





'''simple docstring'''




def 	UpperCAmelCase_							(					__lowercase							:      list[list]       )		->       list[list]:


     '''simple docstring'''



     _UpperCAmelCase     							=   current_set.copy()
     for row_index, row in enumerate(__lowercase       ):
          _UpperCAmelCase     							=   row[0]
          for column_index, column in enumerate(__lowercase       ):
               if magnitude == 0:
                    _UpperCAmelCase     							=   column
                    continue
               _UpperCAmelCase     							=   column / magnitude
    # Subtract to cancel term
     _UpperCAmelCase     							=   current_set[0]
     _UpperCAmelCase     							=   [first_row]
     _UpperCAmelCase     							=   current_set[1::]
     for row in current_set:
          _UpperCAmelCase     							=   []
          # If first term is 0, it is already in form we want, so we preserve it
          if row[0] == 0:
               final_set.append(__lowercase       )
               continue
          for column_index in range(len(__lowercase       )       ):
               temp_row.append(first_row[column_index] - row[column_index]       )
          final_set.append(__lowercase       )
     # Create next recursion iteration set
     if len(final_set[0]       ) != 3:
          _UpperCAmelCase     							=   final_set[0]
          _UpperCAmelCase     							=   []
          _UpperCAmelCase     							=   []
          for row in final_set[1::]:
               current_first_column.append(row[0]       )
               next_iteration.append(row[1::]       )
          _UpperCAmelCase     							=   simplify(__lowercase       )
          for i in range(len(__lowercase       )       ):
               resultant[i].insert(0			,     current_first_column[i]       )
          resultant.insert(0			,     __lowercase       )
          _UpperCAmelCase     							=   resultant
     return final_set
def 	UpperCAmelCase_							(					__lowercase							:      list[list]       )		->       list:


     '''simple docstring'''



     if len(__lowercase       ) == 0:
          raise IndexError("solve_simultaneous() requires n lists of length n+1"       )
     _UpperCAmelCase     							=   len(__lowercase       ) + 1
     if any(len(__lowercase       ) != _length for item in equations       ):
          raise IndexError("solve_simultaneous() requires n lists of length n+1"       )
     for row in equations:
          if any(not isinstance(__lowercase			,     (int, float)       ) for column in row       ):
               raise ValueError("solve_simultaneous() requires lists of integers"       )
     if len(__lowercase       ) == 1:
          return [equations[0][-1] / equations[0][0]]
     _UpperCAmelCase     							=   equations.copy()
     if any(0 in row for row in data_set       ):
          _UpperCAmelCase     							=   data_set.copy()
          _UpperCAmelCase     							=   []
          for row_index, row in enumerate(__lowercase       ):
               if 0 not in row:
                    _UpperCAmelCase     							=   data_set.pop(__lowercase       )
                    break
          if not full_row:
               raise ValueError("solve_simultaneous() requires at least 1 full equation"       )
          data_set.insert(0			,     __lowercase       )
     _UpperCAmelCase     							=   data_set.copy()
     _UpperCAmelCase     							=   simplify(__lowercase       )
     _UpperCAmelCase     							=   simplified[::-1]
     _UpperCAmelCase     							=   []
     for row in simplified:
          _UpperCAmelCase     							=   row[-1]
          if not solutions:
               if row[-2] == 0:
                    solutions.append(0       )
                    continue
               solutions.append(current_solution / row[-2]       )
               continue
          _UpperCAmelCase     							=   row.copy()[: len(__lowercase       ) - 1 :]
          while temp_row[0] == 0:
               temp_row.pop(0       )
          if len(__lowercase       ) == 0:
               solutions.append(0       )
               continue
          _UpperCAmelCase     							=   temp_row[1::]
          _UpperCAmelCase     							=   temp_row[::-1]
          for column_index, column in enumerate(__lowercase       ):
               current_solution -= column * solutions[column_index]
          solutions.append(__lowercase       )
     _UpperCAmelCase     							=   []
     for item in solutions:
          final.append(float(round(__lowercase			,     5       )       )       )
     return final[::-1]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  __SCREAMING_SNAKE_CASE     :Tuple       =				[
      [2, 1, 1, 1, 1, 4],
      [1, 2, 1, 1, 1, 5],
      [1, 1, 2, 1, 1, 6],
      [1, 1, 1, 2, 1, 7],
      [1, 1, 1, 1, 2, 8],
  ]
  print(solve_simultaneous(eq))
  print(solve_simultaneous([[4, 2]]))








# 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

