



"""simple docstring"""







import tempfile

import torch

from diffusers import (
    DEISMultistepScheduler,
    DPMSolverMultistepScheduler,
    DPMSolverSinglestepScheduler,
    UniPCMultistepScheduler,
)

from .test_schedulers import SchedulerCommonTest

class       UpperCamelCase  (					a				):





     """simple docstring"""






     _lowerCamelCase					: List[Any]				   =(DPMSolverMultistepScheduler,)
     _lowerCamelCase					: Optional[Any]				   =(("num_inference_steps", 25),)





     def 						A__  (					self :							Tuple	,      **_lowerCamelCase :							str ):
          A__				=   {
              '''num_train_timesteps''': 1_0_0_0,
              '''beta_start''': 0.0_001,
              '''beta_end''': 0.02,
              '''beta_schedule''': '''linear''',
              '''solver_order''': 2,
              '''prediction_type''': '''epsilon''',
              '''thresholding''': False,
              '''sample_max_value''': 1.0,
              '''algorithm_type''': '''dpmsolver++''',
              '''solver_type''': '''midpoint''',
              '''lower_order_final''': False,
              '''lambda_min_clipped''': -float('''inf''' ),
              '''variance_type''': None,
          }

          config.update(**_lowerCamelCase )
          return config





     def 						A__  (					self :							Optional[int]	,      _lowerCamelCase :							Optional[Any]=0	,      **_lowerCamelCase :							Optional[Any] ):
          A__				=   dict(self.forward_default_kwargs )
          A__				=   kwargs.pop('''num_inference_steps'''	,      _lowerCamelCase )
          A__				=   self.dummy_sample
          A__				=   0.1 * sample
          A__				=   [residual + 0.2, residual + 0.15, residual + 0.10]

          for scheduler_class in self.scheduler_classes:
               A__				=   self.get_scheduler_config(**_lowerCamelCase )
               A__				=   scheduler_class(**_lowerCamelCase )
               scheduler.set_timesteps(_lowerCamelCase )
               # copy over dummy past residuals
               A__				=   dummy_past_residuals[: scheduler.config.solver_order]

               with tempfile.TemporaryDirectory() as tmpdirname:
                    scheduler.save_config(_lowerCamelCase )
                    A__				=   scheduler_class.from_pretrained(_lowerCamelCase )
                    new_scheduler.set_timesteps(_lowerCamelCase )
                    # copy over dummy past residuals
                    A__				=   dummy_past_residuals[: new_scheduler.config.solver_order]

               A__	,     A__				=   sample, sample
               for t in range(_lowerCamelCase	,      time_step + scheduler.config.solver_order + 1 ):
                    A__				=   scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase	,      **_lowerCamelCase ).prev_sample
                    A__				=   new_scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase	,      **_lowerCamelCase ).prev_sample

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





     def 						A__  (					self :							Optional[Any] ):
          pass





     def 						A__  (					self :							List[str]	,      _lowerCamelCase :							Dict=0	,      **_lowerCamelCase :							int ):
          A__				=   dict(self.forward_default_kwargs )
          A__				=   kwargs.pop('''num_inference_steps'''	,      _lowerCamelCase )
          A__				=   self.dummy_sample
          A__				=   0.1 * sample
          A__				=   [residual + 0.2, residual + 0.15, residual + 0.10]

          for scheduler_class in self.scheduler_classes:
               A__				=   self.get_scheduler_config()
               A__				=   scheduler_class(**_lowerCamelCase )
               scheduler.set_timesteps(_lowerCamelCase )

               # copy over dummy past residuals (must be after setting timesteps)
               A__				=   dummy_past_residuals[: scheduler.config.solver_order]

               with tempfile.TemporaryDirectory() as tmpdirname:
                    scheduler.save_config(_lowerCamelCase )
                    A__				=   scheduler_class.from_pretrained(_lowerCamelCase )
                    # copy over dummy past residuals
                    new_scheduler.set_timesteps(_lowerCamelCase )

                    # copy over dummy past residual (must be after setting timesteps)
                    A__				=   dummy_past_residuals[: new_scheduler.config.solver_order]

               A__				=   scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase	,      **_lowerCamelCase ).prev_sample
               A__				=   new_scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase	,      **_lowerCamelCase ).prev_sample

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





     def 						A__  (					self :							str	,      _lowerCamelCase :							Optional[Any]=None	,      **_lowerCamelCase :							Any ):
          if scheduler is None:
               A__				=   self.scheduler_classes[0]
               A__				=   self.get_scheduler_config(**_lowerCamelCase )
               A__				=   scheduler_class(**_lowerCamelCase )

          A__				=   1_0
          A__				=   self.dummy_model()
          A__				=   self.dummy_sample_deter
          scheduler.set_timesteps(_lowerCamelCase )

          for i, t in enumerate(scheduler.timesteps ):
               A__				=   model(_lowerCamelCase	,      _lowerCamelCase )
               A__				=   scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase ).prev_sample

          return sample





     def 						A__  (					self :							Tuple ):
          A__				=   dict(self.forward_default_kwargs )

          A__				=   kwargs.pop('''num_inference_steps'''	,      _lowerCamelCase )

          for scheduler_class in self.scheduler_classes:
               A__				=   self.get_scheduler_config()
               A__				=   scheduler_class(**_lowerCamelCase )

               A__				=   self.dummy_sample
               A__				=   0.1 * sample

               if num_inference_steps is not None and hasattr(_lowerCamelCase	,      '''set_timesteps''' ):
                    scheduler.set_timesteps(_lowerCamelCase )
               elif num_inference_steps is not None and not hasattr(_lowerCamelCase	,      '''set_timesteps''' ):
                    A__				=   num_inference_steps

               # copy over dummy past residuals (must be done after set_timesteps)
               A__				=   [residual + 0.2, residual + 0.15, residual + 0.10]
               A__				=   dummy_past_residuals[: scheduler.config.solver_order]

               A__				=   scheduler.timesteps[5]
               A__				=   scheduler.timesteps[6]

               A__				=   scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase	,      **_lowerCamelCase ).prev_sample
               A__				=   scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase	,      **_lowerCamelCase ).prev_sample

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





     def 						A__  (					self :							Optional[Any] ):
          for timesteps in [2_5, 5_0, 1_0_0, 9_9_9, 1_0_0_0]:
               self.check_over_configs(num_train_timesteps=_lowerCamelCase )





     def 						A__  (					self :							Any ):
          self.check_over_configs(thresholding=_lowerCamelCase )
          for order in [1, 2, 3]:
               for solver_type in ["midpoint", "heun"]:
                    for threshold in [0.5, 1.0, 2.0]:
                         for prediction_type in ["epsilon", "sample"]:
                              self.check_over_configs(
                                  thresholding=_lowerCamelCase	,      prediction_type=_lowerCamelCase	,      sample_max_value=_lowerCamelCase	,      algorithm_type='''dpmsolver++'''	,      solver_order=_lowerCamelCase	,      solver_type=_lowerCamelCase	,      )





     def 						A__  (					self :							Union[str, Any] ):
          for prediction_type in ["epsilon", "v_prediction"]:
               self.check_over_configs(prediction_type=_lowerCamelCase )





     def 						A__  (					self :							Tuple ):
          for algorithm_type in ["dpmsolver", "dpmsolver++", "sde-dpmsolver", "sde-dpmsolver++"]:
               for solver_type in ["midpoint", "heun"]:
                    for order in [1, 2, 3]:
                         for prediction_type in ["epsilon", "sample"]:
                              if algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
                                   if order == 3:
                                        continue
                              else:
                                   self.check_over_configs(
                                       solver_order=_lowerCamelCase	,      solver_type=_lowerCamelCase	,      prediction_type=_lowerCamelCase	,      algorithm_type=_lowerCamelCase	,      )
                              A__				=   self.full_loop(
                                  solver_order=_lowerCamelCase	,      solver_type=_lowerCamelCase	,      prediction_type=_lowerCamelCase	,      algorithm_type=_lowerCamelCase	,      )
                              assert not torch.isnan(_lowerCamelCase ).any(), "Samples have nan numbers"





     def 						A__  (					self :							Any ):
          self.check_over_configs(lower_order_final=_lowerCamelCase )
          self.check_over_configs(lower_order_final=_lowerCamelCase )





     def 						A__  (					self :							Optional[Any] ):
          self.check_over_configs(lambda_min_clipped=-float('''inf''' ) )
          self.check_over_configs(lambda_min_clipped=-5.1 )





     def 						A__  (					self :							str ):
          self.check_over_configs(variance_type=_lowerCamelCase )
          self.check_over_configs(variance_type='''learned_range''' )





     def 						A__  (					self :							Union[str, Any] ):
          for num_inference_steps in [1, 2, 3, 5, 1_0, 5_0, 1_0_0, 9_9_9, 1_0_0_0]:
               self.check_over_forward(num_inference_steps=_lowerCamelCase	,      time_step=0 )





     def 						A__  (					self :							Dict ):
          A__				=   self.full_loop()
          A__				=   torch.mean(torch.abs(_lowerCamelCase ) )

          assert abs(result_mean.item() - 0.3_301 ) < 1E-3





     def 						A__  (					self :							List[Any] ):
          A__				=   self.full_loop(thresholding=_lowerCamelCase	,      dynamic_thresholding_ratio=0.87	,      sample_max_value=0.5 )
          A__				=   torch.mean(torch.abs(_lowerCamelCase ) )

          assert abs(result_mean.item() - 1.1_364 ) < 1E-3





     def 						A__  (					self :							Dict ):
          A__				=   self.full_loop(prediction_type='''v_prediction''' )
          A__				=   torch.mean(torch.abs(_lowerCamelCase ) )

          assert abs(result_mean.item() - 0.2_251 ) < 1E-3





     def 						A__  (					self :							Optional[int] ):
          A__				=   self.full_loop(prediction_type='''v_prediction'''	,      use_karras_sigmas=_lowerCamelCase )
          A__				=   torch.mean(torch.abs(_lowerCamelCase ) )

          assert abs(result_mean.item() - 0.2_096 ) < 1E-3





     def 						A__  (					self :							int ):
          # make sure that iterating over schedulers with same config names gives same results
          # for defaults
          A__				=   DPMSolverMultistepScheduler(**self.get_scheduler_config() )
          A__				=   self.full_loop(scheduler=_lowerCamelCase )
          A__				=   torch.mean(torch.abs(_lowerCamelCase ) )

          assert abs(result_mean.item() - 0.3_301 ) < 1E-3

          A__				=   DPMSolverSinglestepScheduler.from_config(scheduler.config )
          A__				=   UniPCMultistepScheduler.from_config(scheduler.config )
          A__				=   DEISMultistepScheduler.from_config(scheduler.config )
          A__				=   DPMSolverMultistepScheduler.from_config(scheduler.config )

          A__				=   self.full_loop(scheduler=_lowerCamelCase )
          A__				=   torch.mean(torch.abs(_lowerCamelCase ) )

          assert abs(result_mean.item() - 0.3_301 ) < 1E-3





     def 						A__  (					self :							Dict ):
          A__				=   self.scheduler_classes[0]
          A__				=   self.get_scheduler_config(thresholding=_lowerCamelCase	,      dynamic_thresholding_ratio=0 )
          A__				=   scheduler_class(**_lowerCamelCase )

          A__				=   1_0
          A__				=   self.dummy_model()
          A__				=   self.dummy_sample_deter.half()
          scheduler.set_timesteps(_lowerCamelCase )

          for i, t in enumerate(scheduler.timesteps ):
               A__				=   model(_lowerCamelCase	,      _lowerCamelCase )
               A__				=   scheduler.step(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase ).prev_sample

          assert sample.dtype == torch.floataa





     def 						A__  (					self :							List[str]	,      **_lowerCamelCase :							Tuple ):
          for scheduler_class in self.scheduler_classes:
               A__				=   self.get_scheduler_config(**_lowerCamelCase )
               A__				=   scheduler_class(**_lowerCamelCase )

               scheduler.set_timesteps(scheduler.config.num_train_timesteps )
               assert len(scheduler.timesteps.unique() ) == scheduler.num_inference_steps








"""simple docstring"""







from math import factorial



def   a_	(			__a		,							__a      ):
     return factorial(__a      ) / (factorial(__a      ) * factorial(n - r      ))



def   a_	(			):
     A__				=   0

     for i in range(1		,							101      ):
          for j in range(1		,							i + 1      ):
               if combinations(__a		,							__a      ) > 1e6:
                    total += 1
     return total


if __name__ == "__main__":
 print(solution())



