
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


__SCREAMING_SNAKE_CASE     :				Union[str, Any]      	=       logging.get_logger(__name__)  # pylint: disable=invalid-name


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerAncestralDiscrete
class 						__magic_name__				(  snake_case      ):
		_lowerCAmelCase						=		42
		_lowerCAmelCase						=		None



def       UpperCAmelCase__							(    __magic_name__  :       Optional[int]							,					__magic_name__  :       List[Any]=0.999							,					__magic_name__  :       Dict="cosine"							,					):


					'''simple docstring'''

					if alpha_transform_type == "cosine":

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

					elif alpha_transform_type == "exp":

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

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

					lowerCAmelCase						:   Dict							=       []
					for i in range(__magic_name__					):
										lowerCAmelCase						:   Tuple							=       i / num_diffusion_timesteps
										lowerCAmelCase						:   List[Any]							=       (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 						__magic_name__				(  snake_case,			snake_case      ):
		_lowerCAmelCase						=		[e.name for e in KarrasDiffusionSchedulers]
		_lowerCAmelCase						=		1





		@register_to_config
		def __init__(							self      :		int  ,					lowerCamelCase__      :		int = 1_0_0_0  ,					lowerCamelCase__      :		float = 0.0_0_0_1  ,					lowerCamelCase__      :		float = 0.0_2  ,					lowerCamelCase__      :		str = "linear"  ,					lowerCamelCase__      :		Optional[Union[np.ndarray, List[float]]] = None  ,					lowerCamelCase__      :		str = "epsilon"  ,					lowerCamelCase__      :		str = "linspace"  ,					lowerCamelCase__      :		int = 0  ,					):
							if trained_betas is not None:
												lowerCAmelCase						:   Optional[Any]							=       torch.tensor(lowerCamelCase__  ,					dtype=torch.floataa			)
							elif beta_schedule == "linear":
												lowerCAmelCase						:   List[str]							=       torch.linspace(lowerCamelCase__  ,					lowerCamelCase__  ,					lowerCamelCase__  ,					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  ,					lowerCamelCase__  ,					dtype=torch.floataa			) ** 2
												)
							elif beta_schedule == "squaredcos_cap_v2":
												# Glide cosine schedule
												lowerCAmelCase						:   Tuple							=       betas_for_alpha_bar(lowerCamelCase__			)
							else:
												raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''			)

							lowerCAmelCase						:   Optional[int]							=       1.0 - self.betas
							lowerCAmelCase						:   Optional[int]							=       torch.cumprod(self.alphas  ,					dim=0			)

							lowerCAmelCase						:   Union[str, Any]							=       np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
							lowerCAmelCase						:   int							=       np.concatenate([sigmas[::-1], [0.0]]			).astype(np.floataa			)
							lowerCAmelCase						:   int							=       torch.from_numpy(lowerCamelCase__			)

							# setable values
							lowerCAmelCase						:   str							=       None
							lowerCAmelCase						:   str							=       np.linspace(0  ,					num_train_timesteps - 1  ,					lowerCamelCase__  ,					dtype=lowerCamelCase__			)[::-1].copy()
							lowerCAmelCase						:   str							=       torch.from_numpy(lowerCamelCase__			)
							lowerCAmelCase						:   Tuple							=       False





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





		def  _A							(							self      :		Optional[int]  ,					lowerCamelCase__      :		int  ,					lowerCamelCase__      :		Union[str, torch.device] = None			):
							lowerCAmelCase						:   Tuple							=       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						:   int							=       np.linspace(0  ,					self.config.num_train_timesteps - 1  ,					lowerCamelCase__  ,					dtype=lowerCamelCase__			)[
												    ::-1
												].copy()
							elif self.config.timestep_spacing == "leading":
												lowerCAmelCase						:   str							=       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						:   Optional[int]							=       (np.arange(0  ,					lowerCamelCase__			) * step_ratio).round()[::-1].copy().astype(lowerCamelCase__			)
												timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
												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(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\'.'''			)

							lowerCAmelCase						:   Union[str, Any]							=       np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
							lowerCAmelCase						:   Tuple							=       np.interp(lowerCamelCase__  ,					np.arange(0  ,					len(lowerCamelCase__			)			)  ,					lowerCamelCase__			)
							lowerCAmelCase						:   Any							=       np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
							lowerCAmelCase						:   List[str]							=       torch.from_numpy(lowerCamelCase__			).to(device=lowerCamelCase__			)
							if str(lowerCamelCase__			).startswith('''mps'''			):
												# mps does not support float64
												lowerCAmelCase						:   Optional[Any]							=       torch.from_numpy(lowerCamelCase__			).to(lowerCamelCase__  ,					dtype=torch.floataa			)
							else:
												lowerCAmelCase						:   Union[str, Any]							=       torch.from_numpy(lowerCamelCase__			).to(device=lowerCamelCase__			)





		def  _A							(							self      :		List[Any]  ,					lowerCamelCase__      :		torch.FloatTensor  ,					lowerCamelCase__      :		Union[float, torch.FloatTensor]  ,					lowerCamelCase__      :		torch.FloatTensor  ,					lowerCamelCase__      :		Optional[torch.Generator] = None  ,					lowerCamelCase__      :		bool = True  ,					):

							if (
							    isinstance(lowerCamelCase__  ,					lowerCamelCase__			)
							    or isinstance(lowerCamelCase__  ,					torch.IntTensor			)
							    or isinstance(lowerCamelCase__  ,					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(lowerCamelCase__  ,					torch.Tensor			):
												lowerCAmelCase						:   Any							=       timestep.to(self.timesteps.device			)

							lowerCAmelCase						:   List[str]							=       (self.timesteps == timestep).nonzero().item()
							lowerCAmelCase						:   str							=       self.sigmas[step_index]

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
												lowerCAmelCase						:   Union[str, Any]							=       sample - sigma * model_output
							elif self.config.prediction_type == "v_prediction":
												# * c_out + input * c_skip
												lowerCAmelCase						:   Any							=       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						:   Optional[int]							=       self.sigmas[step_index]
							lowerCAmelCase						:   Union[str, Any]							=       self.sigmas[step_index + 1]
							lowerCAmelCase						:   Dict							=       (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
							lowerCAmelCase						:   Optional[int]							=       (sigma_to**2 - sigma_up**2) ** 0.5

							# 2. Convert to an ODE derivative
							lowerCAmelCase						:   Optional[int]							=       (sample - pred_original_sample) / sigma

							lowerCAmelCase						:   str							=       sigma_down - sigma

							lowerCAmelCase						:   str							=       sample + derivative * dt

							lowerCAmelCase						:   int							=       model_output.device
							lowerCAmelCase						:   Union[str, Any]							=       randn_tensor(model_output.shape  ,					dtype=model_output.dtype  ,					device=lowerCamelCase__  ,					generator=lowerCamelCase__			)

							lowerCAmelCase						:   str							=       prev_sample + noise * sigma_up

							if not return_dict:
												return (prev_sample,)

							return EulerAncestralDiscreteSchedulerOutput(
							    prev_sample=lowerCamelCase__  ,					pred_original_sample=lowerCamelCase__			)





		def  _A							(							self      :		List[str]  ,					lowerCamelCase__      :		torch.FloatTensor  ,					lowerCamelCase__      :		torch.FloatTensor  ,					lowerCamelCase__      :		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(lowerCamelCase__			):
												# mps does not support float64
												lowerCAmelCase						:   List[Any]							=       self.timesteps.to(original_samples.device  ,					dtype=torch.floataa			)
												lowerCAmelCase						:   Union[str, Any]							=       timesteps.to(original_samples.device  ,					dtype=torch.floataa			)
							else:
												lowerCAmelCase						:   Tuple							=       self.timesteps.to(original_samples.device			)
												lowerCAmelCase						:   Any							=       timesteps.to(original_samples.device			)

							lowerCAmelCase						:   Union[str, Any]							=       [(schedule_timesteps == t).nonzero().item() for t in timesteps]

							lowerCAmelCase						:   int							=       sigmas[step_indices].flatten()
							while len(sigma.shape			) < len(original_samples.shape			):
												lowerCAmelCase						:   List[Any]							=       sigma.unsqueeze(-1			)

							lowerCAmelCase						:   Any							=       original_samples + noise * sigma
							return noisy_samples





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


def       UpperCAmelCase__							(    __magic_name__  :       int = 99_80_01					):


					'''simple docstring'''

					lowerCAmelCase						:   Tuple							=       0
					for i in range(9_99							,					99							,					-1					):  # 3 digit numbers range from 999 down to 100
										for j in range(9_99							,					99							,					-1					):
															lowerCAmelCase						:   Any							=       str(i * j					)
															if product_string == product_string[::-1] and i * j < n:
																				lowerCAmelCase						:   Optional[int]							=       max(__magic_name__							,					i * j					)
					return answer


if __name__ == "__main__":
		print(f"""{solution() = }""")
