


import sys
def 				UpperCAmelCase_					(							__snake_case						)     ->			str:







 """simple docstring"""


 _lowercase							      =len(__snake_case						)
 _lowercase							      =[[0 for x in range(__snake_case						)] for x in range(__snake_case						)]
 _lowercase							      =[[0 for x in range(__snake_case						)] for x in range(__snake_case						)]

 for chain_length in range(2     ,						__snake_case						):
  for a in range(1     ,						n - chain_length + 1						):
   _lowercase							      =a + chain_length - 1

   _lowercase							      =sys.maxsize
   for c in range(__snake_case     ,						__snake_case						):
    _lowercase							      =(
        matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
    )
    if cost < matrix[a][b]:
     _lowercase							      =cost
     _lowercase							      =c
 return matrix, sol
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case						)     ->			str:







 """simple docstring"""


 if i == j:
  print('''A''' + str(__snake_case						)     ,						end=''' '''						)
 else:
  print('''('''     ,						end=''' '''						)
  print_optiomal_solution(__snake_case     ,						__snake_case     ,						optimal_solution[i][j]						)
  print_optiomal_solution(__snake_case     ,						optimal_solution[i][j] + 1     ,						__snake_case						)
  print(''')'''     ,						end=''' '''						)
def 				UpperCAmelCase_					(							)     ->			Union[str, Any]:







 """simple docstring"""


 _lowercase							      =[30, 35, 15, 5, 10, 20, 25]
 _lowercase							      =len(__snake_case						)
 # Size of matrix created from above array will be
 # 30*35 35*15 15*5 5*10 10*20 20*25
 _lowercase      ,    _lowercase							      =matrix_chain_order(__snake_case						)

 print('''No. of Operation required: ''' + str(matrix[1][n - 1]						)						)
 print_optiomal_solution(__snake_case     ,						1     ,						n - 1						)


if __name__ == "__main__":
  main()





# 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       lowerCamelCase__   (       lowerCAmelCase   ,							lowerCAmelCase):
     SCREAMING_SNAKE_CASE__      			=			1





     @register_to_config
     def __init__(self		,     UpperCAmelCase=2_0_0_0		,     UpperCAmelCase=0.1		,     UpperCAmelCase=2_0		,     UpperCAmelCase=1e-3       )     ->   List[str]:
      _lowercase							      =None
      _lowercase							      =None
      _lowercase							      =None





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase = None       )     ->   str:
      _lowercase							      =torch.linspace(1		,     self.config.sampling_eps		,     UpperCAmelCase		,     device=UpperCAmelCase       )





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase=None       )     ->   Optional[int]:
      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
      _lowercase							      =(
          -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
      )
      _lowercase							      =torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff       )       )
      _lowercase							      =std.flatten()
      while len(std.shape       ) < len(score.shape       ):
       _lowercase							      =std.unsqueeze(-1       )
      _lowercase							      =-score / std

      # compute
      _lowercase							      =-1.0 / len(self.timesteps       )

      _lowercase							      =self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
      _lowercase							      =beta_t.flatten()
      while len(beta_t.shape       ) < len(x.shape       ):
       _lowercase							      =beta_t.unsqueeze(-1       )
      _lowercase							      =-0.5 * beta_t * x

      _lowercase							      =torch.sqrt(UpperCAmelCase       )
      _lowercase							      =drift - diffusion**2 * score
      _lowercase							      =x + drift * dt

      # add noise
      _lowercase							      =randn_tensor(x.shape		,     layout=x.layout		,     generator=UpperCAmelCase		,     device=x.device		,     dtype=x.dtype       )
      _lowercase							      =x_mean + diffusion * math.sqrt(-dt       ) * noise

      return x, x_mean





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

