




'''simple docstring'''

def     __lowercase  (_lowercase     )   ->     Optional[int]:


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


     """simple docstring"""


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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   UpperCAmelCase__						:str          =			[
       [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]]))











'''simple docstring'''

from typing import List, Optional, Tuple, Union

import torch

from ...utils import logging, randn_tensor
from ..pipeline_utils import AudioPipelineOutput, DiffusionPipeline


UpperCAmelCase__						:Dict          =			logging.get_logger(__name__)  # pylint: disable=invalid-name







class 	SCREAMING_SNAKE_CASE	(      lowerCAmelCase_  ):




       def __init__(					self      : int	,    A__      : List[Any]	,    A__      : Tuple					):


            """simple docstring"""







            super().__init__()
            self.register_modules(unet=A__	,    scheduler=A__					)




       @torch.no_grad()
       def __call__(					self      : List[str]	,    A__      : int = 1	,    A__      : int = 100	,    A__      : Optional[Union[torch.Generator, List[torch.Generator]]] = None	,    A__      : Optional[float] = None	,    A__      : bool = True	,    ):


            """simple docstring"""







            if audio_length_in_s is None:
                 __lowerCamelCase						:       Union[str, Any]				   =				self.unet.config.sample_size / self.unet.config.sample_rate

            __lowerCamelCase						:       int				   =				audio_length_in_s * self.unet.config.sample_rate

            __lowerCamelCase						:       List[Any]				   =				2 ** len(self.unet.up_blocks					)
            if sample_size < 3 * down_scale_factor:
                 raise ValueError(
                     f"{audio_length_in_s} is too small. Make sure it's bigger or equal to"
                     f" {3 * down_scale_factor / self.unet.config.sample_rate}."					)

            __lowerCamelCase						:       Any				   =				int(A__					)
            if sample_size % down_scale_factor != 0:
                 __lowerCamelCase						:       Optional[Any]				   =				(
                     (audio_length_in_s * self.unet.config.sample_rate) // down_scale_factor + 1
                 ) * down_scale_factor
                 logger.info(
                     f"{audio_length_in_s} is increased to {sample_size / self.unet.config.sample_rate} so that it can be handled"
                     f" by the model. It will be cut to {original_sample_size / self.unet.config.sample_rate} after the denoising"
                     """ process."""					)
            __lowerCamelCase						:       Dict				   =				int(A__					)

            __lowerCamelCase						:       Optional[int]				   =				next(iter(self.unet.parameters()					)					).dtype
            __lowerCamelCase						:       Optional[Any]				   =				(batch_size, self.unet.config.in_channels, sample_size)
            if isinstance(A__	,    A__					) and len(A__					) != batch_size:
                 raise ValueError(
                     f"You have passed a list of generators of length {len(A__					)}, but requested an effective batch"
                     f" size of {batch_size}. Make sure the batch size matches the length of the generators."					)

            __lowerCamelCase						:       int				   =				randn_tensor(A__	,    generator=A__	,    device=self.device	,    dtype=A__					)

            # set step values
            self.scheduler.set_timesteps(A__	,    device=audio.device					)
            __lowerCamelCase						:       List[Any]				   =				self.scheduler.timesteps.to(A__					)

            for t in self.progress_bar(self.scheduler.timesteps					):
                 # 1. predict noise model_output
                 __lowerCamelCase						:       List[str]				   =				self.unet(A__	,    A__					).sample

                 # 2. compute previous image: x_t -> t_t-1
                 __lowerCamelCase						:       Dict				   =				self.scheduler.step(A__	,    A__	,    A__					).prev_sample

            __lowerCamelCase						:       Optional[int]				   =				audio.clamp(-1	,    1					).float().cpu().numpy()

            __lowerCamelCase						:       int				   =				audio[:, :, :original_sample_size]

            if not return_dict:
                 return (audio,)

            return AudioPipelineOutput(audios=A__					)



