'''simple docstring'''




import torch

from diffusers import EulerDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest


class       UpperCAmelCase__  (       __lowercase			):






   """simple docstring"""
   A							:       List[str]     =    (EulerDiscreteScheduler,)
   A							:       Optional[Any]     =    10
   def 		_lowerCamelCase (self       ,				**_a				)    ->     Union[str, Any]:
        lowercase_					:       Tuple     				=					{
            'num_train_timesteps': 1_100,
            'beta_start': 0.00_01,
            'beta_end': 0.02,
            'beta_schedule': 'linear',
        }

        config.update(**__A				)
        return config
   def 		_lowerCamelCase (self				)    ->     Any:
        for timesteps in [10, 50, 100, 1_000]:
             self.check_over_configs(num_train_timesteps=__A				)
   def 		_lowerCamelCase (self				)    ->     List[Any]:
        for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]       ,				[0.00_02, 0.0_02, 0.02]				):
             self.check_over_configs(beta_start=__A       ,				beta_end=__A				)
   def 		_lowerCamelCase (self				)    ->     List[Any]:
        for schedule in ["linear", "scaled_linear"]:
             self.check_over_configs(beta_schedule=__A				)
   def 		_lowerCamelCase (self				)    ->     str:
        for prediction_type in ["epsilon", "v_prediction"]:
             self.check_over_configs(prediction_type=__A				)
   def 		_lowerCamelCase (self				)    ->     List[str]:
        lowercase_					:       Tuple     				=					self.scheduler_classes[0]
        lowercase_					:       int     				=					self.get_scheduler_config()
        lowercase_					:       List[str]     				=					scheduler_class(**__A				)

        scheduler.set_timesteps(self.num_inference_steps				)

        lowercase_					:       Tuple     				=					torch.manual_seed(0				)

        lowercase_					:       Optional[int]     				=					self.dummy_model()
        lowercase_					:       Optional[int]     				=					self.dummy_sample_deter * scheduler.init_noise_sigma
        lowercase_					:       Optional[Any]     				=					sample.to(__A				)

        for i, t in enumerate(scheduler.timesteps				):
             lowercase_					:       int     				=					scheduler.scale_model_input(__A       ,				__A				)

             lowercase_					:       List[str]     				=					model(__A       ,				__A				)

             lowercase_					:       Dict     				=					scheduler.step(__A       ,				__A       ,				__A       ,				generator=__A				)
             lowercase_					:       Optional[int]     				=					output.prev_sample

        lowercase_					:       Tuple     				=					torch.sum(torch.abs(__A				)				)
        lowercase_					:       Tuple     				=					torch.mean(torch.abs(__A				)				)

        assert abs(result_sum.item() - 10.08_07				) < 1e-2
        assert abs(result_mean.item() - 0.01_31				) < 1e-3
   def 		_lowerCamelCase (self				)    ->     int:
        lowercase_					:       List[Any]     				=					self.scheduler_classes[0]
        lowercase_					:       Optional[int]     				=					self.get_scheduler_config(prediction_type='v_prediction'				)
        lowercase_					:       Union[str, Any]     				=					scheduler_class(**__A				)

        scheduler.set_timesteps(self.num_inference_steps				)

        lowercase_					:       str     				=					torch.manual_seed(0				)

        lowercase_					:       Union[str, Any]     				=					self.dummy_model()
        lowercase_					:       str     				=					self.dummy_sample_deter * scheduler.init_noise_sigma
        lowercase_					:       Any     				=					sample.to(__A				)

        for i, t in enumerate(scheduler.timesteps				):
             lowercase_					:       Optional[int]     				=					scheduler.scale_model_input(__A       ,				__A				)

             lowercase_					:       List[str]     				=					model(__A       ,				__A				)

             lowercase_					:       List[str]     				=					scheduler.step(__A       ,				__A       ,				__A       ,				generator=__A				)
             lowercase_					:       Tuple     				=					output.prev_sample

        lowercase_					:       int     				=					torch.sum(torch.abs(__A				)				)
        lowercase_					:       Tuple     				=					torch.mean(torch.abs(__A				)				)

        assert abs(result_sum.item() - 0.00_02				) < 1e-2
        assert abs(result_mean.item() - 2.2676e-06				) < 1e-3
   def 		_lowerCamelCase (self				)    ->     List[str]:
        lowercase_					:       Optional[Any]     				=					self.scheduler_classes[0]
        lowercase_					:       Optional[Any]     				=					self.get_scheduler_config()
        lowercase_					:       List[str]     				=					scheduler_class(**__A				)

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

        lowercase_					:       Union[str, Any]     				=					torch.manual_seed(0				)

        lowercase_					:       str     				=					self.dummy_model()
        lowercase_					:       List[str]     				=					self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
        lowercase_					:       int     				=					sample.to(__A				)

        for t in scheduler.timesteps:
             lowercase_					:       Optional[int]     				=					scheduler.scale_model_input(__A       ,				__A				)

             lowercase_					:       Dict     				=					model(__A       ,				__A				)

             lowercase_					:       Dict     				=					scheduler.step(__A       ,				__A       ,				__A       ,				generator=__A				)
             lowercase_					:       Optional[int]     				=					output.prev_sample

        lowercase_					:       Tuple     				=					torch.sum(torch.abs(__A				)				)
        lowercase_					:       Tuple     				=					torch.mean(torch.abs(__A				)				)

        assert abs(result_sum.item() - 10.08_07				) < 1e-2
        assert abs(result_mean.item() - 0.01_31				) < 1e-3





   def 		_lowerCamelCase (self				)    ->     str:
        lowercase_					:       Union[str, Any]     				=					self.scheduler_classes[0]
        lowercase_					:       Tuple     				=					self.get_scheduler_config()
        lowercase_					:       Dict     				=					scheduler_class(**__A       ,				use_karras_sigmas=__A				)

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

        lowercase_					:       Any     				=					torch.manual_seed(0				)

        lowercase_					:       int     				=					self.dummy_model()
        lowercase_					:       List[str]     				=					self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
        lowercase_					:       Dict     				=					sample.to(__A				)

        for t in scheduler.timesteps:
             lowercase_					:       Optional[int]     				=					scheduler.scale_model_input(__A       ,				__A				)

             lowercase_					:       Union[str, Any]     				=					model(__A       ,				__A				)

             lowercase_					:       List[Any]     				=					scheduler.step(__A       ,				__A       ,				__A       ,				generator=__A				)
             lowercase_					:       Any     				=					output.prev_sample

        lowercase_					:       Any     				=					torch.sum(torch.abs(__A				)				)
        lowercase_					:       List[Any]     				=					torch.mean(torch.abs(__A				)				)

        assert abs(result_sum.item() - 1_24.52_29_94_99_51_17_19				) < 1e-2
        assert abs(result_mean.item() - 0.1_62_13_93_26_33_39_99_63				) < 1e-3

'''simple docstring'''




import math

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_							):

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5  ,       int(math.sqrt(SCREAMING_SNAKE_CASE_							) + 1							)  ,       6							):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True

def _UpperCamelCase   (       SCREAMING_SNAKE_CASE_ = 10_001							):

     try:
          lowercase_					:       List[Any]     				=					int(SCREAMING_SNAKE_CASE_							)
     except (TypeError, ValueError):
          raise TypeError('Parameter nth must be int or castable to int.'							) from None
     if nth <= 0:
          raise ValueError('Parameter nth must be greater than or equal to one.'							)
     lowercase_					:       list[int]     				=					[]
     lowercase_					:       Optional[int]     				=					2
     while len(SCREAMING_SNAKE_CASE_							) < nth:
          if is_prime(SCREAMING_SNAKE_CASE_							):
               primes.append(SCREAMING_SNAKE_CASE_							)
               num += 1
          else:
               num += 1
     return primes[len(SCREAMING_SNAKE_CASE_							) - 1]


if __name__ == "__main__":
 print(F"""{solution() = }""")




