



def      __snake_case	(			_UpperCAmelCase				):
    return 10 - x * x





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase				):
    # Bolzano theory in order to find if there is a root between a and b
    if equation(_UpperCAmelCase				) * equation(_UpperCAmelCase				) >= 0:
        raise ValueError('''Wrong space!'''				)

    __a						       =				a
    while (b - a) >= 0.01:
        # Find middle point
        __a						       =				(a + b) / 2
        # Check if middle point is root
        if equation(_UpperCAmelCase				) == 0.0:
            break
        # Decide the side to repeat the steps
        if equation(_UpperCAmelCase				) * equation(_UpperCAmelCase				) < 0:
            __a						       =				c
        else:
            __a						       =				c
    return c


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 print(bisection(-2, 5))
 print(bisection(0, 6))










import torch

from diffusers import DDPMParallelScheduler

from .test_schedulers import SchedulerCommonTest

class     _A       (	__UpperCAmelCase    ):
       UpperCamelCase__  :    Tuple											=						(DDPMParallelScheduler,)



       def 		_lowerCamelCase			(		self							:     int     ,		**__SCREAMING_SNAKE_CASE							:     List[Any]):


           '''simple docstring'''

           __a						       =				{
               '''num_train_timesteps''': 1_000,
               '''beta_start''': 0.00_01,
               '''beta_end''': 0.02,
               '''beta_schedule''': '''linear''',
               '''variance_type''': '''fixed_small''',
               '''clip_sample''': True,
           }

           config.update(**__SCREAMING_SNAKE_CASE)
           return config



       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

           for timesteps in [1, 5, 100, 1_000]:
               self.check_over_configs(num_train_timesteps=__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     Tuple):


           '''simple docstring'''

           for beta_start, beta_end in zip([0.00_01, 0.0_01, 0.01, 0.1]     ,		[0.0_02, 0.02, 0.2, 2]):
               self.check_over_configs(beta_start=__SCREAMING_SNAKE_CASE     ,		beta_end=__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

           for schedule in ["linear", "squaredcos_cap_v2"]:
               self.check_over_configs(beta_schedule=__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     Any):


           '''simple docstring'''

           for variance in ["fixed_small", "fixed_large", "other"]:
               self.check_over_configs(variance_type=__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

           for clip_sample in [True, False]:
               self.check_over_configs(clip_sample=__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     str):


           '''simple docstring'''

           self.check_over_configs(thresholding=__SCREAMING_SNAKE_CASE)
           for threshold in [0.5, 1.0, 2.0]:
               for prediction_type in ["epsilon", "sample", "v_prediction"]:
                   self.check_over_configs(
                       thresholding=__SCREAMING_SNAKE_CASE     ,		prediction_type=__SCREAMING_SNAKE_CASE     ,		sample_max_value=__SCREAMING_SNAKE_CASE     ,		)



       def 		_lowerCamelCase			(		self							:     Union[str, Any]):


           '''simple docstring'''

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



       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

           for t in [0, 500, 999]:
               self.check_over_forward(time_step=__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     str):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config()
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           assert torch.sum(torch.abs(scheduler._get_variance(0) - 0.0)) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(487) - 0.0_09_79)) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(999) - 0.02)) < 1E-5



       def 		_lowerCamelCase			(		self							:     Optional[Any]):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config()
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           __a						       =				len(__SCREAMING_SNAKE_CASE)

           __a						       =				self.dummy_model()
           __a						       =				self.dummy_sample_deter
           __a						       =				self.dummy_sample_deter + 0.1
           __a						       =				self.dummy_sample_deter - 0.1

           __a						       =				samplea.shape[0]
           __a						       =				torch.stack([samplea, samplea, samplea]     ,		dim=0)
           __a						       =				torch.arange(__SCREAMING_SNAKE_CASE)[0:3, None].repeat(1     ,		__SCREAMING_SNAKE_CASE)

           __a						       =				model(samples.flatten(0     ,		1)     ,		timesteps.flatten(0     ,		1))
           __a						       =				scheduler.batch_step_no_noise(__SCREAMING_SNAKE_CASE     ,		timesteps.flatten(0     ,		1)     ,		samples.flatten(0     ,		1))

           __a						       =				torch.sum(torch.abs(__SCREAMING_SNAKE_CASE))
           __a						       =				torch.mean(torch.abs(__SCREAMING_SNAKE_CASE))

           assert abs(result_sum.item() - 11_53.18_33) < 1E-2
           assert abs(result_mean.item() - 0.50_05) < 1E-3



       def 		_lowerCamelCase			(		self							:     Dict):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config()
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           __a						       =				len(__SCREAMING_SNAKE_CASE)

           __a						       =				self.dummy_model()
           __a						       =				self.dummy_sample_deter
           __a						       =				torch.manual_seed(0)

           for t in reversed(range(__SCREAMING_SNAKE_CASE)):
               # 1. predict noise residual
               __a						       =				model(__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE)

               # 2. predict previous mean of sample x_t-1
               __a						       =				scheduler.step(__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE     ,		generator=__SCREAMING_SNAKE_CASE).prev_sample

               __a						       =				pred_prev_sample

           __a						       =				torch.sum(torch.abs(__SCREAMING_SNAKE_CASE))
           __a						       =				torch.mean(torch.abs(__SCREAMING_SNAKE_CASE))

           assert abs(result_sum.item() - 2_58.96_06) < 1E-2
           assert abs(result_mean.item() - 0.33_72) < 1E-3



       def 		_lowerCamelCase			(		self							:     Optional[int]):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config(prediction_type='''v_prediction''')
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           __a						       =				len(__SCREAMING_SNAKE_CASE)

           __a						       =				self.dummy_model()
           __a						       =				self.dummy_sample_deter
           __a						       =				torch.manual_seed(0)

           for t in reversed(range(__SCREAMING_SNAKE_CASE)):
               # 1. predict noise residual
               __a						       =				model(__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE)

               # 2. predict previous mean of sample x_t-1
               __a						       =				scheduler.step(__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE     ,		generator=__SCREAMING_SNAKE_CASE).prev_sample

               __a						       =				pred_prev_sample

           __a						       =				torch.sum(torch.abs(__SCREAMING_SNAKE_CASE))
           __a						       =				torch.mean(torch.abs(__SCREAMING_SNAKE_CASE))

           assert abs(result_sum.item() - 2_02.02_96) < 1E-2
           assert abs(result_mean.item() - 0.26_31) < 1E-3



       def 		_lowerCamelCase			(		self							:     Optional[int]):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config()
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           __a						       =				[100, 87, 50, 1, 0]

           scheduler.set_timesteps(timesteps=__SCREAMING_SNAKE_CASE)

           __a						       =				scheduler.timesteps

           for i, timestep in enumerate(__SCREAMING_SNAKE_CASE):
               if i == len(__SCREAMING_SNAKE_CASE) - 1:
                   __a						       =				-1
               else:
                   __a						       =				timesteps[i + 1]

               __a						       =				scheduler.previous_timestep(__SCREAMING_SNAKE_CASE)
               __a						       =				prev_t.item()

               self.assertEqual(__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     Dict):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config()
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           __a						       =				[100, 87, 50, 51, 0]

           with self.assertRaises(__SCREAMING_SNAKE_CASE     ,		msg='''`custom_timesteps` must be in descending order.'''):
               scheduler.set_timesteps(timesteps=__SCREAMING_SNAKE_CASE)



       def 		_lowerCamelCase			(		self							:     Optional[int]):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config()
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           __a						       =				[100, 87, 50, 1, 0]
           __a						       =				len(__SCREAMING_SNAKE_CASE)

           with self.assertRaises(__SCREAMING_SNAKE_CASE     ,		msg='''Can only pass one of `num_inference_steps` or `custom_timesteps`.'''):
               scheduler.set_timesteps(num_inference_steps=__SCREAMING_SNAKE_CASE     ,		timesteps=__SCREAMING_SNAKE_CASE)





       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

           __a						       =				self.scheduler_classes[0]
           __a						       =				self.get_scheduler_config()
           __a						       =				scheduler_class(**__SCREAMING_SNAKE_CASE)

           __a						       =				[scheduler.config.num_train_timesteps]

           with self.assertRaises(
               __SCREAMING_SNAKE_CASE     ,		msg='''`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}'''     ,		):
               scheduler.set_timesteps(timesteps=__SCREAMING_SNAKE_CASE)





