




from __future__ import annotations

class   __a:






    """simple docstring"""





    def __init__(				self       ,_SCREAMING_SNAKE_CASE  )			->		str:
         UpperCAmelCase_      :							List[Any]       =      TypeError(
             '''Matrices must be formed from a list of zero or more lists containing at '''
             '''least one and the same number of values, each of which must be of type '''
             '''int or float.'''  )
         if len(_SCREAMING_SNAKE_CASE  ) != 0:
              UpperCAmelCase_      :							Union[str, Any]       =      len(rows[0]  )
              if cols == 0:
                   raise error
              for row in rows:
                   if len(_SCREAMING_SNAKE_CASE  ) != cols:
                        raise error
                   for value in row:
                        if not isinstance(_SCREAMING_SNAKE_CASE       ,(int, float)  ):
                             raise error
              UpperCAmelCase_      :							Union[str, Any]       =      rows
         else:
              UpperCAmelCase_      :							Optional[Any]       =      []





    def 							a__				(				self  )			->		list[list[int]]:
         return [[row[i] for row in self.rows] for i in range(len(self.rows[0]  )  )]





    @property
    def 							a__				(				self  )			->		int:
         return len(self.rows  )





    @property
    def 							a__				(				self  )			->		int:
         return len(self.rows[0]  )





    @property
    def 							a__				(				self  )			->		tuple[int, int]:
         return (self.num_rows, self.num_columns)





    @property
    def 							a__				(				self  )			->		bool:
         return self.order[0] == self.order[1]





    def 							a__				(				self  )			->		Matrix:
         UpperCAmelCase_      :							Tuple       =      [
             [0 if column_num != row_num else 1 for column_num in range(self.num_rows  )]
             for row_num in range(self.num_rows  )
         ]
         return Matrix(_SCREAMING_SNAKE_CASE  )





    def 							a__				(				self  )			->		int:
         if not self.is_square:
              return 0
         if self.order == (0, 0):
              return 1
         if self.order == (1, 1):
              return int(self.rows[0][0]  )
         if self.order == (2, 2):
              return int(
                  (self.rows[0][0] * self.rows[1][1])
                  - (self.rows[0][1] * self.rows[1][0])  )
         else:
              return sum(
                  self.rows[0][column] * self.cofactors().rows[0][column]
                  for column in range(self.num_columns  )  )





    def 							a__				(				self  )			->		bool:
         return bool(self.determinant()  )





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )			->		int:
         UpperCAmelCase_      :							List[Any]       =      [
             [
                 self.rows[other_row][other_column]
                 for other_column in range(self.num_columns  )
                 if other_column != column
             ]
             for other_row in range(self.num_rows  )
             if other_row != row
         ]
         return Matrix(_SCREAMING_SNAKE_CASE  ).determinant()





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )			->		int:
         if (row + column) % 2 == 0:
              return self.get_minor(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )
         return -1 * self.get_minor(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )





    def 							a__				(				self  )			->		Matrix:
         return Matrix(
             [
                 [self.get_minor(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ) for column in range(self.num_columns  )]
                 for row in range(self.num_rows  )
             ]  )





    def 							a__				(				self  )			->		Matrix:
         return Matrix(
             [
                 [
                     self.minors().rows[row][column]
                     if (row + column) % 2 == 0
                     else self.minors().rows[row][column] * -1
                     for column in range(self.minors().num_columns  )
                 ]
                 for row in range(self.minors().num_rows  )
             ]  )





    def 							a__				(				self  )			->		Matrix:
         UpperCAmelCase_      :							List[str]       =      [
             [self.cofactors().rows[column][row] for column in range(self.num_columns  )]
             for row in range(self.num_rows  )
         ]
         return Matrix(_SCREAMING_SNAKE_CASE  )





    def 							a__				(				self  )			->		Matrix:
         UpperCAmelCase_      :							List[Any]       =      self.determinant()
         if not determinant:
              raise TypeError('''Only matrices with a non-zero determinant have an inverse'''  )
         return self.adjugate() * (1 / determinant)





    def __repr__(				self  )			->		str:
         return str(self.rows  )





    def __str__(				self  )			->		str:
         if self.num_rows == 0:
              return "[]"
         if self.num_rows == 1:
              return "[[" + ". ".join(str(self.rows[0]  )  ) + "]]"
         return (
             "["
             + "\n ".join(
                 [
                     '''[''' + '''. '''.join([str(_SCREAMING_SNAKE_CASE  ) for value in row]  ) + '''.]'''
                     for row in self.rows
                 ]  )
             + "]"
         )





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE = None  )			->		None:
         UpperCAmelCase_      :							List[str]       =      TypeError('''Row must be a list containing all ints and/or floats'''  )
         if not isinstance(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ):
              raise type_error
         for value in row:
              if not isinstance(_SCREAMING_SNAKE_CASE       ,(int, float)  ):
                   raise type_error
         if len(_SCREAMING_SNAKE_CASE  ) != self.num_columns:
              raise ValueError(
                  '''Row must be equal in length to the other rows in the matrix'''  )
         if position is None:
              self.rows.append(_SCREAMING_SNAKE_CASE  )
         else:
              UpperCAmelCase_      :							Union[str, Any]       =      self.rows[0:position] + [row] + self.rows[position:]





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE = None  )			->		None:
         UpperCAmelCase_      :							str       =      TypeError(
             '''Column must be a list containing all ints and/or floats'''  )
         if not isinstance(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ):
              raise type_error
         for value in column:
              if not isinstance(_SCREAMING_SNAKE_CASE       ,(int, float)  ):
                   raise type_error
         if len(_SCREAMING_SNAKE_CASE  ) != self.num_rows:
              raise ValueError(
                  '''Column must be equal in length to the other columns in the matrix'''  )
         if position is None:
              UpperCAmelCase_      :							Optional[Any]       =      [self.rows[i] + [column[i]] for i in range(self.num_rows  )]
         else:
              UpperCAmelCase_      :							Union[str, Any]       =      [
                  self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                  for i in range(self.num_rows  )
              ]





    def __eq__(				self       ,_SCREAMING_SNAKE_CASE  )			->		bool:
         if not isinstance(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ):
              return NotImplemented
         return self.rows == other.rows





    def __ne__(				self       ,_SCREAMING_SNAKE_CASE  )			->		bool:
         return not self == other





    def __neg__(				self  )			->		Matrix:
         return self * -1





    def __add__(				self       ,_SCREAMING_SNAKE_CASE  )			->		Matrix:
         if self.order != other.order:
              raise ValueError('''Addition requires matrices of the same order'''  )
         return Matrix(
             [
                 [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns  )]
                 for i in range(self.num_rows  )
             ]  )





    def __sub__(				self       ,_SCREAMING_SNAKE_CASE  )			->		Matrix:
         if self.order != other.order:
              raise ValueError('''Subtraction requires matrices of the same order'''  )
         return Matrix(
             [
                 [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns  )]
                 for i in range(self.num_rows  )
             ]  )





    def __mul__(				self       ,_SCREAMING_SNAKE_CASE  )			->		Matrix:
         if isinstance(_SCREAMING_SNAKE_CASE       ,(int, float)  ):
              return Matrix(
                  [[int(element * other  ) for element in row] for row in self.rows]  )
         elif isinstance(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ):
              if self.num_columns != other.num_rows:
                   raise ValueError(
                       '''The number of columns in the first matrix must '''
                       '''be equal to the number of rows in the second'''  )
              return Matrix(
                  [
                      [Matrix.dot_product(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ) for column in other.columns()]
                      for row in self.rows
                  ]  )
         else:
              raise TypeError(
                  '''A Matrix can only be multiplied by an int, float, or another matrix'''  )





    def __pow__(				self       ,_SCREAMING_SNAKE_CASE  )			->		Matrix:
         if not isinstance(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ):
              raise TypeError('''A Matrix can only be raised to the power of an int'''  )
         if not self.is_square:
              raise ValueError('''Only square matrices can be raised to a power'''  )
         if other == 0:
              return self.identity()
         if other < 0:
              if self.is_invertable():
                   return self.inverse() ** (-other)
              raise ValueError(
                  '''Only invertable matrices can be raised to a negative power'''  )
         UpperCAmelCase_      :							List[Any]       =      self
         for _ in range(other - 1  ):
              result *= self
         return result





    @classmethod
    def 							a__				(				cls       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )			->		int:
         return sum(row[i] * column[i] for i in range(len(_SCREAMING_SNAKE_CASE  )  )  )


if __name__ == "__main__":
     import doctest

     doctest.testmod()





import tempfile

import torch

from diffusers import IPNDMScheduler

from .test_schedulers import SchedulerCommonTest

class   __a(					_a       ):






    """simple docstring"""





    lowerCAmelCase        =				(IPNDMScheduler,)
    lowerCAmelCase        =				(('''num_inference_steps''', 50),)





    def 							a__				(				self       ,**_SCREAMING_SNAKE_CASE  )			->		int:
         UpperCAmelCase_      :							Tuple       =      {'''num_train_timesteps''': 1_000}
         config.update(**_SCREAMING_SNAKE_CASE  )
         return config





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE=0       ,**_SCREAMING_SNAKE_CASE  )			->		Union[str, Any]:
         UpperCAmelCase_      :							Optional[int]       =      dict(self.forward_default_kwargs  )
         UpperCAmelCase_      :							int       =      kwargs.pop('''num_inference_steps'''       ,_SCREAMING_SNAKE_CASE  )
         UpperCAmelCase_      :							str       =      self.dummy_sample
         UpperCAmelCase_      :							Optional[Any]       =      0.1 * sample
         UpperCAmelCase_      :							Optional[int]       =      [residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

         for scheduler_class in self.scheduler_classes:
              UpperCAmelCase_      :							Tuple       =      self.get_scheduler_config(**_SCREAMING_SNAKE_CASE  )
              UpperCAmelCase_      :							Optional[int]       =      scheduler_class(**_SCREAMING_SNAKE_CASE  )
              scheduler.set_timesteps(_SCREAMING_SNAKE_CASE  )
              # copy over dummy past residuals
              UpperCAmelCase_      :							Optional[Any]       =      dummy_past_residuals[:]

              if time_step is None:
                   UpperCAmelCase_      :							Tuple       =      scheduler.timesteps[len(scheduler.timesteps  ) // 2]

              with tempfile.TemporaryDirectory() as tmpdirname:
                   scheduler.save_config(_SCREAMING_SNAKE_CASE  )
                   UpperCAmelCase_      :							List[Any]       =      scheduler_class.from_pretrained(_SCREAMING_SNAKE_CASE  )
                   new_scheduler.set_timesteps(_SCREAMING_SNAKE_CASE  )
                   # copy over dummy past residuals
                   UpperCAmelCase_      :							Optional[int]       =      dummy_past_residuals[:]

              UpperCAmelCase_      :							List[Any]       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample
              UpperCAmelCase_      :							str       =      new_scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample

              assert torch.sum(torch.abs(output - new_output  )  ) < 1e-5, "Scheduler outputs are not identical"

              UpperCAmelCase_      :							Union[str, Any]       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample
              UpperCAmelCase_      :							Optional[int]       =      new_scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample

              assert torch.sum(torch.abs(output - new_output  )  ) < 1e-5, "Scheduler outputs are not identical"





    def 							a__				(				self  )			->		List[Any]:
         pass





    def 							a__				(				self       ,_SCREAMING_SNAKE_CASE=0       ,**_SCREAMING_SNAKE_CASE  )			->		List[Any]:
         UpperCAmelCase_      :							List[str]       =      dict(self.forward_default_kwargs  )
         UpperCAmelCase_      :							Tuple       =      kwargs.pop('''num_inference_steps'''       ,_SCREAMING_SNAKE_CASE  )
         UpperCAmelCase_      :							int       =      self.dummy_sample
         UpperCAmelCase_      :							Tuple       =      0.1 * sample
         UpperCAmelCase_      :							int       =      [residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

         for scheduler_class in self.scheduler_classes:
              UpperCAmelCase_      :							str       =      self.get_scheduler_config()
              UpperCAmelCase_      :							str       =      scheduler_class(**_SCREAMING_SNAKE_CASE  )
              scheduler.set_timesteps(_SCREAMING_SNAKE_CASE  )

              # copy over dummy past residuals (must be after setting timesteps)
              UpperCAmelCase_      :							Tuple       =      dummy_past_residuals[:]

              if time_step is None:
                   UpperCAmelCase_      :							Dict       =      scheduler.timesteps[len(scheduler.timesteps  ) // 2]

              with tempfile.TemporaryDirectory() as tmpdirname:
                   scheduler.save_config(_SCREAMING_SNAKE_CASE  )
                   UpperCAmelCase_      :							Optional[int]       =      scheduler_class.from_pretrained(_SCREAMING_SNAKE_CASE  )
                   # copy over dummy past residuals
                   new_scheduler.set_timesteps(_SCREAMING_SNAKE_CASE  )

                   # copy over dummy past residual (must be after setting timesteps)
                   UpperCAmelCase_      :							str       =      dummy_past_residuals[:]

              UpperCAmelCase_      :							Tuple       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample
              UpperCAmelCase_      :							Optional[int]       =      new_scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample

              assert torch.sum(torch.abs(output - new_output  )  ) < 1e-5, "Scheduler outputs are not identical"

              UpperCAmelCase_      :							str       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample
              UpperCAmelCase_      :							List[str]       =      new_scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample

              assert torch.sum(torch.abs(output - new_output  )  ) < 1e-5, "Scheduler outputs are not identical"





    def 							a__				(				self       ,**_SCREAMING_SNAKE_CASE  )			->		List[Any]:
         UpperCAmelCase_      :							Tuple       =      self.scheduler_classes[0]
         UpperCAmelCase_      :							List[Any]       =      self.get_scheduler_config(**_SCREAMING_SNAKE_CASE  )
         UpperCAmelCase_      :							Tuple       =      scheduler_class(**_SCREAMING_SNAKE_CASE  )

         UpperCAmelCase_      :							Any       =      10
         UpperCAmelCase_      :							Tuple       =      self.dummy_model()
         UpperCAmelCase_      :							List[str]       =      self.dummy_sample_deter
         scheduler.set_timesteps(_SCREAMING_SNAKE_CASE  )

         for i, t in enumerate(scheduler.timesteps  ):
              UpperCAmelCase_      :							int       =      model(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )
              UpperCAmelCase_      :							Union[str, Any]       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ).prev_sample

         for i, t in enumerate(scheduler.timesteps  ):
              UpperCAmelCase_      :							Optional[int]       =      model(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  )
              UpperCAmelCase_      :							Dict       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE  ).prev_sample

         return sample





    def 							a__				(				self  )			->		str:
         UpperCAmelCase_      :							List[Any]       =      dict(self.forward_default_kwargs  )

         UpperCAmelCase_      :							Any       =      kwargs.pop('''num_inference_steps'''       ,_SCREAMING_SNAKE_CASE  )

         for scheduler_class in self.scheduler_classes:
              UpperCAmelCase_      :							int       =      self.get_scheduler_config()
              UpperCAmelCase_      :							List[Any]       =      scheduler_class(**_SCREAMING_SNAKE_CASE  )

              UpperCAmelCase_      :							Optional[int]       =      self.dummy_sample
              UpperCAmelCase_      :							List[Any]       =      0.1 * sample

              if num_inference_steps is not None and hasattr(_SCREAMING_SNAKE_CASE       ,'''set_timesteps'''  ):
                   scheduler.set_timesteps(_SCREAMING_SNAKE_CASE  )
              elif num_inference_steps is not None and not hasattr(_SCREAMING_SNAKE_CASE       ,'''set_timesteps'''  ):
                   UpperCAmelCase_      :							Union[str, Any]       =      num_inference_steps

              # copy over dummy past residuals (must be done after set_timesteps)
              UpperCAmelCase_      :							str       =      [residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]
              UpperCAmelCase_      :							int       =      dummy_past_residuals[:]

              UpperCAmelCase_      :							List[Any]       =      scheduler.timesteps[5]
              UpperCAmelCase_      :							Dict       =      scheduler.timesteps[6]

              UpperCAmelCase_      :							List[Any]       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample
              UpperCAmelCase_      :							Dict       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample

              self.assertEqual(output_a.shape       ,sample.shape  )
              self.assertEqual(output_a.shape       ,output_a.shape  )

              UpperCAmelCase_      :							List[Any]       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample
              UpperCAmelCase_      :							Dict       =      scheduler.step(_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,_SCREAMING_SNAKE_CASE       ,**_SCREAMING_SNAKE_CASE  ).prev_sample

              self.assertEqual(output_a.shape       ,sample.shape  )
              self.assertEqual(output_a.shape       ,output_a.shape  )





    def 							a__				(				self  )			->		Any:
         for timesteps in [100, 1_000]:
              self.check_over_configs(num_train_timesteps=_SCREAMING_SNAKE_CASE       ,time_step=_SCREAMING_SNAKE_CASE  )





    def 							a__				(				self  )			->		Union[str, Any]:
         for t, num_inference_steps in zip([1, 5, 10]       ,[10, 50, 100]  ):
              self.check_over_forward(num_inference_steps=_SCREAMING_SNAKE_CASE       ,time_step=_SCREAMING_SNAKE_CASE  )





    def 							a__				(				self  )			->		Union[str, Any]:
         UpperCAmelCase_      :							Optional[int]       =      self.full_loop()
         UpperCAmelCase_      :							str       =      torch.mean(torch.abs(_SCREAMING_SNAKE_CASE  )  )

         assert abs(result_mean.item() - 2_540_529  ) < 10