
"""simple docstring"""
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 SchedulerMixin


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




@dataclass
class  _snake_case	(    __UpperCAmelCase							):
							SCREAMING_SNAKE_CASE		  =    42






class  _snake_case	(    __UpperCAmelCase			,					__UpperCAmelCase							):
							SCREAMING_SNAKE_CASE		  =    1






							@register_to_config
							def __init__(       self    :      int    ,			snake_case__    :      int = 4_0    ,			snake_case__    :      float = 0.002    ,			snake_case__    :      float = 80.0    ,			snake_case__    :      float = 0.5    ,			snake_case__    :      float = 1.0    ,			snake_case__    :      float = 7.0    ,			snake_case__    :      bool = True    ,			):






												"""simple docstring"""



												__a:    List[Any]		     =       sigma_max

												__a:    str		     =       np.linspace(0    ,			1    ,			__snake_case     )
												__a:    Tuple		     =       self._convert_to_karras(__snake_case     )
												__a:    Optional[int]		     =       self.sigma_to_t(__snake_case     )

												# setable values
												__a:    Optional[Any]		     =       None
												__a:    Optional[int]		     =       torch.from_numpy(__snake_case     )
												__a:    Tuple		     =       torch.from_numpy(__snake_case     )
												__a:    str		     =       False
												__a:    List[str]		     =       False






							def 				__lowercase	(       self    :      int    ,			snake_case__    :      Optional[Any]    ,			snake_case__    :      Optional[int]=None     ):






												"""simple docstring"""



												if schedule_timesteps is None:
																	__a:    Optional[Any]		     =       self.timesteps

												__a:    str		     =       (schedule_timesteps == timestep).nonzero()
												return indices.item()






							def 				__lowercase	(       self    :      Dict    ,			snake_case__    :      torch.FloatTensor    ,			snake_case__    :      Union[float, torch.FloatTensor]     ):






												"""simple docstring"""



												if isinstance(__snake_case    ,			torch.Tensor     ):
																	__a:    Dict		     =       timestep.to(self.timesteps.device     )
												__a:    int		     =       self.index_for_timestep(__snake_case     )
												__a:    List[Any]		     =       self.sigmas[step_idx]

												__a:    Dict		     =       sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

												__a:    Optional[int]		     =       True
												return sample






							def 				__lowercase	(       self    :      Any    ,			snake_case__    :      Union[float, np.ndarray]     ):






												"""simple docstring"""



												if not isinstance(__snake_case    ,			np.ndarray     ):
																	__a:    Union[str, Any]		     =       np.array(__snake_case    ,			dtype=np.floataa     )

												__a:    List[str]		     =       1_0_0_0 * 0.25 * np.log(sigmas + 1e-44     )

												return timesteps






							def 				__lowercase	(       self    :      Any    ,			snake_case__    :      Optional[int] = None    ,			snake_case__    :      Union[str, torch.device] = None    ,			snake_case__    :      Optional[List[int]] = None    ,			):






												"""simple docstring"""



												if num_inference_steps is None and timesteps is None:
																	raise ValueError("""Exactly one of `num_inference_steps` or `timesteps` must be supplied."""     )

												if num_inference_steps is not None and timesteps is not None:
																	raise ValueError("""Can only pass one of `num_inference_steps` or `timesteps`."""     )

												# Follow DDPMScheduler custom timesteps logic
												if timesteps is not None:
																	for i in range(1    ,			len(__snake_case     )     ):
																						if timesteps[i] >= timesteps[i - 1]:
																											raise ValueError("""`timesteps` must be in descending order."""     )

																	if timesteps[0] >= self.config.num_train_timesteps:
																						raise ValueError(
																						    f"""`timesteps` must start before `self.config.train_timesteps`:"""
																						    f""" {self.config.num_train_timesteps}."""     )

																	__a:    Any		     =       np.array(__snake_case    ,			dtype=np.intaa     )
																	__a:    Dict		     =       True
												else:
																	if num_inference_steps > self.config.num_train_timesteps:
																						raise ValueError(
																						    f"""`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"""
																						    f""" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"""
																						    f""" maximal {self.config.num_train_timesteps} timesteps."""     )

																	__a:    Optional[Any]		     =       num_inference_steps

																	__a:    Optional[int]		     =       self.config.num_train_timesteps // self.num_inference_steps
																	__a:    Optional[Any]		     =       (np.arange(0    ,			__snake_case     ) * step_ratio).round()[::-1].copy().astype(np.intaa     )
																	__a:    Tuple		     =       False

												# Map timesteps to Karras sigmas directly for multistep sampling
												# See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
												__a:    Tuple		     =       self.config.num_train_timesteps
												__a:    Optional[int]		     =       timesteps[::-1].copy()
												__a:    str		     =       ramp / (num_train_timesteps - 1)
												__a:    Optional[int]		     =       self._convert_to_karras(__snake_case     )
												__a:    List[Any]		     =       self.sigma_to_t(__snake_case     )

												__a:    Optional[Any]		     =       np.concatenate([sigmas, [self.sigma_min]]     ).astype(np.floataa     )
												__a:    Any		     =       torch.from_numpy(__snake_case     ).to(device=__snake_case     )

												if str(__snake_case     ).startswith("""mps"""     ):
																	# mps does not support float64
																	__a:    int		     =       torch.from_numpy(__snake_case     ).to(__snake_case    ,			dtype=torch.floataa     )
												else:
																	__a:    Optional[int]		     =       torch.from_numpy(__snake_case     ).to(device=__snake_case     )






							def 				__lowercase	(       self    :      Tuple    ,			snake_case__    :      Union[str, Any]     ):






												"""simple docstring"""



												__a:    float		     =       self.config.sigma_min
												__a:    float		     =       self.config.sigma_max

												__a:    str		     =       self.config.rho
												__a:    Tuple		     =       sigma_min ** (1 / rho)
												__a:    Optional[Any]		     =       sigma_max ** (1 / rho)
												__a:    Dict		     =       (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
												return sigmas






							def 				__lowercase	(       self    :      int    ,			snake_case__    :      Dict     ):






												"""simple docstring"""



												__a:    List[Any]		     =       self.config.sigma_data

												__a:    Optional[Any]		     =       sigma_data**2 / (sigma**2 + sigma_data**2)
												__a:    Tuple		     =       sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
												return c_skip, c_out






							def 				__lowercase	(       self    :      Optional[int]    ,			snake_case__    :      Optional[int]     ):






												"""simple docstring"""



												__a:    Optional[Any]		     =       self.config.sigma_min
												__a:    List[Any]		     =       self.config.sigma_data

												__a:    Optional[int]		     =       sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
												__a:    List[Any]		     =       (sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
												return c_skip, c_out






							def 				__lowercase	(       self    :      Optional[int]    ,			snake_case__    :      torch.FloatTensor    ,			snake_case__    :      Union[float, torch.FloatTensor]    ,			snake_case__    :      torch.FloatTensor    ,			snake_case__    :      Optional[torch.Generator] = None    ,			snake_case__    :      bool = True    ,			):






												"""simple docstring"""



												if (
												    isinstance(__snake_case    ,			__snake_case     )
												    or isinstance(__snake_case    ,			torch.IntTensor     )
												    or isinstance(__snake_case    ,			torch.LongTensor     )
												):
																	raise ValueError(
																	    (
																	        """Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"""
																	        f""" `{self.__class__}.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(__snake_case    ,			torch.Tensor     ):
																	__a:    Optional[int]		     =       timestep.to(self.timesteps.device     )

												__a:    Optional[int]		     =       self.config.sigma_min
												__a:    List[str]		     =       self.config.sigma_max

												__a:    str		     =       self.index_for_timestep(__snake_case     )

												# sigma_next corresponds to next_t in original implementation
												__a:    Optional[int]		     =       self.sigmas[step_index]
												if step_index + 1 < self.config.num_train_timesteps:
																	__a:    str		     =       self.sigmas[step_index + 1]
												else:
																	# Set sigma_next to sigma_min
																	__a:    int		     =       self.sigmas[-1]

												# Get scalings for boundary conditions
												__a:    Dict		     =       self.get_scalings_for_boundary_condition(__snake_case     )

												# 1. Denoise model output using boundary conditions
												__a:    Any		     =       c_out * model_output + c_skip * sample
												if self.config.clip_denoised:
																	__a:    Any		     =       denoised.clamp(-1    ,			1     )

												# 2. Sample z ~ N(0, s_noise^2 * I)
												# Noise is not used for onestep sampling.
												if len(self.timesteps     ) > 1:
																	__a:    Tuple		     =       randn_tensor(
																	    model_output.shape    ,			dtype=model_output.dtype    ,			device=model_output.device    ,			generator=__snake_case     )
												else:
																	__a:    Tuple		     =       torch.zeros_like(__snake_case     )
												__a:    Dict		     =       noise * self.config.s_noise

												__a:    List[Any]		     =       sigma_next.clamp(min=__snake_case    ,			max=__snake_case     )

												# 3. Return noisy sample
												# tau = sigma_hat, eps = sigma_min
												__a:    Optional[int]		     =       denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

												if not return_dict:
																	return (prev_sample,)

												return CMStochasticIterativeSchedulerOutput(prev_sample=__snake_case     )






							def 				__lowercase	(       self    :      Optional[int]    ,			snake_case__    :      torch.FloatTensor    ,			snake_case__    :      torch.FloatTensor    ,			snake_case__    :      torch.FloatTensor    ,			):






												"""simple docstring"""



												__a:    Any		     =       self.sigmas.to(device=original_samples.device    ,			dtype=original_samples.dtype     )
												if original_samples.device.type == "mps" and torch.is_floating_point(__snake_case     ):
																	# mps does not support float64
																	__a:    Tuple		     =       self.timesteps.to(original_samples.device    ,			dtype=torch.floataa     )
																	__a:    Optional[Any]		     =       timesteps.to(original_samples.device    ,			dtype=torch.floataa     )
												else:
																	__a:    Optional[int]		     =       self.timesteps.to(original_samples.device     )
																	__a:    List[str]		     =       timesteps.to(original_samples.device     )

												__a:    Dict		     =       [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

												__a:    Tuple		     =       original_samples + noise * sigma
												return noisy_samples






							def __len__(       self    :      str     ):






												"""simple docstring"""



												return self.config.num_train_timesteps







'''simple docstring'''






def    lowercase_   (		lowercase__ = 400_0000    ) ->int:

						if n <= 1:
												return 0
						_snake_case: Union[str, Any]	       =		0
						_snake_case: List[Any]	       =		2
						_snake_case: Any	       =		0
						while 4 * b + a <= n:
												_snake_case       ,    _snake_case: int	       =		b, 4 * b + a
												count += a
						return count + b


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





