'''simple docstring'''

def __UpperCamelCase( ):
   '''simple docstring'''
   return [list(range(10_00 - i	,      -10_00 - i	,      -1     )     ) for i in range(10_00     )]


UpperCamelCase__  :						Optional[int]					=      generate_large_matrix()
UpperCamelCase__  :						Optional[int]					=      (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)







def __UpperCamelCase( _A       :					list[list[int]]     ):
   '''simple docstring'''
   assert all(row == sorted(_A	,      reverse=_A     ) for row in grid     )
   assert all(list(_A     ) == sorted(_A	,      reverse=_A     ) for col in zip(*_A     )     )







def __UpperCamelCase( _A       :					list[int]     ):
   '''simple docstring'''
   UpperCAmelCase__				:					Dict 					=	0
   UpperCAmelCase__				:					Union[str, Any] 					=	len(_A     ) - 1

   # Edge cases such as no values or all numbers are negative.
   if not array or array[0] < 0:
      return 0

   while right + 1 > left:
      UpperCAmelCase__				:					Optional[Any] 					=	(left + right) // 2
      UpperCAmelCase__				:					Dict 					=	array[mid]

      # Num must be negative and the index must be greater than or equal to 0.
      if num < 0 and array[mid - 1] >= 0:
         return mid

      if num >= 0:
         UpperCAmelCase__				:					Tuple 					=	mid + 1
      else:
         UpperCAmelCase__				:					str 					=	mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
   return len(_A     )







def __UpperCamelCase( _A       :					list[list[int]]     ):
   '''simple docstring'''
   UpperCAmelCase__				:					List[Any] 					=	0
   UpperCAmelCase__				:					Dict 					=	len(grid[0]     )

   for i in range(len(_A     )     ):
      UpperCAmelCase__				:					List[Any] 					=	find_negative_index(grid[i][:bound]     )
      total += bound
   return (len(_A     ) * len(grid[0]     )) - total







def __UpperCamelCase( _A       :					list[list[int]]     ):
   '''simple docstring'''
   return len([number for row in grid for number in row if number < 0]     )







def __UpperCamelCase( _A       :					list[list[int]]     ):
   '''simple docstring'''
   UpperCAmelCase__				:					List[Any] 					=	0
   for row in grid:
      for i, number in enumerate(_A     ):
         if number < 0:
            total += len(_A     ) - i
            break
   return total







def __UpperCamelCase( ):
   '''simple docstring'''
   from timeit import timeit

   print('''Running benchmarks'''     )
   UpperCAmelCase__				:					List[Any] 					=	(
       "from __main__ import count_negatives_binary_search, "
       "count_negatives_brute_force, count_negatives_brute_force_with_break, grid"
   )
   for func in (
       "count_negatives_binary_search",  # took 0.7727 seconds
       "count_negatives_brute_force_with_break",  # took 4.6505 seconds
       "count_negatives_brute_force",  # took 12.8160 seconds
   ):
      UpperCAmelCase__				:					Union[str, Any] 					=	timeit(F'''{func}(grid=grid)'''	,      setup=_A	,      number=5_00     )
      print(F'''{func}() took {time:0.4f} seconds'''     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  benchmark()








"""simple docstring"""



import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest







class _lowerCAmelCase							( snake_case_      ):
   __UpperCAmelCase					:			List[str]				    =    (KDPMaDiscreteScheduler,)
   __UpperCAmelCase					:			List[Any]				    =    10







   def 					lowerCamelCase						(      self		,      **UpperCamelCase__		)      ->						Optional[int]:

       '''simple docstring'''




       snake_case       : List[str]    =       {
           "num_train_timesteps": 1100,
           "beta_start": 0.0001,
           "beta_end": 0.02,
           "beta_schedule": "linear",
       }

       config.update(**UpperCamelCase__		)
       return config







   def 					lowerCamelCase						(      self		)      ->						Optional[int]:

       '''simple docstring'''




       for timesteps in [10, 50, 100, 1000]:
           self.check_over_configs(num_train_timesteps=UpperCamelCase__		)







   def 					lowerCamelCase						(      self		)      ->						str:

       '''simple docstring'''




       for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]		,      [0.0002, 0.002, 0.02]		):
           self.check_over_configs(beta_start=UpperCamelCase__		,      beta_end=UpperCamelCase__		)







   def 					lowerCamelCase						(      self		)      ->						Optional[Any]:

       '''simple docstring'''




       for schedule in ["linear", "scaled_linear"]:
           self.check_over_configs(beta_schedule=UpperCamelCase__		)







   def 					lowerCamelCase						(      self		)      ->						List[str]:

       '''simple docstring'''




       for prediction_type in ["epsilon", "v_prediction"]:
           self.check_over_configs(prediction_type=UpperCamelCase__		)







   def 					lowerCamelCase						(      self		)      ->						Optional[Any]:

       '''simple docstring'''




       snake_case       : str    =       self.scheduler_classes[0]
       snake_case       : str    =       self.get_scheduler_config(prediction_type="v_prediction"		)
       snake_case       : Dict    =       scheduler_class(**UpperCamelCase__		)

       scheduler.set_timesteps(self.num_inference_steps		)

       snake_case       : List[Any]    =       self.dummy_model()
       snake_case       : List[str]    =       self.dummy_sample_deter * scheduler.init_noise_sigma
       snake_case       : Optional[Any]    =       sample.to(UpperCamelCase__		)

       for i, t in enumerate(scheduler.timesteps		):
           snake_case       : int    =       scheduler.scale_model_input(UpperCamelCase__		,      UpperCamelCase__		)

           snake_case       : int    =       model(UpperCamelCase__		,      UpperCamelCase__		)

           snake_case       : Optional[Any]    =       scheduler.step(UpperCamelCase__		,      UpperCamelCase__		,      UpperCamelCase__		)
           snake_case       : Optional[Any]    =       output.prev_sample

       snake_case       : Optional[Any]    =       torch.sum(torch.abs(UpperCamelCase__		)		)
       snake_case       : Any    =       torch.mean(torch.abs(UpperCamelCase__		)		)

       if torch_device in ["cpu", "mps"]:
           assert abs(result_sum.item() - 4.6934e-07		) < 1e-2
           assert abs(result_mean.item() - 6.1112e-10		) < 1e-3
       else:
           # CUDA
           assert abs(result_sum.item() - 4.693_4286_5017_0972e-07		) < 1e-2
           assert abs(result_mean.item() - 0.0002		) < 1e-3







   def 					lowerCamelCase						(      self		)      ->						Dict:

       '''simple docstring'''




       if torch_device == "mps":
           return
       snake_case       : Optional[Any]    =       self.scheduler_classes[0]
       snake_case       : Optional[int]    =       self.get_scheduler_config()
       snake_case       : Dict    =       scheduler_class(**UpperCamelCase__		)

       scheduler.set_timesteps(self.num_inference_steps		)

       snake_case       : List[Any]    =       self.dummy_model()
       snake_case       : Union[str, Any]    =       self.dummy_sample_deter * scheduler.init_noise_sigma
       snake_case       : List[str]    =       sample.to(UpperCamelCase__		)

       for i, t in enumerate(scheduler.timesteps		):
           snake_case       : List[Any]    =       scheduler.scale_model_input(UpperCamelCase__		,      UpperCamelCase__		)

           snake_case       : Optional[int]    =       model(UpperCamelCase__		,      UpperCamelCase__		)

           snake_case       : Optional[int]    =       scheduler.step(UpperCamelCase__		,      UpperCamelCase__		,      UpperCamelCase__		)
           snake_case       : int    =       output.prev_sample

       snake_case       : int    =       torch.sum(torch.abs(UpperCamelCase__		)		)
       snake_case       : Union[str, Any]    =       torch.mean(torch.abs(UpperCamelCase__		)		)

       if torch_device in ["cpu", "mps"]:
           assert abs(result_sum.item() - 20.4125		) < 1e-2
           assert abs(result_mean.item() - 0.0266		) < 1e-3
       else:
           # CUDA
           assert abs(result_sum.item() - 20.4125		) < 1e-2
           assert abs(result_mean.item() - 0.0266		) < 1e-3







   def 					lowerCamelCase						(      self		)      ->						Optional[int]:

       '''simple docstring'''




       if torch_device == "mps":
           return
       snake_case       : Any    =       self.scheduler_classes[0]
       snake_case       : Any    =       self.get_scheduler_config()
       snake_case       : Union[str, Any]    =       scheduler_class(**UpperCamelCase__		)

       scheduler.set_timesteps(self.num_inference_steps		,      device=UpperCamelCase__		)

       snake_case       : Optional[Any]    =       self.dummy_model()
       snake_case       : Optional[int]    =       self.dummy_sample_deter.to(UpperCamelCase__		) * scheduler.init_noise_sigma

       for t in scheduler.timesteps:
           snake_case       : Optional[Any]    =       scheduler.scale_model_input(UpperCamelCase__		,      UpperCamelCase__		)

           snake_case       : Any    =       model(UpperCamelCase__		,      UpperCamelCase__		)

           snake_case       : List[Any]    =       scheduler.step(UpperCamelCase__		,      UpperCamelCase__		,      UpperCamelCase__		)
           snake_case       : Dict    =       output.prev_sample

       snake_case       : Dict    =       torch.sum(torch.abs(UpperCamelCase__		)		)
       snake_case       : str    =       torch.mean(torch.abs(UpperCamelCase__		)		)

       if str(UpperCamelCase__		).startswith("cpu"		):
           # The following sum varies between 148 and 156 on mps. Why?
           assert abs(result_sum.item() - 20.4125		) < 1e-2
           assert abs(result_mean.item() - 0.0266		) < 1e-3
       else:
           # CUDA
           assert abs(result_sum.item() - 20.4125		) < 1e-2
           assert abs(result_mean.item() - 0.0266		) < 1e-3





