





'''simple docstring'''




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

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch

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







@dataclass
class   A_	(  lowerCAmelCase_			):
 _lowerCamelCase  : torch.FloatTensor
 _lowerCamelCase  : torch.FloatTensor







class   A_	(  lowerCAmelCase_							,						lowerCAmelCase_			):
 _lowerCamelCase  : Tuple           =							1




 @register_to_config
 def __init__(					self       :    Dict	,			snake_case_       :    int = 2_0_0_0	,			snake_case_       :    float = 0.1_5	,			snake_case_       :    float = 0.0_1	,			snake_case_       :    float = 1_3_4_8.0	,			snake_case_       :    float = 1e-5	,			snake_case_       :    int = 1	,			):
      # standard deviation of the initial noise distribution
      _UpperCAmelCase     							=   sigma_max

      # setable values
      _UpperCAmelCase     							=   None

      self.set_sigmas(snake_case_	,			snake_case_	,			snake_case_	,			snake_case_    )




 def      lowercase	(					self       :    Union[str, Any]	,			snake_case_       :    torch.FloatTensor	,			snake_case_       :    Optional[int] = None    ):
      return sample




 def      lowercase	(					self       :    Tuple	,			snake_case_       :    int	,			snake_case_       :    float = None	,			snake_case_       :    Union[str, torch.device] = None    ):
      _UpperCAmelCase     							=   sampling_eps if sampling_eps is not None else self.config.sampling_eps

      _UpperCAmelCase     							=   torch.linspace(1	,			snake_case_	,			snake_case_	,			device=snake_case_    )




 def      lowercase	(					self       :    Any	,			snake_case_       :    int	,			snake_case_       :    float = None	,			snake_case_       :    float = None	,			snake_case_       :    float = None    ):
      _UpperCAmelCase     							=   sigma_min if sigma_min is not None else self.config.sigma_min
      _UpperCAmelCase     							=   sigma_max if sigma_max is not None else self.config.sigma_max
      _UpperCAmelCase     							=   sampling_eps if sampling_eps is not None else self.config.sampling_eps
      if self.timesteps is None:
           self.set_timesteps(snake_case_	,			snake_case_    )

      _UpperCAmelCase     							=   sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
      _UpperCAmelCase     							=   torch.exp(torch.linspace(math.log(snake_case_    )	,			math.log(snake_case_    )	,			snake_case_    )    )
      _UpperCAmelCase     							=   torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]    )




 def      lowercase	(					self       :    Optional[int]	,			snake_case_       :    Union[str, Any]	,			snake_case_       :    int    ):
      return torch.where(
          timesteps == 0	,			torch.zeros_like(t.to(timesteps.device    )    )	,			self.discrete_sigmas[timesteps - 1].to(timesteps.device    )	,			)




 def      lowercase	(					self       :    Union[str, Any]	,			snake_case_       :    torch.FloatTensor	,			snake_case_       :    int	,			snake_case_       :    torch.FloatTensor	,			snake_case_       :    Optional[torch.Generator] = None	,			snake_case_       :    bool = True	,			):
      if self.timesteps is None:
           raise ValueError(
               "`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"    )

      _UpperCAmelCase     							=   timestep * torch.ones(
          sample.shape[0]	,			device=sample.device    )  # torch.repeat_interleave(timestep, sample.shape[0])
      _UpperCAmelCase     							=   (timestep * (len(self.timesteps    ) - 1)).long()

      # mps requires indices to be in the same device, so we use cpu as is the default with cuda
      _UpperCAmelCase     							=   timesteps.to(self.discrete_sigmas.device    )

      _UpperCAmelCase     							=   self.discrete_sigmas[timesteps].to(sample.device    )
      _UpperCAmelCase     							=   self.get_adjacent_sigma(snake_case_	,			snake_case_    ).to(sample.device    )
      _UpperCAmelCase     							=   torch.zeros_like(snake_case_    )
      _UpperCAmelCase     							=   (sigma**2 - adjacent_sigma**2) ** 0.5

      # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
      # also equation 47 shows the analog from SDE models to ancestral sampling methods
      _UpperCAmelCase     							=   diffusion.flatten()
      while len(diffusion.shape    ) < len(sample.shape    ):
           _UpperCAmelCase     							=   diffusion.unsqueeze(-1    )
      _UpperCAmelCase     							=   drift - diffusion**2 * model_output

      #  equation 6: sample noise for the diffusion term of
      _UpperCAmelCase     							=   randn_tensor(
          sample.shape	,			layout=sample.layout	,			generator=snake_case_	,			device=sample.device	,			dtype=sample.dtype    )
      _UpperCAmelCase     							=   sample - drift  # subtract because `dt` is a small negative timestep
      # TODO is the variable diffusion the correct scaling term for the noise?
      _UpperCAmelCase     							=   prev_sample_mean + diffusion * noise  # add impact of diffusion field g

      if not return_dict:
           return (prev_sample, prev_sample_mean)

      return SdeVeOutput(prev_sample=snake_case_	,			prev_sample_mean=snake_case_    )




 def      lowercase	(					self       :    str	,			snake_case_       :    torch.FloatTensor	,			snake_case_       :    torch.FloatTensor	,			snake_case_       :    Optional[torch.Generator] = None	,			snake_case_       :    bool = True	,			):
      if self.timesteps is None:
           raise ValueError(
               "`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"    )

      # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
      # sample noise for correction
      _UpperCAmelCase     							=   randn_tensor(sample.shape	,			layout=sample.layout	,			generator=snake_case_    ).to(sample.device    )

      # compute step size from the model_output, the noise, and the snr
      _UpperCAmelCase     							=   torch.norm(model_output.reshape(model_output.shape[0]	,			-1    )	,			dim=-1    ).mean()
      _UpperCAmelCase     							=   torch.norm(noise.reshape(noise.shape[0]	,			-1    )	,			dim=-1    ).mean()
      _UpperCAmelCase     							=   (self.config.snr * noise_norm / grad_norm) ** 2 * 2
      _UpperCAmelCase     							=   step_size * torch.ones(sample.shape[0]    ).to(sample.device    )
      # self.repeat_scalar(step_size, sample.shape[0])

      # compute corrected sample: model_output term and noise term
      _UpperCAmelCase     							=   step_size.flatten()
      while len(step_size.shape    ) < len(sample.shape    ):
           _UpperCAmelCase     							=   step_size.unsqueeze(-1    )
      _UpperCAmelCase     							=   sample + step_size * model_output
      _UpperCAmelCase     							=   prev_sample_mean + ((step_size * 2) ** 0.5) * noise

      if not return_dict:
           return (prev_sample,)

      return SchedulerOutput(prev_sample=snake_case_    )




 def      lowercase	(					self       :    Any	,			snake_case_       :    torch.FloatTensor	,			snake_case_       :    torch.FloatTensor	,			snake_case_       :    torch.FloatTensor	,			):
      # Make sure sigmas and timesteps have the same device and dtype as original_samples
      _UpperCAmelCase     							=   timesteps.to(original_samples.device    )
      _UpperCAmelCase     							=   self.discrete_sigmas.to(original_samples.device    )[timesteps]
      _UpperCAmelCase     							=   (
          noise * sigmas[:, None, None, None]
          if noise is not None
          else torch.randn_like(snake_case_    ) * sigmas[:, None, None, None]
      )
      _UpperCAmelCase     							=   noise + original_samples
      return noisy_samples




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







'''simple docstring'''






from __future__ import annotations


def 		_A     (    A__      ):






 """simple docstring"""



 __lowercase							  = len(A__      )
 # We need to create solution object to save path.
 __lowercase							  = [[0 for _ in range(A__      )] for _ in range(A__      )]
 __lowercase							  = run_maze(A__     ,				0     ,				0     ,				A__      )
 if solved:
  print('''\n'''.join(str(A__      ) for row in solutions      )      )
 else:
  print('''No solution exists!'''      )
 return solved


def 		_A     (    A__     ,				A__     ,				A__     ,				A__      ):






 """simple docstring"""



 __lowercase							  = len(A__      )
 # Final check point.
 if i == j == (size - 1):
  __lowercase							  = 1
  return True

 __lowercase							  = (not i < 0) and (not j < 0)  # Check lower bounds
 __lowercase							  = (i < size) and (j < size)  # Check upper bounds

 if lower_flag and upper_flag:
  # check for already visited and block points.
  __lowercase							  = (not solutions[i][j]) and (not maze[i][j])
  if block_flag:
   # check visited
   __lowercase							  = 1

   # check for directions
   if (
       run_maze(A__     ,				i + 1     ,				A__     ,				A__      )
       or run_maze(A__     ,				A__     ,				j + 1     ,				A__      )
       or run_maze(A__     ,				i - 1     ,				A__     ,				A__      )
       or run_maze(A__     ,				A__     ,				j - 1     ,				A__      )
   ):
    return True

   __lowercase							  = 0
   return False
 return False


if __name__ == "__main__":
 import doctest

 doctest.testmod()

