


# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin



class A__     ( A__				,		A__  ):



  """simple docstring"""



  _lowercase									=		1

  @register_to_config
  def __init__( self			:  Optional[Any]				,				lowerCamelCase__			:  int=2_000				,				lowerCamelCase__			:  List[str]=0.1				,				lowerCamelCase__			:  Tuple=20				,				lowerCamelCase__			:  Dict=1E-3       ):
        a__	:  Union[str, Any]     =   None
        a__	:  Dict     =   None
        a__	:  List[str]     =   None

  def    _UpperCamelCase( self			:  str				,				lowerCamelCase__			:  Optional[Any]				,				lowerCamelCase__			:  Union[str, torch.device] = None       ):
        a__	:  Optional[Any]     =   torch.linspace(1				,				self.config.sampling_eps				,				lowerCamelCase__				,				device=lowerCamelCase__       )

  def    _UpperCamelCase( self			:  Any				,				lowerCamelCase__			:  Optional[Any]				,				lowerCamelCase__			:  Dict				,				lowerCamelCase__			:  List[str]				,				lowerCamelCase__			:  Tuple=None       ):
        if self.timesteps is None:
              raise ValueError(
                  "`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"       )

        # TODO(Patrick) better comments + non-PyTorch
        # postprocess model score
        a__	:  Optional[int]     =   (
            -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
        )
        a__	:  Optional[Any]     =   torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff       )       )
        a__	:  Any     =   std.flatten()
        while len(std.shape       ) < len(score.shape       ):
              a__	:  Union[str, Any]     =   std.unsqueeze(-1       )
        a__	:  int     =   -score / std

        # compute
        a__	:  List[Any]     =   -1.0 / len(self.timesteps       )

        a__	:  List[str]     =   self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
        a__	:  Any     =   beta_t.flatten()
        while len(beta_t.shape       ) < len(x.shape       ):
              a__	:  int     =   beta_t.unsqueeze(-1       )
        a__	:  Any     =   -0.5 * beta_t * x

        a__	:  Tuple     =   torch.sqrt(lowerCamelCase__       )
        a__	:  int     =   drift - diffusion**2 * score
        a__	:  int     =   x + drift * dt

        # add noise
        a__	:  Optional[int]     =   randn_tensor(x.shape				,				layout=x.layout				,				generator=lowerCamelCase__				,				device=x.device				,				dtype=x.dtype       )
        a__	:  str     =   x_mean + diffusion * math.sqrt(-dt       ) * noise

        return x, x_mean

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



"""simple docstring"""




from __future__ import annotations

import typing
from collections import Counter




def 			_lowerCAmelCase		(		_UpperCamelCase    ):






  """simple docstring"""



  _lowercase:      typing.Counter[int]   			=  Counter()
  for base in range(1			,					max_perimeter + 1    ):
    for perpendicular in range(_UpperCamelCase			,					max_perimeter + 1    ):
      _lowercase:      str   			=  (base * base + perpendicular * perpendicular) ** 0.5
      if hypotenuse == int(_UpperCamelCase    ):
        _lowercase:      str   			=  int(base + perpendicular + hypotenuse    )
        if perimeter > max_perimeter:
          continue
        triplets[perimeter] += 1
  return triplets




def 			_lowerCAmelCase		(		_UpperCamelCase = 1_000    ):






  """simple docstring"""



  _lowercase:      int   			=  pythagorean_triple(_UpperCamelCase    )
  return triplets.most_common(1    )[0][0]


if __name__ == "__main__":
  print(f"""Perimeter {solution()} has maximum solutions""")
