
"""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


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







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class 		lowerCamelCase__					(					__magic_name__				):





			'''simple docstring'''
			lowerCamelCase  					=		42
			lowerCamelCase  					=		None







def     _lowerCamelCase(__UpperCamelCase    , __UpperCamelCase=0.9_99    , __UpperCamelCase="cosine"    , )				-> int:
	if alpha_transform_type == "cosine":

		def alpha_bar_fn(__UpperCamelCase       ):
			return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2       ) ** 2

	elif alpha_transform_type == "exp":

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

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

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







class 		lowerCamelCase__					(					__magic_name__ ,	__magic_name__				):





			'''simple docstring'''
			lowerCamelCase  					=		[e.name for e in KarrasDiffusionSchedulers]
			lowerCamelCase  					=		1



			@register_to_config
			def __init__(							self     ,     __UpperCAmelCase = 10_00     ,     __UpperCAmelCase = 0.0_0_0_1     ,     __UpperCAmelCase = 0.0_2     ,     __UpperCAmelCase = "linear"     ,     __UpperCAmelCase = None     ,     __UpperCAmelCase = "epsilon"     ,     __UpperCAmelCase = "linear"     ,     __UpperCAmelCase = False     ,     __UpperCAmelCase = "linspace"     ,     __UpperCAmelCase = 0     ,     ) ->     Optional[int]:
				if trained_betas is not None:
					_lowerCAmelCase								=torch.tensor(__UpperCAmelCase     ,     dtype=torch.floataa  )
				elif beta_schedule == "linear":
					_lowerCAmelCase								=torch.linspace(__UpperCAmelCase     ,     __UpperCAmelCase     ,     __UpperCAmelCase     ,     dtype=torch.floataa  )
				elif beta_schedule == "scaled_linear":
					# this schedule is very specific to the latent diffusion model.
					_lowerCAmelCase								=(
					    torch.linspace(beta_start**0.5     ,     beta_end**0.5     ,     __UpperCAmelCase     ,     dtype=torch.floataa  ) ** 2
					)
				elif beta_schedule == "squaredcos_cap_v2":
					# Glide cosine schedule
					_lowerCAmelCase								=betas_for_alpha_bar(__UpperCAmelCase  )
				else:
					raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''  )

				_lowerCAmelCase								=1.0 - self.betas
				_lowerCAmelCase								=torch.cumprod(self.alphas     ,     dim=0  )

				_lowerCAmelCase								=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
				_lowerCAmelCase								=np.concatenate([sigmas[::-1], [0.0]]  ).astype(np.floataa  )
				_lowerCAmelCase								=torch.from_numpy(__UpperCAmelCase  )

				# setable values
				_lowerCAmelCase								=None
				_lowerCAmelCase								=np.linspace(0     ,     num_train_timesteps - 1     ,     __UpperCAmelCase     ,     dtype=__UpperCAmelCase  )[::-1].copy()
				_lowerCAmelCase								=torch.from_numpy(__UpperCAmelCase  )
				_lowerCAmelCase								=False
				_lowerCAmelCase								=use_karras_sigmas



			@property
			def 					_lowerCAmelCase		(							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 					_lowerCAmelCase		(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase  ) ->     torch.FloatTensor:
				if isinstance(__UpperCAmelCase     ,     torch.Tensor  ):
					_lowerCAmelCase								=timestep.to(self.timesteps.device  )
				_lowerCAmelCase								=(self.timesteps == timestep).nonzero().item()
				_lowerCAmelCase								=self.sigmas[step_index]

				_lowerCAmelCase								=sample / ((sigma**2 + 1) ** 0.5)

				_lowerCAmelCase								=True
				return sample



			def 					_lowerCAmelCase		(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase = None  ) ->     List[Any]:
				_lowerCAmelCase								=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								=np.linspace(0     ,     self.config.num_train_timesteps - 1     ,     __UpperCAmelCase     ,     dtype=__UpperCAmelCase  )[
					    ::-1
					].copy()
				elif self.config.timestep_spacing == "leading":
					_lowerCAmelCase								=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								=(np.arange(0     ,     __UpperCAmelCase  ) * step_ratio).round()[::-1].copy().astype(__UpperCAmelCase  )
					timesteps += self.config.steps_offset
				elif self.config.timestep_spacing == "trailing":
					_lowerCAmelCase								=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								=(np.arange(self.config.num_train_timesteps     ,     0     ,     -step_ratio  )).round().copy().astype(__UpperCAmelCase  )
					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								=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
				_lowerCAmelCase								=np.log(__UpperCAmelCase  )

				if self.config.interpolation_type == "linear":
					_lowerCAmelCase								=np.interp(__UpperCAmelCase     ,     np.arange(0     ,     len(__UpperCAmelCase  )  )     ,     __UpperCAmelCase  )
				elif self.config.interpolation_type == "log_linear":
					_lowerCAmelCase								=torch.linspace(np.log(sigmas[-1]  )     ,     np.log(sigmas[0]  )     ,     num_inference_steps + 1  ).exp()
				else:
					raise ValueError(
					    f'''{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'''
					    """ 'linear' or 'log_linear'"""  )

				if self.use_karras_sigmas:
					_lowerCAmelCase								=self._convert_to_karras(in_sigmas=__UpperCAmelCase     ,     num_inference_steps=self.num_inference_steps  )
					_lowerCAmelCase								=np.array([self._sigma_to_t(__UpperCAmelCase     ,     __UpperCAmelCase  ) for sigma in sigmas]  )

				_lowerCAmelCase								=np.concatenate([sigmas, [0.0]]  ).astype(np.floataa  )
				_lowerCAmelCase								=torch.from_numpy(__UpperCAmelCase  ).to(device=__UpperCAmelCase  )
				if str(__UpperCAmelCase  ).startswith("""mps"""  ):
					# mps does not support float64
					_lowerCAmelCase								=torch.from_numpy(__UpperCAmelCase  ).to(__UpperCAmelCase     ,     dtype=torch.floataa  )
				else:
					_lowerCAmelCase								=torch.from_numpy(__UpperCAmelCase  ).to(device=__UpperCAmelCase  )



			def 					_lowerCAmelCase		(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase  ) ->     Optional[int]:
				# get log sigma
				_lowerCAmelCase								=np.log(__UpperCAmelCase  )

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

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

				_lowerCAmelCase								=log_sigmas[low_idx]
				_lowerCAmelCase								=log_sigmas[high_idx]

				# interpolate sigmas
				_lowerCAmelCase								=(low - log_sigma) / (low - high)
				_lowerCAmelCase								=np.clip(__UpperCAmelCase     ,     0     ,     1  )

				# transform interpolation to time range
				_lowerCAmelCase								=(1 - w) * low_idx + w * high_idx
				_lowerCAmelCase								=t.reshape(sigma.shape  )
				return t



			def 					_lowerCAmelCase		(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase  ) ->     torch.FloatTensor:
				_lowerCAmelCase								=in_sigmas[-1].item()
				_lowerCAmelCase								=in_sigmas[0].item()

				_lowerCAmelCase								=7.0  # 7.0 is the value used in the paper
				_lowerCAmelCase								=np.linspace(0     ,     1     ,     __UpperCAmelCase  )
				_lowerCAmelCase								=sigma_min ** (1 / rho)
				_lowerCAmelCase								=sigma_max ** (1 / rho)
				_lowerCAmelCase								=(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
				return sigmas



			def 					_lowerCAmelCase		(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase     ,     __UpperCAmelCase     ,     __UpperCAmelCase = 0.0     ,     __UpperCAmelCase = 0.0     ,     __UpperCAmelCase = float("""inf"""  )     ,     __UpperCAmelCase = 1.0     ,     __UpperCAmelCase = None     ,     __UpperCAmelCase = True     ,     ) ->     Union[EulerDiscreteSchedulerOutput, Tuple]:

				if (
				    isinstance(__UpperCAmelCase     ,     __UpperCAmelCase  )
				    or isinstance(__UpperCAmelCase     ,     torch.IntTensor  )
				    or isinstance(__UpperCAmelCase     ,     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(__UpperCAmelCase     ,     torch.Tensor  ):
					_lowerCAmelCase								=timestep.to(self.timesteps.device  )

				_lowerCAmelCase								=(self.timesteps == timestep).nonzero().item()
				_lowerCAmelCase								=self.sigmas[step_index]

				_lowerCAmelCase								=min(s_churn / (len(self.sigmas  ) - 1)     ,     2**0.5 - 1  ) if s_tmin <= sigma <= s_tmax else 0.0

				_lowerCAmelCase								=randn_tensor(
				    model_output.shape     ,     dtype=model_output.dtype     ,     device=model_output.device     ,     generator=__UpperCAmelCase  )

				_lowerCAmelCase								=noise * s_noise
				_lowerCAmelCase								=sigma * (gamma + 1)

				if gamma > 0:
					_lowerCAmelCase								=sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

				# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
				# NOTE: "original_sample" should not be an expected prediction_type but is left in for
				# backwards compatibility
				if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
					_lowerCAmelCase								=model_output
				elif self.config.prediction_type == "epsilon":
					_lowerCAmelCase								=sample - sigma_hat * model_output
				elif self.config.prediction_type == "v_prediction":
					# * c_out + input * c_skip
					_lowerCAmelCase								=model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
				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
				_lowerCAmelCase								=(sample - pred_original_sample) / sigma_hat

				_lowerCAmelCase								=self.sigmas[step_index + 1] - sigma_hat

				_lowerCAmelCase								=sample + derivative * dt

				if not return_dict:
					return (prev_sample,)

				return EulerDiscreteSchedulerOutput(prev_sample=__UpperCAmelCase     ,     pred_original_sample=__UpperCAmelCase  )



			def 					_lowerCAmelCase		(							self     ,     __UpperCAmelCase     ,     __UpperCAmelCase     ,     __UpperCAmelCase     ,     ) ->     torch.FloatTensor:
				# Make sure sigmas and timesteps have the same device and dtype as original_samples
				_lowerCAmelCase								=self.sigmas.to(device=original_samples.device     ,     dtype=original_samples.dtype  )
				if original_samples.device.type == "mps" and torch.is_floating_point(__UpperCAmelCase  ):
					# mps does not support float64
					_lowerCAmelCase								=self.timesteps.to(original_samples.device     ,     dtype=torch.floataa  )
					_lowerCAmelCase								=timesteps.to(original_samples.device     ,     dtype=torch.floataa  )
				else:
					_lowerCAmelCase								=self.timesteps.to(original_samples.device  )
					_lowerCAmelCase								=timesteps.to(original_samples.device  )

				_lowerCAmelCase								=[(schedule_timesteps == t).nonzero().item() for t in timesteps]

				_lowerCAmelCase								=sigmas[step_indices].flatten()
				while len(sigma.shape  ) < len(original_samples.shape  ):
					_lowerCAmelCase								=sigma.unsqueeze(-1  )

				_lowerCAmelCase								=original_samples + noise * sigma
				return noisy_samples



			def __len__(							self  ) ->     Any:
				return self.config.num_train_timesteps





"""simple docstring"""


def     _lowerCamelCase(__UpperCamelCase = 4000000       )				-> int:
	_lowerCAmelCase								=1
	_lowerCAmelCase								=2
	_lowerCAmelCase								=0
	while j <= n:
		if j % 2 == 0:
			total += j
		_lowerCAmelCase						,							_lowerCAmelCase								=j, i + j

	return total


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



