0

    # compute interpolated sigmas
    __lowerCamelCase	:	Dict   	=			sigmas.log().lerp(sigmas_down.log()      ,     0.5       ).exp()
    __lowerCamelCase	:	Tuple   	=			0.0

    # set sigmas
    __lowerCamelCase	:	Tuple   	=			torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2       ), sigmas[-1:]]       )
    __lowerCamelCase	:	Tuple   	=			torch.cat(
        [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2       ), sigmas_interpol[-1:]]       )
    __lowerCamelCase	:	List[str]   	=			torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2       ), sigmas_up[-1:]]       )
    __lowerCamelCase	:	List[str]   	=			torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2       ), sigmas_down[-1:]]       )

    if str(_a       ).startswith('mps'       ):
      # mps does not support float64
      __lowerCamelCase	:	Union[str, Any]   	=			torch.from_numpy(_a       ).to(_a      ,     dtype=torch.floataa       )
    else:
      __lowerCamelCase	:	Dict   	=			torch.from_numpy(_a       ).to(_a       )

    __lowerCamelCase	:	Any   	=			self.sigma_to_t(_a       ).to(_a      ,     dtype=timesteps.dtype       )
    __lowerCamelCase	:	Dict   	=			torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])      ,     dim=-1       ).flatten()

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

    __lowerCamelCase	:	Any   	=			None

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




  def 						_lowercase					(			self				:     List[Any]      ,     _a				:     Optional[int]       ) -> int:
    # get log sigma
    __lowerCamelCase	:	Optional[int]   	=			sigma.log()

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

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

    __lowerCamelCase	:	int   	=			self.log_sigmas[low_idx]
    __lowerCamelCase	:	int   	=			self.log_sigmas[high_idx]

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

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




  @property
  def 						_lowercase					(			self				:     List[str]       ) -> Any:
    return self.sample is None




  def 						_lowercase					(			self				:     Any      ,     _a				:     Union[torch.FloatTensor, np.ndarray]      ,     _a				:     Union[float, torch.FloatTensor]      ,     _a				:     Union[torch.FloatTensor, np.ndarray]      ,     _a				:     Optional[torch.Generator] = None      ,     _a				:     bool = True      ,     ) -> Union[SchedulerOutput, Tuple]:
    __lowerCamelCase	:	Optional[Any]   	=			self.index_for_timestep(_a       )

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

    if self.state_in_first_order:
      __lowerCamelCase	:	Dict   	=			self.sigmas[step_index]
      __lowerCamelCase	:	Union[str, Any]   	=			self.sigmas_interpol[step_index]
      __lowerCamelCase	:	Union[str, Any]   	=			self.sigmas_up[step_index]
      __lowerCamelCase	:	Optional[int]   	=			self.sigmas_down[step_index - 1]
    else:
      # 2nd order / KPDM2's method
      __lowerCamelCase	:	str   	=			self.sigmas[step_index - 1]
      __lowerCamelCase	:	Union[str, Any]   	=			self.sigmas_interpol[step_index - 1]
      __lowerCamelCase	:	int   	=			self.sigmas_up[step_index - 1]
      __lowerCamelCase	:	Tuple   	=			self.sigmas_down[step_index - 1]

    # 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	:	List[Any]   	=			sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

    __lowerCamelCase	:	Union[str, Any]   	=			model_output.device
    __lowerCamelCase	:	List[str]   	=			randn_tensor(model_output.shape      ,     dtype=model_output.dtype      ,     device=_a      ,     generator=_a       )

    # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
    if self.config.prediction_type == "epsilon":
      __lowerCamelCase	:	Dict   	=			sigma_hat if self.state_in_first_order else sigma_interpol
      __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_interpol
      __lowerCamelCase	:	str   	=			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
      __lowerCamelCase	:	Optional[int]   	=			(sample - pred_original_sample) / sigma_hat
      # 3. delta timestep
      __lowerCamelCase	:	Optional[Any]   	=			sigma_interpol - sigma_hat

      # store for 2nd order step
      __lowerCamelCase	:	Any   	=			sample
      __lowerCamelCase	:	Union[str, Any]   	=			dt
      __lowerCamelCase	:	str   	=			sample + derivative * dt
    else:
      # DPM-Solver-2
      # 2. Convert to an ODE derivative for 2nd order
      __lowerCamelCase	:	Optional[Any]   	=			(sample - pred_original_sample) / sigma_interpol
      # 3. delta timestep
      __lowerCamelCase	:	Union[str, Any]   	=			sigma_down - sigma_hat

      __lowerCamelCase	:	Optional[int]   	=			self.sample
      __lowerCamelCase	:	Tuple   	=			None

      __lowerCamelCase	:	Union[str, Any]   	=			sample + derivative * dt
      __lowerCamelCase	:	Optional[Any]   	=			prev_sample + noise * sigma_up

    if not return_dict:
      return (prev_sample,)

    return SchedulerOutput(prev_sample=_a       )




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

    __lowerCamelCase	:	Optional[Any]   	=			[self.index_for_timestep(_a      ,     _a       ) for t in timesteps]

    __lowerCamelCase	:	List[str]   	=			sigmas[step_indices].flatten()
    while len(sigma.shape       ) < len(original_samples.shape       ):
      __lowerCamelCase	:	Union[str, Any]   	=			sigma.unsqueeze(-1       )

    __lowerCamelCase	:	Optional[int]   	=			original_samples + noise * sigma
    return noisy_samples




  def __len__(			self				:     Union[str, Any]       ) -> List[Any]:
    return self.config.num_train_timesteps










'''simple docstring'''





import random






class  lowerCamelCase_   :
  """simple docstring"""




  def __init__(			self				:     Union[str, Any]      ,     _a				:     float      ,     _a				:     float       ) -> None:
    __lowerCamelCase	:	Optional[int]   	=			x
    __lowerCamelCase	:	Union[str, Any]   	=			y




  def 						_lowercase					(			self				:     Tuple       ) -> bool:
    return (self.x**2 + self.y**2) <= 1




  @classmethod
  def 						_lowercase					(			cls				:     List[Any]       ) -> Optional[int]:
    return cls(x=random.random()      ,     y=random.random()       )




def 	a_					(							_lowerCAmelCase	)				->				float:
  if number_of_simulations < 1:
    raise ValueError('At least one simulation is necessary to estimate PI.'	)

  __lowerCamelCase	:	Optional[int]   	=			0
  for _ in range(_lowerCAmelCase	):
    __lowerCamelCase	:	Dict   	=			Point.random_unit_square()

    if random_point.is_in_unit_circle():
      number_in_unit_circle += 1

  return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
   # import doctest

   # doctest.testmod()
   from math import pi

   _UpperCamelCase							    =						'Please enter the desired number of Monte Carlo simulations: '
   _UpperCamelCase							    =						estimate_pi(int(input(prompt).strip()))
   print(f'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')






