





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

import numpy as np
import torch
from scipy import integrate

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




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 				_a		(   _lowerCAmelCase       ):
				UpperCamelCase			=					42
				UpperCamelCase			=					None





def  a_       (							_lowercase ,		_lowercase=0.999 ,		_lowercase="cosine" ,		):
						if alpha_transform_type == "cosine":

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

						elif alpha_transform_type == "exp":

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

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

						_UpperCamelCase    :      List[Any]						     =					[]
						for i in range(_lowercase     ):
												_UpperCamelCase    :      Dict						     =					i / num_diffusion_timesteps
												_UpperCamelCase    :      Dict						     =					(i + 1) / num_diffusion_timesteps
												betas.append(min(1 - alpha_bar_fn(_lowercase     ) / alpha_bar_fn(_lowercase     ) ,		_lowercase     )     )
						return torch.tensor(_lowercase ,		dtype=torch.floataa     )






class 				_a		(   _lowerCAmelCase			,       _lowerCAmelCase       ):
				UpperCamelCase			=					[e.name for e in KarrasDiffusionSchedulers]
				UpperCamelCase			=					1






				@register_to_config
				def __init__(				self	:					int,				lowerCAmelCase__	:					int = 1_0_0_0,				lowerCAmelCase__	:					float = 0.0_001,				lowerCAmelCase__	:					float = 0.02,				lowerCAmelCase__	:					str = "linear",				lowerCAmelCase__	:					Optional[Union[np.ndarray, List[float]]] = None,				lowerCAmelCase__	:					Optional[bool] = False,				lowerCAmelCase__	:					str = "epsilon",				lowerCAmelCase__	:					str = "linspace",				lowerCAmelCase__	:					int = 0,				)			->   List[str]:




										'''simple docstring'''



										if trained_betas is not None:
																_UpperCamelCase    :      str						     =					torch.tensor(lowerCAmelCase__,				dtype=torch.floataa							)
										elif beta_schedule == "linear":
																_UpperCamelCase    :      int						     =					torch.linspace(lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__,				dtype=torch.floataa							)
										elif beta_schedule == "scaled_linear":
																# this schedule is very specific to the latent diffusion model.
																_UpperCamelCase    :      Optional[Any]						     =					(
																    torch.linspace(beta_start**0.5,				beta_end**0.5,				lowerCAmelCase__,				dtype=torch.floataa							) ** 2
																)
										elif beta_schedule == "squaredcos_cap_v2":
																# Glide cosine schedule
																_UpperCamelCase    :      Optional[Any]						     =					betas_for_alpha_bar(lowerCAmelCase__							)
										else:
																raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""							)

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

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

										# setable values
										_UpperCamelCase    :      Optional[int]						     =					None
										_UpperCamelCase    :      Optional[int]						     =					use_karras_sigmas
										self.set_timesteps(lowerCAmelCase__,				lowerCAmelCase__							)
										_UpperCamelCase    :      Any						     =					[]
										_UpperCamelCase    :      Union[str, Any]						     =					False






				@property
				def        snake_case			(				self	:					Tuple							)			->   List[str]:




										'''simple docstring'''



										if self.config.timestep_spacing in ["linspace", "trailing"]:
																return self.sigmas.max()

										return (self.sigmas.max() ** 2 + 1) ** 0.5






				def        snake_case			(				self	:					Optional[int],				lowerCAmelCase__	:					torch.FloatTensor,				lowerCAmelCase__	:					Union[float, torch.FloatTensor]							)			->   torch.FloatTensor:




										'''simple docstring'''



										if isinstance(lowerCAmelCase__,				torch.Tensor							):
																_UpperCamelCase    :      Optional[Any]						     =					timestep.to(self.timesteps.device							)
										_UpperCamelCase    :      int						     =					(self.timesteps == timestep).nonzero().item()
										_UpperCamelCase    :      Dict						     =					self.sigmas[step_index]
										_UpperCamelCase    :      Union[str, Any]						     =					sample / ((sigma**2 + 1) ** 0.5)
										_UpperCamelCase    :      str						     =					True
										return sample






				def        snake_case			(				self	:					List[Any],				lowerCAmelCase__	:					Optional[int],				lowerCAmelCase__	:					Optional[Any],				lowerCAmelCase__	:					Optional[int]							)			->   Any:




										'''simple docstring'''



										def lms_derivative(lowerCAmelCase__	:					Tuple							):
																_UpperCamelCase    :      Dict						     =					1.0
																for k in range(lowerCAmelCase__							):
																						if current_order == k:
																												continue
																						prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
																return prod

										_UpperCamelCase    :      int						     =					integrate.quad(lowerCAmelCase__,				self.sigmas[t],				self.sigmas[t + 1],				epsrel=1e-4							)[0]

										return integrated_coeff






				def        snake_case			(				self	:					int,				lowerCAmelCase__	:					int,				lowerCAmelCase__	:					Union[str, torch.device] = None							)			->   Tuple:




										'''simple docstring'''



										_UpperCamelCase    :      str						     =					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":
																_UpperCamelCase    :      List[Any]						     =					np.linspace(0,				self.config.num_train_timesteps - 1,				lowerCAmelCase__,				dtype=lowerCAmelCase__							)[
																    ::-1
																].copy()
										elif self.config.timestep_spacing == "leading":
																_UpperCamelCase    :      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
																_UpperCamelCase    :      Optional[int]						     =					(np.arange(0,				lowerCAmelCase__							) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__							)
																timesteps += self.config.steps_offset
										elif self.config.timestep_spacing == "trailing":
																_UpperCamelCase    :      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
																_UpperCamelCase    :      Optional[Any]						     =					(np.arange(self.config.num_train_timesteps,				0,				-step_ratio							)).round().copy().astype(lowerCAmelCase__							)
																timesteps -= 1
										else:
																raise ValueError(
																    f"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""							)

										_UpperCamelCase    :      Any						     =					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
										_UpperCamelCase    :      Optional[Any]						     =					np.log(lowerCAmelCase__							)
										_UpperCamelCase    :      Tuple						     =					np.interp(lowerCAmelCase__,				np.arange(0,				len(lowerCAmelCase__							)							),				lowerCAmelCase__							)

										if self.use_karras_sigmas:
																_UpperCamelCase    :      Dict						     =					self._convert_to_karras(in_sigmas=lowerCAmelCase__							)
																_UpperCamelCase    :      List[str]						     =					np.array([self._sigma_to_t(lowerCAmelCase__,				lowerCAmelCase__							) for sigma in sigmas]							)

										_UpperCamelCase    :      Optional[int]						     =					np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)

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

										_UpperCamelCase    :      Union[str, Any]						     =					[]






				def        snake_case			(				self	:					Optional[int],				lowerCAmelCase__	:					Union[str, Any],				lowerCAmelCase__	:					Union[str, Any]							)			->   Any:




										'''simple docstring'''



										_UpperCamelCase    :      str						     =					np.log(lowerCAmelCase__							)

										# get distribution
										_UpperCamelCase    :      str						     =					log_sigma - log_sigmas[:, np.newaxis]

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

										_UpperCamelCase    :      str						     =					log_sigmas[low_idx]
										_UpperCamelCase    :      List[Any]						     =					log_sigmas[high_idx]

										# interpolate sigmas
										_UpperCamelCase    :      List[str]						     =					(low - log_sigma) / (low - high)
										_UpperCamelCase    :      Union[str, Any]						     =					np.clip(lowerCAmelCase__,				0,				1							)

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






				def        snake_case			(				self	:					str,				lowerCAmelCase__	:					torch.FloatTensor							)			->   torch.FloatTensor:




										'''simple docstring'''



										_UpperCamelCase    :      float						     =					in_sigmas[-1].item()
										_UpperCamelCase    :      float						     =					in_sigmas[0].item()

										_UpperCamelCase    :      Tuple						     =					7.0  # 7.0 is the value used in the paper
										_UpperCamelCase    :      Optional[int]						     =					np.linspace(0,				1,				self.num_inference_steps							)
										_UpperCamelCase    :      Dict						     =					sigma_min ** (1 / rho)
										_UpperCamelCase    :      List[Any]						     =					sigma_max ** (1 / rho)
										_UpperCamelCase    :      Optional[int]						     =					(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
										return sigmas






				def        snake_case			(				self	:					int,				lowerCAmelCase__	:					torch.FloatTensor,				lowerCAmelCase__	:					Union[float, torch.FloatTensor],				lowerCAmelCase__	:					torch.FloatTensor,				lowerCAmelCase__	:					int = 4,				lowerCAmelCase__	:					bool = True,				)			->   Union[LMSDiscreteSchedulerOutput, Tuple]:




										'''simple docstring'''



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

										if isinstance(lowerCAmelCase__,				torch.Tensor							):
																_UpperCamelCase    :      Union[str, Any]						     =					timestep.to(self.timesteps.device							)
										_UpperCamelCase    :      Optional[int]						     =					(self.timesteps == timestep).nonzero().item()
										_UpperCamelCase    :      List[str]						     =					self.sigmas[step_index]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
																_UpperCamelCase    :      Union[str, Any]						     =					sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
																# * c_out + input * c_skip
																_UpperCamelCase    :      Tuple						     =					model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
										elif self.config.prediction_type == "sample":
																_UpperCamelCase    :      List[str]						     =					model_output
										else:
																raise ValueError(
																    f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"""							)

										# 2. Convert to an ODE derivative
										_UpperCamelCase    :      List[Any]						     =					(sample - pred_original_sample) / sigma
										self.derivatives.append(lowerCAmelCase__							)
										if len(self.derivatives							) > order:
																self.derivatives.pop(0							)

										# 3. Compute linear multistep coefficients
										_UpperCamelCase    :      List[str]						     =					min(step_index + 1,				lowerCAmelCase__							)
										_UpperCamelCase    :      List[Any]						     =					[self.get_lms_coefficient(lowerCAmelCase__,				lowerCAmelCase__,				lowerCAmelCase__							) for curr_order in range(lowerCAmelCase__							)]

										# 4. Compute previous sample based on the derivatives path
										_UpperCamelCase    :      Dict						     =					sample + sum(
										    coeff * derivative for coeff, derivative in zip(lowerCAmelCase__,				reversed(self.derivatives							)							)							)

										if not return_dict:
																return (prev_sample,)

										return LMSDiscreteSchedulerOutput(prev_sample=lowerCAmelCase__,				pred_original_sample=lowerCAmelCase__							)






				def        snake_case			(				self	:					Union[str, Any],				lowerCAmelCase__	:					torch.FloatTensor,				lowerCAmelCase__	:					torch.FloatTensor,				lowerCAmelCase__	:					torch.FloatTensor,				)			->   torch.FloatTensor:




										'''simple docstring'''



										_UpperCamelCase    :      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(lowerCAmelCase__							):
																# mps does not support float64
																_UpperCamelCase    :      str						     =					self.timesteps.to(original_samples.device,				dtype=torch.floataa							)
																_UpperCamelCase    :      Dict						     =					timesteps.to(original_samples.device,				dtype=torch.floataa							)
										else:
																_UpperCamelCase    :      List[str]						     =					self.timesteps.to(original_samples.device							)
																_UpperCamelCase    :      int						     =					timesteps.to(original_samples.device							)

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

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

										_UpperCamelCase    :      List[Any]						     =					original_samples + noise * sigma
										return noisy_samples






				def __len__(				self	:					Any							)			->   int:




										'''simple docstring'''



										return self.config.num_train_timesteps










"""simple docstring"""




def  a_       (							_lowercase ,		_lowercase ,		_lowercase ,		_lowercase     ):
						return len_board * len_board_column * row + column





def  a_       (							_lowercase ,		_lowercase ,		_lowercase ,		_lowercase ,		_lowercase ,		_lowercase ,		):

						if board[row][column] != word[word_index]:
												return False

						if word_index == len(_lowercase     ) - 1:
												return True

						_UpperCamelCase    :      Union[str, Any]						     =					[(0, 1), (0, -1), (-1, 0), (1, 0)]
						_UpperCamelCase    :      List[str]						     =					len(_lowercase     )
						_UpperCamelCase    :      Optional[Any]						     =					len(board[0]     )
						for direction in traverts_directions:
												_UpperCamelCase    :      Union[str, Any]						     =					row + direction[0]
												_UpperCamelCase    :      List[Any]						     =					column + direction[1]
												if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
																		continue

												_UpperCamelCase    :      Optional[Any]						     =					get_point_key(_lowercase ,		_lowercase ,		_lowercase ,		_lowercase     )
												if key in visited_points_set:
																		continue

												visited_points_set.add(_lowercase     )
												if exits_word(_lowercase ,		_lowercase ,		_lowercase ,		_lowercase ,		word_index + 1 ,		_lowercase     ):
																		return True

												visited_points_set.remove(_lowercase     )

						return False





def  a_       (							_lowercase ,		_lowercase     ):
						_UpperCamelCase    :      Optional[Any]						     =					(
						    '''The board should be a non empty matrix of single chars strings.'''
						)

						_UpperCamelCase    :      int						     =					len(_lowercase     )
						if not isinstance(_lowercase ,		_lowercase     ) or len(_lowercase     ) == 0:
												raise ValueError(_lowercase     )

						for row in board:
												if not isinstance(_lowercase ,		_lowercase     ) or len(_lowercase     ) == 0:
																		raise ValueError(_lowercase     )

												for item in row:
																		if not isinstance(_lowercase ,		_lowercase     ) or len(_lowercase     ) != 1:
																								raise ValueError(_lowercase     )

    # Validate word
						if not isinstance(_lowercase ,		_lowercase     ) or len(_lowercase     ) == 0:
												raise ValueError(
												    '''The word parameter should be a string of length greater than 0.'''     )

						_UpperCamelCase    :      List[str]						     =					len(board[0]     )
						for i in range(_lowercase     ):
												for j in range(_lowercase     ):
																		if exits_word(
																		    _lowercase ,		_lowercase ,		_lowercase ,		_lowercase ,		0 ,		{get_point_key(_lowercase ,		_lowercase ,		_lowercase ,		_lowercase     )}     ):
																								return True

						return False


if __name__ == "__main__":
						import doctest

						doctest.testmod()



