






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  UpperCamelCase    (			snake_case_   ):
 UpperCamelCase      : torch.FloatTensor
 UpperCamelCase      : Optional[torch.FloatTensor]    =      None







def     lowerCAmelCase__  (  UpperCamelCase__  ,     UpperCamelCase__=0.999  ,     UpperCamelCase__="cosine"  ,     ):



  '''simple docstring'''
  if alpha_transform_type == "cosine":

    def alpha_bar_fn(UpperCamelCase__       ):
      return math.cos((t + 0.008) / 1.008 * 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}"""       )

  _a						: List[Any]    =			[]
  for i in range(UpperCamelCase__       ):
    _a						: List[str]    =			i / num_diffusion_timesteps
    _a						: Any    =			(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  UpperCamelCase    (			snake_case_	,  snake_case_   ):
 UpperCamelCase      : int    =      [e.name for e in KarrasDiffusionSchedulers]
 UpperCamelCase      : Optional[Any]    =      1


 @register_to_config
 def __init__(  self	:		Union[str, Any]							,		UpperCAmelCase__	:		int = 1000							,		UpperCAmelCase__	:		float = 0.0_0_0_1							,		UpperCAmelCase__	:		float = 0.0_2							,		UpperCAmelCase__	:		str = "linear"							,		UpperCAmelCase__	:		Optional[Union[np.ndarray, List[float]]] = None							,		UpperCAmelCase__	:		Optional[bool] = False							,		UpperCAmelCase__	:		str = "epsilon"							,		UpperCAmelCase__	:		str = "linspace"							,		UpperCAmelCase__	:		int = 0							,		)      -> Tuple:
   if trained_betas is not None:
     _a						: Any    =			torch.tensor(UpperCAmelCase__							,		dtype=torch.floataa							)
   elif beta_schedule == "linear":
     _a						: Union[str, Any]    =			torch.linspace(UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__							,		dtype=torch.floataa							)
   elif beta_schedule == "scaled_linear":
     # this schedule is very specific to the latent diffusion model.
     _a						: Optional[int]    =			(
         torch.linspace(beta_start**0.5							,		beta_end**0.5							,		UpperCAmelCase__							,		dtype=torch.floataa							) ** 2
     )
   elif beta_schedule == "squaredcos_cap_v2":
     # Glide cosine schedule
     _a						: List[str]    =			betas_for_alpha_bar(UpperCAmelCase__							)
   else:
     raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""							)

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

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

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


 @property
 def _lowercase			(  self	:		Any							)      -> 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	:		Optional[int]							,		UpperCAmelCase__	:		torch.FloatTensor							,		UpperCAmelCase__	:		Union[float, torch.FloatTensor]							)      -> torch.FloatTensor:
   if isinstance(UpperCAmelCase__							,		torch.Tensor							):
     _a						: Optional[Any]    =			timestep.to(self.timesteps.device							)
   _a						: int    =			(self.timesteps == timestep).nonzero().item()
   _a						: Optional[int]    =			self.sigmas[step_index]
   _a						: Optional[int]    =			sample / ((sigma**2 + 1) ** 0.5)
   _a						: str    =			True
   return sample


 def _lowercase			(  self	:		List[str]							,		UpperCAmelCase__	:		Optional[int]							,		UpperCAmelCase__	:		Tuple							,		UpperCAmelCase__	:		Optional[Any]							)      -> Optional[int]:

   def lms_derivative(UpperCAmelCase__	:		Optional[Any]							):
     _a						: Any    =			1.0
     for k in range(UpperCAmelCase__							):
       if current_order == k:
         continue
       prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
     return prod

   _a						: Any    =			integrate.quad(UpperCAmelCase__							,		self.sigmas[t]							,		self.sigmas[t + 1]							,		epsrel=1E-4							)[0]

   return integrated_coeff


 def _lowercase			(  self	:		Any							,		UpperCAmelCase__	:		int							,		UpperCAmelCase__	:		Union[str, torch.device] = None							)      -> Dict:
   _a						: Optional[int]    =			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":
     _a						: Any    =			np.linspace(0							,		self.config.num_train_timesteps - 1							,		UpperCAmelCase__							,		dtype=UpperCAmelCase__							)[
         ::-1
     ].copy()
   elif self.config.timestep_spacing == "leading":
     _a						: 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
     _a						: List[Any]    =			(np.arange(0							,		UpperCAmelCase__							) * step_ratio).round()[::-1].copy().astype(UpperCAmelCase__							)
     timesteps += self.config.steps_offset
   elif self.config.timestep_spacing == "trailing":
     _a						: Tuple    =			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
     _a						: str    =			(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'."""							)

   _a						: List[Any]    =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
   _a						: str    =			np.log(UpperCAmelCase__							)
   _a						: Dict    =			np.interp(UpperCAmelCase__							,		np.arange(0							,		len(UpperCAmelCase__							)							)							,		UpperCAmelCase__							)

   if self.use_karras_sigmas:
     _a						: int    =			self._convert_to_karras(in_sigmas=UpperCAmelCase__							)
     _a						: Optional[int]    =			np.array([self._sigma_to_t(UpperCAmelCase__							,		UpperCAmelCase__							) for sigma in sigmas]							)

   _a						: List[str]    =			np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)

   _a						: int    =			torch.from_numpy(UpperCAmelCase__							).to(device=UpperCAmelCase__							)
   if str(UpperCAmelCase__							).startswith("""mps"""							):
     # mps does not support float64
     _a						: Tuple    =			torch.from_numpy(UpperCAmelCase__							).to(UpperCAmelCase__							,		dtype=torch.floataa							)
   else:
     _a						: int    =			torch.from_numpy(UpperCAmelCase__							).to(device=UpperCAmelCase__							)

   _a						: Any    =			[]


 def _lowercase			(  self	:		Any							,		UpperCAmelCase__	:		Optional[Any]							,		UpperCAmelCase__	:		Any							)      -> Dict:
   # get log sigma
   _a						: Union[str, Any]    =			np.log(UpperCAmelCase__							)

   # get distribution
   _a						: Union[str, Any]    =			log_sigma - log_sigmas[:, np.newaxis]

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

   _a						: Optional[int]    =			log_sigmas[low_idx]
   _a						: Any    =			log_sigmas[high_idx]

   # interpolate sigmas
   _a						: int    =			(low - log_sigma) / (low - high)
   _a						: List[str]    =			np.clip(UpperCAmelCase__							,		0							,		1							)

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


 def _lowercase			(  self	:		List[str]							,		UpperCAmelCase__	:		torch.FloatTensor							)      -> torch.FloatTensor:
   _a						: float    =			in_sigmas[-1].item()
   _a						: float    =			in_sigmas[0].item()

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


 def _lowercase			(  self	:		Dict							,		UpperCAmelCase__	:		torch.FloatTensor							,		UpperCAmelCase__	:		Union[float, torch.FloatTensor]							,		UpperCAmelCase__	:		torch.FloatTensor							,		UpperCAmelCase__	:		int = 4							,		UpperCAmelCase__	:		bool = True							,		)      -> Union[LMSDiscreteSchedulerOutput, Tuple]:
   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(UpperCAmelCase__							,		torch.Tensor							):
     _a						: Optional[Any]    =			timestep.to(self.timesteps.device							)
   _a						: str    =			(self.timesteps == timestep).nonzero().item()
   _a						: int    =			self.sigmas[step_index]

   # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
   if self.config.prediction_type == "epsilon":
     _a						: Optional[Any]    =			sample - sigma * model_output
   elif self.config.prediction_type == "v_prediction":
     # * c_out + input * c_skip
     _a						: Dict    =			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
   elif self.config.prediction_type == "sample":
     _a						: Tuple    =			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
   _a						: Dict    =			(sample - pred_original_sample) / sigma
   self.derivatives.append(UpperCAmelCase__							)
   if len(self.derivatives							) > order:
     self.derivatives.pop(0							)

   # 3. Compute linear multistep coefficients
   _a						: Optional[Any]    =			min(step_index + 1							,		UpperCAmelCase__							)
   _a						: Tuple    =			[self.get_lms_coefficient(UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__							) for curr_order in range(UpperCAmelCase__							)]

   # 4. Compute previous sample based on the derivatives path
   _a						: Optional[Any]    =			sample + sum(
       coeff * derivative for coeff, derivative in zip(UpperCAmelCase__							,		reversed(self.derivatives							)							)							)

   if not return_dict:
     return (prev_sample,)

   return LMSDiscreteSchedulerOutput(prev_sample=UpperCAmelCase__							,		pred_original_sample=UpperCAmelCase__							)


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

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

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

   _a						: str    =			original_samples + noise * sigma
   return noisy_samples







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









"""simple docstring"""




from __future__ import annotations

import sys

def     lowerCAmelCase__  (  UpperCamelCase__       ):



  '''simple docstring'''
  if n < 0:
    raise ValueError("""Negative arguments are not supported"""       )
  return _fib(UpperCamelCase__       )[0]

def     lowerCAmelCase__  (  UpperCamelCase__       ):



  '''simple docstring'''
  if n == 0:  # (F(0), F(1))
    return (0, 1)

  # F(2n) = F(n)[2F(n+1) − F(n)]
  # F(2n+1) = F(n+1)^2+F(n)^2
  _a   ,						_a						: Dict    =			_fib(n // 2       )
  _a						: Dict    =			a * (b * 2 - a)
  _a						: Optional[Any]    =			a * a + b * b
  return (d, c + d) if n % 2 else (c, d)


if __name__ == "__main__":
 _snake_case					   =     int(sys.argv[1])
 print(F'''fibonacci({n}) is {fibonacci(n)}''')

